source,target The results for these cases (not shown) indicate that the VLA can detect them out to z8 and bevond =—30. respectively. while the SIVA caneasily detect ihem bevond z—30.," The results for these cases (not shown) indicate that the VLA can detect them out to $z \sim 8$ and beyond $z \sim 30$, respectively, while the SKA caneasily detect them beyond $z \sim 30$." Figure 13. shows the light curves of the energetic Ην afterglows at 2:=6 and v~200 MIIz and at z19 and ν~100 MlIz. as well as the 5o sensitivities of the VLA. LOFAR and SIVA.," Figure \ref{fig:HN} shows the light curves of the energetic HN afterglows at $z=6$ and $\nu \sim 200$ MHz and at $z=13$ and $\nu \sim 100$ MHz, as well as the $5 \sigma$ sensitivities of the VLA, LOFAR and SKA." This shows that the VLA. LOFAR and SIXÀ can detect such HN alterglows at low frequencies e100 MlIZ and high redshifts 2~10.," This shows that the VLA, LOFAR and SKA can detect such HN afterglows at low frequencies $\sim 100$ MHz and high redshifts $z \sim 10$." " The peak flux indicated is about ~107-10"" jeJv at the redshifted 21 cm frequenev. p=1420/(1+2) MIIz. for 2=6."," The peak flux indicated is about $\sim 10^{2}$ $10^{3}$ $\mu$ Jy at the redshifted 21 cm frequency, $\nu=1420/(1+z)$ MHz, for $z \simg 6$." The reverse shock enission is comparable to the forward shock emission. aud the redshilt dependence is weak.," The reverse shock emission is comparable to the forward shock emission, and the redshift dependence is weak." We also calculated the moderate energy LIN case E~1077 erg and the high density HEN case ncLO? Ὁ to find that the peak flux at ~100 MIIz in both cases is about an order of magnitude below the flix in Figure 13.., We also calculated the moderate energy HN case $E \sim 10^{53}$ erg and the high density HN case $n \sim 10^{2}$ $^{-3}$ to find that the peak flux at $\sim 100$ MHz in both cases is about an order of magnitude below the flux in Figure \ref{fig:HN}. One caveat about the ΗΝ emission is (hat one may. have no prior information about the sky position because of the preponderant lack of detected gamma-ray emission., One caveat about the HN emission is that one may have no prior information about the sky position because of the preponderant lack of detected gamma-ray emission. However the number of ΗΝ alterglows at 26 on the skv is estimated as ~10 events 107. where brea~101 days is the peak time of the IINe. and we assume a fraction f.~50% of all GRBs on the sky originating at 26 (Bromm&Loeb2002) and. a ratio of the ΗΝ rate to the GRB one fus;conp~ 1.," However the number of HN afterglows at $z \simg 6$ on the sky is estimated as $\sim 10^{3}$ events $^{-1} \times t_{\rm peak} f_{z} f_{\rm HN/GRB} \sim 10^{3}$ , where $t_{\rm peak} \sim 10^{3}$ days is the peak time of the HNe, and we assume a fraction $f_{z} \sim 50$ of all GRBs on the sky originating at $z \simg 6$ \citep{bromm02a} and a ratio of the HN rate to the GRB one $f_{\rm HN/GRB}\sim 1$ ." Thus the imaging of ~40 deg? of sky would lead to one IIN afterglow at zZ 6. while the field of view of the SIVA may be larger than this.," Thus the imaging of $\sim 40$ $^{2}$ of sky would lead to one HN afterglow at $z \simg 6$ , while the field of view of the SKA may be larger than this." Thus. LIN alterelows could be detected as a by-product of other related or unrelated observing prograis.," Thus, HN afterglows could be detected as a by-product of other related or unrelated observing programs." llowever. the sensitivity of the M67 TO morpholoey iuplies that also other effects may influence dt. apart from the metallicity.,"However, the sensitivity of the M67 TO morphology implies that also other effects may influence it, apart from the metallicity." The nuclear reaction rates were already ineutioued., The nuclear reaction rates were already mentioned. Other possible aspects could be the amount of overshooting. atomic diffusion. aud the pre-nian sequence historv.," Other possible aspects could be the amount of overshooting, atomic diffusion, and the pre-main sequence history." Last. but not least. technical details of the stellar evolution codes may play a role.," Last, but not least, technical details of the stellar evolution codes may play a role." It is therefore necessary to show that our results do not depend ou the particular numerical code., It is therefore necessary to show that our results do not depend on the particular numerical code. " As a first. aud crucial step. we have successfully attempted to reproduce the key result by ο,"," As a first, and crucial step, we have successfully attempted to reproduce the key result by VG07." This will also show where changes to their procedure are indicated., This will also show where changes to their procedure are indicated. The first step concerns the solar model calibration., The first step concerns the solar model calibration. Tere. as for the M67 models. VGOT used NACRE unclear reaction rates. the OPAL (Telesias&Rogers1996) and Fergusonctal.(2005) opacities (as is done iu our code). but ignored diffusion.," Here, as for the M67 models, VG07 used NACRE nuclear reaction rates, the OPAL \citep{ri:96} and \citet{af:05} opacities (as is done in our code), but ignored diffusion." This point is crucial. as we will show later on.," This point is crucial, as we will show later on." Some amount of convective overshooting (see L.1)) was included for the M67 models. but is uot relevant— for the solar calibration.," Some amount of convective overshooting (see \ref{s:over}) ) was included for the M67 models, but is not relevant for the solar calibration." For the atimospheres they used the MARCS iodcel (Gustafsson20033., For the atmospheres they used the MARCS model \citep{marcs:2003}. .. In this respect we differ. since we use standard Eddington grey atinospheres.," In this respect we differ, since we use standard Eddington grey atmospheres." However. as shown by VaudeuBerectal.(2008).. this has in our resent case no significant ifiueuce on the tracks ou the nain-sequeuce and subeiaut brauch.," However, as shown by \citet{veeg:2008}, this has in our present case no significant influence on the tracks on the main-sequence and subgiant branch." Table contains in the first two rows the resulting solar model parameters by VOOT and in rows 3 aud | he equivalent ones obtained with our code., Table \ref{t:ssm} contains in the first two rows the resulting solar model parameters by VG07 and in rows 3 and 4 the equivalent ones obtained with our code. Additionally. we also show the results when using the Dartinouth and LPCODE codes L3)).," Additionally, we also show the results when using the Dartmouth and LPCODE codes \ref{s:codecomp}) )." Note that the iuixiug cheth paramecters can never be compared idu their absolute values due to the different formulations of MILT., Note that the mixing length parameters can never be compared in their absolute values due to the different formulations of MLT. Overall. the agreement with VGOT for the initial abundances is within with our codes returning systematically lower iuitial metallicities (by 35€)) for the ACSU5 mixture.," Overall, the agreement with VG07 for the initial abundances is within, with our codes returning systematically lower initial metallicities (by ) for the AGS05 mixture." Although a small effect. it additionally disfavors the appearance of a convective core in the M67 TO.," Although a small effect, it additionally disfavors the appearance of a convective core in the M67 TO." Usine these initial composition values we calculated stellar tracks and isochrones for M67. which we show in Fieure 1.," Using these initial composition values we calculated stellar tracks and isochrones for M67, which we show in Figure \ref{f:vgrep}." The πιο values for distance aud reddening are ddeutieal Ίσα].to WOOT., The numerical values for distance and reddening are identical to VG07. The boest-fitting isochrones have somewhat higher ages (by 0.3 Car)., The best-fitting isochrones have somewhat higher ages (by 0.3 Gyr). The TO aatss is 1.229 respectively 1.200Αν for the old aud Lew conipositiou.," The TO mass is $1.229$ respectively $1.200\,\msun$ for the old and new composition." One recognizes the same basic result as in VCO: for the ACGSO05 mixture. the isochrone does rot show the characteristic hook.," One recognizes the same basic result as in VG07: for the AGS05 mixture, the isochrone does not show the characteristic hook." However. it cisplavs a slight iuclination indicating the presence of a very small convective core at the TO amass.," However, it displays a slight inclination indicating the presence of a very small convective core at the TO mass." " Consistent with this norphological sigu. the TO mass is mareinally higher han Mo; which is L175AL... while in the case of the CSOS nüxture it is clearly above A44,=1.139AL..."," Consistent with this morphological sign, the TO mass is marginally higher than $M_\mathrm{ccc}$, which is $1.175\,\msun$, while in the case of the GS98 mixture it is clearly above $M_\mathrm{ccc}=1.139\,\msun$." These values appear to be very similar to those found w (ιο (see their Table 1)., These values appear to be very similar to those found by VG07 (see their Table 1). " This exercise deimoustrates hat we are able to reproduce correctly VGOT and that heir result is independent of the stellar evolution code used,", This exercise demonstrates that we are able to reproduce correctly VG07 and that their result is independent of the stellar evolution code used. VQGOT already emphasized. that atomic diffusion (effectively sedimentation) could modify this result as it leads to an increase of metallicity iu the core over time., VG07 already emphasized that atomic diffusion (effectively sedimentation) could modify this result as it leads to an increase of metallicity in the core over time. As explained in the previous subsection. this will favor the occurrence of a convective core and reduce Aloe.," As explained in the previous subsection, this will favor the occurrence of a convective core and reduce $M_\mathrm{ccc}$." However. the solar model calibration should also iuclude diffusion. as it was shown that onlv with this plivsical effect the best agreement with the seismic Sun can be achieved.," However, the solar model calibration should also include diffusion, as it was shown that only with this physical effect the best agreement with the seismic Sun can be achieved." Ouly in this case the solar parameters. in particular the initial composition is determined as accurately as possible.," Only in this case the solar parameters, in particular the initial composition is determined as accurately as possible." The corresponding results are listed in Table 1 as, The corresponding results are listed in Table \ref{t:ssm} as quautum uumber of magnetic [lux tubes Np = eo (ch))—2zLE S) =—,quantum number of magnetic flux tubes N_B = e /( c ) = ) =. "uec This quautuim uumber is tlie ""hair: an observer at infinity cau measure the correspoucding Poyutiug flux aud infer the nunuber Ny.", This quantum number is the “hair”: an observer at infinity can measure the corresponding Poynting flux and infer the number $N_B$. The conserved poloidal magnetice flux (2.3)) implies a oon the horizon of the =aT(GADPPOBySR —— Sp6πῶςPN (T, The conserved poloidal magnetic flux \ref{NB}) ) implies a on the horizon of the = = 6 (. hepJ) We cau then verify that the resulting wwill have no problem in breaking the vacuum: the rotation of the leads to the appearance of the iuductive wwith a total potential drop within the ool the order sae = GPRSDUE (i, We can then verify that the resulting will have no problem in breaking the vacuum: the rotation of the leads to the appearance of the inductive with a total potential drop within the of the order a e = = (. SEU This is sufficiently high. to break the vacutun via radiative effects aud produce a highly conducting plasma., This is sufficiently high to break the vacuum via radiative effects and produce a highly conducting plasma. Iu additiou. even iu the relatively weak [n]eravitatioual field of astar. the eeneral relativistic effects of the rotatiou of space-time (the Lense-Thirring precessiou) domiuate the accelerating," In addition, even in the relatively weak gravitational field of a, the general relativistic effects of the rotation of space-time (the Lense-Thirring precession) dominate the accelerating" Opportunity observations carried out with the Swift N-ray Telescope (XRT) aud Ultraviolet and Optical Telescope (UVOT). as well as with 0.1300 GeV fluxes iude public by the Fermi Science Support Center.,"Opportunity observations carried out with the Swift X-ray Telescope (XRT) and Ultraviolet and Optical Telescope (UVOT), as well as with 0.1–300 GeV fluxes made public by the Fermi Science Support Center." The observations are described in Section 2.., The observations are described in Section \ref{sec:obs}. The light curves. correlation functious. aud SED are discussed iu Section 3..," The light curves, correlation functions, and SED are discussed in Section \ref{sec:results}." Photometric monitoring of wwas carried out on the 1 telescope located at Cerro Tololo Tateramerican Observatory (CTIO) with the ANDIC'ANT instiuueut., Photometric monitoring of was carried out on the 1.3m telescope located at Cerro Tololo Interamerican Observatory (CTIO) with the ANDICAM instrument. " ANDICAAT is a dual-channel nuager with a dichroic that feeds au optical CCD aud an IR imager. which can obtain simultancous data from 0.1 to 2.2 ji,"," ANDICAM is a dual-channel imager with a dichroic that feeds an optical CCD and an IR imager, which can obtain simultaneous data from 0.4 to 2.2 $\mu$." Our campaign began with observations in D. VOR aud Jebauds with a cadeuce of oue observation every 2 nights.," Our campaign began with observations in B, V, R and J-bands with a cadence of one observation every 2 nights." After it became clear that 3€ 1513 was exhibiting interesting and varied behavior. we added Is-band observations and increased the cadence to one observation every night.," After it became clear that 3C 454.3 was exhibiting interesting and varied behavior, we added K-band observations and increased the cadence to one observation every night." The SATARTS photometric data and light curves for aas well as all other Fermi/LAT monitored blazars visible from CTIO are made publicly available on a 1-2 dav timescale ou tle web., The SMARTS photometric data and light curves for as well as all other Fermi/LAT monitored blazars visible from CTIO are made publicly available on a 1-2 day timescale on the web. Optical data were bias-subtracted. oversean-subtracted. and flat— fielded— usine —in IRAF.," Optical data were bias-subtracted, overscan-subtracted, and flat fielded using in IRAF." The optical photometry was calibrated using published juaenitudes of a secondary standard in the field of 3€ 1513 (Craine1977:Auegioue1971:Fioruccietal. 1998).," The optical photometry was calibrated using published magnitudes of a secondary standard in the field of 3C 454.3 \citep{craine71, angione71, fiorucci98}." . Infrared data were skv-subtracted. flat fielded. aud dithered images combined using in-house IRAF scripts," Infrared data were sky-subtracted, flat fielded, and dithered images combined using in-house IRAF scripts." The infrared. photometry was calibrated using 2\TASS inagnuitudes of a secondary. standard star (the same star used in optical photometry calibration) im the field of 3€ 151.3., The infrared photometry was calibrated using 2MASS magnitudes of a secondary standard star (the same star used in optical photometry calibration) in the field of 3C 454.3. We estimated photometric errors by calculating the 1-0 variation in magnitude of comparison stars with comparable magnitude to 3€ 151.3., We estimated photometric errors by calculating the $\sigma$ variation in magnitude of comparison stars with comparable magnitude to 3C 454.3. " These are as follows: By, = 0.02 mae. Vay = 0.02 mae. R44 = 0.02. Jor — 0.01 mae. and Kay = 0.0L mae."," These are as follows: $_{\rm err}$ = 0.02 mag, $_{\rm err}$ = 0.02 mag, $_{\rm err}$ = 0.02, $_{\rm err}$ = 0.04 mag, and $_{\rm err}$ = 0.04 mag." Figue 3. shows the D-baud lieht curve normalized ο its flux at JD 2151700., Figure \ref{fig:lc} shows the B-band light curve normalized to its flux at JD 2454700. Figure 3. shows two SEDs orISLS: one averaged over the actively faring xxiod up to JD 2151750. aud a second averaged over the relatively quiesceut period after that dav.," Figure \ref{fig:sed} shows two SEDs for: one averaged over the actively flaring period up to JD 2454750, and a second averaged over the relatively quiescent period after that day." To compute the Huxes. mmeuitiudes were dereddened using the extinction relations in Cardellietal.(1989) together with the value or Ap eiven by Schlegeletal.(1998). aud converted into Hux deusitics using the zero-poiut fluxes even by Desselletal.(1998). and Beckwithetal.(1976) The Fermi Space Telescope (formerly GLAST) was launched ou 11. June 2008.," To compute the fluxes, magnitudes were dereddened using the extinction relations in \citet{cardelli89} together with the value for $_{\rm B}$ given by \citet{schlegel98} and converted into flux densities using the zero-point fluxes given by \citet{bessell98} and \citet{beckwith76} The Fermi Space Telescope (formerly GLAST) was launched on 11 June 2008." " The Fermi observatory Large Area Telescope (LAT) is designed to measure tle cosmic eanuna-rav flux up to ~ 300 (ιο, The LAT is au nuage. wide feld-ofview high-enerew pair conversiou telescope with οπσον range frou ~ 20 MeV to z 300 GeV. and survevs the sky every three hours2007)."," The Fermi observatory Large Area Telescope (LAT) is designed to measure the cosmic gamma-ray flux up to $\sim$ 300 GeV. The LAT is an imaging, wide field-of-view high-energy pair conversion telescope with energy range from $\sim$ 20 MeV to $\gsim$ 300 GeV, and surveys the sky every three hours." . As a service to the commuuity and im order to support correlated wunltiwaveleneth observations. the LAT Instrument Science Operations Center provides daily aud weekly averaged fluxes for a uuuber of blazars. of which iis onc.," As a service to the community and in order to support correlated multiwavelength observations, the LAT Instrument Science Operations Center provides daily and weekly averaged fluxes for a number of blazars, of which is one." Fluxes aud lo uncertainties for three bands. 0.1300 GeV. 0.3.1 GeV. and 1300 GeV. using preliminary iustruinent response functions and calibrations. are made available online roughly once per week. with the caveat that the carly flux estimates are not absolutely calibrated. aud. aay have variatious of up to due to uncorrected systematic effects.," Fluxes and $\sigma$ uncertainties for three bands, 0.1--300 GeV, 0.3–1 GeV, and 1–300 GeV, using preliminary instrument response functions and calibrations, are made available online roughly once per week, with the caveat that the early flux estimates are not absolutely calibrated, and may have variations of up to due to uncorrected systematic effects." Because the observed variations are well correlated witli independently iieasured IB. optical. aud UV variations. we conclude the ezuuinia-ray variations will not chauge senificautlv even if they are eventually recalibrated. and in any case. our key results are robust against fluctuations im gauunia-rav intensity.," Because the observed variations are well correlated with independently measured IR, optical, and UV variations, we conclude the gamma-ray variations will not change significantly even if they are eventually recalibrated, and in any case, our key results are robust against fluctuations in gamma-ray intensity." We show the ]lieht curve in the 0.1300 GeV band in Figure 3 normalized to its photon fux at JD 2151700., We show the light curve in the 0.1–300 GeV band in Figure \ref{fig:lc} normalized to its photon flux at JD 2454700. Fluxes shown in Fieure 3. are computed from the publicly released data in the 0.81 GeV and 1300 Ce bands by assundue a power-law spectru of photon iudex [=2., Fluxes shown in Figure \ref{fig:sed} are computed from the publicly released data in the 0.3–1 GeV and 1–300 GeV bands by assuming a power-law spectrum of photon index $\Gamma$ =2. Since being identified in June 2008 as an extraordinarily bright eamuna-rav source (Vittorinietal.2008:Crasparriui 2008).. hhas been the subject of umimerous Swift target of opportunity observations. mceludiug one by PI Douniug covering 22 September - 02 October. 2008.," Since being identified in June 2008 as an extraordinarily bright gamma-ray source \citep{vittorini08, gasparrini08}, has been the subject of numerous Swift target of opportunity observations, including one by PI Bonning covering 22 September - 02 October, 2008." The Swift satellite (Coliyelsetal.2001). has three. instruments: a codedanask Burst Alert Telescope (BAT.Dartheluival. 2005).. an N-rav Telescope covering the euergv range 0.220 keV (XRT.Durrowsctal.2005j.. aud an Ultraviolet/Optical Telescope covering 170600 uu (UVOT.Romingetal.2005).," The Swift satellite \citep{gehrels04} has three instruments: a coded-mask Burst Alert Telescope \citep[BAT,][]{barthelmy05}, an X-ray Telescope covering the energy range 0.2–20 keV \citep[XRT,][]{burrows05}, and an Ultraviolet/Optical Telescope covering 170–600 nm \citep[UVOT,][]{roming05}." Swift data are made public to the community within a few davs of the observations: therefore we were able to collect all available data within the period of our SMARTS observations., Swift data are made public to the community within a few days of the observations; therefore we were able to collect all available data within the period of our SMARTS observations. We reduced the data from the ταν telescope (XRT) aud the Ultraviolet Optical Telescope (CVOT) according to the standard recipes given by the Swift data analysis maunals., We reduced the data from the X-ray telescope (XRT) and the Ultraviolet Optical Telescope (UVOT) according to the standard recipes given by the Swift data analysis manuals. For each obsid. the UVOT data for each exposure were co-added with the taskΙ," For each obsid, the UVOT data for each exposure were co-added with the task." "Ο, The source magnitudes were then computed from a source region of 5.5 arcsec using the taskveotsorrce, which performs aperture photometry on the source aud returns the count rate. fux density. and magnitude in the Swift/UVOT photometric svstem (Pooleetal.2008)."," The source magnitudes were then computed from a source region of 5.5 arcsec using the task, which performs aperture photometry on the source and returns the count rate, flux density, and magnitude in the Swift/UVOT photometric system \citep{poole08}." . We correct these for interstellar extinction as described iu Section 2.1.., We correct these for interstellar extinction as described in Section \ref{sec:smarts}. Lieht curves from the UVOT D and WI bands are shown in Figure 3. and average fluxes before aud after JD 2151750 in Figure 3..," Light curves from the UVOT B and W1 bands are shown in Figure \ref{fig:lc}, and average fluxes before and after JD 2454750 in Figure \ref{fig:sed}." For each obsid. the NRT level2 event list was eenerated via0.41.5. with the default filtering and screening criteria. sclecting photon counting (PC) data with NRT event evades 0-12.," For each obsid, the XRT level-2 event list was generated via with the default filtering and screening criteria, selecting photon counting (PC) data with XRT event grades 0-12." We extracted the source spectrum from a region centered at the source with a radius of 60 arcsec aud subtracted the backerouud ποια a nearby source-free region., We extracted the source spectrum from a region centered at the source with a radius of 60 arcsec and subtracted the background from a nearby source-free region. Spectra were rebiuned to 25 cts/bin. fit with an absorbed power hav. aud the," Spectra were rebinned to 25 cts/bin, fit with an absorbed power law, and the" The discovery of “eaps” along the blue horizoutal brauch (IB) in globular clusters as well as of loug extensions towards higher temperatures has trieeered several spectroscopic investigations (Moohler 1999 and referencest therein) vieldineo the followineoO results:tCt Two scenarios. have been sugeested to account for. the DIID stars: by a combinatio,The discovery of “gaps” along the blue horizontal branch (HB) in globular clusters as well as of long extensions towards higher temperatures has triggered several spectroscopic investigations (Moehler \cite{moeh99} and references therein) yielding the following results: Two scenarios have been suggested to account for the low gravities of BHB stars: The discovery of “eaps” along the blue horizoutal brauch (IB) in globular clusters as well as of loug extensions towards higher temperatures has trieeered several spectroscopic investigations (Moohler 1999 and referencest therein) vieldineo the followineoO results:tCt Two scenarios. have been sugeested to account for. the DIID stars: by a combination,The discovery of “gaps” along the blue horizontal branch (HB) in globular clusters as well as of long extensions towards higher temperatures has triggered several spectroscopic investigations (Moehler \cite{moeh99} and references therein) yielding the following results: Two scenarios have been suggested to account for the low gravities of BHB stars: where 7=0 and £1 (sec YLUS: YLPOs).,where $n=0$ and $\pm 1$ (see YL08; YLP08). Using Equatious(C.1)) for (C1)) combined with (09)). we obtain Πο for the evro-resonaut acceleration à2+1. aud d?k=2z42dkdi has been used for fast modes.," Using Equations\ref{fast}) ) for \ref{eq:gyroapp}) ) combined with \ref{eq:Rn}) ), we obtain (w)] for the gyro-resonant acceleration $n=\pm 1$, and $d^{3}k=2\pi k^{2}dk d\eta$ has been used for fast modes." " Iu the above equation. £ is the injection scale of turbulence. w=kpey(Qo=μμKL.HRchusο,dV?Vi. y=cos. his the cut-off of turbulence cascade due to damping. and J, is second order Bessel function."," In the above equation, $L$ is the injection scale of turbulence, $w={k_{\perp} v_{\perp}}/{\Omega}, x=k/k_{\min}=kL, R=vk_{\min}/\Omega, M_{\A}^{2}= \delta V^{2}/V_{\A}^{2}$, $\eta=\cos\theta$, $k_{c}$ is the cut-off of turbulence cascade due to damping, and $J_{n}$ is second order Bessel function." MÀ For the trausit time acceleration (TTD). 7=0. we obtain where £ isthe injection scale of turbulence. «=Ape/O0c=khuRELRchu.AR—óp?Vi.," For the transit time acceleration (TTD), $n=0$, we obtain where $L$ isthe injection scale of turbulence, $w={k_{\perp} v_{\perp}}/{\Omega}, x=k/k_{\min}=kL, R=vk_{\min}/\Omega, M_{\A}^{2}= \delta V^{2}/V_{\A}^{2}$." " Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fe"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )." " Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )." " Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee "," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )." " Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee 1"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )." " Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee 15"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )." " Iu the QLT. HR, is replaced by 6 fiction. Equations (C10)) aud (C'L1)) become aud fee 15)"," In the QLT, $R_{n}$ is replaced by $\delta$ function, Equations \ref{eq:appdpg}) ) and \ref{eq:appdpt})) become and )." We caleulate the mass of A1644 in two wavs.,We calculate the mass of A1644 in two ways. " Our first mass estimate depends on the ""eaustic technique of Diaferio&Geller(1997).", Our first mass estimate depends on the “caustic” technique of \citet{dia97}. . A hierarchical clustering model predicts (he existence of two caustic curves with amplitude C2) approximately equal to the escape velocity from the cluster at racius A., A hierarchical clustering model predicts the existence of two caustic curves with amplitude $A(R)$ approximately equal to the escape velocity from the cluster at radius $R$ . Dialerio(1999). shows that ACH) is related to the mass of the cluster interior to 2: We use the techniques of Dialerio(1999) wilh smoothing parameter q=25 lo calculate the caustics of A1644 (Figure 8))., \citet{dia99} shows that $A(R)$ is related to the mass of the cluster interior to $R$ : We use the techniques of \citet{dia99} with smoothing parameter $q=25$ to calculate the caustics of A1644 (Figure \ref{fig-caust}) ). Of the 141 presumed cluster members. 127 lie within the causties; the lourteen remaining galaxies may in fact be outliers.," Of the 141 presumed cluster members, 127 lie within the caustics; the fourteen remaining galaxies may in fact be outliers." Equation 2 automatically excludes these outliers from the caustic mass determination.," Equation \ref{eqn-caustic} automatically excludes these outliers from the caustic mass determination." Our second mass estimate uses a virial estimator (Dinnev&Tremaine1987): where cj; is the radial velocity of each galaxy. with respect to the cluster mean and H;is the galaxys position relative to the ¢D. This estimator assumes that (he galaxies are embedded in a dilfuse dark matter distribution. and that the spatial arrangement of galaxies traces the dark matter.," Our second mass estimate uses a virial estimator \citep{bin87}: where $v_{p,i}$ is the radial velocity of each galaxy with respect to the cluster mean and is the galaxy's position relative to the cD. This estimator assumes that the galaxies are embedded in a diffuse dark matter distribution, and that the spatial arrangement of galaxies traces the dark matter." The virial mass is verv sensitive to outliers., The virial mass is very sensitive to outliers. " In Figure 9. we first plot M,j,;,; using the 141 galaxies with 10.000 km |«ez<20.000 knis !."," In Figure \ref{fig-massdiff} we first plot $M_{virial}$ using the 141 galaxies with 10,000 km $^{-1}100 yan. The Galactic background emissiou is extended compared to the LAWS beam. and therefore gives rise to strong frineineC»o in both the on- and off-source spectra.," Galactic background flux levels were only significant for $\lambda \ge 100$ $\mu$ m. The Galactic background emission is extended compared to the LWS beam, and therefore gives rise to strong fringing in both the on- and off-source spectra." The 1ckeround-subtracted spectra do not show friugiug. oexdicatiug tha the ΟΠΤΗ stars are point-like to the LAWS. as expected.," The background-subtracted spectra do not show fringing, indicating that the OH/IR stars are point-like to the LWS, as expected." After averaging and backerouud subtraction (1f llOCCSSIaYV). each observation consisted of ten subspectra (one per detector). which were rescaled by sinall factors to eive the cousisteut fluxes in regions of overlap. auc merged to eive a final spectrum.," After averaging and background subtraction (if necessary), each observation consisted of ten subspectra (one per detector), which were rescaled by small factors to give the consistent fluxes in regions of overlap, and merged to give a final spectrum." " One of the main eoals of this ar is to study the overall ISO spectra of the selectedi""objects.", One of the main goals of this article is to study the overall ISO spectra of the selected objects. Therefore. it Is necessary to jolu he SWS ancl S spectra m such a way that the flux levels and slopes o the spectra agree for xti LWS and SWS.," Therefore, it is necessary to join the SWS and LWS spectra in such a way that the flux levels and slopes of the spectra agree for both LWS and SWS." " Differences in the fux levels of the IWS and SWS προςra are mostly due to flux calibration Tucerantis,", Differences in the flux levels of the LWS and SWS spectra are mostly due to flux calibration uncertainties. Although the spectral shape is very reliable. 1e absolute flux calibration wucertainty is for the SWS at ja (Schaeidt et al. 1996)).," Although the spectral shape is very reliable, the absolute flux calibration uncertainty is for the SWS at 45 $\mu$ m (Schaeidt et al. \cite{schaeidt}) )," and for 1ο TAS at the sue waveleneth (Swinvard et al. 1998) , and for the LWS at the same wavelength (Swinyard et al. \cite{swin98}) ). Therefore. differences between the flux levels of LAWS aud SWS which are smaller than are acceptable within ie linuts of the combined error bars.," Therefore, differences between the flux levels of LWS and SWS which are smaller than are acceptable within the limits of the combined error bars." The SWS and IWS spectra were scaled according to 111 fluxcs in the overlap region., The SWS and LWS spectra were scaled according to their fluxes in the overlap region. Generally this resulted iu a shift of less than (see Table 1})., Generally this resulted in a shift of less than (see Table \ref{obs}) ). In the case of Mira and WX Psc. a iimch larger shift was required. prestmably due to the laree time interval between the SWS aud LAWS observations of these variable stars.," In the case of Mira and WX Psc, a much larger shift was required, presumably due to the large time interval between the SWS and LWS observations of these variable stars." The combined spectra are presented in Fig. l.," The combined spectra are presented in Fig. \ref{fig1}," iu AFA units., in $\lambda F_\lambda$ units. The spectra are ordered by increasing optical depth in the observed 10-42 silicate absorption. z. aud hence are in approximate order of increasing mass-loss rate. assundue roughlv simular hwunuinosities.," The spectra are ordered by increasing optical depth in the observed $\mu$ m silicate absorption, $\tau_{\rm s}$, and hence are in approximate order of increasing mass-loss rate, assuming roughly similar luminosities." By anocdelling the oeifrared excess cluission of O-rich AGB stars. Schutte Ticlens (1989)) aud Justtanout Ticlens (1992)) have determined the dust nass loss rates for several oexdividual O-rich ACB stars.," By modelling the infrared excess emission of O-rich AGB stars, Schutte Tielens \cite{schutte}) ) and Justtanont Tielens \cite{justtiel}) ) have determined the dust mass loss rates for several individual O-rich AGB stars." Their results are sumunarizec in Table 2.. where our sources are listed in the same order as in Fig. 1," Their results are summarized in Table \ref{massloss}, where our sources are listed in the same order as in Fig. \ref{fig1}." According to Table 2.. our saniple is indeed ordered with increasiug mass loss rate. excludiug WX Psc.," According to Table \ref{massloss}, our sample is indeed ordered with increasing mass loss rate, excluding WX Psc." " The values of z, measured frou the spectra are the apparent optical depth compared to our continua fit to the overall SED. or to an assiuned silicate emission profile for CRE 2199 and WX Psc."," The values of $\tau_{\rm s}$ measured from the spectra are the apparent optical depth compared to our continuum fit to the overall SED, or to an assumed silicate emission profile for CRL 2199 and WX Psc." " ""They therefore represent only a part of the total L0-jau silicate optical depth owardls the sources.", They therefore represent only a part of the total $\mu$ m silicate optical depth towards the sources. This is evident from Table 2.. where the measured Τ. are quoted. along with he optical depths derived for some of our sources by DmJusttanont Tieleus (1992)). using radiative transter modelling.," This is evident from Table \ref{massloss}, where the measured $\tau_{\rm s}$ are quoted, along with the $\mu$ m optical depths derived for some of our sources by Justtanont Tielens \cite{justtiel}) ), using radiative transfer modelling." A, A A ανασα]. classification scheme for miuor bodies in the outer solar svstem is preseuted by Claciuaetal.(2008) (hereafter GMIV).,A dynamical classification scheme for minor bodies in the outer solar system is presented by \citet{GlaMarVan08} (hereafter GMV). " Thev define inner classical belt objects as those that have semünajor axes ως than 39.1 AU. are not Centaurs, are not scattered disk objects. and are not in resonant orbits."," They define inner classical belt objects as those that have semimajor axes less than 39.4 AU, are not Centaurs, are not scattered disk objects, and are not in resonant orbits." " As explained in (ΛΙ, he stable tuner classical belt is not disconuecte from the main classical belt. which contains objects on stable. uon-resonanut orbits with @= I8 AU."," As explained in GMV, the stable inner classical belt is not disconnected from the main classical belt, which contains objects on stable, non-resonant orbits with = $-$ 48 AU." GAIV only classify objects that moet certain criteria for having sufficient astrometrv a9 of May 2006., GMV only classify objects that met certain criteria for having sufficient astrometry as of May 2006. Thev list 17 as inner classical Iuiper belt objects (hereafter ICKBO) objects. and over 250 main classical Kuiper belt objects (hereafter MCTISBOs)., They list 17 as inner classical Kuiper belt objects (hereafter ICKBO) objects and over 250 main classical Kuiper belt objects (hereafter MCKBOs). As more recent astromietry is available. we searched the continuously updated listing ofthe Deep Ecliptic Survey (DES) team (Elliotal.2005) for possible ICKDOs in additioa to those identified i CADW.," As more recent astrometry is available, we searched the continuously updated listing of the Deep Ecliptic Survey (DES) team \citep{Elliot05} for possible ICKBOs in addition to those identified in GMV." We searched for objects with < 39.1 AU which the DES team defiuitivelv classifies as “classical” objects based on their detailed orbital integrations.," We searched for objects with $<$ 39.4 AU which the DES team definitively classifies as “classical"" objects based on their detailed orbital integrations." Two adcditioua ΠΟΡΟΣ of the iuner classical belt (111897. anc Ww103 QAÀ92) were found in this wav., Two additional members of the inner classical belt (144897 and 2003 QA92) were found in this way. Neither of jese objects are classified in (ΛΑΟ, Neither of these objects are classified in GMV. ", Of the 17 ICKBOs identified in CATV. five are classified by the DES teal as “scatteres jer"" objects. rather than classical objects."," Of the 17 ICKBOs identified in GMV, five are classified by the DES team as “scattered near"" objects, rather than classical objects." Al five of these objects have orbital inclinations over1, All five of these objects have orbital inclinations over. "05, Thus. there is some disagreenieut over the classification of some objects in the < 39.1 AU region."," Thus, there is some disagreement over the classification of some objects in the $<$ 39.4 AU region." " However. all but one of the objects for which colors are available have orbital inclinatious less than103, and so are probably members of the iuner classical belt."," However, all but one of the objects for which colors are available have orbital inclinations less than, and so are probably members of the inner classical belt." If we use he CATV classification. augmented by the 2 additional objects. the iuner classical velt has 19 known objects.," If we use the GMV classification, augmented by the 2 additional objects, the inner classical belt has 19 known objects." INavelaarsetal.(2009) estimates that the inner disk KDBOs max have a population 10 to 20 times zinaller than the main belt., \citet{CFEPS09} estimates that the inner disk KBOs may have a population 10 to 20 times smaller than the main belt. " Evidence that the main classical Kuiper Belt is composed of a ""coll aud “lot” population has been presented bv Brown(2001)."," Evidence that the main classical Kuiper Belt is composed of a “cold"" and “hot"" population has been presented by \citet{Brown01}." .. There is sole evidence of differences in the physical properties between the cold auc hot populations (see. Peisinho.LacerdaaudJewitt(2008) andl references therein)., There is some evidence of differences in the physical properties between the cold and hot populations (see \citet{Pei08} and references therein). However the dividing liue iu inclination between the cold aud hot populations is not sharp. and indeed a simple dividing liue may uot be useful. as the two populations may overlap.," However the dividing line in inclination between the cold and hot populations is not sharp, and indeed a simple dividing line may not be useful, as the two populations may overlap." Drown(2001) models the two populatious as separate Gaussians in inclination. with the cold population having == aaud the hot having aaround177.," \citet{Brown01} models the two populations as separate Gaussians in inclination, with the cold population having = and the hot having around." . Culbis.ElliotaudKane(2006) use a inclination of about tto separate cold (core) and hot (halo) classical objects., \citet{Gulbis06} use a inclination of about to separate cold (core) and hot (halo) classical objects. Towever. Poeixiulho.LacerdaaudJewitt(2008) fud that tli colors of classical main belt objects are uniforiuly red up to an inclination of 12°-- that is. they do not see a break iu colors at57.," However, \citet{Pei08} find that the colors of classical main belt objects are uniformly red up to an inclination of - that is, they do not see a break in colors at." . Our initial eoa was fo measure the color of ICKDOs with he lowest values of aud as these could ο an extension of the main cold classical belt awards the Sun.," Our initial goal was to measure the color of ICKBOs with the lowest values of and, as these could be an extension of the main cold classical belt towards the Sun." If this were the case. the inner objects would exteud the seniunajor axis range of the classical belt aud provide a larger range of sciunmajor axis in which to look for correlations between seniuajor axis and plivsical properties than the «range provided bv the main cold classical belt KBOs alone.," If this were the case, the inner objects would extend the semimajor axis range of the classical belt and provide a larger range of semimajor axis in which to look for correlations between semimajor axis and physical properties than the range provided by the main cold classical belt KBOs alone." However. new results on the structure of the Ixuiper Belt obtained from surveys analyzed with observational biases taken iuto account (Navelaarsetal.2009) indicate the possibility that the iucr t objects are not analogous to the cold main belt but are perhaps more analogous to the hot classical volt objects;," However, new results on the structure of the Kuiper Belt obtained from surveys analyzed with observational biases taken into account \citep{CFEPS09} indicate the possibility that the inner belt objects are not analogous to the cold main belt but are perhaps more analogous to the hot classical belt objects." Such ho objects originate αἲ siguificantlv different heliocentrie distances upared to thei prescut locations., Such hot objects originated at significantly different heliocentric distances compared to their present locations. Iavelaarsetal.(2009) argue. from the uuuber of expectec and observed Πιο disk objects at low.. that the ιο disk is most likely devoid of a col coniponcnt. bu this conclusion is uncertain due to the small uuuber of Πο disk objects fou so far in their survey.," \citet{CFEPS09} argue, from the number of expected and observed inner disk objects at low, that the inner disk is most likely devoid of a cold component, but this conclusion is uncertain due to the small number of inner disk objects found so far in their survey." Tn contradiction to the I&aveliuusetal.(2009) results. LykawkaaudMui(2007) specifically posit a cold πιο disk.," In contradiction to the \citet{CFEPS09} results, \citet{LykMuk07} specifically posit a inner disk." These authors state that cold classical KBOs ave located in the inucr disk reeion- 37 AU 8 we recover 20 I07/C08 associations with one discrepant (SXDF850.10), translating to a completeness rate, with reliability."," For a reasonable evidence threshold, i.e. ln $B_{tot}>8$ we recover 20 I07/C08 associations with one discrepant (SXDF850.10), translating to a completeness rate, with reliability." " However it is possible, if not likely, that some of the associations presented in 107/C08 are not correct."," However it is possible, if not likely, that some of the associations presented in I07/C08 are not correct." " In fact C08 go so far as to indicate which associations they are not confident in; SXDF850.14, SXDF850.24, SXDF850.69, SXDF850.74 SXDF850.88."," In fact C08 go so far as to indicate which associations they are not confident in; SXDF850.14, SXDF850.24, SXDF850.69, SXDF850.74 SXDF850.88." Of these we only recover one with reasonable evidence (SXDF850.14)., Of these we only recover one with reasonable evidence (SXDF850.14). If we exclude these associations from our 107/C08 “truth” list then our completeness improves to72%., If we exclude these associations from our I07/C08 “truth” list then our completeness improves to. . Encouragingly these completeness and reliability rates are very close to those predicted from simulations in the previous section., Encouragingly these completeness and reliability rates are very close to those predicted from simulations in the previous section. A comparison of the photo-z estimates between C08 and here is given in Table 3.., A comparison of the $z$ estimates between C08 and here is given in Table \ref{tab:scubaresults}. " There is some level of agreement with the C08 photo-z measurements, although in a few cases the redshifts are clearly discrepant."," There is some level of agreement with the C08 photo-z measurements, although in a few cases the redshifts are clearly discrepant." " This is more clearly seen in Figure 4,, where the distribution of both sets of photo-z estimates is shown."," This is more clearly seen in Figure \ref{fig:zhist}, where the distribution of both sets of $z$ estimates is shown." Also shown is the redshift distribution for spectroscopically confirmed SCUBA galaxies from Chapman (2005)., Also shown is the redshift distribution for spectroscopically confirmed SCUBA galaxies from \nocite{Chapman2005}{ (2005). " The median redshift for associations presented here is z—1.73, slightly higher than the C08 measure of the same sample (z— 1.44) and significantly lowerthan the Chapman et al."," The median redshift for associations presented here is $z=1.73$, slightly higher than the C08 measure of the same sample $z=1.44$ ) and significantly lowerthan the Chapman et al." sample which has a median of z— 2.5., sample which has a median of $z=2.5$ . frequencies (IF. or equivalently. baseband converters) were recorded in each polarization. with 8 Ally per IF. and a total aggregate bit rate of 128 Mbits/s. The data were correlated bv the VLBA correlator in Soccoro.,"frequencies (IF, or equivalently, baseband converters) were recorded in each polarization, with 8 MHz per IF, and a total aggregate bit rate of 128 Mbits/s. The data were correlated by the VLBA correlator in Soccoro." The preliminary calibration. [ringe fitting. polarization calibration and imaging were done using the Astronomical Image Processing Svstem (AIPS) following standard methods.," The preliminary calibration, fringe fitting, polarization calibration and imaging were done using the Astronomical Image Processing System (AIPS) following standard methods." The global VLBI array used for the February 23. 1993 observations included the Effelsberg (EB). Green Bank (GB). and Medicina (AIC) telescopes. the phased Very Large Array (Y¥27). and the Hancock (LIN). North Liberty (NL). Brewster (BR) and Owens Valley (OV) VLBA antennas.," The global VLBI array used for the February 23, 1993 observations included the Effelsberg (EB), Green Bank (GB), and Medicina (MC) telescopes, the phased Very Large Array (Y27), and the Hancock (HN), North Liberty (NL), Brewster (BR) and Owens Valley (OV) VLBA antennas." Ellelshere was used as the reference antenna al all stages of the calibration., Effelsberg was used as the reference antenna at all stages of the calibration. The unpolarized source OQ 208 was used as the instrumental polarization (D-term) calibrator in the AIPS taskLPC'AL., The unpolarized source OQ 208 was used as the instrumental polarization $D$ -term) calibrator in the AIPS task. The absolute electric-vector polarization angle (EVPA or Y) calibration was performed by comparing the total VLBI-scale and (simultaneously measured) VLA core polarizations for the compact polarized source OJ 287., The absolute electric-vector polarization angle (EVPA or $\chi$ ) calibration was performed by comparing the total VLBI-scale and (simultaneously measured) VLA core polarizations for the compact polarized source OJ 287. The July 13. 1995 and June 23. 1993 observations were obtained using the ten telescopes ol the American VLBA.," The July 13, 1995 and June 28, 1998 observations were obtained using the ten telescopes of the American VLBA." Los Alamos was used as the reference antenna at all stages of the calibration., Los Alamos was used as the reference antenna at all stages of the calibration. " The unpolarized source 3C84 and the nearly unresolved polarized. source O749+540 were used for the D-term calibration for the July 1995 and June 1998 observations. respectively,"," The unpolarized source 3C84 and the nearly unresolved polarized source 0749+540 were used for the $D$ -term calibration for the July 1995 and June 1998 observations, respectively." Short 53-minute VLA snapshots of LO HEDLs. including five of the four lIBLs for which 1995.53 images are presented here. were made al 4.9. 8.4. and 15.0 GIIz on July 18. 1995. onlv a few davs after the July 1995 VLBA observations.," Short 2–3-minute VLA snapshots of 10 HBLs, including five of the four HBLs for which 1995.53 images are presented here, were made at 4.9, 8.4, and 15.0 GHz on July 18, 1995, only a few days after the July 1995 VLBA observations." We used the results of these 4.9 GlIIz observations lor OJ287 for the EVPA calibration of the VLBA data. assuming (hat the polarization position angle of OJ287 did not vary between the VLA and VLBI observations.," We used the results of these 4.9 GHz observations for OJ287 for the EVPA calibration of the VLBA data, assuming that the polarization position angle of OJ287 did not vary between the VLA and VLBI observations." Unfortunatelv. we did not have integrated. polarization measurements of any compact polarized sources observed during our June 1993 VLBA run nearby in time to those VLBA observations.," Unfortunately, we did not have integrated polarization measurements of any compact polarized sources observed during our June 1998 VLBA run nearby in time to those VLBA observations." Instead. we applied the EVPA calibration determined for VLBA observations in March. and April 1005. based on integrated polarization measurements within a lew davs of those experiments and using the same reference antenna (Los Alamos).," Instead, we applied the EVPA calibration determined for VLBA observations in March and April 1998, based on integrated polarization measurements within a few days of those experiments and using the same reference antenna (Los Alamos)." The EVPA, The EVPA surface of cach excised sphere: ὃν ia Eq.,surface of each excised sphere: $\partial/\partial r$ in Eq. denotes the radial derivative in a coordinate svstem centered. at the center of sphere 7., denotes the radial derivative in a coordinate system centered at the center of sphere $i$ . Figure | sketches the domain decomposition used for the computational domain D., Figure \ref{fig:Domains-BBH} sketches the domain decomposition used for the computational domain $\cal D$. We surround each excised sphere with a spherical shell., We surround each excised sphere with a spherical shell. These two splerical shells are matched together with 5«3 rectangular blocks. where the two blocks that contain the excised splieres Sy. are removed.," These two spherical shells are matched together with $5\times 3\times 3$ rectangular blocks, where the two blocks that contain the excised spheres $S_{1,2}$ are removed." Finally. we surround this structure with a third spherical shell extending to very large outer radius.," Finally, we surround this structure with a third spherical shell extending to very large outer radius." This gives a total of 16 subdomains. namely 3 shells aud. 13 rectangular blocks.," This gives a total of 46 subdomains, namely 3 shells and 43 rectangular blocks." Iu the iuner spheres we use a log mapping for the radial coordinate., In the inner spheres we use a log mapping for the radial coordinate. In the rectangular blocks. a combination of linear aud οσααπο mappings 1s used similar to the 2D example iu figure 2..," In the rectangular blocks, a combination of linear and logarithmic mappings is used similar to the 2D example in figure \ref{fig:SketchRectangles}." In the outer sphere an inverse mapping is used which is well adapted to the fall-off behavior c~1|ar++++ for laree radii +.," In the outer sphere an inverse mapping is used which is well adapted to the fall-off behavior $\psi\sim 1+a\,r^{-1}+\cdots$ for large radii $r$." The outer radius of the outer spherical shell is chosen to be 10? or 1019 and a Dirichlet boundary condition c= Lis used to approximate Eq., The outer radius of the outer spherical shell is chosen to be $10^9$ or $10^{10}$ and a Dirichlet boundary condition $\psi=1$ is used to approximate Eq. (55).. We now present two solutionswith different sizes aud locatious of the excised spheres., We now present two solutionswith different sizes and locations of the excised spheres. Iu sections 1.2.3 to 1.2.6. we then discuss several topics including preconcditioniug and parallelization.," In sections \ref{sec:Example2-Preconditioning} to \ref{sec:Example2-ParallelExecution}, we then discuss several topics including preconditioning and parallelization." First we choose two equal sized spheres with radi ry=ro1., First we choose two equal sized spheres with radii $r_1=r_2=1$. " The separation between the centers of the spheres is chosen to be 10. the outer radius of the outer sphereis 10°,"," The separation between the centers of the spheres is chosen to be 10, the outer radius of the outer sphereis $10^9$ ." (2001).,. ".. The advantage of this imiechauisni is that the oscillatory state is expected to be active only in a very narrow range of radi from r,,2rs tor, =les and hence a siunall rauge of accretion rates. as we observed for the 1 Tz QPO (see 3.2))."," The advantage of this mechanism is that the oscillatory state is expected to be active only in a very narrow range of radii from $r_{m}\simeq r_{c}$ to $r_{m}=1.5r_{c}$ and hence a small range of accretion rates, as we observed for the 1 Hz QPO (see \ref{fastdecayjump}) )." The Spruit-Taai instability could modulate the accretion flow at high amplitude. which would fit the observations of very high fractional rius amplitudes for the QPO.," The Spruit-Taam instability could modulate the accretion flow at high amplitude, which would fit the observations of very high fractional rms amplitudes for the QPO." The instability would also be compatible with the continued presence of accretion-powered pulsations. since accretion could still be fimneled even if the ier edee of the disk were oscillating.," The instability would also be compatible with the continued presence of accretion-powered pulsations, since accretion could still be funneled even if the inner edge of the disk were oscillating." Finally. the frequency of the iustabilitv has a weak depeudeuce on the mass accretion rate (see Fie.," Finally, the frequency of the instability has a weak dependence on the mass accretion rate (see Fig." " Lin Spruit&Taam 1993)). rising or falling whether r,, is greater or less than +..."," 4 in \citealt{spr93}) ), rising or falling whether $r_{m}$ is greater or less than $r_{c}$." This weak dependence las been observed in JLs0s (Fig. 7)), This weak dependence has been observed in J1808 (Fig. \ref{rms-flux-freq}) ) with thefrequency rising with X-ray fux. thus sugeestiug Fuzd," with thefrequency rising with X-ray flux, thus suggesting $r_{m}>r_{c}$." Tu sunu. most of the miecliauisiis examined eauuot. based on our current understanding of how thev work. explain key features of the 1 Wz OPO (see Table 2).," In summary, most of the mechanisms examined cannot, based on our current understanding of how they work, explain key features of the 1 Hz QPO (see Table 2)." The mechanisius that remain plausible are all associated with. or fine-tuned by. the onset of the propeller regime.," The mechanisms that remain plausible are all associated with, or fine-tuned by, the onset of the propeller regime." There are a nunibber of other pieces of evidence (ch 77)), There are a number of other pieces of evidence (cf. \ref{1Hz:intro}) ) that also point to major chanees in the accretion enviroment at the huuinositv where the 1 Uz QPO sets iu (Wijnandsctal.2001.. Wijuands 2003.. Campanactal. 2008)) - changes which might be explained by the onset of the propeller.," that also point to major changes in the accretion environment at the luminosity where the 1 Hz QPO sets in \citealt{wij01}, \citealt{wij03}, \citealt{cam08}) ) - changes which might be explained by the onset of the propeller." Ina addition there are timime results sugeesting a major clhauee iu disk structure around this time. such as the ~0.2 phase dift in the fundamental (arguiug for a major chauge iu the disk cnviromment around this time). the change iu the soft lag behavior (artimanetal.20095).. ancl the (debated) detection of an accretion torque (Burderiotal.2006:Tartinanet 2008).," In addition there are timing results suggesting a major change in disk structure around this time, such as the $\sim0.2$ phase drift in the fundamental (arguing for a major change in the disk environment around this time), the change in the soft lag behavior \citep{har09b}, and the (debated) detection of an accretion torque \citep{bur06, har08}." . The mechanism proposed by Spruit&Taam(1993) seclus to be the most promusing candidate to explain the Lz QPO. although the precise details of the time scales for this iustabilitv in the situation when funnel flows are relevant remain to be worked out.," The mechanism proposed by \citet{spr93} seems to be the most promising candidate to explain the 1 Hz QPO, although the precise details of the time scales for this instability in the situation when funnel flows are relevant remain to be worked out." It has a precise ouset point associated with the carly propeller regiae. should remain relatively stable iu frequency as accretion rate varies slightly aud is only expected in a narrow rauge of accretion rates.," It has a precise onset point associated with the early propeller regime, should remain relatively stable in frequency as accretion rate varies slightly and is only expected in a narrow range of accretion rates." Other mechanisius may also plav a role. perhaps in concert with the Spruit-Taam mstabilitv.," Other mechanisms may also play a role, perhaps in concert with the Spruit-Taam instability." In 1.2.0 we ueutioned that new classes of interchange iustabilities uieht operate near the propeller transition. perhaps cading to sporadic accretion.," In \ref{interchange} we mentioned that new classes of interchange instabilities might operate near the propeller transition, perhaps leading to sporadic accretion." In 1.2.0 we discussed he possibility of the ionization instability trigecring on short leugthseales in the inner regions of the disk once he source cuters the[um propeller regime., In \ref{thermalvisc} we discussed the possibility of the ionization instability triggering on short lengthscales in the inner regions of the disk once the source enters the propeller regime. This possibility is xuwtieularlv plausible if the disk is already close to the ransition frou outburst to quiescence., This possibility is particularly plausible if the disk is already close to the transition from outburst to quiescence. The ionization instability imuüsht reiutorce the Spruit-Taam instability uechanisia. and could also fine-tune the onset coucditious or the 1 Tz OPO (see ?27)).," The ionization instability might reinforce the Spruit-Taam instability mechanism, and could also fine-tune the onset conditions for the 1 Hz QPO (see \ref{1808etal}) )." The number of empty ficlds in Table 2 refiects the scale of the modeling work required to resolve these questions., The number of empty fields in Table 2 reflects the scale of the modeling work required to resolve these questions. Tt is hard to uuderstaud why the 1 Wz QPO does not appear diving the faint re-flares m the 2008 outburst., It is hard to understand why the 1 Hz QPO does not appear during the faint re-flares in the 2008 outburst. 8 out of 5? observations were in the 2-15 mCrab rauge diving the re-flaring state., 8 out of 57 observations were in the 2-15 mCrab range during the re-flaring state. The reason why the 1 IIz ΟΡΟ is uot observed in these 8 observations is aa open problem., The reason why the 1 Hz QPO is not observed in these 8 observations is an open problem. Although poorly coustrained. the 1998 outburst exhibited a similar behavior. aud on several occasions diving the 2000. 2002 aud 2005 outbursts the 1 Πε QPO also remained undetected even for fluxes iu the 2-15 mCrab ranec. with fractional ruis amplitude upper Μιάτς of ~105€.," Although poorly constrained, the 1998 outburst exhibited a similar behavior, and on several occasions during the 2000, 2002 and 2005 outbursts the 1 Hz QPO also remained undetected even for fluxes in the 2-15 mCrab range, with fractional rms amplitude upper limits of $\sim 10\%$." Clearly the 1 ITz QPO inechanisin is not always triggeredoo even in the 215 mCrab range in 1505., Clearly the 1 Hz QPO mechanism is not always triggered even in the 2–15 mCrab range in J1808. " Iu order to cuter the propeller regime. JlsO0S needs ο be at the point where r,,r.."," In order to enter the propeller regime, J1808 needs to be at the point where $r_m \sim r_c$ ." Equatiug the crude expressious elven in eq.(3)) aud CL). we obtain a relation οποσα accretion rate. magnetic field and spin rate.," Equating the crude expressions given in \ref{rc}) ) and \ref{rm}) ), we obtain a relation between accretion rate, magnetic field and spin rate." Figure 1) shows the conditions for propeller onset for articular combination of these parameters., Figure \ref{propeller} shows the conditions for propeller onset for particular combination of these parameters. " Clearly this Is Very approxinate. siuce it is based on the simplest estimates of r,, and 57. and ignores cependeucies on nass and radius. but suffücieut to uuderstaud whether he propeller scenario is a realistic possibility."," Clearly this is very approximate, since it is based on the simplest estimates of $r_m$ and $r_c$, and ignores dependencies on mass and radius, but sufficient to understand whether the propeller scenario is a realistic possibility." We plot the mass accretion rate values of three well shown AMNDPs: NTE J18507-291 (spin frequency 190 Tz). Jls0s (101 Wz) aud Τι J00291|291 (599 Iz).," We plot the mass accretion rate values of three well known AMXPs: XTE J1807-294 (spin frequency 190 Hz), J1808 (401 Hz) and IGR J00291+294 (599 Hz)." The first object was chosen because its spin frequency is one of the owest known annone AMINPs aud its outburst spans a wide range of Iuuünosities., The first object was chosen because its spin frequency is one of the lowest known among AMXPs and its outburst spans a wide range of luminosities. ICR 00291|29£ vas chose )ecause its neutron star has the hiehest spin frequency shown anone AMINPs., IGR J00291+294 was chosen because its neutron star has the highest spin frequency known among AMXPs. The mass accretion rates uxed in Fig., The mass accretion rates used in Fig. 10. are calculated Or N-rav fluxes in the 210 keV enerey baud. bx assuniue a neutron star imass of l. 1A. and an efficiency of for the conversion of rest mass enerev of the accreted imuaterial into N-rawv flux.," \ref{propeller} are calculated for X-ray fluxes in the 2–10 keV energy band, by assuming a neutron star mass of 1.4 $M_{\odot}$ and an efficiency of for the conversion of rest mass energy of the accreted material into X-ray flux." Since these lass accretion rates do not refer to bolometric fluxes. they have to be considered lower limits.," Since these mass accretion rates do not refer to bolometric fluxes, they have to be considered lower limits." We also marked the bolometric bpuuinositv of cach source (as reported in Cderlinskietal.2002.. Falaugaetal. 2005a.b)) for assunied distances of 8.5 kpe (IGR and NTE J1807-291) and 3.5 kpe (11505).," We also marked the bolometric luminosity of each source (as reported in \citealt{gie02}, \citealt{fal05a, fal05b}) ) for assumed distances of 8.5 kpc (IGR and XTE J1807-294) and 3.5 kpc (J1808)." The very broad range of luuinositics of JISOS are observed thanks to the deeper observations of 31. Campanactal. 2008)) and (AVijuaucls 2003).," The very broad range of luminosities of J1808 are observed thanks to the deeper observations of \ref{re-flarings}, \citealt{cam08}) ) and \citep{wij03}." . For all three sources. the couditious for propeller ouset should be encountered if the field streneth is ~105 Ci For JisOS. with a spin of LOL IIz aud an accretion rate that runs from a few percent of Eddington at peak. down to less than 0.001 iu the dips between the re-flares. the svsteni must always cuter the propeller regnuue at sane accretion rate. while for B«109 C the system will not cuter the propeller regiae in the observed rauge of mass accretion rates.," For all three sources, the conditions for propeller onset should be encountered if the field strength is $\sim 10^{8}$ G. For J1808, with a spin of 401 Hz and an accretion rate that runs from a few percent of Eddington at peak, down to less than 0.001 in the dips between the re-flares, the system must always enter the propeller regime at same accretion rate, while for $B<10^{6}$ G the system will not enter the propeller regime in the observed range of mass accretion rates." The range of magnetic fields is (B~OL 1.5« 105€) as reported by Hartinanetal. 2009a)..," The range of magnetic fields is $B\sim 0.4$ $1.5\times 10^{8}$ G) as reported by \citet{har08, har09}. ." The rauge of accretion rates for which the 1IIz QPO appears (iuferred from the 2-15 ιατα Nara flux. 3.2)) lies just below this range.," The range of accretion rates for which the 1 Hz QPO appears (inferred from the 2-15 mCrab X-ray flux,\ref{fastdecayjump}) ) lies just below this range." This coiucideuce is quite impressive since the accretion rates are lower limits., This coincidence is quite impressive since the accretion rates are lower limits. feature is blended with an line that strengthens toward the later (vpes (as do the other lines from (he latter ion). interfering with the visual trend: this blend is elucidated at a larger scale in Figure 5.,"feature is blended with an line that strengthens toward the later types (as do the other lines from the latter ion), interfering with the visual trend; this blend is elucidated at a larger scale in Figure 5." Finally. the trend is relatively weak throughout this range. although the ratio reverses between (he extreme cases of WD 150136 ad ;2 Cru (the spectrogram of ILD 93250 has lower S/N and is unreliable al the longer wavelengths).," Finally, the trend is relatively weak throughout this range, although the ratio reverses between the extreme cases of HD 150136 and $\beta$ Cru (the spectrogram of HD 93250 has lower S/N and is unreliable at the longer wavelengths)." The large N/O ratios in ¢ Pup and € Per are most likely abundance effects in processed material. as previously derived in the former spectrum by Kahn et ((2001) in agreement with prior photospheric/wind analyses: see also Oskinova. et ((2006).," The large N/O ratios in $\zeta$ Pup and $\xi$ Per are most likely abundance effects in processed material, as previously derived in the former spectrum by Kahn et (2001) in agreement with prior photospheric/wind analyses; see also Oskinova et (2006)." Note that the behaviors of the ionization ratios are themselves an ionization effect. with the intermediate Ne lines providing the best response to the relevant parameter range.," Note that the behaviors of the ionization ratios are themselves an ionization effect, with the intermediate Ne lines providing the best response to the relevant parameter range." Quantitative measurements (and corresponding uncertainties) of these line ratios. as well as the implied temperatures. are given by Waldron Cassinelli (2007).," Quantitative measurements (and corresponding uncertainties) of these line ratios, as well as the implied temperatures, are given by Waldron Cassinelli (2007)." We present measurements of the Ne ratios below., We present measurements of the Ne ratios below. It is noteworthy that the binary nature of several objects. which may have colliding winds. does not interfere with these observed trends. although it may contribute to some ol the scatter in them.," It is noteworthy that the binary nature of several objects, which may have colliding winds, does not interfere with these observed trends, although it may contribute to some of the scatter in them." Neither does the light to moderate range of interstellar extinctions among them (Table 1). for whieh no correction has been made here.," Neither does the light to moderate range of interstellar extinctions among them (Table 1), for which no correction has been made here." The seven stars with E(B-V) between 0.3 and 0.5 are expected to have emission features longward of 15 eexlincted by [actors up to 23., The seven stars with E(B-V) between 0.3 and 0.5 are expected to have emission features longward of 18 extincted by factors up to 2–3. One might be concerned that the earlier (wpe normal stars tend to have the higher interstellar extinctions. but ¢ Pup provides the counterexample with an early (vpe and low extinction that fits the X-ray line sequence well.," One might be concerned that the earlier type normal stars tend to have the higher interstellar extinctions, but $\zeta$ Pup provides the counterexample with an early type and low extinction that fits the X-ray line sequence well." OF course. wind or interstellar extinction always affects the longer wavelengths more. so it cannot cause the relatively weaker high ionization leatures at the later (vpes.," Of course, wind or interstellar extinction always affects the longer wavelengths more, so it cannot cause the relatively weaker high ionization features at the later types." Neither would it affect the ratios of the close pairs of IH-like to IHe-like lines significantly., Neither would it affect the ratios of the close pairs of H-like to He-like lines significantly. The present sample is not adequate to investigate Iuminosity effects in detail. but there are a [ew suggestive indications of an ionization correlation with that dimension as well.," The present sample is not adequate to investigate luminosity effects in detail, but there are a few suggestive indications of an ionization correlation with that dimension as well." As noted above. the line persists to a slighilv later (wpe in (he supergiants.," As noted above, the line persists to a slightly later type in the supergiants." More svstematically. it can be seen that the and lines remain stronger al later (vpes in the supergiants than on (he main sequence (see also Waldron Cassinelli 2007).," More systematically, it can be seen that the and lines remain stronger at later types in the supergiants than on the main sequence (see also Waldron Cassinelli 2007)." Indeed. + Ori rather breaks these trends in Figure 3. which may well be due to its giant nature.," Indeed, $\iota$ Ori rather breaks these trends in Figure 3, which may well be due to its giant nature." More extensive coverage of intermediate luminosity Classes wilh N-rav data of this equality is required to determine whether (hese effects correlate in detail with that dimension., More extensive coverage of intermediate luminosity classes with X-ray data of this quality is required to determine whether these effects correlate in detail with that dimension. burst. then the source decreased. by nearly four orders of magnitude in lux in one dav!,"burst, then the source decreased by nearly four orders of magnitude in flux in one day!" However. with the current data it cannot be assessed whether or not the source had a similar ecay rate in the time between the tvpe-I X-ray burst and vw start of the NRL observations.," However, with the current data it cannot be assessed whether or not the source had a similar decay rate in the time between the type-I X-ray burst and the start of the XRT observations." Furthermore. it is also unclear if the occurrence of the burst in some way triggered the decay. of the source or if the two are unrelated.," Furthermore, it is also unclear if the occurrence of the burst in some way triggered the decay of the source or if the two are unrelated." The observed tentative change in spectral shape has been seen for many neutron-star X-ray transients., The observed tentative change in spectral shape has been seen for many neutron-star X-ray transients. Phose systems typically change their spectral shape from thermally dominated. to non-thermal dominated: around a few times LO’? erg s (seec.g.Maccarone&Coppi2003:Gladstonectal.2007).. which is close to the X-ray. luminosity at which we observe the spectral shape of Swift J1749.4.2807 to change.," Those systems typically change their spectral shape from thermally dominated to non-thermal dominated around a few times $10^{36}$ erg $^{-1}$ \citep[see e.g.][]{2003MNRAS.338..189M,2007MNRAS.378...13G}, which is close to the X-ray luminosity at which we observe the spectral shape of Swift J1749.4–2807 to change." The exact duration of the outburst is also unclear., The exact duration of the outburst is also unclear. Lt is possible that the source was active for a considerable amount of time (clavs to even weeks) before the BAT burst occurred., It is possible that the source was active for a considerable amount of time (days to even weeks) before the BAT burst occurred. LW true. the 210 keV. tux of the source before the burst should not have been much above approximately 5.10 ος (corresponding to a few times 107 erg +) otherwise we would have detected the source with the ΑΗΑΡΑ," If true, the 2–10 keV flux of the source before the burst should not have been much above approximately $5 \times 10^{-10}$ erg $^{-1}$ (corresponding to a few times $10^{36}$ erg $^{-1}$ ) otherwise we would have detected the source with the /ASM." Lt is also possible that the rise and the peak were as fast as the decay observed in this source., It is also possible that the rise and the peak were as fast as the decay observed in this source. For a type- X-ray burst to occur. a certain amount of matter must be accreted.," For a type-I X-ray burst to occur, a certain amount of matter must be accreted." However. for ordinary neutron star LAINBs the bursts can recur within hours to a clay when they have luminosities similar to those observed for our source when the burst occurred (Gallowayetal.2006)...," However, for ordinary neutron star LMXBs the bursts can recur within hours to a day when they have luminosities similar to those observed for our source when the burst occurred \citep{2006astro.ph..8259G}." Pherefore. it is possible that the source was active for only a day or so and still accumulated enough matter to exhibit the burst. and then disappeared. again.," Therefore, it is possible that the source was active for only a day or so and still accumulated enough matter to exhibit the burst and then disappeared again." Sources which exhibit such short outbursts are easily missed by monitoring instruments., Sources which exhibit such short outbursts are easily missed by monitoring instruments. This could then indicate that a significant number of similar systems may be present in our Galaxy but which are usually missed when they are in outburst., This could then indicate that a significant number of similar systems may be present in our Galaxy but which are usually missed when they are in outburst. Their faint accretion luminosity and their short outbursts might make them very clillicult to detect with monitoring instruments: their bright tvpe X-ray bursts might also easily be Interestingly. there is one class of neutron-star X-ray binaries which might be such a class of sources and. which might be related to Swift J1749.4.2807: ve so-called: burst-only sources (seeCornelisseetal.2004.foranoverviewofthese sources).," Their faint accretion luminosity and their short outbursts might make them very difficult to detect with monitoring instruments; their bright type-I X-ray bursts might also easily be Interestingly, there is one class of neutron-star X-ray binaries which might be such a class of sources and which might be related to Swift J1749.4–2807: the so-called burst-only sources \cite[see][for an overview of these sources]{2004NuPhS.132..518C}." These svstenis are accreting neutron star sources which were discovered (mostly withBeppoSAX but also with INTEGRAL) because à type-L X-ray burst was detected. from them but which could not be detected outside the bursts with any of the monitoring instruments in orbit., These systems are accreting neutron star sources which were discovered (mostly with but also with ) because a type-I X-ray burst was detected from them but which could not be detected outside the bursts with any of the monitoring instruments in orbit. The accretion luminosities of these sources at the time of the tvpe-bE: X-ray bursts. should. be below ~107 erg s+ for them to remain uneetectable., The accretion luminosities of these sources at the time of the type-I X-ray bursts should be below $\sim$$10^{36}$ erg $^{-1}$ for them to remain undetectable. More. sensitive follow-up observations with for example or found that although some are. persistent sources with very low luminosities. most of them were likely neutron-star transients which most of the time were in a very dim cquiescent state (with X-ray luminosities of the order of 107 erg 5 or less: see Cornelisseetal.2002b.2004)).," More sensitive follow-up observations with for example or found that although some are persistent sources with very low luminosities, most of them were likely neutron-star transients which most of the time were in a very dim quiescent state (with X-ray luminosities of the order of $10^{32}$ erg $^{-1}$ or less; see \citealt{2002A&A...392..931C,2004NuPhS.132..518C}) )." In such systems. the tvpe-I bursts were seen during one of their very-faint X-ray outbursts.," In such systems, the type-I bursts were seen during one of their very-faint X-ray outbursts." " One of these burst-only sources (called SAX J2224.915421: Cornelissectal.2002a)) was of particular interest because within S hours after the Wide Field Camera ofBeppoS discovered. it through its burst""... AX pointed. at the sourceusing the Narrow Field. Instrument (NEL) and could detect the source only at a2 10 keV flux of ~13510Pores Lom 7 (Antonellietal.1999) resulting in a luminosity of Ss.1077 erg s (assumingadistanceof7.1kpe:Cornelisseetal. 2002a).."," One of these burst-only sources (called SAX J2224.9+5421; \citealt{2002A&A...392..885C}) ) was of particular interest because within 8 hours after the Wide Field Camera of discovered it through its , pointed at the sourceusing the Narrow Field Instrument (NFI) and could detect the source only at a 2–10 keV flux of $\sim 1.3\times 10^{-13}$ erg $^{-1}$ $^{-2}$ \citep{1999GCN...445....1A} resulting in a luminosity of $\sim 8 \times 10^{32}$ erg $^{-1}$ \citep[assuming a distance of 7.1 kpc;][]{2002A&A...392..885C}. ." This detection of the source at à very faint level only 8 hours after the occurrence of the burst is very reminiscent of what we have observed for Swift JI749.-42807., This detection of the source at a very faint level only 8 hours after the occurrence of the burst is very reminiscent of what we have observed for Swift J1749.4–2807. Only ~S hours after the burst. the ARP 210 keV Dux of Swift τι2807 had. decreased already to around 510 eres tem 7. which is of the same order of magnitude as the [lux observed. for SAN J22?P4.9|5421 outside its burst.," Only $\sim$ 8 hours after the burst, the XRT 2–10 keV flux of Swift J1749.4–2807 had decreased already to around $5\times 10^{-13}$ erg $^{-1}$ $^{-2}$, which is of the same order of magnitude as the flux observed for SAX J2224.9+5421 outside its burst." Cornelisseetal.(20025) suggested. that SAX 2224.9|5421 could be bursting at very low (near quiescent) X-ray luminosities. but our results on Swilt 1749.4.2807 also suggest that both sources could be very similar sources which exhibit a relatively faint (but not very faint) outburst but they decay. very. rapidly after the occurrence of their tvpe-E X-ray bursts.," \citet{2002A&A...392..931C} suggested that SAX J2224.9+5421 could be bursting at very low (near quiescent) X-ray luminosities, but our results on Swift J1749.4–2807 also suggest that both sources could be very similar sources which exhibit a relatively faint (but not very faint) outburst but they decay very rapidly after the occurrence of their type-I X-ray bursts." Determining the exact accretion. luminosity at which the bursts occur is important in understanding the burst physics since the burst. properties depend: strongly on the accretion rate at the time the burst occurs., Determining the exact accretion luminosity at which the bursts occur is important in understanding the burst physics since the burst properties depend strongly on the accretion rate at the time the burst occurs. Although the accretion situation is evident for Swift 1749.42807. it remains unclear lor SAN 2224.9|5421.," Although the accretion situation is evident for Swift J1749.4–2807, it remains unclear for SAX J2224.9+5421." Clearly. for these svstems and others similar to them. the very short slew time available with is necessary to distinguish between the cillerent scenarios.," Clearly, for these systems and others similar to them, the very short slew time available with is necessary to distinguish between the different scenarios." Swift J1749.4.2807 decaved rapidly to a constant level which was verv similar to what saw [rom he source six vears before the occurrence of the burst and our months after it., Swift J1749.4–2807 decayed rapidly to a constant level which was very similar to what saw from the source six years before the occurrence of the burst and four months after it. Therefore. this constant [Dux level very ikelv represents the quiescent [ux of the source which. for a distance of 6.7 προ results in à 210 keV luminosityof A5LO «1075 erg * (seealsoHalpern2006)..," Therefore, this constant flux level very likely represents the quiescent flux of the source which, for a distance of 6.7 kpc, results in a 2–10 keV luminosityof 0.5–1.0 $\times 10^{33}$ erg $^{-1}$ \citep[see also][]{2006GCN..5210....1H}." " ""Phis is very similar to the quiescent Luminosity seen for other neutron-star N-rav. transients in their quiescent state.", This is very similar to the quiescent luminosity seen for other neutron-star X-ray transients in their quiescent state. Sadly. due to he faintness of the source no spectral information could x obtained but the high Ny (as measured. in outburst with the NICE) in-front. of the source makes it cüllicult to detect any soft. thermal component and it is very likely that he emission we observe is (mostlv) due to a non-thermal component.," Sadly, due to the faintness of the source no spectral information could be obtained but the high $N_{\rm H}$ (as measured in outburst with the XRT) in-front of the source makes it difficult to detect any soft, thermal component and it is very likely that the emission we observe is (mostly) due to a non-thermal component." With the current data no sensible upper limits can be obtained on any thermal component with which we could test cooling mocels for acerction-heatec neutron stars., With the current data no sensible upper limits can be obtained on any thermal component with which we could test cooling models for accretion-heated neutron stars. A longer exposureobservation with (with thesource on-axis) or a deep observation (with its much lowerbackground) is needed to study the quiescent emission of this source with the detall necessary to allow, A longer exposureobservation with (with thesource on-axis) or a deep observation (with its much lowerbackground) is needed to study the quiescent emission of this source with the detail necessary to allow been observed with the IRS: 19 are in our program 40038. 4 in archival program 20125 (G. Lagache. PI.) one in archival program 20083. (M. Lacy. P.I.) and one in archival program 40539 (G. Helou. P.I.).,"been observed with the IRS: 19 are in our program 40038, 4 in archival program 20128 (G. Lagache, P.I.) one in archival program 20083 (M. Lacy, P.I.) and one in archival program 40539 (G. Helou, P.I.)." Characteristics and observational details of these 25 sources are 5given in Table I., Characteristics and observational details of these 25 sources are given in Table 1. Spilzer spectroscopic observations were made with the Short Low module in orders Land 2 (SLI and οἱ) and with the Long Low module in orders 1: and 2 (LL1 and LL2). described in Ποιοetal.(2004).," $Spitzer$ spectroscopic observations were made with the Short Low module in orders 1 and 2 (SL1 and SL2) and with the Long Low module in orders 1 and 2 (LL1 and LL2), described in \citet{hou04}." .. These give low resolution spectral coverage [rom 5 to 35πμ]., These give low resolution spectral coverage from $\sim$ to $\sim$. For our new observations. sources were placed on the slit by using the IRS peakup mocle with the blue camera < A « 18.7jmm)).," For our new observations, sources were placed on the slit by using the IRS peakup mode with the blue camera $<$ $\lambda$ $<$ )." All images when the source was in one of the two nod positions on each slit were coadded (o obtain the image of the source spectrum., All images when the source was in one of the two nod positions on each slit were coadded to obtain the image of the source spectrum. The background. whieh was subtracted was determined. from coacldecl background. images that added both nod positions having the source in the other slit (i.e.. both nods on the LL1 slit when the source is in the LL? slit produce LL1 images of background only).," The background which was subtracted was determined from coadded background images that added both nod positions having the source in the other slit (i.e., both nods on the LL1 slit when the source is in the LL2 slit produce LL1 images of background only)." The difference between coadded source images minus coadded background images was used [or the spectral extraction. eiving (wo independent extractions of the spectrum for each order.," The difference between coadded source images minus coadded background images was used for the spectral extraction, giving two independent extractions of the spectrum for each order." These independent spectra were compared to reject anv hiehlv outlving pixels in either spectrum. and a final mean spectrum was produced.," These independent spectra were compared to reject any highly outlying pixels in either spectrum, and a final mean spectrum was produced." The extraction of one dimensional spectra Irom the two dimensional images was done with the SMART analvsis package (Iigdonetal.2004).. beginning with the Basie Calibrated Data products. version 15. of the Spitzer [ux calibration pipeline.," The extraction of one dimensional spectra from the two dimensional images was done with the SMART analysis package \citep{hig04}, beginning with the Basic Calibrated Data products, version 15, of the $Spitzer$ flux calibration pipeline." Final spectra were to the approximate resolution of the different URS modules for SLI and SL2. for LL2. and [or LL1).," Final spectra were boxcar-smoothed to the approximate resolution of the different IRS modules for SL1 and SL2, for LL2, and for LL1)." Spectra for all FLS sources in Table 1 are illustrated among the spectra in Figures 1-4., Spectra for all FLS sources in Table 1 are illustrated among the spectra in Figures 1-4. Spectra for FLS starbursts are in Figure 1 and are truncated al in the rest [rame because of the absence of any significant features in the low resolution spectra bevond that wavelength: most Bootes starburst spectra were illustrated in (2007)., Spectra for FLS starbursts are in Figure 1 and are truncated at in the rest frame because of the absence of any significant features in the low resolution spectra beyond that wavelength; most Bootes starburst spectra were illustrated in \citet{hou07}. . Spectra for Bootes and FLS AGN in Table 3 are illustrated in Figures 2-4., Spectra for Bootes and FLS AGN in Table 3 are illustrated in Figures 2-4. Measured spectral parameters for all starbursts with URS spectra Irom FLS and Bootes, Measured spectral parameters for all starbursts with IRS spectra from FLS and Bootes for the seunple of Murphy: Webb et al.,"for the sample of Murphy, Webb et al." "tt. ""This result implies that B>>££). ancl therefore. it also means that the NLED contribution is quite negligible for this sample given the present estimate D,=(0.008+=0.002) μα CMbelek οἱ al."," This result implies that $B \gg B_1$, and therefore, it also means that the NLED contribution is quite negligible for this sample given the present estimate $B_1 = \left(0.008 \pm 0.002 \right)~\mu$ G (Mbelek et al." 2006)., 2006). Thus. we conclude from the measurements of Webb et al.," Thus, we conclude from the measurements of Webb et al." and Murphy et al., and Murphy et al. that over the redshift range 0.2 B_{c}$ (case of Murphy, Webb et al." samples). 0.5 trucem 3) a positive variation of eon. should be observed from any sample of absorbing intergalactic gas cloud such that D«D. (case of Levshakov ct al.," samples), 0.5 truecm 3) a positive variation of $\alpha_{\rm obs}$ should be observed from any sample of absorbing intergalactic gas cloud such that $B < B_{c}$ (case of Levshakov et al." sample)., sample). Aleanwhile. notice that the LL column densities are provided. neither by Srianand ct al.," Meanwhile, notice that the HI column densities are provided neither by Srianand et al.," Chand et. al., Chand et al. nor bv Levshakov et al., nor by Levshakov et al. for their studies on the cosmological variation of the fine structure constant., for their studies on the cosmological variation of the fine structure constant. However. Srianand et al.," However, Srianand et al." pointed. out. that. they have avoided. sub-Damped Lyman Alpha systems. ie. NCL)z10277 7 (Srianand et al.," pointed out that they have avoided sub-Damped Lyman Alpha systems, i. e., $N(HI) \geq 10^{19}$ $^{-2}$ (Srianand et al." 2004)., 2004). " Nevertheless. Boksenberg and Snijders (1981) derived limits to the neutral hvdrogen column density of 510! « Vf) 2en. from their observations of the 2.5,=15251 richest absorpsion system. identified: in the optical region towarels OQ 1101-264."," Nevertheless, Boksenberg and Snijders (1981) derived limits to the neutral hydrogen column density of 5 < N(H) 2, from their observations of the $z_{abs} = 1.8387$ richest absorpsion system identified in the optical region towards Q 1101-264." llence. on account that /N(£44)~INCIE)/1000. « AGIT): which implies 0.060 ; DLIUE recen in accordance with the magnitude of the magnetic field RETO rtereel ο. 1.1 « « −⋅2.6m derived from relation SSS(27)) and the new measurement of <$ by Levshakov et al. (" 2007).,2007). We have estimated the distances of the gas. cloud absorbers from the Llubble law by using Jf=68 km s Alpe+., We have estimated the distances of the gas cloud absorbers from the Hubble law by using $H_{0} = 68$ km $^{-1}$ $^{-1}$. We emphasize that the estimates of D. in relations (25)) and (30)) are consistent with the avalaible astrophysical data on the magnetic field strength within intergalactic gas clouds., We emphasize that the estimates of $B$ in relations \ref{le-champ-intensite}) ) and \ref{b-field-limit}) ) are consistent with the avalaible astrophysical data on the magnetic field strength within intergalactic gas clouds. By using a nonlinear eletrodvnamiücs theory in. which the ellective Lagrangian is the first. order. approximation (after. Alaxwell’s term) of a polynomial series of inverse powers of the electromagnetic invariant quantity δν we have presented a consistent explanation of the controversial results regarding a hypotctical variation of the fine structure constant à since the recombination era.," By using a nonlinear eletrodynamics theory in which the effective Lagrangian is the first order approximation (after Maxwell's term) of a polynomial series of inverse powers of the electromagnetic invariant quantity $F$, we have presented a consistent explanation of the controversial results regarding a hypotetical variation of the fine structure constant $\alpha $ since the recombination era." In these lines. one can state that the large set of observations of quasar absorption svstems are mapping the structure of the intergalactic magnetic field in several directions between the Earth ane absorbers in the sky. in addition to the expansion of the universe as a whole.," In these lines, one can state that the large set of observations of quasar absorption systems are mapping the structure of the intergalactic magnetic field in several directions between the Earth and absorbers in the sky, in addition to the expansion of the universe as a whole." In other words. the fact that the ballpark of the observations seem to be controversial could. be interpreted. as an indication that the strength of the local magnetic field in cach of the observed. systems is most likely different from each other.," In other words, the fact that the ballpark of the observations seem to be controversial could be interpreted as an indication that the strength of the local magnetic field in each of the observed systems is most likely different from each other." Lenee. any conclusive statement on the actual cosmological evolution of the fine structure constant à rests on a better understanding of the interealactic magnetic field. strength and structure over the whole sky. ancl also on more accurate measurements of the relative magnitude of the fine splitting between resonance absorption lines from far away (quasars.," Hence, any conclusive statement on the actual cosmological evolution of the fine structure constant $\alpha$ rests on a better understanding of the intergalactic magnetic field strength and structure over the whole sky, and also on more accurate measurements of the relative magnitude of the fine splitting between resonance absorption lines from far away quasars." he Av emission from those regions is partly due to voung stars (Ixnapen et al.,the $K$ emission from those regions is partly due to young stars (Knapen et al. 1995a.b).," 1995a,b)." Our NIB. imaging confirms he location of dust lanes and suspected SE regions. shown * Ixnapen et al. (," Our NIR imaging confirms the location of dust lanes and suspected SF regions, shown by Knapen et al. (" 1995a) in their £A colour index map.,1995a) in their $I-K$ colour index map. The locus of the cireumnuclear ring-like structure shows up ominentlv in all racial. profiles., The locus of the circumnuclear ring-like structure shows up prominently in all radial profiles. Unfortunatelv. noA/S Jt images are available.," Unfortunately, no NIR images are available." NGC 5248 is a galaxy with anHii nucleus and a lot of SE activity in the CNR., NGC 5248 is a galaxy with an nucleus and a lot of SF activity in the CNR. Elmeereen et al. (, Elmegreen et al. ( 1997) found very conspicuous central spiral arms. ancl several hotspots that form a ring-like spiral pattern.,"1997) found very conspicuous central spiral arms, and several hotspots that form a ring-like spiral pattern." Buta and Crocker (1993) detected a nuclear ring with a diameter of 10.17 aresec., Buta and Crocker (1993) detected a nuclear ring with a diameter of 10–17 arcsec. This activity shows up clearly in our broad-band NUR images. as well as in our colour index maps (Fig.," This activity shows up clearly in our broad-band NIR images, as well as in our colour index maps (Fig." 2k)., 2k). Spiral structure with star-forming arms. accompanied by dust lanes. is the dominant feature.," Spiral structure with star-forming arms, accompanied by dust lanes, is the dominant feature." The western spiral arm has colours which are redder by about 0.1 mag in JA than its counterpart in the east., The western spiral arm has colours which are redder by about 0.1 mag in $J-K$ than its counterpart in the east. Our J.A image has been published: earlier bv Laine et al. (, Our $J-K$ image has been published earlier by Laine et al. ( 1999).,1999). hey. compared it with the images obtained using adaptive optics. which show a nuclear erauxd-design spiral structure.," They compared it with the images obtained using adaptive optics, which show a nuclear grand-design spiral structure." This nuclear spiral. at scales of tens of pc. is not expected to show up in a single broad-band NIB image. even at.LEST resolution. and in fact does not. show up (Fig.," This nuclear spiral, at scales of tens of pc, is not expected to show up in a single broad-band NIR image, even at resolution, and in fact does not show up (Fig." 1)., 1). PheAST H-band image does show a wealth of structure in the CNR. again in the form of emitting regions distributed along spiral arm fragments. and accompanied by less Luminous regions which mav well be dusty.," The $H$ -band image does show a wealth of structure in the CNR, again in the form of emitting regions distributed along spiral arm fragments, and accompanied by less luminous regions which may well be dusty." As in other galaxies. we can see the signature of the ring asa peak at a radius of 7 arcsec in all radial profiles.," As in other galaxies, we can see the signature of the ring as a peak at a radius of $\sim7$ arcsec in all radial profiles." Phere is no evidence for nested bars., There is no evidence for nested bars. The dust structure in the cireumnuclear ring is the mos conspicuous feature in our JA colour index map. bu the star-forming regions in the ring can also be seen in the broad-band images (Fig.," The dust structure in the circumnuclear ring is the most conspicuous feature in our $J-K$ colour index map, but the star-forming regions in the ring can also be seen in the broad-band images (Fig." 2D., 2l). Phe bar dust lanes connect to this nuclear ring in the northeast and. southwest., The bar dust lanes connect to this nuclear ring in the northeast and southwest. Severa sites of SE are located along the ring. and its presence is also seen in the ellipticity and PA profiles. as well as in al other profiles (rig.," Several sites of SF are located along the ring, and its presence is also seen in the ellipticity and PA profiles, as well as in all other profiles (Fig." 21)., 2l). We can also see à blue ring at about 2 aresec. within the red. nuclear ring surrounding it.," We can also see a blue ring at about 2 arcsec, within the red nuclear ring surrounding it." Εις blue ring shows up as a dip in the JJ.A profile., This blue ring shows up as a dip in the $J-K$ profile. Its nature is not. clear. and needs further study.," Its nature is not clear, and needs further study." Ehe /-band image. used also by Pérrez ct al. (," The $H$ -band image, used also by Pérrez et al. (" 2000). shows a picture also seen in. e.g.. NGC 3351 and NGC 4314. namely of bright emitting knots,"2000), shows a picture also seen in, e.g., NGC 3351 and NGC 4314, namely of bright emitting knots" reaclions are taken from ?..,reactions are taken from \citet{caselli02}. The rates are temperature dependent and (he reaction rate between (wo species. / and j. is given by where 5;; = Los ο is the activation barrier to (he reaction). Vy is the total number of sites on the surface of the grain and vy is the grain number densitv.," The rates are temperature dependent and the reaction rate between two species, $i$ and $j$, is given by where $\kappa_{ij}$ = $^{-E_a/kT_{gr}}$ $E_a$ is the activation barrier to the reaction), $N_s$ is the total number of sites on the surface of the grain and $n_d$ is the grain number density." The rate at which 7 and j scan the surface of the grain is given by /; and /;: where £j is the binding energy (from Table 7)) aud i is given by Equation 5.., The rate at which $i$ and $j$ scan the surface of the grain is given by $t_i$ and $t_j$: where $E_D$ is the binding energy (from Table \ref{tab:be}) ) and $\nu_0$ is given by Equation \ref{eq:nu0}. Important parameters are (he binding energies of I1 and D atoms and (heir reaction rates on the grains., Important parameters are the binding energies of H and D atoms and their reaction rates on the grains. For the formation rate of I» we have used the work of ?? who developed a moclel of (his process that fits (he experimental data for the reaction of (vo hydrogen atoms on silicate and amorphous carbon grains.," For the formation rate of $_2$ we have used the work of \cite{ct02,ct04} who developed a model of this process that fits the experimental data for the reaction of two hydrogen atoms on silicate and amorphous carbon grains." Thev find that I» formation can be efficient. at temperatures up to 5500 Ix on these surfaces., They find that $_2$ formation can be efficient at temperatures up to 500 K on these surfaces. This model takes into account the possibility of both chemi- aud physi-sorption ancl assumes a high binding energy. of GOO Ix. [or atomic hvedrogen atoms adsorbed onto a silicate surface., This model takes into account the possibility of both chemi- and physi-sorption and assumes a high binding energy of 600 K for atomic hydrogen atoms adsorbed onto a silicate surface. This value of Ep(II) is rather higher than the 350 IN 72. which we have assumed in our previous work. and which results in a greatly reduced IH» formation rate at 7/2 15 IX. For deuterium atoms we follow ?. and take Ep(D) = Eph + 21 Ix (21 Ix is the zero point energy difference between the hydrogen and deuterium atoms).," This value of $E_D$ (H) is rather higher than the 350 K \cite{ta87} which we have assumed in our previous work, and which results in a greatly reduced $_2$ formation rate at $T$ $>$ 15 K. For deuterium atoms we follow \citet{caselli02} and take $E_D$ (D) = $E_D$ (H) + 21 K (21 K is the zero point energy difference between the hydrogen and deuterium atoms)." Recent caleulations of the binding energy of HE:atoms adsorbed onto water ice have founcl values ranging rom ~ 400 Ix (2). to ~ 575 Ix (2)..," Recent calculations of the binding energy of H–atoms adsorbed onto water ice have found values ranging from $\sim$ 400 K \citep{alh} to $\sim$ 575 K \citep{perets05}." Our choice of 600 IX is therefore a little high. but consistent with the larger of these calculatecl values.," Our choice of 600 K is therefore a little high, but consistent with the larger of these calculated values." Given the uncertainty in {11} we compare the results for Zp(Il) = 600 Ix with those for ZZp(Il) = 350 Ix in section 3.1.5 to determine the effects of our choice on the chemistry., Given the uncertainty in $E_D$ (H) we compare the results for $E_D$ (H) = 600 K with those for $E_D$ (H) = 350 K in Section \ref{sec:h_be} to determine the effects of our choice on the chemistry. lonization in the disk can arise from several sources:, Ionization in the disk can arise from several sources: "multiplicity the smaller the distortion to the interloper distribution compared to the normal one, whether oblate or prolate.","multiplicity the smaller the distortion to the interloper distribution compared to the normal one, whether oblate or prolate." Another interesting outcome of these simulations is we find a hard limit for the observable ellipsoid as a function of multiplicity and interloper rate (see Figure 7 for the prolate limits)., Another interesting outcome of these simulations is we find a hard limit for the observable ellipsoid as a function of multiplicity and interloper rate (see Figure \ref{limits} for the prolate limits). " The observable limit is smallest for groups with the lowest interloper rates and multiplicities, and worst for those with the highest interloper rates and highest multiplicities."," The observable limit is smallest for groups with the lowest interloper rates and multiplicities, and worst for those with the highest interloper rates and highest multiplicities." " The dependence on interloper rates is how one might expect, but the relation to multiplicity might not be so obvious."," The dependence on interloper rates is how one might expect, but the relation to multiplicity might not be so obvious." 'These trends are observed strongly for both prolate and oblate shapes., These trends are observed strongly for both prolate and oblate shapes. " A significant issue is the confusion effect: does the presence of interlopers make a prolate distribution look oblate and vica-versa, and how does multiplicity and the interloper rate affect the possibility of confusion?"," A significant issue is the confusion effect: does the presence of interlopers make a prolate distribution look oblate and vica-versa, and how does multiplicity and the interloper rate affect the possibility of confusion?" " When confusion occurs it is generally at the largest axial ratios, an understandable result since as prolate and oblate shapes move closer to spherical it requires à smaller amount of random distortion to transform one distribution into the other, and hence it doesn't affect prolate or oblate groups worse."," When confusion occurs it is generally at the largest axial ratios, an understandable result since as prolate and oblate shapes move closer to spherical it requires a smaller amount of random distortion to transform one distribution into the other, and hence it doesn't affect prolate or oblate groups worse." " It becomes easier to distinguish populations when the axial ratios are lower ( 0.5), however this improvement is lost when axial ratios are very small (less than the effective observable limit) because the distributions become very hard to fit at all"," It becomes easier to distinguish populations when the axial ratios are lower $\sim0.5$ ), however this improvement is lost when axial ratios are very small (less than the effective observable limit) because the distributions become very hard to fit at all." " The distortion is particularly evident for higher multiplicities, as can be seen in Figure 8.."," The distortion is particularly evident for higher multiplicities, as can be seen in Figure \ref{distortions}." " Here all the input axial ratios are 0.1 and the interloper rate is only596,, and yet the amount of distortion becomes quite significant as a function of multiplicity."," Here all the input axial ratios are 0.1 and the interloper rate is only, and yet the amount of distortion becomes quite significant as a function of multiplicity." " In contrast the quality of fitting for axial ratios of 0.7 is very good even when interloper rates are at20%,, as is evident from the QQ-plots in Figure 9.."," In contrast the quality of fitting for axial ratios of 0.7 is very good even when interloper rates are at, as is evident from the QQ-plots in Figure \ref{qqplots}." " 'The last finding of note is that interloper rates alone account for some degree of distribution broadening, on top of the aforementioned shift to more spherical populations."," The last finding of note is that interloper rates alone account for some degree of distribution broadening, on top of the aforementioned shift to more spherical populations." " T'his is understandable simply because we are modeling a binomial distribution (every Monte-Carlo galaxy has a chance of being an interloper as described by the interloper and as such there will be an associated spread in rate),observed shapes since when there are many interlopers a given group will appear more"," This is understandable simply because we are modeling a binomial distribution (every Monte-Carlo galaxy has a chance of being an interloper as described by the interloper rate), and as such there will be an associated spread in observed shapes since when there are many interlopers a given group will appear more" as archival of large. photometric catalogues. gravitational ensing and image cde-projection.,"as archival of large photometric catalogues, gravitational lensing and image de-projection." " .X precise method. to measure the shear induced by weak lensing on galaxy iniages is presented in an adjoining paper (Itefregier Bacon 2001. ""aper HD."," A precise method to measure the shear induced by weak lensing on galaxy images is presented in an adjoining paper (Refregier Bacon 2001, Paper II)." The application of Shapelets to interferometric images will be presented in Chang Itefregier (2001)., The application of Shapelets to interferometric images will be presented in Chang Refregier (2001). The analvtical results derived in this paper may also be useful or any application using the Edgeworth expansion. such as. for instance. the study of the growth. of cosmological »erturbations (Juskiewicg et al.," The analytical results derived in this paper may also be useful for any application using the Edgeworth expansion, such as, for instance, the study of the growth of cosmological perturbations (Juskiewicz et al." 1995 and reference therein)., 1995 and reference therein). This paper is organised as follows., This paper is organised as follows. " In refone,g. . wedeseribethemeainpropertiesofl dimensionalshapeletsanddiseusstheirconnectiontolhec(4 O."," In \\ref{one_d}, we describe the main properties of 1-dimensional shapelets and discuss their connection to the QHO." 1nt lwogquarlesian..weshowhow2 dimensionalshapelelscanbe formedandderiveanumberof practicalanalgl ical resulls.," In \\ref{two_d_cartesian}, we show how 2-dimensional shapelets can be formed and derive a number of practical analytical results." dnt refeonvolulion.. wediscusshowlheshapeletstatesbehaveunderceonvolulions.," In \\ref{convolution}, we discuss how the shapelet states behave under convolutions." IEnt wederivepolarshapeletsfromthecartesianbasisfunclionsanddescribesomcoftheirproperlics.," In \\ref{two_d_polar}, we derive polar shapelets from the cartesian basis functions and describe some of their properties." Int .wediscussseveraldirectapplicalionsofshapelelbs.," In \\ref{applications}, we discuss several direct applications of shapelets." Ourconclusionsarepresentedint conclusion., Our conclusions are presented in \\ref{conclusion}. We [first consider the description. of a. localisecl object in l-dimension., We first consider the description of a localised object in 1-dimension. " For this purpose. we first define the cimensionless basis functions where n is a non-negative integer and Z4,Gr) is a hermite polynomial of order η."," For this purpose, we first define the dimensionless basis functions where $n$ is a non-negative integer and $H_{n}(x)$ is a hermite polynomial of order $n$." These functions are orthonormal in the sense that where ον is the Kronecker delta symbol., These functions are orthonormal in the sense that where $\delta_{mn}$ is the Kronecker delta symbol. Phe first few functions are plotted on figure 1.., The first few functions are plotted on figure \ref{fig:hermite}. These functions. which we call “Shapelets’. can be thought of as shape perturbations around the gaussian Oy). Jo describe an object in. practice. we use the dimensional basis functions where 3 ds a characteristic scale. which is typically. chosen to be close to the size of the object.," These functions, which we call `Shapelets', can be thought of as shape perturbations around the gaussian $\phi_{0}(x)$, To describe an object in practice, we use the dimensional basis functions where $\beta$ is a characteristic scale, which is typically chosen to be close to the size of the object." These functions are also orthonormal. i.c. This infinite set of functions forms a complete basis for smooth and integrable Functions.," These functions are also orthonormal, i.e. This infinite set of functions forms a complete basis for smooth and integrable functions." Thus. a (sullicicntly well behaved) object. profile f(r) can be expanded as From the orthonormality condition (eq. 4].," Thus, a (sufficiently well behaved) object profile $f(x)$ can be expanded as From the orthonormality condition (Eq. \ref{eq:orthonorm}] ])," the shapelet coellicients are given hy In practice. the series of Equation (5)) will converge quickly if the object f(re) is sullieiently localised. and if: and the origin. =0 are not too cdilferent [rom the size and location of the object.," the shapelet coefficients are given by In practice, the series of Equation \ref{eq:decompose}) ) will converge quickly if the object $f(x)$ is sufficiently localised, and if $\beta$ and the origin $x=0$ are not too different from the size and location of the object." This series representation is referred to as the Gram-Charlicr series. or. in its asymptotic form. as the I5dgeworth expansion (see eg.," This series representation is referred to as the Gram-Charlier series, or, in its asymptotic form, as the Edgeworth expansion (see eg." Juiszkiewicz 1995 and reference therein), Juiszkiewicz 1995 and reference therein). These basis functions have a number of useful. properties., These basis functions have a number of useful properties. " Let us first consider their Fourier transform. which. for an arbitrary function. fr). is defined as With these conventions. the Fourier transform: of the dimensionless basis function ó,(£) is Thus. up to a phase factor. the dimensionless basis functions are invariant under Fourier transforms."," Let us first consider their Fourier transform, which, for an arbitrary function $f(x)$, is defined as With these conventions, the Fourier transform of the dimensionless basis function $\phi_{n}(\xi)$ is Thus, up to a phase factor, the dimensionless basis functions are invariant under Fourier transforms." This very useful property can be understood in physical terms from the analogy with the quantum harmonic oscillator (see relqho))., This very useful property can be understood in physical terms from the analogy with the quantum harmonic oscillator (see \\ref{qho}) ). The Fourier transform of the dimensional basis function (μη9) is given by ‘Thus. the Fourier transform acts on the basis Functions with an unsurprising change of scale ο tf.," The Fourier transform of the dimensional basis function $B_{n}(x;\beta)$ is given by Thus, the Fourier transform acts on the basis functions with an unsurprising change of scale $\beta \rightarrow \beta^{-1}$ ." correction to the GJ4436 photometry with the linear trend determined from the average of both reference stars yielded marginally smaller residuals from the light curve fit so it was utilized in the primary reduction.,correction to the 436 photometry with the linear trend determined from the average of both reference stars yielded marginally smaller residuals from the light curve fit so it was utilized in the primary reduction. The next step was to normalize the 4436 data to the same relative flux scale., The next step was to normalize the 436 data to the same relative flux scale. We were not successful at this no matter which combination of reference star data we used and the differences in the relative flux levels between visits were obvious by eye., We were not successful at this no matter which combination of reference star data we used and the differences in the relative flux levels between visits were obvious by eye. We believe that the primary reason for this is due to the varying position of 4436 in the instrument’s FOV., We believe that the primary reason for this is due to the varying position of 436 in the instrument's FOV. This happened because the two gyro guiding mode for the prevented the same spacecraft roll angle to be used for all the visits., This happened because the two gyro guiding mode for the prevented the same spacecraft roll angle to be used for all the visits. " The visit groups 1, 2, and 3 — 6 were each obtained at different rolls."," The visit groups 1, 2, and 3 – 6 were each obtained at different rolls." " The FGS FOV must not have a flat photometric response at the level our data are sensitive to in addition to the well studied variance in position aberration (i.e.theopticalfieldangledistortion, ?).."," The FGS FOV must not have a flat photometric response at the level our data are sensitive to in addition to the well studied variance in position aberration \citep[i.e. the optical field angle distortion,][]{mcarthur02}." " Examination of the un-normalized data for the multi-visit set obtained at the same roll show consistent, but still not perfect, relative flux levels."," Examination of the un-normalized data for the multi-visit set obtained at the same roll show consistent, but still not perfect, relative flux levels." This supports our hypothesis about the FOV variance., This supports our hypothesis about the FOV variance. The lower level disagreement for this group could be a result of still small variances in FOV position even among visits carried out with the same roll or the effects of stellar activity (?).., The lower level disagreement for this group could be a result of still small variances in FOV position even among visits carried out with the same roll or the effects of stellar activity \citep{demory07}. We see no way to distinguish between the these two effects with the current data., We see no way to distinguish between the these two effects with the current data. " The reference stars were never placed in the same position in the FOV as 4436, and indeed this would not have been possible due to guiding and FGS pointing restrictions."," The reference stars were never placed in the same position in the FOV as 436, and indeed this would not have been possible due to guiding and FGS pointing restrictions." " Therefore, the reference star data cannot be used to correct the relative flux levels of 4436."," Therefore, the reference star data cannot be used to correct the relative flux levels of 436." The time dependent response correction described above is still valid because that variance is most likely due to the thermal settling of the telescope itself and should be similar for all the targets., The time dependent response correction described above is still valid because that variance is most likely due to the thermal settling of the telescope itself and should be similar for all the targets. Our solution to the relative flux correction problem was to introduce normalization parameters for the data obtained in each of the visits that were solved for during the light curve analysis described in $3., Our solution to the relative flux correction problem was to introduce normalization parameters for the data obtained in each of the visits that were solved for during the light curve analysis described in 3. The relative flux levels for the visits determined from this analysis are given in Table 1.., The relative flux levels for the visits determined from this analysis are given in Table \ref{t1}. At this point in the reduction we had two time series (X and Y axes) for each of the six visits., At this point in the reduction we had two time series (X and Y axes) for each of the six visits. We summed the two sets to make a single time series and analyzed the data as described in $3., We summed the two sets to make a single time series and analyzed the data as described in 3. This analysis yielded very poor results., This analysis yielded very poor results. The residuals were much larger than expected from counting statistics and clearly correlated (trends and jumps) on ~ mminute timescales., The residuals were much larger than expected from counting statistics and clearly correlated (trends and jumps) on $\sim$ minute timescales. Inspection of the data revealed that the source for most of the unusual noise was the X axis data., Inspection of the data revealed that the source for most of the unusual noise was the X axis data. " When the data from the two axes were analyzed separately, we found that X axis data had residuals twice as large as those from the Y axis despite nearly identical count rates."," When the data from the two axes were analyzed separately, we found that X axis data had residuals twice as large as those from the Y axis despite nearly identical count rates." " Furthermore, the Y axis transit model residuals do not exhibit obvious correlations like the X axis data."," Furthermore, the Y axis transit model residuals do not exhibit obvious correlations like the X axis data." We don't have a definitive explanation for the lower quality of the X axis data., We don't have a definitive explanation for the lower quality of the X axis data. We note that since beginning science observations with the FGSIr in 2000 we have consistently (thousands of independent observations) obtained position residuals ~35% higher in X axis data compared to Y axis data when using the instrument for high-precision relative astrometry even though corrections determined from extensive calibration efforts are applied for this work (e.g.??)..," We note that since beginning science observations with the FGS1r in 2000 we have consistently (thousands of independent observations) obtained position residuals $\sim$ higher in X axis data compared to Y axis data when using the instrument for high-precision relative astrometry even though corrections determined from extensive calibration efforts are applied for this work \citep[e.g.][]{benedict07,bean07}." This discrepancy is similar in magnitude but opposite what was seen in data from FGS3 when it was used for science observations., This discrepancy is similar in magnitude but opposite what was seen in data from FGS3 when it was used for science observations. " The effect we see in the 4436 photometry is likely related to this issue, but relatively larger possibly due to a lack of any sort of known applicable correction."," The effect we see in the 436 photometry is likely related to this issue, but relatively larger possibly due to a lack of any sort of known applicable correction." We ultimately decided to set aside the X axis data because the expected V2 reduction in counting noise from including these data is more than negatively compensated by the larger errors introduced by using it., We ultimately decided to set aside the X axis data because the expected $\sqrt{2}$ reduction in counting noise from including these data is more than negatively compensated by the larger errors introduced by using it. " The final time series that we analyzed as described in $3 was created by binning only the Y axis HHz measurements to 60ss samples, which yielded 180 data points."," The final time series that we analyzed as described in 3 was created by binning only the Y axis Hz measurements to s samples, which yielded 180 data points." The adopted values for each bin were the average of the counts and the initial error estimate was the error in the mean., The adopted values for each bin were the average of the counts and the initial error estimate was the error in the mean. " These data are given in Table 2, which is only available electronically from the CDS."," These data are given in Table 2, which is only available electronically from the CDS." We modeled the obtained photometric time series of 4436 using the exact analytic formulae given by ? for a planetary transit., We modeled the obtained photometric time series of 436 using the exact analytic formulae given by \citet{mandel02} for a planetary transit. To account for the stellar limb darkening we calculated flux-weighted theoretical spectra for 18 different angles from the central line of sight and integrated them over the unique bandpass of the FGS with the F583W filter., To account for the stellar limb darkening we calculated flux-weighted theoretical spectra for 18 different angles from the central line of sight and integrated them over the unique bandpass of the FGS with the F583W filter. " We used the latest version of the PHOENIX model atmosphere code (?) for these calculations with the stellar parameters given by ? as determined from a spectral synthesis analysis (T.7 = KK, log g = 4.92, and [M/H] = -0.33)."," We used the latest version of the PHOENIX model atmosphere code \citep{hauschildt99} for these calculations with the stellar parameters given by \citet{bean06} as determined from a spectral synthesis analysis $T_{eff}$ = K, log g = 4.92, and [M/H] = -0.33)." We fitted the calculated, We fitted the calculated (,. "68) Here, we have multiplied the spectrum (52)) by normalization constant 32/9; such that the total energy radiated matches that given by Larmor’s formula (40)): ."," Here, we have multiplied the spectrum \ref{HyperAllmu}) ) by normalization constant $32/9\pi$ such that the total energy radiated matches that given by Larmor's formula \ref{larmor}) ):." " If the details of the emission on angular scales a*/L are unimportant, a 6-function’ aapproximation can be used."," If the details of the emission on angular scales $\accel/L$ are unimportant, a $\delta$ approximation can be used." " While the integration over solid angle cannot be found, a simple function that approximates the angular integrated spectrum is fracc3wa*),"," While the integration over solid angle cannot be found, a simple function that approximates the angular integrated spectrum is ),." The accuracy Lobof ATDthis approximation can be seen in Figure 2 where the function is plotted together with the numerically integrated value of (67)) for a range of L/a*.," The accuracy of this approximation can be seen in Figure \ref{HyperApproxFig} where the function is plotted together with the numerically integrated value of \ref{Hyperestimate}) ) for a range of $L/\accel$." The maximum photon energy produced can be reasonably approximated as mc2-LÉ[[a* =enspace., The maximum photon energy produced can be reasonably approximated as = = . ". As we discuss in section 5,, this that each electron that traverses the gap from x=0 to impliesx= produces on average ας photons of frequency ω~Wmax, Lwhere ar is the fine-structure constant."," As we discuss in section \ref{pulsars}, this implies that each electron that traverses the gap from $x=0$ to $x=L$ produces on average $\alpha_{\rm f}$ photons of frequency $\omega\sim\omega_{\rm max}$, where $\alpha_{\rm f}$ is the fine-structure constant." In this section we consider two special cases for which approximate or analytic expressions can be found., In this section we consider two special cases for which approximate or analytic expressions can be found. The first is an isolated structure containing a reversal of the the electric field., The first is an isolated structure containing a reversal of the the electric field. " To facilitate the analysis, we choose a particle orbit of the form with ((Q,))75)|Bo|<1, i.e., the particle starts and finishes its orbit at rest, while its position suffers a displacement of 20β0/Ώρ."," To facilitate the analysis, we choose a particle orbit of the form _0 ) with $\left|\beta_0\right|<1$, i.e., the particle starts and finishes its orbit at rest, while its position suffers a displacement of $2c\beta_0/\Omega_0$." The maximum particle speed is co., The maximum particle speed is $c\beta_0$. The electric field at the position of the particle isenspace., The electric field at the position of the particle is. ". Of the many functions E(x,f) that can provide such a trajectory, those representing an isolated structure that is either static or moving at constant, subluminal velocity (which is nowhere equal to the particle speed) are perhaps the that are physically realistic."," Of the many functions $E(x,t)$ that can provide such a trajectory, those representing an isolated structure that is either static or moving at constant, subluminal velocity (which is nowhere equal to the particle speed) are perhaps the simplest that are physically realistic." " In the static case, the electric simplestfield is simply E(x)="," In the static case, the electric field is simply E(x) =" bimodal. aud this division is somewhat arbitrary.,"bimodal, and this division is somewhat arbitrary." More precise age estimates will be enabled with the use of UV and/or Ho imaging: such data already exist [or a portion of the observed fielcl and will be utilized in a future paper., More precise age estimates will be enabled with the use of UV and/or $\alpha$ imaging; such data already exist for a portion of the observed field and will be utilized in a future paper. Of the 2920 star cluster candidates in our sample. 1877 (051) are blue. with 0.45.," Of the 2920 star cluster candidates in our sample, 1877 ) are blue, with $(B-V)_0<0.45$ ." The effect of our 7=23.5 magnitude limit is such that our cluster sample contains [aint clusters only if they are red., The effect of our $I=23.5$ magnitude limit is such that our cluster sample contains faint clusters only if they are red. The bluest clusters in our sample have V—722—0.5. so (he sample is not color-biased above V.—23 (Ady=—6.1).," The bluest clusters in our sample have $V-I \approx -0.5$, so the sample is not color-biased above $V=23$ $(M_V=-6.1)$." To this limit. there are 1715 cluster candidates of which 1260 (73%)) are blue.," To this limit, there are 1715 cluster candidates of which 1260 ) are blue." Figure 4. shows the spatial distribution of the MIOLI candidates. both the complete sample and the bright (V.«23) red and blue subsamples.," Figure \ref{color-spat} shows the spatial distribution of the M101 candidates, both the complete sample and the bright $V<23$ ) red and blue subsamples." The spiral pattern of the galaxy is more apparent in the blue clusters., The spiral pattern of the galaxy is more apparent in the blue clusters. This is consistent with them being vounger and associated with star formation in (he spiral aruis. and indeed the bluest clusters ((2—V)< 0.2) trace the arms even more clearly.," This is consistent with them being younger and associated with star formation in the spiral arms, and indeed the bluest clusters $(B-V)<0.2$ ) trace the arms even more clearly." Observed color distributions for the candidates ave shown in Figure 5.., Observed color distributions for the candidates are shown in Figure \ref{2color}. The left panel of this ligure compares the colors lor M1OI clusters to those in other nearby spirals: M81 (Chandaretal.2001a).. M33 (Mochejskaetal.1993).. and M51. (Biketal.2003): these colors have not been corrected [or reddening.," The left panel of this figure compares the colors for M101 clusters to those in other nearby spirals: M81 \citep{cft1}, M33 \citep{m98}, and M51 \citep{bik03}; these colors have not been corrected for reddening." The color distribution of MIOLI candidates is most similar to that of the M33 candidates. which is unsurprising given that the (wo galaxies are the same IIubble type ancl have a similar specilic star formation rate.," The color distribution of M101 candidates is most similar to that of the M33 candidates, which is unsurprising given that the two galaxies are the same Hubble type and have a similar specific star formation rate." ALLOL has [fewer blue elusters than M51. and fewer red. clusters than M81., M101 has fewer blue clusters than M51 and fewer red clusters than M81. This is broadly consistent. with a picture in which the proportion of blue to red clusters reflects the recent star formation rate (M51 might be expected (to have enhanced star formation due to encounters will its companion). and the number of red clusters is proportional to the galaxy. bulge mass (which is larger for M81. an earlier-tvpe galaxy (han MIOL).," This is broadly consistent with a picture in which the proportion of blue to red clusters reflects the recent star formation rate (M51 might be expected to have enhanced star formation due to encounters with its companion), and the number of red clusters is proportional to the galaxy bulge mass (which is larger for M81, an earlier-type galaxy than M101)." Chandaretal.(2001b) interpret the separation of M81 cluster colors into (wo groups (al D—V220.5 and V—J£22 1.0) as a separation in age., \citet{cft2} interpret the separation of M81 cluster colors into two groups (at $B-V\approx0.5$ and $V-I\approx1.0$ ) as a separation in age. No such clear separation is apparent in the MIOLI cluster candidates., No such clear separation is apparent in the M101 cluster candidates. In the right panel of Figure 5. we compare colors of red. MIOL cluster candidates (o those of globular clusters in the Milky Way (ILarris1996).. M31 (Darmbyοἱal.2000)... and elobular cluster candidates in MIOI itself from Chandaretal.(2004).," In the right panel of Figure \ref{2color} we compare colors of red M101 cluster candidates to those of globular clusters in the Milky Way \citep{h96}, M31 \citep{b00}, and globular cluster candidates in M101 itself from \citet{cwl04}." . The median colors ol MIOL cluster candidates are clearly consistent with those of the elobulars in the other ealaxies. indicating thal we have indeed detected a population of old elobular clusters in AI101.," The median colors of M101 cluster candidates are clearly consistent with those of the globulars in the other galaxies, indicating that we have indeed detected a population of old globular clusters in M101." The larger scatter of the ALLOL colors presumably reflects the larger photometric or recldenine-correction errors., The larger scatter of the M101 colors presumably reflects the larger photometric or reddening-correction errors. enough ions are present in the dissipation region. as we show below. then a source of anomalous resistivity can be established.,"enough ions are present in the dissipation region, as we show below, then a source of anomalous resistivity can be established." We argue that the energy. released. during the precursor was enough to heat the crust to a point where a barvon [aver was evaporated into the magnetosphere., We argue that the energy released during the precursor was enough to heat the crust to a point where a baryon layer was evaporated into the magnetosphere. TD95 provide an upper limit to the mass of the barvon laver ablated during a burst by comparing the thermal energy of the burst to that of the potential energy of the mass laver where we have assumed a more conservative estimate of fey., TD95 provide an upper limit to the mass of the baryon layer ablated during a burst by comparing the thermal energy of the burst to that of the potential energy of the mass layer where we have assumed a more conservative estimate of $E_{\rm th}$. Then. assuming that AZ amount of barvonic mass. in the form of protons. was injected into the magnetospheric volume of ~2? vielding a barvon number density of Even with the large amount of barvons. (the magnetospheric plasma is still. collisionless.," Then, assuming that $\Delta M$ amount of baryonic mass, in the form of protons, was injected into the magnetospheric volume of $\sim R_{\star}^3$ yielding a baryon number density of Even with the large amount of baryons, the magnetospheric plasma is still collisionless." " Phe Spitzer resistivity for a quasi-neutral clectron-ion plasma is only a function of the electron. temperature -x7, which for electron temperatures as high as 107 Ix vields a negligible resistivity."," The Spitzer resistivity for a quasi-neutral electron-ion plasma is only a function of the electron temperature $\propto T_e^{-3/2}$, which for electron temperatures as high as $\sim 10^8$ K yields a negligible resistivity." " For plasma temperatures higher than T3510"" Is. he reconnecting current laver turns into a super-hot urbulent current laver. (SIEECL). for which the theory ix been well developed by and. documented. in. (Somov 2006.. pp."," For plasma temperatures higher than $T>3\times10^7$ K, the reconnecting current layer turns into a super-hot turbulent current layer (SHTCL), for which the theory has been well developed by and documented in \citealt{Somov2006}, pp." 129-151)., 129-151). The anomalous resistivity in the current aver arises due to wave-particle interactions. where the ions interact with field [luctuations in the waves.," The anomalous resistivity in the current layer arises due to wave-particle interactions, where the ions interact with field fluctuations in the waves." As a result. the resistivity and other transport coellicients of the asma are altered.," As a result, the resistivity and other transport coefficients of the plasma are altered." " “Phe electrons are the current. carriers and participate mainlv in the heat conductive cooling of he οο,", The electrons are the current carriers and participate mainly in the heat conductive cooling of the SHTCL. " The current [laver is assumed to have been venetrated by a relatively weak transverse magnetic Lele component (transverse to the electric field in the current aver) where Dj,Bo with Do as the strength. of he external dipole field."," The current layer is assumed to have been penetrated by a relatively weak transverse magnetic field component (transverse to the electric field in the current layer), where $B_\perp\ll B_0$ with $B_0$ as the strength of the external dipole field." In the two temperature model. where the electrons and ions are allowed to have dissimilar emperatures. the ellective anomalous resistivity is generally a combination of two terms.," In the two temperature model, where the electrons and ions are allowed to have dissimilar temperatures, the effective anomalous resistivity is generally a combination of two terms." One resulting from the ion-acoustic turbulence and the other from the ion-evelotron urbulence., One resulting from the ion-acoustic turbulence and the other from the ion-cyclotron turbulence. In addition. cach turbulent instability has two separate regimes — marginal and saturated.," In addition, each turbulent instability has two separate regimes – marginal and saturated." The former applies when the wave-particle interactions are described by quasilinear equations. and the latter becomes important in the case of strong electric fields when the nonlinear contributions can no longer be ignored (see for e.g. Somov1992. pp.," The former applies when the wave-particle interactions are described by quasilinear equations, and the latter becomes important in the case of strong electric fields when the nonlinear contributions can no longer be ignored (see for e.g. \citealt{Somov1992} pp." 115-217 for a detailed description)., 115-217 for a detailed description). For an equal. temperature plasma (Z5.~ 77). the saturated: ion-evelotron turbulent instability makes the dominant contribution to the cllective resistivity.," For an equal temperature plasma $T_e\sim T_i$ ), the saturated ion-cyclotron turbulent instability makes the dominant contribution to the effective resistivity." Thus. we ignore any other terms corresponding to the ion-acoustic instability.," Thus, we ignore any other terms corresponding to the ion-acoustic instability." " Phe effective resistivity in the present case is given as (Somoy2006).. depending on the dimensionless temperature parameter 6—T,/1;. where a=rose is the cllective reconnection rate determined bv the inflow Εις velocity ey into the current [aver. and the rest of the variables in equation (12)) retain their usual meaning."," The effective resistivity in the present case is given as \citep{Somov2006}, depending on the dimensionless temperature parameter $\theta\equiv T_e/T_i$, where $\alpha\equiv v_0/c$ is the effective reconnection rate determined by the inflow fluid velocity $v_0$ into the current layer, and the rest of the variables in equation \ref{eq:effectiveEta}) ) retain their usual meaning." Equation (16)) conveys the frozen-in field condition., Equation \ref{eq:frozenin}) ) conveys the frozen-in field condition. Next. we write the magnetic diffusivity of the plasma due to the effective anomalous resistivity ↾↓∖∪≼⇍⋜↧↓≼⇍⊔↓⋜⋯⊾∣↓↕∢⋅⊲↓⊔∐∪∖∖⊽↓≻⇂⋜↧⊳∖⊔⋯∖⇁⋖⋅⇂∪≼⋰∐∙∖⇁⊳∖∖⊽∢⊾⋜↧⊳∖⊳∖⊔⊔↓⋖⋅ ↿↓⋯↿⇂↓↥∢⊾∺∐↾↓∖≺⊲∟↕⊳∖∢⋅⊔↓∣⋡⋯⇂∠⇂⋖⋅∠⇂∐↕⋜↧⊔↓⋯⇍↓⋅∪⊳∖≼∙∪↓≻⋠⊔∙∺∖∖⊽∢⋅∢⋅↥− Parker current. laver.," Next, we write the magnetic diffusivity of the plasma due to the effective anomalous resistivity To calculate the inflow plasma velocity, we assume that the SHTCL is embedded in a macroscopic Sweet-Parker current layer." The. primary. role of the. SITECIL is to provide enough resistivity in a collisionless plasma so that the magnetic field. lines can diffuse through it. and ultimately undergo reconnection., The primary role of the SHTCL is to provide enough resistivity in a collisionless plasma so that the magnetic field lines can diffuse through it and ultimately undergo reconnection. From equation. (7)) we know that for a Sweet-Parker current laver the inflow [uid velocity is regulated by the aspect ratio of the current Laver., From equation \ref{eq:vin}) ) we know that for a Sweet-Parker current layer the inflow fluid velocity is regulated by the aspect ratio of the current layer. The outllow: velocity is limited by the speed. of light., The outflow velocity is limited by the speed of light. By expressing the width of the Sweet-Parker current. [aver in terms of the magnetic dilfusivitv. we find that the inflow velocity has to be on the order of ej~10ems+ (so that ocx 1). with the width of the laver given as where the transverse magnetic field is By~10.Dy. and L is the length of the current laver.," By expressing the width of the Sweet-Parker current layer in terms of the magnetic diffusivity, we find that the inflow velocity has to be on the order of $v_0\sim10^3\mbox{ cm s}^{-1}$ (so that $\alpha\ll1$ ), with the width of the layer given as where the transverse magnetic field is $B_\perp\sim10^{-3}B_0$, and $L$ is the length of the current layer." The size of the SLUPCL can now be obtained from the following where e and b are. respectively. the half-width and the," The size of the SHTCL can now be obtained from the following where $a$ and $b$ are, respectively, the half-width and the" Low-power radio galaxies appear to be tuned such that their average jet kinetic powers. which are dictated by the rate of accretion onto a central supermassive black hole. provide the heating and momentum input required to limit star formation in their host galaxies by keeping the gas hot (e.g.. 2007)..,"Low-power radio galaxies appear to be tuned such that their average jet kinetic powers, which are dictated by the rate of accretion onto a central supermassive black hole, provide the heating and momentum input required to limit star formation in their host galaxies by keeping the gas hot \citep[e.g.,][]{granato, kawata, best, schawinski}." This adds to the interest in studying jets and their lifecycles. and one issue of importance in the study of this feedback process is how the kinetic power of individual sources varies with time.," This adds to the interest in studying jets and their lifecycles, and one issue of importance in the study of this feedback process is how the kinetic power of individual sources varies with time." Historically the radio emission has been used as a probe., Historically the radio emission has been used as a probe. However. the loss lifetimes of electrons responsible for the radiation exceed flow times along many resolvable jet structures. and thus the radiation that is observed holds only a time-averaged trace of changes to the central power output and local environmental effects along the jet.," However, the loss lifetimes of electrons responsible for the radiation exceed flow times along many resolvable jet structures, and thus the radiation that is observed holds only a time-averaged trace of changes to the central power output and local environmental effects along the jet." X-ray studies of low-power radio galaxies came into omruition withChandra. whose aresec-scale resolution (Weisskopfαal.2000). supports the common detection of resolved X-ray ynehrotron emission from their kpe-seale jets (Worrall.Birkin-ynaw&Hardeastle 20013..," X-ray studies of low-power radio galaxies came into fruition with, whose arcsec-scale resolution \citep{weisskopf} supports the common detection of resolved X-ray synchrotron emission from their kpc-scale jets \citep*{worrall01}. ." For X-ray emission the electron energy- lifetimes are short compared with light travel times over the Palructures that are detected. and a focus of much current work is therefore the use of X-ray emission as a probe of distributed particle acceleration (seeWorrall2009.forareview).," For X-ray emission the electron energy-loss lifetimes are short compared with light travel times over the structures that are detected, and a focus of much current work is therefore the use of X-ray emission as a probe of distributed particle acceleration \citep[see][for a review]{worrall}." Most resolved X-ray jets in low-power radio sources correspond to the brighter radio jet onlv. indicating that the X-rays are notdetected without the assistance of relativistic boosting," Most resolved X-ray jets in low-power radio sources correspond to the brighter radio jet only, indicating that the X-rays are notdetected without the assistance of relativistic boosting" We have introduced and presented a method dubbed that removes instrumental artefacts from CoRoT data and demonstrated its usefulness in some practical applications.,We have introduced and presented a method dubbed that removes instrumental artefacts from CoRoT data and demonstrated its usefulness in some practical applications. We emphasize that the algorithm can be used to prepares CoRoT data for any transit detection but should not be used for transit analysis because it can remove real signal., We emphasize that the algorithm can be used to prepares CoRoT data for any transit detection but should not be used for transit analysis because it can remove real signal. This is not of course a problem for the detection inasmuch as instrumental jumps affect far more the light curve., This is not of course a problem for the detection inasmuch as instrumental jumps affect far more the light curve. " From our study of 1030 light curves in the first CoRoT field (IRao01), we found that only very few light curves have no instrumentally caused features and remain as they are, while the vast majority of light curves are appreciably improved."," From our study of 1030 light curves in the first CoRoT field (IRao01), we found that only very few light curves have no instrumentally caused features and remain as they are, while the vast majority of light curves are appreciably improved." We have presented some examples that show how the algorithm affects the light curves., We have presented some examples that show how the algorithm affects the light curves. " Our main conclusion is that instrumental jumps substantially affect the CoRoT light curves, making a transit detection in fainter stars impossible."," Our main conclusion is that instrumental jumps substantially affect the CoRoT light curves, making a transit detection in fainter stars impossible." " To illustrate how the algorithm affect the data of the full sample, we calculated the median absolute deviation (MAD) before and after applying 13 "," To illustrate how the algorithm affect the data of the full sample, we calculated the median absolute deviation (MAD) before and after applying \ref{fig9} " We solve equation at several resolutions.,We solve equation at several resolutions. The hieliest resolution uses 297 collocation points in each rectangular block. 29«2112 collocation points (radial. ϐ and o directions) iu the iucr spherical shells aud 29«1632 im the outer spherical shell.," The highest resolution uses $29^3$ collocation points in each rectangular block, $29\times 21\times 42$ collocation points (radial, $\theta$ and $\phi$ directions) in the inner spherical shells and $29\times 16\times 32$ in the outer spherical shell." We use the differeuce in the solutions at neieliboriug resolutious as a iucasure of the error., We use the difference in the solutions at neighboring resolutions as a measure of the error. We denote the pointwise maxinuun of this difference bv {νε aud the rootziueau-square of the grid point values by £o., We denote the pointwise maximum of this difference by $L_{inf}$ and the root-mean-square of the grid point values by $L_2$. We also compute at cach resolution the quantity which is the total mass of the binary black hole system., We also compute at each resolution the quantity which is the total mass of the binary black hole system. AL will be needed iu the comparison to a finite difference code below., $M$ will be needed in the comparison to a finite difference code below. The difference AM between AL at ucieliboriug resolutions is again a measure of the error of the solution., The difference $\Delta M$ between $M$ at neighboring resolutions is again a measure of the error of the solution. Figure 5. shows the couvergeuce of the solution c with increasing resolution., Figure \ref{fig:Convergence-BBH} shows the convergence of the solution $\psi$ with increasing resolution. Since the rectangular blocks aud the spheres have ciffereut ummbers of collocation points. the cube root of the total number of degrees of freedom. Nog is used to label the w-asis.," Since the rectangular blocks and the spheres have different numbers of collocation points, the cube root of the total number of degrees of freedom, $N_{DF}^{1/3}$ is used to label the $x$ -axis." The exponential convergence is apparent., The exponential convergence is apparent. Because of the exponcutial convergence. and because Linf. L2 and AA utilize differences to the next lower resolution. the errors given iu figure 5 are esseutially the errors of the nextlower resolution.," Because of the exponential convergence, and because Linf, L2 and $\Delta M$ utilize differences to the next lower resolution, the errors given in figure \ref{fig:Convergence-BBH} are essentially the errors of the next resolution." " Note that at the highest resolutious the approximation of the outer boundary condition bv a Dirichlet bouudiryv coudition at finite outer radius 109 becomes appareut: If we move the outer boundary to 1010, AZ changes by 2-10.? which is of order 1/109 as expected."," Note that at the highest resolutions the approximation of the outer boundary condition by a Dirichlet boundary condition at finite outer radius $10^9$ becomes apparent: If we move the outer boundary to $10^{10}$, $M$ changes by $2\cdot 10^{-9}$ which is of order $1/10^9$ as expected." Ou the coarsest resolution c= Lis used as the initial euess;, On the coarsest resolution $\psi=1$ is used as the initial guess. Newtou-Raplsou then needs six iterations to converge., Newton-Raphson then needs six iterations to converge. On the finer resolutions we use the result of the previous level as the initial guess., On the finer resolutions we use the result of the previous level as the initial guess. These initial guesses are so good that one Newtou-Raplson iteration is sufficient on cach resolution., These initial guesses are so good that one Newton-Raphson iteration is sufficient on each resolution. "No Stokes I or V variability has been found forJ1354-0206,, neither for the several sources close toVir.","No Stokes I or V variability has been found for, neither for the several sources close to." . Dynamical spectra are shown in Fig. 1.., Dynamical spectra are shown in Fig. \ref{spe}. " Heliocentric rotational phases, computed by using the ephemerisby Pyperetal.(1998),, indicate that the peak ""a"" of April 23rd and the ""b"" of April 30th occur at the same phase (¢z 0.55), when the star is oriented in space in the same way relatively to the Earth."," Heliocentric rotational phases, computed by using the ephemerisby \citet{pyp98}, indicate that the peak ""a"" of April 23rd and the ""b"" of April 30th occur at the same phase $\phi\approx 0.55$ ), when the star is oriented in space in the same way relatively to the Earth." Fig., Fig. " 2 shows the polarized flux average in the two bands as a function of the rotational phase, stressing the coincidence in phase of ""à"" and ""b"" events and a significant level of variability between the two observations."," \ref{phase} shows the polarized flux average in the two bands as a function of the rotational phase, stressing the coincidence in phase of ""a"" and ""b"" events and a significant level of variability between the two observations." " All the three events last approximately 1 hour each; ""c"" exhibits a single peak of flux levels of about 20 mJy; ""a"" and ""b"" lower and broader emission, with two components in the ""b"" event."," All the three events last approximately 1 hour each; ""c"" exhibits a single peak of flux levels of about 20 mJy; ""a"" and ""b"" lower and broader emission, with two components in the ""b"" event." " The phase difference between ""a"" (or ""b"") and ""c"" events is about 0.4."," The phase difference between ""a"" (or ""b"") and ""c"" events is about 0.4." " This allows to recognize the same peaks of emission reported by Trigilioetal. (2000),, Trigilioetal.(2008) and"," This allows to recognize the same peaks of emission reported by \citet{tri00}, , \citet{tri08} and" We may relate the outer vertical scale of the turbulence L- to the height of the disk H by introducing yet another parameter L- = mss where #j-«I.,We may relate the outer vertical scale of the turbulence $L_z$ to the height of the disk $H$ by introducing yet another parameter L_z = H where $\eta_z< 1$ . " Recalling that H/A,~7. the wave temperature becomestau;-2n."," Recalling that $H/\lambda_p \simeq \tau$, the wave temperature becomes." Now. we may write the turbulent v-parameter as ye _(64) where nduip<| and 7? was chosen since 7>| for thin disks.," Now, we may write the turbulent $y$ -parameter as ) ) where $\eta^{2r}_R\,\eta^{2s}_{\phi}\,\eta^{2n}_z\leq 1 $ and $\tau^2$ was chosen since $\tau > 1$ for thin disks." Interestingly. eq. (61))," Interestingly, eq. \ref{reducedtemp}) )" " tells us that 744,9.»Z4) if ", tells us that $T_w(\lambda_p)\rightarrow T_w(\lambda_0)$ if 1. This is only possible near the inner-edge since for thin disks., This is only possible near the inner-edge since for thin disks. " Close to the hole. where a large fraction of the disk’s power is released. A, approaches Ao as long as 7/ and n are sufficiently large."," Close to the hole, where a large fraction of the disk's power is released, $\lambda_p$ approaches $\lambda_0$ as long as ${\dot m}$ and $\alpha$ are sufficiently large." " When this is the case. v, is roughly given by the product of the wave temperature on the outer scale T.(Ao) and the square of the optical depth tau"," When this is the case, $y_w$ is roughly given by the product of the wave temperature on the outer scale $T_w(\lambda_0)$ and the square of the optical depth ^2." Equations (40)) and (68)) then allow us to writeC, Equations \ref{kerrwavetemp}) ) and \ref{tau}) ) then allow us to write. "A*(72) That is. when A,~Ao. the turbulent y-parameter is approximatelyr"," That is, when $\lambda_p\sim\lambda_0$ , the turbulent $y$ -parameter is approximately." "adius, Figure 1. shows turbulent wave temperatures for maximally spinning black holes of varying 7 and o.", Figure \ref{fig:wavetemp} shows turbulent wave temperatures for maximally spinning black holes of varying ${\dot m}$ and $\alpha$. " The radius at which 7; reaches its maximum value coincides with the most luminous radius of the disk. a consequence of 7), directly scaling with the aceretion stress."," The radius at which $T_w$ reaches its maximum value coincides with the most luminous radius of the disk, a consequence of $T_w$ directly scaling with the accretion stress." " The curves shown in Figure 1. are independent of black hole mass. a result of c, and 7 being independent of black hole mass."," The curves shown in Figure \ref{fig:wavetemp} are independent of black hole mass, a result of $c_s$ and $\tau$ being independent of black hole mass." " The curve labeled ""c"" depicts turbulent wave temperatures for vi and a = 0.1.", The curve labeled “c” depicts turbulent wave temperatures for ${\dot m}$ and $\alpha$ = 0.1. For this particular case. the turbulence was confined to the upper-most 1/10 of the disk.," For this particular case, the turbulence was confined to the upper-most 1/10 of the disk." Confinement of the turbulence to a thin upper layer may be possible since regions of large magnetic pressure will be relatively buoyant., Confinement of the turbulence to a thin upper layer may be possible since regions of large magnetic pressure will be relatively buoyant. Identical wave temperatures and y-parameters may be attained for a given jn by reducing «| by afactor £ while confining the turbulence to a narrow upper layer whose optical thickness is 7/f. implying that the local turbulentstresses are f£ times larger than the vertically averaged value.," Identical wave temperatures and $y$ -parameters may be attained for a given ${\dot m}$ by reducing $\alpha$ by a factor $f$ while confining the turbulence to a narrow upper layer whose optical thickness is $\tau/f$, implying that the local turbulentstresses are $f$ times larger than the vertically averaged value." Of course. this onlyapplies for our constant density disk atmosphere model where each optical depth occupies an equal amount of height.," Of course, this onlyapplies for our constant density disk atmosphere model where each optical depth occupies an equal amount of height." (A1240) = 0.6 7+0.07 and Lyo (AL216) = 0.87 + 0.03.,$\lambda$ 1240) = 0.67 $\pm$ 0.07 and $\alpha$ $\lambda$ 1216) = 0.87 $\pm$ 0.03. Fhree important conclusions arise [rom these results., Three important conclusions arise from these results. First. we clo not obtain any [αἱ correlation between the DaA values and the waveleneth/ceeree of ionization.," First, we do not obtain any fair correlation between the $B/A$ values and the wavelength/degree of ionization." Second. the average of the five measurements is z 0.75. Le. totally consistent with the macrolens ratio.," Second, the average of the five measurements is $\approx$ 0.75, i.e., totally consistent with the macrolens ratio." Third. for each pair of lines. there are several individual channes (at some wavelenghs within the integrationD interval) leading5 to {ux ratios in disagreement with the macrolens ratio.," Third, for each pair of lines, there are several individual channels (at some wavelengths within the integration interval) leading to flux ratios in disagreement with the macrolens ratio." " T""herefore. it is not suroising to infer an anomalous [ux ratio from a refatively small collection of channels."," Therefore, it is not surprising to infer an anomalous flux ratio from a relatively small collection of channels." For example. due o the resolution of the gratings and the presence of prominent absorption features and blending. theIL. and Lye lines are studied through 317 channels.," For example, due to the resolution of the gratings and the presence of prominent absorption features and blending, the, and $\alpha$ lines are studied through 13–17 channels." However. we use 3637 channels or the and lines (see Table 1).," However, we use 36–37 channels for the and lines (see Table 1)." We interpret the continuumemission lines results in the following wav: while the bro:wlline emission region (BLIZIU) does not experience cilerential extinction as a whole. the continuum source and some substructures of the BLER do suller it.," We interpret the continuum/emission lines results in the following way: while the broad–line emission region (BLER) does not experience differential extinction as a whole, the continuum source and some substructures of the BLER do suffer it." Thus. a network of com»wt clusty clouds in he lens galaxy secms to be involved.," Thus, a network of compact dusty clouds in the lens galaxy seems to be involved." The longimescale evolution of D/:A in the £2? optical filter agrees with our interpretation (Oscoz et al., The long–timescale evolution of $B/A$ in the $R$ optical filter agrees with our interpretation (Oscoz et al. 2002)., 2002). Phe lack of microlensing in the continuum ratios suggests that no stars are present within the dusty regions crossing the A and D images., The lack of microlensing in the continuum ratios suggests that no stars are present within the dusty regions crossing the A and B images. Hence. the ckμις do not seem to be associated to stars and the network is probably embedded in the elliptical galaxy dark halo.," Hence, the clouds do not seem to be associated to stars and the network is probably embedded in the elliptical galaxy dark halo." Spectroscopy. and multiband photometry of lensecl quasars ave throwing light on the cdillerential extinction. and microlensing of the continuum and emission line regions., Spectroscopy and multiband photometry of lensed quasars are throwing light on the differential extinction and microlensing of the continuum and emission line regions. Apart from our concusions on the CER and BLER of QSO 0957|561 (there is clillerential extinction of the CLR and some substructures of the BLER. but no gravitational microlensing) there are other very recent results on the subject.," Apart from our conclusions on the CER and BLER of QSO 0957+561 (there is differential extinction of the CER and some substructures of the BLER, but no gravitational microlensing) there are other very recent results on the subject." For example. Wucknitz ct αἱ. (," For example, Wucknitz et al. (" 2003) analvzed data of QSO LE 3329.,2003) analyzed data of QSO HE $-$ 3329. Assuming that the emission line [lux ratios are only alfected by dillercntial extinction. the authors properly. corrected. the continuum flux ratios and found evidence for a microlensed CLR.," Assuming that the emission line flux ratios are only affected by differential extinction, the authors properly corrected the continuum flux ratios and found evidence for a microlensed CER." Wavth. ODowd Webster (2005) also reported [ux ratios of QSO 237|0305.," Wayth, O'Dowd Webster (2005) also reported flux ratios of QSO 2237+0305." After applying corrections for cilferential extinction. they argued that both the CER and BLER must be microlensed.," After applying corrections for differential extinction, they argued that both the CER and BLER must be microlensed." We note that the four images of the system cross the bulge of a faceon Sab spiral galaxy., We note that the four images of the system cross the bulge of a face–on Sab spiral galaxy. Finally. from data of," Finally, from data of" of 400 s. We do this to avoid apparent Dux variations due to the ROSA wobble period of about 400 s. Brinkmann et al. (,of 400 s. We do this to avoid apparent flux variations due to the $ROSAT$ wobble period of about 400 s. Brinkmann et al. ( 1994) have shown that [lux determination in wobble mocde is good to within 4 per cent when binning over integer multiples of the 400 s wobble period.,1994) have shown that flux determination in wobble mode is good to within $\sim$ 4 per cent when binning over integer multiples of the 400 s wobble period. Moreover. for each time scale a careful analysis of the background. was mace to ensure that observed. variability is not due to a change in the background rate.," Moreover, for each time scale a careful analysis of the background was made to ensure that observed variability is not due to a change in the background rate." The light curve of all the sources obtained with a bin of 3600 s are shown in Figure 1., The light curve of all the sources obtained with a bin of 3600 s are shown in Figure 1. For each observation we report the source light curve (top panel) and. [or comparison. the background light curve (lower panel).," For each observation we report the source light curve (top panel) and, for comparison, the background light curve (lower panel)." 1n order to understand and to interpret the properties, In order to understand and to interpret the properties "Unfortunately, |Zu/IE| estimates exist for only six DLAS of the sample aud for oulv one low T. syste (the :~0.395 absorber towards PISS 1229-021) (Boisséetal.1998.Pettiui1991.Pettini1997.Aleveretal.1989.Mever&York 1992)).","Unfortunately, [Zn/H] estimates exist for only six DLAS of the sample and for only one low ${\rm T_s}$ system (the $z \sim 0.395$ absorber towards PKS 1229-021) \cite{boisse98,pettini94,pettini97,meyer89,meyer92}) )." These values are plotted agaimst spin teniperature in Fie. 5:, These values are plotted against spin temperature in Fig. \ref{fig:znts}; it can be seen that the low Ty system has the highest |Zu/II| ratio of all six absorbers., it can be seen that the low ${\rm T_s}$ system has the highest [Zn/H] ratio of all six absorbers. It would be very interesting to test whether this trend persists. for the other absorbers in the salple.," It would be very interesting to test whether this trend persists, for the other absorbers in the sample." Fies., Figs. 6 and 7 plot the velocity spreac AV (ful width between uulls) of the syvstenus with detecte 21 cin absorption against redshift aud spin temperature. respectively. (," \ref{fig:vel} and \ref{fig:vel_ts} plot the velocity spread $\dV$ (full width between nulls) of the systems with detected 21 cm absorption against redshift and spin temperature, respectively. (" The total velocity spread is used. imstead of the EFWIIM of the absorption profile. to account for the possibility that a sinele line of sight intersects multiple clouds. as is typical iu spiral οealaxics.),"The total velocity spread is used, instead of the FWHM of the absorption profile, to account for the possibility that a single line of sight intersects multiple clouds, as is typical in spiral galaxies.)" The plot of AV versus redshift indicates that aree velocity spreads (AV>100 lan ?) ave not found for :=2. while both large and simall spreads are seen at low redshift.," The plot of $\dV$ versus redshift indicates that large velocity spreads $\Delta V > 100$ km $^{-1}$ ) are not found for $z \ga 2$, while both large and small spreads are seen at low redshift." Similarly. Fig.," Similarly, Fig." 9. shows that. while both low aud high T. values are obtained at low redshift. oulv high values are obtained for 21.5.," \ref{fig:tvsz} shows that, while both low and high ${\rm T_s}$ values are obtained at low redshift, only high values are obtained for $z \ga 1.5$." This is qualitatively consistent with what is expected in hierarchical clustering models (e.g. Ixauffinaun 1996). in which svstems with low circular volocities dominate the absorption cross-section at high redshift. while svstenis with both high and low circular velocities are found at low :.," This is qualitatively consistent with what is expected in hierarchical clustering models (e.g. Kauffmann 1996), in which systems with low circular velocities dominate the absorption cross-section at high redshift, while systems with both high and low circular velocities are found at low $z$." Next. Fig.," Next, Fig." 7 shows a possible correlation between the velocity width and the spin temperature of the absorbers. with oulv one svstei (the 2=0.3127 absorber towards PINS 1127-115) havine both a large 21 cin velocity spread aud a high temperature: all other systems with large (AV100 kins 1) velocity widths are identified with low T. spirals.," \ref{fig:vel_ts} shows a possible correlation between the velocity width and the spin temperature of the absorbers, with only one system (the $z = 0.3127$ absorber towards PKS 1127-145) having both a large 21 cm velocity spread and a high temperature; all other systems with large $\dV > 100$ km $^{-1}$ ) velocity widths are identified with low ${\rm T_s}$ spirals." The svsteia towards PISS 1127-115 is likely to be tidally disturbed, The system towards PKS 1127-145 is likely to be tidally disturbed Old accreting neutron stars. NSs. in low mass ο binaries. LAINRBs. display a colmplex variety of quasi-periodic oscillation. QPO. modes in their N-ray flux.,"Old accreting neutron stars, NSs, in low mass X-ray binaries, LMXRBs, display a complex variety of quasi-periodic oscillation, QPO, modes in their X-ray flux." The QPOs (~1100 IIz) that were discovered and studied frou hieh huninosity Z-sources in the cighties ave further classified iuto horizoutal. normal aud flaring brauch oscillations (ITIBOs. NBOs iud FBOs. respectively). depending on the simultaneous position occupied by a source in the X-ray colour-colour diagram (for a review see van der Klis 1995).," The QPOs $\sim 1-100$ Hz) that were discovered and studied from high luminosity Z-sources in the eighties are further classified into horizontal, normal and flaring branch oscillations (HBOs, NBOs and FBOs, respectively), depending on the simultaneous position occupied by a source in the X-ray colour-colour diagram (for a review see van der Klis 1995)." The κ QPOs (~0.2 to ~1.3 kIIz) that were revealed aud investigated with RATE in a uuuber of NS LAUINRBs (see van der Iklis 1998. 1999. 2000 aud refereuces therein) involve timescales simular to the dvnamucal timescales close to the NS.," The kHz QPOs $\sim 0.2$ to $\sim 1.3$ kHz) that were revealed and investigated with RXTE in a number of NS LMXRBs (see van der Klis 1998, 1999, 2000 and references therein) involve timescales similar to the dynamical timescales close to the NS." A coununion phenomenon is the presence of a pair of kIlz QPOs (centroid fequencies of 24 aud v2) which drift in frequency while mantaining their frequeney difference AvSr.νι250.360 Tz roughly coustaut., A common phenomenon is the presence of a pair of kHz QPOs (centroid frequencies of $\nu_1$ and $\nu_2$ ) which drift in frequency while mantaining their frequency difference $\Delta\nu \equiv \nu_2 - \nu_1 \approx 250-360$ Hz roughly constant. Detailed studies showed that in four sources A» decreases siguificautlv (by up to 100 Tz) as po Increases: these are Sco N-1 (van der Klis et al., Detailed studies showed that in four sources $\Delta\nu$ decreases significantly (by up to $\sim 100$ Hz) as $\nu_2$ increases; these are Sco X-1 (van der Klis et al. 1997). IU1608-52 (Mondez ot al.," 1997), 4U1608-52 (Mendez et al." 1998a.b). IU1735-II (Ford et al.," 1998a,b), 4U1735-44 (Ford et al." 1998) aud £U1728-31 (Mendez vau der Ilis 1999)., 1998) and 4U1728-34 (Mendez van der Klis 1999). Owing to poor statistics. a similar variation of A» in other sources would have remained undetected (Psaltis et al.," Owing to poor statistics, a similar variation of $\Delta\nu$ in other sources would have remained undetected (Psaltis et al." 1998)., 1998). κας OPOs show remarkably similar properties across NS LAINRBs of the Z and, kHz QPOs show remarkably similar properties across NS LMXRBs of the Z and GRBs column density of neutral gas can still be traced by weakly ionised. metal lines (e.g. Zn Hl. Si HD. which in fact is a more logical method of comparing absorption in N.rays and the optical. given that the XNrays are absorbed by metals and not neutral hydrogen (e.g.Schady et al.,"GRBs column density of neutral gas can still be traced by weakly ionised metal lines (e.g. Zn II, Si II), which in fact is a more logical method of comparing absorption in X–rays and the optical, given that the X–rays are absorbed by metals and not neutral hydrogen (e.g. Schady et al." 2011)., 2011). The X-shooter instrument mounted at the ESO/VLET ollers the best opportunities for these studies., The X-shooter instrument mounted at the ESO/VLT offers the best opportunities for these studies. Alaking use of the sox computed by Melandri et al. (, Making use of the $\beta_{OX}$ computed by Melandri et al. ( 2011). we found a strong correlation between GlIUD darkness and Xrav absorbing column densities.,"2011), we found a strong correlation between GRB darkness and X–ray absorbing column densities." Since metals. are a kev ingredient for dust production (Draine 2003). our findings are consistent with a picture in which the darkness ofa GRB is in most cases due to absorption by circumburst material.," Since metals are a key ingredient for dust production (Draine 2003), our findings are consistent with a picture in which the darkness of a GRB is in most cases due to absorption by circumburst material." SC thanks Darach Watson anc Phil Evans for useful conversations., SC thanks Darach Watson and Phil Evans for useful conversations. Fhis work has been supported by ASL erant Lfoo4/11/0., This work has been supported by ASI grant I/004/11/0. This work macle use of data supplied by the Ulx Science Data Centre at the University of Leicester., This work made use of data supplied by the UK Science Data Centre at the University of Leicester. tell us iu qualitative teris wren the amount of absorber was hieher or lower. bu it is tot possible to interpret the column density values «)btaiued in a simple way.,"tell us in qualitative terms when the amount of absorber was higher or lower, but it is not possible to interpret the column density values obtained in a simple way." If the change in fiux is real then. given that f naguctospleric radius Sis a functio1r οἳ the acevetion rate (RinneονMPO )tus nuelt iauplv an iucrease in f uagnetospherie radiis by about 1tal.," If the change in flux is real then, given that the magnetospheric radius is a function of the accretion rate $R_{\rm mag} \propto \dot{M}^{-2/7}$ ) this might imply an increase in the magnetospheric radius by about $10\%$." That iu um nieht allow the lower nae’uctic pole of he white dwart to IO nore visible. as wel as reducing the contribution from he impact regio ua the outer οςoo of the «isc.," That in turn might allow the lower magnetic pole of the white dwarf to be more visible, as well as reducing the contribution from the impact region at the outer edge of the disc." These wo changes togeher could then coiceivablv explain some of the chauges iu he brond orvital modiation ad some of the chauges in the spin pulse profile that are seen., These two changes together could then conceivably explain some of the changes in the broad orbital modulation and some of the changes in the spin pulse profile that are seen. However. trose Modulatious do not simMv chauge svsteimnaticallv from before to afOr the outburst.," However, those modulations do not simply change systematically from before to after the outburst." We therefore couclude that there is no conipelliug evidence for a sienificautly altered X-rav flux or coluun density between auv of the various N-raxv observations of NY Avi in quiescence., We therefore conclude that there is no compelling evidence for a significantly altered X-ray flux or column density between any of the various X-ray observations of XY Ari in quiescence. So we iust look or other causes of the changes in orbital modulation aud spin pulse profile., So we must look for other causes of the changes in orbital modulation and spin pulse profile. The broad orbital modulation secu from NY Avi was prominent when the object was observed byGinga.ASCA. aud between 1989 aud 2000.," The broad orbital modulation seen from XY Ari was prominent when the object was observed by, and between 1989 and 2000." By the time of the second observation in 2001. the broad modulation was less apparent with a siguificaut decrease in the low energy modulation depth.," By the time of the second observation in 2001, the broad modulation was less apparent with a significant decrease in the low energy modulation depth." In the most recent observatious. withRATE. the broad modulation is," In the most recent observations, with, the broad modulation is" subject of SSCs in external galaxies. we refer the reader to Whitmore (2000).,"subject of SSCs in external galaxies, we refer the reader to Whitmore (2000)." While a lot of effort is beiug devoted to understanding he properties of SSCs. /NICAIOS imaging has ouly recently revealed a population of bright regions iu two LIRGs. Arp 299 and NGC 1611 (CAATIO0: AATIOL).," While a lot of effort is being devoted to understanding the properties of SSCs, /NICMOS imaging has only recently revealed a population of bright regions in two LIRGs, Arp 299 and NGC 1614 (AAH00; AAH01)." A larec yaction of these regions show Iuninosities iu excess of hat of 30 Doradus. the prototypical giant region.," A large fraction of these regions show luminosities in excess of that of 30 Doradus, the prototypical giant region." One of the main difficulties in quautitving the age of the stellar xo»pulatious in LIRGs aud interacting galaxies is breaking he age-extinction degencracy., One of the main difficulties in quantifying the age of the stellar populations in LIRGs and interacting galaxies is breaking the age-extinction degeneracy. This usually translates iuto ouly rough age estimates for SSCs (from photometric data) ranging between 5 aud 900ATIr (sce the recent review x Whitmore 2000)., This usually translates into only rough age estimates for SSCs (from photometric data) ranging between 5 and Myr (see the recent review by Whitmore 2000). regions. on the other haud. will üehlieht the vouugest regions of star formation. with ages of«5 10XMvr. as these are the lifetimes of the O aud D stars required to ionize the eas.," regions, on the other hand, will highlight the youngest regions of star formation, with ages of $< 5-10\,$ Myr, as these are the lifetimes of the O and B stars required to ionize the gas." Clearly. understaudiug he properties of regions and SSCs. aud their relation at Ligh spatial resolution will provide further insight iuto he nature of the star formation processes in LIRCis.," Clearly, understanding the properties of regions and SSCs, and their relation at high spatial resolution will provide further insight into the nature of the star formation processes in LIRGs." Iu this paper we present a study of thedetailed (tens toa ew hundred parsecs) properties of the star forming regions regions aud star clusters) of a sample of 8 LIRGs., In this paper we present a study of the (tens to a few hundred parsecs) properties of the star forming regions regions and star clusters) of a sample of 8 LIRGs. This paper is organized as follows., This paper is organized as follows. Section (2) describes the observations. data reduction aud the production of the region aud star cluster catalogs.," Section (2) describes the observations, data reduction and the production of the region and star cluster catalogs." Iu Section (3) we establish the overall morphology of star forming regions i LIRCs and its relation with the dvuaimical stage of the galaxy., In Section (3) we establish the overall morphology of star forming regions in LIRGs and its relation with the dynamical stage of the galaxy. Iu Section (1) the statistical properties of regious iu LIRGs are analyzed and compared with those of normal ealaxies observed at comparable spatial resolutions., In Section (4) the statistical properties of regions in LIRGs are analyzed and compared with those of normal galaxies observed at comparable spatial resolutions. The spatial distribution of regions and star clusters. their relative numbers and the age sequence are analyzed in Section (5).," The spatial distribution of regions and star clusters, their relative numbers and the age sequence are analyzed in Section (5)." Our conclusions are preseuted in Section (6)., Our conclusions are presented in Section (6). The large amount of extinction routinely present in LIRGs. aud in particular. the fact that active star forming regions are expected to contain non-neelieible amounts of dust. prompted us to search theLEST archive for infrared observations.," The large amount of extinction routinely present in LIRGs, and in particular, the fact that active star forming regions are expected to contain non-negligible amounts of dust, prompted us to search the archive for infrared observations." " The obvious choice was narrow-band Pan and broad-band continua duaecine to identity regions and star clusters respectively,", The obvious choice was narrow-band $\alpha$ and broad-band continuum imaging to identify regions and star clusters respectively. This resulted im a sample of cight LIRGs., This resulted in a sample of eight LIRGs. " The sample covers a range of mfrared huninositices between logLy;=LOOLL.. and logLy;=11.82L.. aswellasa varietv of dynamical stages: isolated ealaxies. close pairs of interacting galaxies and advanced increers,"," The sample covers a range of infrared luminosities –between $\log L_{\rm IR} = 10.94\,{\rm L}_\odot$ and $\log L_{\rm IR} = 11.82\,{\rm L}_\odot$ – as well as a variety of dynamical stages: isolated galaxies, close pairs of interacting galaxies and advanced mergers." The sample is presented in Table in increasing order of tufrared Ininositv., The sample is presented in Table in increasing order of infrared luminosity. The observations of the LIRGS analyzed in this paper were obtained as part of a varietv of ZZST/NICMOS GTO and GO programs. listed in Table 1.," The observations of the LIRGS analyzed in this paper were obtained as part of a variety of /NICMOS GTO and GO programs, listed in Table 1." The Pao |continua inages were taken with the NIC2 aud NICS cameras (pixel size iid 1. respectively) using the narrow-band filter FLOON filter.," The $\alpha$ +continuum images were taken with the NIC2 and NIC3 cameras (pixel size $^{-1}$ and $^{-1}$, respectively) using the narrow-band filter F190N filter." At the distances of the ΤΠ sample. this filter (AA/Ac 1%) contains the Pao cussion line aud the adjacent coutinuuni at 1.90 gan. For the continua subtraction. inages through the F187N filter were usec. except for NCC 5653 and NGC. 6808 (from Bolsker et al.," At the distances of the LIRG sample, this filter $\Delta \lambda/\lambda \simeq 1\%$ ) contains the $\alpha$ emission line and the adjacent continuum at $1.90\,\mu$ m. For the continuum subtraction, images through the F187N filter were used, except for NGC 5653 and NGC 6808 (from Bökker et al." 1999 survey) for which broud-baud F160W filter observations were einiploved instead., 1999 survey) for which broad-band F160W filter observations were employed instead. " The field of view of the images is 19.5""« and 51.2""« for the NIC2 and NIC3 observations. respectively."," The field of view of the images is $19.5\arcsec \times 19.5\arcsec$ and $51.2\arcsec \times 51.2\arcsec$ for the NIC2 and NIC3 observations, respectively." All the continuuni miaeses used to identify the star clusters were observed through the FIGOW filter which represeuts a eood compromise between the better spatial resolution at shorter wavelengths and lower extinction at longer wavelengths., All the continuum images used to identify the star clusters were observed through the F160W filter which represents a good compromise between the better spatial resolution at shorter wavelengths and lower extinction at longer wavelengths. Iu Table 1 for cach galaxy we list the iufrared Iunuinosity. distance (assunuüug Sty=Thkus!Mpe lj. lareo. scale morphology. cameras aud filters used. the corresponding linear scale iu parsec per pixel aud the MST program," In Table 1 for each galaxy we list the infrared luminosity, distance (assuming $H_0 = 75\,{\rm km\,s}^{-1}\, {\rm Mpc}^{-1}$ ), large scale morphology, cameras and filters used, the corresponding linear scale in parsec per pixel and the program" mechanisms that can produce such powerful AGN wines in El.,mechanisms that can produce such powerful AGN winds in \ref{sec:discussion}. In the subgrid LSAT model of SLIO3. gas with densities above the star formation threshold approaches an ellective thermal energy. Hepp. set by a balance between cooling. and. the feedback from star formation.," In the subgrid ISM model of SH03, gas with densities above the star formation threshold approaches an effective thermal energy, $u_{eff}$, set by a balance between cooling and the feedback from star formation." LW processes such as shocks or aciabatic expansion/compression cause the internal energy to deviate [rom ρε. the differences decay on the timescale given by eq. (," If processes such as shocks or adiabatic expansion/compression cause the internal energy to deviate from $u_{eff}$, the differences decay on the timescale given by eq. (" 12) of SLII03.,12) of SH03. This decay timescale is set by the προς! model rather than the true cooling time of the gas., This decay timescale is set by the subgrid model rather than the true cooling time of the gas. One consequence of SII03s. ISM. model. ijs that sullicienthy dense shock heated: gas does not cool on its cooling timescale., One consequence of SH03's ISM model is that sufficiently dense shock heated gas does not cool on its cooling timescale. In this paper we show that ACN winds can shock heat gas in the ISM to above the escape speed his contributes to driving a galactic wind., In this paper we show that AGN winds can shock heat gas in the ISM to above the escape speed – this contributes to driving a galactic wind. " To ensure that he cooling of the shock heated. gas is correct. we mocified he ISM model of SLI03 to better match the expected cooling rate for gas with roughly a solar metallicity,"," To ensure that the cooling of the shock heated gas is correct, we modified the ISM model of SH03 to better match the expected cooling rate for gas with roughly a solar metallicity." To compute he local cooling rate we use a fit to 2? for gas with solar metallicity., To compute the local cooling rate we use a fit to \cite{sutherland93} for gas with solar metallicity. The fit is essentially eq. (, The fit is essentially eq. ( 12) of 7. but with he cooling rate increased by a factor of two when the cmperature is between ~3103 I and 3.10* Ix (to account or solar metallicity).,12) of \cite{sharma10} but with the cooling rate increased by a factor of two when the temperature is between $\sim 3 \times 10^4$ K and $3 \times 10^7$ K (to account for solar metallicity). From this cooling rate we compute a cooling time. ἑρμως dillerences between the thermal energy and the subgrid Πρ decay on fi4455feoot.," From this cooling rate we compute a cooling time, $t_{cool}$; differences between the thermal energy and the subgrid $u_{eff}$ decay on $t_{relax} = t_{cool}$." lor most of the relevant range of temperature ancl density in our simulations. this cooling time is shorter than the relaxation time of SLLOS.," For most of the relevant range of temperature and density in our simulations, this cooling time is shorter than the relaxation time of SH03." 1n addition to the above mocification to the cooling rale. we also consider the role. of. inverse Compton coolingheating.," In addition to the above modification to the cooling rate, we also consider the role of inverse Compton cooling/heating." To do so. we modify the cooling/relaxation timescale of the gas to be where the (non-relativistic) Compton time is given by ∖∖⋰↓↿↓↕∫↘⋟↿↓↥⋖⋅∠∐⊳∖⋜↧⊔≼∼⋖⋅↿∪⇂↓↥∢⊾∐∐⋜⋯∠⇂∠↿↓∐⋅⋜↧⊳∖⊳∖⋯∷↓⋜⋯⋅∠⇂ ⇀∖≺∶↓∖⊽↓⇂⇂↓," To do so, we modify the cooling/relaxation timescale of the gas to be where the (non-relativistic) Compton time is given by with $R$ the distance to the BH and $L$ the associated AGN luminosity." ↥↓↕↓↥∢≱≻↕⇂∙∖⇁⊳∖∖⊽∢⊾∠⇂∪⊔∪⇂≼⇍∪⊔⊳∖⊲⊔⇂⋖⊾↓⋅⋜⋯∙∖⇁↓⋅⋯⇂⊲↓⋜⊔⊲↓∖⇁⋖⋅↿↓⋅⋜⋯⊳∖⇂⋅∢⋅↓⋅ ⋖⋅∐⋅⋯∼⇂⊳∖↕↓↕↿↓↕↕≻↓≻⋜↧↓≻⋖⊾↓⋅⊳∖∖⋎↓↥↕≼∼↓↕↕↓↕↓⋅⋖⋅⋜↧↓↕↿∙∖⇁≼⇍⋜↧⊔⊔↓⋯⇂∐⋮∖⇁∣⋯↿↓⊔↓↕∢⋅ Iuminosity L seen at a given radius and the local Compton temperature at a given radius.," We do not consider any radiative transfer effects in this paper, which in reality can modify both the luminosity $L$ seen at a given radius and the local Compton temperature at a given radius." Instead. we take the Compton temperature to be that appropriate for the mean spectrum of luminous AGN. including the ellects of obscuration: 2.]0 K(T)," Instead, we take the Compton temperature to be that appropriate for the mean spectrum of luminous AGN, including the effects of obscuration: $T_C \simeq 2 \times 10^7$ K \citep{sazonov04}." " In the limit that the Compton timescale is. short compared to the two-body cooling time. we no longer relax the thermal energy. of the gas to the elfective equation of state value for the energy. i,rg. but rather to ne:=MK. ‘T"," In the limit that the Compton timescale is short compared to the two-body cooling time, we no longer relax the thermal energy of the gas to the effective equation of state value for the energy, $u_{eff}$, but rather to $u_C = 3/2 k T_C$." o transition between these two limits. we in general let the thermal energve of ogas relax to: For dense gas. atomic cooling dominates ancl the eas rather quickly approaches the sound: speed: associated with the effective. equation of state.," To transition between these two limits, we in general let the thermal energy of gas relax to: For dense gas, atomic cooling dominates and the gas rather quickly approaches the sound speed associated with the effective equation of state." For. gas. densities characteristic of the ESAL in the central kpe of our mocel galaxies (~10.10% 7) the sound speeds are 40knis and thus the gas is primarily rotationally supported rather than pressure supported., For gas densities characteristic of the ISM in the central kpc of our model galaxies $\sim 10-10^3$ $^{-3}$ ) the sound speeds are $\sim 40 \kms$ and thus the gas is primarily rotationally supported rather than pressure supported. This justifies our use of the viscous accretion rate in equation 1.., This justifies our use of the viscous accretion rate in equation \ref{eqn:Mdvisc}. Table. 1 lists the parameters of the galaxy merger simulations presented in this work., Table \ref{tab:simparm} lists the parameters of the galaxy merger simulations presented in this work. We consider a single galaxy mass and merger orbit (see 2.1)). ancl explore the elects of including ACN wind feedback. both with ancl without radiation. pressure.," We consider a single galaxy mass and merger orbit (see \ref{sec:ICs}) ), and explore the effects of including AGN wind feedback, both with and without radiation pressure." For the GN. winds. we vary both the total momentum Hux in the wind (τι) are the wind speed c. with ficucial values of τν=5 ane ry=10.000kms," For the AGN winds, we vary both the total momentum flux in the wind $\tau_w$ ) and the wind speed $v_w$, with fiducial values of $\tau_w = 5$ and $v_w = 10,000 \kms$." In varving the AGN wind. paranieters. we are no e&uaranteed that the resulting DII mass will be consisten with the AJeywoo relation.," In varying the AGN wind parameters, we are not guaranteed that the resulting BH mass will be consistent with the $M_{BH}-\sigma$ relation." In such cases. the effects of the AGN wind might not be realistic because of the unphysica Bll mass.," In such cases, the effects of the AGN wind might not be realistic because of the unphysical BH mass." To quantify this. we present results with ane without the radiation pressure feedback model explored. in DOM.," To quantify this, we present results with and without the radiation pressure feedback model explored in DQM." Our simple model of radiation. pressure. feedback xocduces model galaxies roughly on the observed Alpy0 correlation for 7~20. the value used. here (DOM.," Our simple model of radiation pressure feedback produces model galaxies roughly on the observed $M_{\rm BH}-\sigma$ correlation for $\tau \sim 20$, the value used here (DQM)." For he present purposes these calculations are useful primarily recause they allow us to study the ellects of AGN wind eedback for svstems in which the DII is guaranteed to be approximately on the lew—0 relation., For the present purposes these calculations are useful primarily because they allow us to study the effects of AGN wind feedback for systems in which the BH is guaranteed to be approximately on the $M_{BH}-\sigma$ relation. We also separately carey out simulations with wind feedback. alone., We also separately carry out simulations with wind feedback alone. " Figure 1. shows the net accretion rate into the black hole. Al;,. and the star formation rate. Al,. as a function of time (summed over both galaxies) for three dillerent simulations: the ficlucial simulation (black curve) with radiation pressure (r= 20) and AGN wind feedback (7,=5 and e,=]0.000kms +). a run identical to the fiducial run but without the wind feedback (grav) and a run with both wind and radiation pressure feedback that includes Compton heating/cooling in the thermodyvnamics of the gas (blue)."," Figure \ref{fig:mdotfid} shows the net accretion rate into the black hole, $\dot{M}_{in}$ , and the star formation rate, $\dot{M}_{*}$, as a function of time (summed over both galaxies) for three different simulations: the fiducial simulation (black curve) with radiation pressure $\tau=20$ ) and AGN wind feedback $\tau_w = 5$ and $v_w = 10,000 \kms$ ), a run identical to the fiducial run but without the wind feedback (gray), and a run with both wind and radiation pressure feedback that includes Compton heating/cooling in the thermodynamics of the gas (blue)." We first describe the cllects of the AGN wind and later return to the role of Compton heating/cooling., We first describe the effects of the AGN wind and later return to the role of Compton heating/cooling. The inclusion of the wind feedback has little effect on either the accretion or star formation rate before the final coalescence of the two galaxies at /~1.7 Cyr., The inclusion of the wind feedback has little effect on either the accretion or star formation rate before the final coalescence of the two galaxies at $t \sim 1.7$ Gyr. This is surprising because equation (6)) implies that [or a given set of conditions at large radii (that determines Meise) the BLL accretion rate at small radii is a [actor of Loloreqefes=16 smaller for the simulation with ACN winds than for the run with just radiation pressure., This is surprising because equation \ref{eqn:Mdin}) ) implies that for a given set of conditions at large radii (that determines $\dot M_{\rm visc}$ ) the BH accretion rate at small radii is a factor of $1+ \tau_w\eta c/v_w =16$ smaller for the simulation with AGN winds than for the run with just radiation pressure. After a small number of time steps. however. the feedback due to radiation pressure is so effective in all of the simulations in ligure 1. that the physical conditions at small racii quickly adjust so that there is à balance between radiation pressure and eravity.," After a small number of time steps, however, the feedback due to radiation pressure is so effective in all of the simulations in Figure \ref{fig:mdotfid} that the physical conditions at small radii quickly adjust so that there is a balance between radiation pressure and gravity." " This sets the BIL accretion. rate Ali, to be ~στ(one) (2) independent of the presence ofthe ACN wind removing mass from the nuclear region (where fjand"," This sets the BH accretion rate $\dot M_{in}$ to be $\sim f_g \sigma^4/(\tau \eta c G)$ \citep{debuhr10} independent of the presence of the AGN wind removing mass from the nuclear region (where $f_g$and" effect of the variable airmass and sky transparency in the NIR. we performed differential aperture photometry of CI against three comparison stars in its field.,"effect of the variable airmass and sky transparency in the NIR, we performed differential aperture photometry of C1 against three comparison stars in its field." The instrumental magnitude difference between the comparison stars was found to be constant within the photometric errors. hence to the accuracy of our photometry (~0.02 mag) these stars can be considered non-vartable.," The instrumental magnitude difference between the comparison stars was found to be constant within the photometric errors, hence to the accuracy of our photometry $\sim$ 0.02 mag) these stars can be considered non-variable." Their magnitudes were calibrated against a standard star observed at the same airmass as one of the frames., Their magnitudes were calibrated against a standard star observed at the same airmass as one of the frames. In Fig. 4..," In Fig. \ref{curves}," we present the light curves obtained., we present the light curves obtained. Both curves exhibit random variations that are fully consistent with photometric uncertainties., Both curves exhibit random variations that are fully consistent with photometric uncertainties. A Lomb-Scargle periodogram does not display any periodicity. indicating that the data are consistent with a constant source.," A Lomb-Scargle periodogram does not display any periodicity, indicating that the data are consistent with a constant source." We also searched for long-term variability. using. the observations on April 18. 21. and 28 and July 22 to monitor possible magnitude changes on scales of days or months.," We also searched for long-term variability, using the observations on April 18, 21, and 28 and July 22 to monitor possible magnitude changes on scales of days or months." " Figure 5. shows that these changes do occur in Cl. which was brighter in the NIR in mid April. fading later by ~0.2 mag in both H and K,."," Figure \ref{longcurve} shows that these changes do occur in C1, which was brighter in the NIR in mid April, fading later by $\sim$ 0.2 mag in both $H$ and $K_{\mathrm s}$." The / band data present the opposite behavior. displaying a marginal brightening in this. band.," The $J$ band data present the opposite behavior, displaying a marginal brightening in this band." None of the other two counterpart candidates (C2—C3) shows magnitude variations between April and July 2005., None of the other two counterpart candidates (C2–C3) shows magnitude variations between April and July 2005. " The long-term variability of Cl m the NIR bands is interesting. and in addition to the properties discussed in former sections of the present work. makes a strong case forJ16281083-4838560..G335.3268+00.1016.. and being different emissions of the same astrophysical system,"," The long-term variability of C1 in the NIR bands is interesting, and in addition to the properties discussed in former sections of the present work, makes a strong case for, and being different emissions of the same astrophysical system." " NIR polarimetry in the A, band was performed using the observations taken with the Wollaston prism at different position. angles.", NIR polarimetry in the $K_{\mathrm s}$ band was performed using the observations taken with the Wollaston prism at different position angles. Images were reduced using the procedure described in the SOFI user manual., Images were reduced using the procedure described in the SOFI user manual. Aperture photometry was performed for candidate Cl and several stars in the field to determine their fluxes., Aperture photometry was performed for candidate C1 and several stars in the field to determine their fluxes. Standard unpolarized (HD 125184) and polarized stars (HD 150193. P=1.68+0.02% at a position angle of 60x 1°) were also observed to ensure that instrumental and sky polarization were appropriately removed.," Standard unpolarized (HD 125184) and polarized stars (HD 150193, $P = 1.68 \pm 0.02\%$ at a position angle of $60 \pm 1\degr$ ) were also observed to ensure that instrumental and sky polarization were appropriately removed." The measurement of field stars allowed us to estimate the foreground interstellar polarization. obtaining a value of P;=3.7+0.5% at a position angle (north through east) of 33+1," The measurement of field stars allowed us to estimate the foreground interstellar polarization, obtaining a value of $P_{\mathrm f} = 3.7 \pm 0.5\%$ at a position angle (north through east) of $33 \pm 1\degr$." A deviation of CI polarization from this value would indicate an intrinsic. polarization. of the source., A deviation of C1 polarization from this value would indicate an intrinsic polarization of the source. For Cl. we obtained," For C1, we obtained" "where3;,j is the IXronecker delta. eT=Obrs,+ο dHobiloΊνα Ξαιfee. bao) is the Laplace coellicient. ∖∖⋎↓↥⋖⊾↓⋅∢⋅∣⋎∶∕∖⊥∕∖⊐⋡ bt This equation includes no secular terms since these are higher order in the eccentricity.","where$\delta_{i,j}$ is the Kronecker delta, $c^{\pm}_j=\partial_\alpha b^{(j)}_{1/2}\pm 2jb^{(j)}_{1/2}$ , $d^{\pm}_j=c^{\pm}_j+b^{(j)}_{1/2}(\alpha)$, $\alpha = a_1/a_2$, $b^{(j)}_{1/2}(\alpha)$ is the Laplace coefficient, where $\psi=\lambda_1-\lambda_2$, and This equation includes no secular terms since these are higher order in the eccentricity." Note that since we have only included the first order terms in the eccentricity. the resonant arguments which appear have ratios j|1:j and j:j 1 for the mean lonegituces.," Note that since we have only included the first order terms in the eccentricity, the resonant arguments which appear have ratios $j+1$ $j$ and $j$ $j+1$ for the mean longitudes." " The perturbecl semi-major axis is given in ?.. and we compute the perturbed eccentricity and. longitude of periastron using P,=ejsinze, and Ay=e,cosz,."," The perturbed semi-major axis is given in \citet{mal93b}, and we compute the perturbed eccentricity and longitude of periastron using $h_1=e_1\sin{\varpi_1}$ and $k_1=e_1\cos{\varpi_1}$." " Weeping all the resonance terms that exist to first order in the eccentricities gives the equations of motion for hj.Aj. Vo find the ciunge in the transit timing we use the orbital elements to compute the variation in 6,."," Keeping all the resonance terms that exist to first order in the eccentricities gives the equations of motion for $h_1, k_1$, To find the change in the transit timing we use the orbital elements to compute the variation in $\dot\theta_1$ ." " ""To first order in e, Since we begin with zero eccentricitv. we ignore perturbations to A in the sin ancl cos terms in this equation."," To first order in $e_1$ Since we begin with zero eccentricity, we ignore perturbations to $\lambda$ in the $\sin$ and $\cos$ terms in this equation." " As in equation (22)) where 060,—6,njo. we integrate this equation to find where p, and no are taken at their initial values. Ajo=ALU0). AsoAs(E—0). &=2/0(110). (4} is the complete elliptic integral. (0) is defined in the appendix of 7.. and we havedropped any terms which vary linearly. with time."," As in equation \ref{eclipsetime}) ) where $\delta \dot\theta_1 = \dot\theta_1 -n_{10}$, we integrate this equation to find where $n_1$ and $n_2$ are taken at their initial values, $\lambda_{10}=\lambda_1(t=0)$, $\lambda_{20}=\lambda_2(t=0)$, $k=2\sqrt{\alpha}/(1+\alpha)$, $K(k)$ is the complete elliptic integral, $Q(\psi)$ is defined in the appendix of \citet{mal93b}, , and we havedropped any terms which vary linearly with time." AX similar calculation canbe carried out for perturbations by a planet interior to the transitingὃν planet.," A similar calculation canbe carried out for perturbations by a planet interior to the transiting planet," A programme has been. started. using the recently commissioned. Nagova-South African. 14m Infrared Survey Facility (RSE) at SAO Sutherland. to study the stellar populations. evolution and structures of Local. Ciroup galaxies.,"A programme has been started, using the recently commissioned Nagoya-South African 1.4m Infrared Survey Facility (IRSF) at SAAO Sutherland, to study the stellar populations, evolution and structures of Local Group galaxies." One aim of this programme is to detect long period variables (Miras ancl other types) in these svstems aid to derive their infrared light curves., One aim of this programme is to detect long period variables (Miras and other types) in these systems and to derive their infrared light curves. “Phe programme will necessarily take several vears to complete., The programme will necessarily take several years to complete. In. the present communication we discuss the light that initial observations of the dwarf spheroidal galaxy. Leo lL. throw on the AGB star population of that galaxy.," In the present communication we discuss the light that initial observations of the dwarf spheroidal galaxy, Leo I, throw on the AGB star population of that galaxy." The IRSE is a 1.4-2m telescope constructed and operated in terms of an agreement. between SAAQO and the Ciraduate School of Science and School of Science. Nagova University. to carry out specialized. surveys of the southern sky. in the infrared.," The IRSF is a 1.4-m telescope constructed and operated in terms of an agreement between SAAO and the Graduate School of Science and School of Science, Nagoya University, to carry out specialized surveys of the southern sky in the infrared." Phe telescope is equipped with a 3-channel camera. SIRIUS. constructed jointly by Nagova University and the National Astronomical Observatory of Japan (Nagashima et al.," The telescope is equipped with a 3-channel camera, SIRIUS, constructed jointly by Nagoya University and the National Astronomical Observatory of Japan (Nagashima et al." 1999). that allows and images to be obtained simultaneously.," 1999), that allows and images to be obtained simultaneously." The field of view is 7.8 arcmin square with a scale of 0.45 arcsec/pixel., The field of view is 7.8 arcmin square with a scale of 0.45 arcsec/pixel. Images centred on Leo LE (referred to hereafter as field A) were obtained at two epochs. 2001-01-16 ancl 2001-12-19. and processed by means of the standard. IRSE pipeline (Nakajima. private communication).," Images centred on Leo I (referred to hereafter as field A) were obtained at two epochs, 2001-01-16 and 2001-12-19, and processed by means of the standard IRSF pipeline (Nakajima, private communication)." A single image comprises 10 ditherecdl 30-5 exposures., A single image comprises 10 dithered 30-s exposures. Three such sets of frames were combined to give an elfective 900-8 exposure in each of and A. at both epochs., Three such sets of frames were combined to give an effective 900-s exposure in each of and $ K_{s}$ at both epochs. At this stage. the clleetive field. of view is reduced to 7.2 aremin square.," At this stage, the effective field of view is reduced to 7.2 arcmin square." Standard stars from Persson οἱ al. (, Standard stars from Persson et al. ( 1998) were observed on each night and the results presented here are in the natural system of the SIRIUS camera. but with the zero point of the Persson ct al.,"1998) were observed on each night and the results presented here are in the natural system of the SIRIUS camera, but with the zero point of the Persson et al." standards., standards. At the first epoch. we obtained a supplementary set. of images of an adjacent.field. (field," At the first epoch, we obtained a supplementary set of images of an adjacentfield (field" the cluster X-ray emission (Fig.,the cluster X-ray emission (Fig. 1 and Fig., 1 and Fig. 2)., 2). The optical spectrum. of nonstellar Light is characterized. by. weak. Iow-ionization emission lines (Baum et al 1988: Tadhbunter οἱ al 1993).," The optical spectrum of nonstellar light is characterized by weak, low-ionization emission lines (Baum et al 1988; Tadhunter et al 1993)." Fig., Fig. 7 shows the radio image of 3€353 taken in the NRAO/VLA Sky Survey (NVSS. Condon et al 1998). in contour superposed on the SIS full band image.," 7 shows the radio image of 3C353 taken in the NRAO/VLA Sky Survey (NVSS, Condon et al 1998) in contour superposed on the SIS full band image." The radio image was taken bv the VLA at 20 em at resolution of 45 aresec., The radio image was taken by the VLA at 20 cm at resolution of 45 arcsec. In this low resolution image. the radio source appears to be triple while much higher resolution images such that in Morganti. Killeen Tacdhunter (1993) and Swain. Briclle Baum (1998) reveal more details in the radio structure as well as the weak radio core at the nucleus.," In this low resolution image, the radio source appears to be triple while much higher resolution images such that in Morganti, Killeen Tadhunter (1993) and Swain, Bridle Baum (1998) reveal more details in the radio structure as well as the weak radio core at the nucleus." point-like X-ray source coincides with the nucleus of the radio galaxy which is located at the centre between the radio lobes., A point-like X-ray source coincides with the nucleus of the radio galaxy which is located at the centre between the radio lobes. The brightero jet ὃνgoingo towards the cluster emission. terminates at à hot spot ancl the surface brightness of the jet-sicle Lobe steeply declines in front. of the bright cluster emission., The brighter jet going towards the cluster emission terminates at a hot spot and the surface brightness of the jet-side lobe steeply declines in front of the bright cluster emission. The cluster medium may be acting as a working surface of the radio jet. or it is merely an orientation elfect of the jet.," The cluster medium may be acting as a working surface of the radio jet, or it is merely an orientation effect of the jet." As suggested from the image analysis. the X-ray. spectrum of 30353 is very hard.," As suggested from the image analysis, the X-ray spectrum of 3C353 is very hard." A likely explanation is an absorbed X-ray source of an active nucleus in the radio galaxy., A likely explanation is an absorbed X-ray source of an active nucleus in the radio galaxy. To minimize the contamination from the cluster enission. we use the SIS data for a spectral study as the SIS provides better spatial resolution. and the data were collected. from. a small region with a radius of 1.5 aremin on the two SIS detectors centred on the hard X-ray source.," To minimize the contamination from the cluster emission, we use the SIS data for a spectral study as the SIS provides better spatial resolution, and the data were collected from a small region with a radius of 1.5 arcmin on the two SIS detectors centred on the hard X-ray source." Halt of the total photons from 3€C353 should be contained in the region. when the point spread. function of the ASCA ARP for a point source is assumed.," Half of the total photons from 3C353 should be contained in the region, when the point spread function of the ASCA XRT for a point source is assumed." The background. data were taken from a region where the cluster emission is weak., The background data were taken from a region where the cluster emission is weak. The obtained spectrum should. therefore contain some cluster emission in he soft. X-ray band., The obtained spectrum should therefore contain some cluster emission in the soft X-ray band. The SIS spectrum can be fitted with a very Hat. power- of DP-—0.60+0.24 (Fig., The SIS spectrum can be fitted with a very flat power-law of $\Gamma = 0.60\pm 0.24$ (Fig. 5), 8). llowever. a realistic xeture of the spectrum is a sum of the cluster emission and an absorbed: power-law from an AGN.," However, a realistic picture of the spectrum is a sum of the cluster emission and an absorbed power-law from an AGN." Since soft. X-ray emission from the radio galaxy is very weak. as illustrated w the HERE imageὃν and the soft band GIS image.o the energye xuid below 2 keV in the spectrum. is dominated by. the diffuse cluster emission.," Since soft X-ray emission from the radio galaxy is very weak, as illustrated by the HRI image and the soft band GIS image, the energy band below 2 keV in the spectrum is dominated by the diffuse cluster emission." Fitting with a model consisting of a thermal emission spectrum (MISIAL) with A7=4.3 keV and metallicity of aand an absorbed power-law with a photon-index of 1.7 gives an absorption column density ης51070m, Fitting with a model consisting of a thermal emission spectrum (MEKAL) with $kT=4.3$ keV and metallicity of and an absorbed power-law with a photon-index of 1.7 gives an absorption column density $ = 5\times 10^{22}$. The contribution from the cluster emission (as modelled by the MISIAL component) is found to be about GO per cent in the 0.52 keV energy range., The contribution from the cluster emission (as modelled by the MEKAL component) is found to be about 60 per cent in the 0.5–2 keV energy range. The absorption-corrected 2.10 keV luminosity of the N-rav source is 8LO , The absorption-corrected 2–10 keV luminosity of the X-ray source is $8\times 10^{42}$. An ASCA spectral study of a sample of radio galaxies including 3C353 will be reported. elsewhere. (see also Sambruna. Eracleous Mushotzky. 1999).," An ASCA spectral study of a sample of radio galaxies including 3C353 will be reported elsewhere (see also Sambruna, Eracleous Mushotzky 1999)." Compared. with the other “cnission-line selected radio. galaxies. ὃς2039 appears to be underluminous in N-ravs for its radio power.," Compared with the other `emission-line selected' radio galaxies, 3C353 appears to be underluminous in X-rays for its radio power." We have shown that the extended. emission. around. the powerful radio galaxy 3C35335 is a cluster. with highly disturbed: morphology of the X-ray emission. which might allect the radiojets of 80353., We have shown that the extended emission around the powerful radio galaxy 3C353 is a cluster with highly disturbed morphology of the X-ray emission which might affect the radio jets of 3C353. The large racio power of 3€353, The large radio power of 3C353 "With no clear optical association we cannot positively classify this source, but the time-scales between the NVSS detection and MOST detection and non-detection rule out RSNe and GRB afterglows.","With no clear optical association we cannot positively classify this source, but the time-scales between the NVSS detection and MOST detection and non-detection rule out RSNe and GRB afterglows." The light curve for SUMSS J062636—425807 (seeAppendix has a detection and a non-detection separated by almost a [B))year., The light curve for SUMSS $-$ 425807 (seeAppendix \ref{sec:light_curves_transients}) ) has a detection and a non-detection separated by almost a year. " The optical counterpart is point like and the colours are red, with B-K — 5."," The optical counterpart is point like and the colours are red, with B-K = 5." The source is most likely an AGN scintillating above our noise threshold., The source is most likely an AGN scintillating above our noise threshold. " The light curve for J135304—363726 (see Appendix [B)) is consistent with a flaring source, or a variable source occasionally appearing above our sensitivity limit."," The light curve for $-$ 363726 (see Appendix \ref{sec:light_curves_transients}) ) is consistent with a flaring source, or a variable source occasionally appearing above our sensitivity limit." " It is marginally detected in the SuperCOSMOS R plates and not detected in B or I, or any 2MASS images."," It is marginally detected in the SuperCOSMOS R plates and not detected in B or I, or any 2MASS images." This source is likely an optically faint AGN scintillating above our noise threshold., This source is likely an optically faint AGN scintillating above our noise threshold. " Some 25 per cent of the variable sources have a clear point- or marginally resolved optical counterpart most of which have red colours, with 0«B—R2."," Some 25 per cent of the variable sources have a clear point-like or marginally resolved optical counterpart most of which have red colours, with $0 < B-R < 2$." " The optical point source and radio detection would typically imply AGN, but the colour distribution is unusual for AGN, for which the vast majority have B—R<1 (?).."," The optical point source and radio detection would typically imply AGN, but the colour distribution is unusual for AGN, for which the vast majority have $B-R<1$ \citep{Croom04}. ." The reddest sources are, The reddest sources are "minimun racial bin. H,,5,. to x.","minimum radial bin, $R_{min}$, to $\infty$." In practice. one only has shear data covering a range from Ryriy lO μι.," In practice, one only has shear data covering a range from $R_{min}$ to $R_{max}$." " Wereler to the parts of (he integrals Irom 10,4, lo x: as endpoint corrections: (hey must be added to the parts of the integrals (hat we can actually perform by interpolating the data.", We refer to the parts of the integrals from $R_{max}$ to $\infty$ as endpoint corrections; they must be added to the parts of the integrals that we can actually perform by interpolating the data. Consider Equation 12. as an example: we can rewrite il as where 75 and Te stand for Data ancl Correction., Consider Equation \ref{eq:delta-rho} as an example; we can rewrite it as where $T_D$ and $T_C$ stand for Data and Correction. To estimate the magnitude of each term. consider an isothermal sphere. AN~A1: in this case. the integrals can be computed analvticallv. leading to For the outermost data point. r=ει (he correction term gives the whole result. and one cannot learn anvihing about the density al this point.," To estimate the magnitude of each term, consider an isothermal sphere, $\Delta\Sigma \sim R^{-1}$; in this case, the integrals can be computed analytically, leading to For the outermost data point, $r=R_{max}$, the correction term gives the whole result, and one cannot learn anything about the density at this point." " ILowever. lor smaller scales. r$ 0.7 objects for observation; however, in this paper we utilize the DEEP2 sample in the Extended Groth Strip, for which no colour cuts have been applied." DEEP2 collected. spectra typically covering the wavelength range .1C)OA [or z 50.000 objects.," DEEP2 collected spectra typically covering the wavelength range $-$ 9,100 for $>$ 50,000 objects." From the survey we select the 6.55552 ealaxies lor which single-system ugriz photometry exists from the ΕΙΤΙ) Legacy Survey (field and for which the DELP2ZQUALITY Lag is either 3 or dC or confidence that the redshift is correct. respectively).," From the survey we select the 6,552 galaxies for which single-system $ugriz$ photometry exists from the CFHT Legacy Survey (field and for which the DEEP2 flag is either 3 or 4 $>$ or confidence that the redshift is correct, respectively)." Thus the dimensionality. of colour-space for these data is p = 4., Thus the dimensionality of colour-space for these data is $p$ = 4. We further remove data for which the redshift error. or any magnitude or magnitude error. is not provided. leaving 6.418 galaxies: after outlier removal. the final sample size is 6.067.," We further remove data for which the redshift error, or any magnitude or magnitude error, is not provided, leaving 6,418 galaxies; after outlier removal, the final sample size is 6,067." Lowe restrict ourselves to data for whichZQUALITY = 4. the sample size is 5.223.," If we restrict ourselves to data for which = 4, the sample size is 5,223." Application of the algorithm outlined in. 882.1-2.2 vields tuning parameter estimates (6.71) = (0.002.850) for = 4 and (0.002.1050) forZQUALITY = 3.," Application of the algorithm outlined in 2.1-2.2 yields tuning parameter estimates $(\epshat,\mhat)$ = (0.002,850) for = 4 and (0.002,1050) for $\geq$ 3." We display our results in Table 1. and Fig. 6:, We display our results in Table \ref{tab:results} and Fig. \ref{fig:deep2}; note that because we do not apply the Nystrómm extension here (but rather. fit to the data directly alter (ο.0i) are determined). the observed scatter is smaller than we would observe with a larger. Nystrómnmr-eextended dataset.," note that because we do not apply the Nyströmm extension here (but rather, fit to the data directly after $(\epshat,\mhat)$ are determined), the observed scatter is smaller than we would observe with a larger, Nyströmm-extended dataset." In both cases. we exclude of the objects from analysis as outlicrs.," In both cases, we exclude of the objects from analysis as outliers." In Fig. 6..," In Fig. \ref{fig:deep2}," " we observe that the quality of the fits below Zs 0.15 (Fic = 0.038 forZQUALITY = 4) is superior to that athigher redshifts ""Tom 0.064).", we observe that the quality of the fits below $Z \approx$ 0.75 $\Rhat$ = 0.038 for = 4) is superior to that athigher redshifts $\Rhat$ = 0.064). To understand why this is so. we examine the DEEP? colour data (Eig. 7)).," To understand why this is so, we examine the DEEP2 colour data (Fig. \ref{fig:deep2colours}) )." " Pick an object at Zz0.75. and compute the Euclidean distance in colour-space to a random object at any other redshift, Z0.1.5]."," Pick an object at $Z \approx 0.75$, and compute the Euclidean distance in colour-space to a random object at any other redshift $Z \in [0,1.5]$." This distance is a nearly constant function of AZ: thus for values o£ « similar to those chosen in the SDSS analyses. there is only a slightly lesser probability of cüllusing from Z= 0.75 to. eg. Z= (2asto. eg. Z= 0.74.," This distance is a nearly constant function of $\Delta Z$; thus for values of $\epsilon$ similar to those chosen in the SDSS analyses, there is only a slightly lesser probability of diffusing from $Z =$ 0.75 to, e.g., $Z =$ 0.2 as to, e.g., $Z =$ 0.74." To achieve aceurate predictions at Ze0.75. « must be mace smaller (lessening the probability of large AZ jumps): this is what our optimization vields.," To achieve accurate predictions at $Z \approx 0.75$, $\epsilon$ must be made smaller (lessening the probability of large $\Delta Z$ jumps); this is what our optimization yields." A consequence of a smaller € is that the weighted graph of the DEIEP2 objects is not fully connected (see diseussion around. equation 1))., A consequence of a smaller $\epshat$ is that the weighted graph of the DEEP2 objects is not fully connected (see discussion around equation \ref{eqn:weighted}) ). One can discern connectedness by examining the vector of eigenvalues: for € = 0.002. the first zz 20 eigenvalues are all c 0.95. implvingthe presence of several disconnected. ebumps on the graph.," One can discern connectedness by examining the vector of eigenvalues; for $\epshat$ = 0.002, the first $\approx$ 20 eigenvalues are all $>$ 0.95, implyingthe presence of several disconnected clumps on the graph." he most. visually obvious manifestation of disconnectedness in the DIZIEP2 analysis is the presence of a markecl knee in the predictions at Zz 0.75 for small values of m (see Fig. 8)):, The most visually obvious manifestation of disconnectedness in the DEEP2 analysis is the presence of a marked knee in the predictions at $Z \approx$ 0.75 for small values of $m$ (see Fig. \ref{fig:deep2ev}) ); the dominant eigenvectors describe the low redshift data well. but not the high redshift data.," the dominant eigenvectors describe the low redshift data well, but not the high redshift data." As m increases. the knee straightens out: however. because of the bias-variance (ρασος i can only increase so much before Rey begins to increase as well. due to increasing variance.," As $m$ increases, the knee straightens out; however, because of the bias-variance tradeoff, $m$ can only increase so much before $\Rhat$ begins to increase as well, due to increasing variance." For m = S50(ZQUALITY = +) we have not vet achieved an optimal description for the hieh-redshift data., For $\mhat$ = 850 = 4) we have not yet achieved an optimal description for the high-redshift data. To demonstrate that we can achieve a better description of these data. we split the full dataset into Iow- and high-recshift sets (at. eg. Zou = 0.9) and compute diffusion maps for cach.," To demonstrate that we can achieve a better description of these data, we split the full dataset into low- and high-redshift sets (at, e.g., $Z_{\rm cut}$ = 0.9) and compute diffusion maps for each." We find that we can achieve. e.g.. Rey8: 0.035 for hieh-redshift data with as [ew as 40 eigenvectors. while the predictions at low redshifts change only slightly.," We find that we can achieve, e.g., $\Rhat \approx$ 0.035 for high-redshift data with as few as 40 eigenvectors, while the predictions at low redshifts change only slightly." While splitting the data vields better results for our DELP? sample. we do not propose such splitting as part of our general dilfusion map framework. for multiple reasons: (a) it acids a tuning parameter (Zou). (b) it complicates the Nystrómam extension (to which data split do we assign a new object?).," While splitting the data yields better results for our DEEP2 sample, we do not propose such splitting as part of our general diffusion map framework, for multiple reasons: (a) it adds a tuning parameter $Z_{\rm cut}$ ), (b) it complicates the Nyströmm extension (to which data split do we assign a new object?)," and. most importantly (ο) a data split. can be rendered. moot with the inclusion of new data in other banclpasses (e.g.. the inclusion of near-It data in the DEEP? sample would mitigate the Iuclidean-cdistance issue seen at Ze 0.15).," and most importantly (c) a data split can be rendered moot with the inclusion of new data in other bandpasses (e.g., the inclusion of near-IR data in the DEEP2 sample would mitigate the Euclidean-distance issue seen at $Z \approx 0.75$ )." Concentrating on the regime Z 0.75. we find that our result Rey80.035 with ηez compares favorably with that of bertetal. (2006).. who train a template-based photometric redshift code using 2.867 spectroscopic redshifts from the VIMOS VLE Deep Survey (VVDS) in the ΕΙΤὸ DI field and obtain σ= and 5g= (sce their. 86.3 and fig.," Concentrating on the regime $Z \la 0.75$ , we find that our result $\Rhat \approx 0.035$ with $\eta \approx$ compares favorably with that of \cite{Ilbert06}, , who train a template-based photometric redshift code using 2,867 spectroscopic redshifts from the VIMOS VLT Deep Survey (VVDS) in the CFHTLS D1 field and obtain $\sigma = 0.032$ and $\eta =$ (see their 6.3 and fig." 14)., 14). Our, Our to a space-filling pattern of shorter LCSs that look more favourable for widespread reconnection.,to a space-filling pattern of shorter LCSs that look more favourable for widespread reconnection. The observed velocity field is found to have comparable [V-v| and |Vxv]. and the observed c field is in qualitative agreement with a combined model incorporating both effects.," The observed velocity field is found to have comparable $|\nabla\cdot{\bf v}|$ and $|\nabla\times{\bf v}|$, and the observed $\sigma$ field is in qualitative agreement with a combined model incorporating both effects." In the combined case. the appearance of the «c and Q fields follows that of the diverging flow model: the diverging part of the velocity acts to quickly stretch and deform the picture.," In the combined case, the appearance of the $\sigma$ and $Q$ fields follows that of the diverging flow model: the diverging part of the velocity acts to quickly stretch and deform the picture." " However. the rate of increase of integrated log,,Q in the combined model is double that of the original model. and we hypothesise that the vortical structure remains ""hidden"" in the magnetic field topology."," However, the rate of increase of integrated $\log_{10}Q$ in the combined model is double that of the original model, and we hypothesise that the vortical structure remains “hidden” in the magnetic field topology." " We have demonstrated how the vortical part may be extracted from an observed velocity field. but further study is required to determine whether the vortical part is a more appropriate predictor of subsequent reconnection,"," We have demonstrated how the vortical part may be extracted from an observed velocity field, but further study is required to determine whether the vortical part is a more appropriate predictor of subsequent reconnection." Due to the limitations of the observational technique used for the demonstration in this paper. the typical flow speeds measured were only 0.1kms'. a factor of 5—10 slower than real granular flows.," Due to the limitations of the observational technique used for the demonstration in this paper, the typical flow speeds measured were only $0.1\,\textrm{km}\,\textrm{s}^{-1}$, a factor of $5-10$ slower than real granular flows." From investigation of the analytical model. we predict that faster flow speeds (for the same size and lifetime of granules) will result in. significantly faster development of strong gradients in the magnetic field.," From investigation of the analytical model, we predict that faster flow speeds (for the same size and lifetime of granules) will result in significantly faster development of strong gradients in the magnetic field." Our initial results are therefore very much a lower bound for the complexity that we expect to develop in the coronal magnetic field over this time., Our initial results are therefore very much a lower bound for the complexity that we expect to develop in the coronal magnetic field over this time. The model also indicates that. if the real vorticity is also larger. then the combined c field will show greater infilling of LCSs.," The model also indicates that, if the real vorticity is also larger, then the combined $\sigma$ field will show greater infilling of LCSs." " In this case. the mixing of trajectories is sufficient that the model begins to show a process of ""homogenisation"" of the «c field as found in simulations of turbulence(?)."," In this case, the mixing of trajectories is sufficient that the model begins to show a process of “homogenisation” of the $\sigma$ field as found in simulations of turbulence." . A proper investigation of the rate of this mixing will require higher resolution. velocity data. but the simple model indicates that it is likely to be effective on timescales much shorter than the observed 12 hours.," A proper investigation of the rate of this mixing will require higher resolution velocity data, but the simple model indicates that it is likely to be effective on timescales much shorter than the observed 12 hours." Realistic numerical simulations of photospheric convection could also give tighter constraints on the expected magnetic structure., Realistic numerical simulations of photospheric convection could also give tighter constraints on the expected magnetic structure. Finally. the method proposed here—which. assumes a perfectly ideal evolution in the corona—will break down if and when sufficiently high magnetic gradients have formed for magnetic reconnection to set in.," Finally, the method proposed here—which assumes a perfectly ideal evolution in the corona—will break down if and when sufficiently high magnetic gradients have formed for magnetic reconnection to set in." Determining this threshold for reconnection will likely require detailed study of numerical MHD simulations., Determining this threshold for reconnection will likely require detailed study of numerical MHD simulations. To this end. we have proposed a method for reconstructing a 3D magnetic. field with the inferred field line mapping.," To this end, we have proposed a method for reconstructing a 3D magnetic field with the inferred field line mapping." This field is neither unique nor (likely) in equilibrium. but it has the significant advantage over existing extrapolation techniques of having the correct field line topology.," This field is neither unique nor (likely) in equilibrium, but it has the significant advantage over existing extrapolation techniques of having the correct field line topology." The method outlined in this paper infers the magnetic field line mapping from a photospheric flow., The method outlined in this paper infers the magnetic field line mapping from a photospheric flow. However. the field line mapping defines the 3D magnetic field B only up to an ideal deformation.," However, the field line mapping defines the 3D magnetic field ${\bf B}$ only up to an ideal deformation." In particular. a hypothetical plasma flow in the volume. which vanishes on the photospheric boundaries. can deform B while leaving the field line mapping invariant.," In particular, a hypothetical plasma flow in the volume, which vanishes on the photospheric boundaries, can deform ${\bf B}$ while leaving the field line mapping invariant." Conversely. two fields B resulting from applying the same photospheric footpoint motions to the same initial magnetic field can differ at most by an ideal deformation.," Conversely, two fields ${\bf B}$ resulting from applying the same photospheric footpoint motions to the same initial magnetic field can differ at most by an ideal deformation." It would be useful for future investigations to generate a particular magnetic field of the required topology., It would be useful for future investigations to generate a particular magnetic field of the required topology. Here we present a general method for constructing such a field., Here we present a general method for constructing such a field. Given a velocity field να.v.7). the strategy is to set so that the field lines of B are simply the trajectories of v with z corresponding to time.," Given a velocity field ${\bf v}(x,y,t)$, the strategy is to set so that the field lines of ${\bf B}$ are simply the trajectories of ${\bf v}$ with $z$ corresponding to time." The scalar function Jt 1s then adjusted to make B divergence-free and match a given normal component B-CG.y.0) on the lower boundary.," The scalar function $\lambda$ is then adjusted to make ${\bf B}$ divergence-free and match a given normal component $B_z(x,y,0)$ on the lower boundary." From V.B=0 we find where the z-derivative is taken along a magnetic field line and A=V-v as before., From $\nabla\cdot{\bf B}=0$ we find where the $z$ -derivative is taken along a magnetic field line and $\Delta\equiv\nabla\cdot{\bf v}$ as before. Integrating from ¢=0 to f=z along the field line fGvo.vo.4) gives | ," Integrating from $t=0$ to $t=z$ along the field line ${\bf f}(x_0,y_0,t)$ gives \ref{fig:suspend} " Perhaps one of the most useful tools for describing the nature of observed. galactic populations is the luminosity function.,Perhaps one of the most useful tools for describing the nature of observed galactic populations is the luminosity function. The relative numbers of galaxies of different luminosities oller a quantitative description of the result of the structure formation scenario of the universe. nowaclays available for inspection even as a function of redshift.," The relative numbers of galaxies of different luminosities offer a quantitative description of the result of the structure formation scenario of the universe, nowadays available for inspection even as a function of redshift." The luminosity function. or mass function of galaxies. once a modeling of star formation histories ancl cust is include ο vield mass to light ratios. is indeed. one of the principa constraints against which cosmological simulations ane structure formation theories in general are tested.," The luminosity function, or mass function of galaxies, once a modeling of star formation histories and dust is included to yield mass to light ratios, is indeed one of the principal constraints against which cosmological simulations and structure formation theories in general are tested." Often star ormation elliciencics and histories are calibrated: through a fitting of predicted. halo mass functions. anc observec uminosity functions e.g. Davis ct al. (, Often star formation efficiencies and histories are calibrated through a fitting of predicted halo mass functions and observed luminosity functions e.g. Davis et al. ( 1985) and references 1ereof[.,1985) and references thereof. Galaxies however. have many more properties than jus wir mass. most notably. ealactic classification schemes 'enter on sorting galaxies as cllipticals. lenticulars and EsXrals. subdividing the latter again into types. tvpically dong the Llubhle sequence.," Galaxies however, have many more properties than just their mass, most notably, galactic classification schemes center on sorting galaxies as ellipticals, lenticulars and spirals, subdividing the latter again into types, typically along the Hubble sequence." " In spite of the many well known P""irtues of this classification scheme. its somewhat subjective. ualitative and relative nature. has mace it. dillicult to use in comparisons against. cosmological simulations. where the ‘twpe of a modeled galaxy is rather dillieult to assess. in terms of Llubble’s classification scheme."," In spite of the many well known virtues of this classification scheme, its somewhat subjective, qualitative and relative nature, has made it difficult to use in comparisons against cosmological simulations, where the 'type' of a modeled galaxy is rather difficult to assess, in terms of Hubble's classification scheme." " Inspired. by varied theoretical studies which invariably identify the A spin parameter of a host halo as the principal physical. parameter in determining the morphological and visual characteristics of a spiral galaxy. which are then subjectively integrated. into the qualitative assignment of ""spe. in Hernandez Cervantes-Sodi (2006) two of us derived a simple estimate of A for any observed spiral."," Inspired by varied theoretical studies which invariably identify the $\lambda$ spin parameter of a host halo as the principal physical parameter in determining the morphological and visual characteristics of a spiral galaxy, which are then subjectively integrated into the qualitative assignment of 'type', in Hernandez Cervantes-Sodi (2006) two of us derived a simple estimate of $\lambda$ for any observed spiral." Phere it was shown that the scalings of the derived. A against various ἵνρο determining properties such as colour. disk hickness and bulge to disk ratio. are comparable to the corresponding scalings of these parameters against. Hubble vpe. using a large sample of nearby. spirals.," There it was shown that the scalings of the derived $\lambda$ against various type determining properties such as colour, disk thickness and bulge to disk ratio, are comparable to the corresponding scalings of these parameters against Hubble type, using a large sample of nearby spirals." ]t is interesting that a generic prediction of cosmological body simulations over the past 2 decades has been the functional formi and. parameters which define the predicted distribution. of A for dark matter halos c.g. Bullock et al. (, It is interesting that a generic prediction of cosmological N-body simulations over the past 2 decades has been the functional form and parameters which define the predicted distribution of $\lambda$ for dark matter halos e.g. Bullock et al. ( 2001).,2001). Nevertheless. it. has not been easy {ο test his prediction directly. as A is not a straight forward observable feature of a real galaxy.," Nevertheless, it has not been easy to test this prediction directly, as $\lambda$ is not a straight forward observable feature of a real galaxy." Not only is a measurable A distribution relevant as a test of the general. structure ormation scheme. but also as a further way of independentIv," Not only is a measurable $\lambda$ distribution relevant as a test of the general structure formation scheme, but also as a further way of independently" in Niteróii. Brazil. has been in operation.,"in Niteróii, Brazil, has been in operation." " Due to a limited aperture (9.5"" of opening angle). the TUPI telescope is on the boundary. between telescopes with a very small field of view. like (he air Cherenkov telescopes. and (he small air shower arrays. characterized by a large field of view."," Due to a limited aperture $9.5^0$ of opening angle), the TUPI telescope is on the boundary between telescopes with a very small field of view, like the air Cherenkov telescopes, and the small air shower arrays, characterized by a large field of view." On (he other hand. a muon telescope at ground level can be used as an astronomical telescope even if (he muons parent particles are neutral. such as photons.," On the other hand, a muon telescope at ground level can be used as an astronomical telescope even if the muon's parent particles are neutral, such as photons." " Muons are expected as products of cosmic rav (protons. nuclei) interaction with the nuclei of the atmosphere via a= production followed by the decay a=—j7v,."," Muons are expected as products of cosmic ray (protons, nuclei) interaction with the nuclei of the atmosphere via $\pi^{\pm}$ production followed by the decay $\pi^{\pm} \to \mu^{\pm} \nu_{\mu}$." However. a small fraction of nmons have (heir origin in photonuclear reactions induced by eamma ravs.," However, a small fraction of muons have their origin in photonuclear reactions induced by gamma rays." The abilitv to disünguish these photonuclear muons from background muons depends upon statistics. the strength and energy spectrum of the emitting source and some characteristic of (he experiment such as (he angular resolution.," The ability to distinguish these ""photonuclear"" muons from background muons depends upon statistics, the strength and energy spectrum of the emitting source and some characteristic of the experiment such as the angular resolution." In order to increase (he sensitivity of TUPI telescope. an up-grade of the acquisition svslen was made on December. 2003 ancl included: a new (on-line) discrimination level to increase (he counting rate background [rom approximately oie per 20 second to approximately 18 per 10 second.," In order to increase the sensitivity of TUPI telescope, an up-grade of the acquisition system was made on December, 2003 and included a new (on-line) discrimination level to increase the counting rate background from approximately one per 20 second to approximately 18 per 10 second." In addition. as the experiment uses scintillator plastics and due to other indtations (see section 3) the counting rate has a dependence with the (on-line) pulse-heieht discrimination and this new data acquisition allows us to build a noise filter.," In addition, as the experiment uses scintillator plastics and due to other limitations (see section 3) the counting rate has a dependence with the (on-line) pulse-height discrimination and this new data acquisition allows us to build a noise filter." The aim of this yamework is to make a consistent analvsis of ground. level events. observed as very. sharp peaks above the count rate background and found during a study of a possible non excess rom the galactic center.," The aim of this framework is to make a consistent analysis of ground level events, observed as very sharp peaks above the count rate background and found during a study of a possible muon excess from the galactic center." In this article we report (wo GLEs detected on December 2003 aud obtained. under these new conditions., In this article we report two GLEs detected on December 2003 and obtained under these new conditions. We give emphasis to the study of their origin. including the temporal characteristics on the basis of the time profile shapes of the GLEs and duration.," We give emphasis to the study of their origin, including the temporal characteristics on the basis of the time profile shapes of the GLEs and duration." We show. that the first GLE has a strong correlation with solar flares.," We show, that the first GLE has a strong correlation with solar flares." Because the second GLE has an unknown origin. (wo possibilities are analvzed.," Because the second GLE has an unknown origin, two possibilities are analyzed." The paper is organized as follows: In section 2. we present the TUPI telescope characteristics.," The paper is organized as follows: In section 2, we present the TUPI telescope characteristics." In section 3. (he raster search. technique is presented.," In section 3, the raster search technique is presented." The analvsis of the two GLEs is presented in section 4., The analysis of the two GLEs is presented in section 4. In section 5 the local effects are analvzed., In section 5 the local effects are analyzed. In section 6 the possible existence of a window to observe GIRDs at the eround is discussed and finally in section 1 we present our conclusions., In section 6 the possible existence of a window to observe GRBs at the ground is discussed and finally in section 7 we present our conclusions. The TUPI muon telescope is installed on the campus of (he Universidade Federal Fluminense. Niteróii. Rio de Janeiro-Brazil.," The TUPI muon telescope is installed on the campus of the Universidade Federal Fluminense, Niteróii, Rio de Janeiro-Brazil." " The position is: latitude: 2275433"" S. longitude:"," The position is: latitude: $22^0 54'33''$ S, longitude:" "elc) was done with standard tools inIAE"".",etc) was done with standard tools in. .. After correction for optical distortions. each individual spectrum was extracted using the APALL task in the SPECRED package in IRAF.," After correction for optical distortions, each individual spectrum was extracted using the APALL task in the SPECRED package in IRAF." Following wavelength calibration based on are lanips mounted within the spectrograph. small zero-point corrections (13D A)) were applied by measuring the [Ol skvlines at ((blue spectra) and (red spectra).," Following wavelength calibration based on arc lamps mounted within the spectrograph, small zero-point corrections (1–3 ) were applied by measuring the ] skylines at (blue spectra) and (red spectra)." Finally. flux. calibration was applied and the individual spectra of each object were summed.," Finally, flux calibration was applied and the individual spectra of each object were summed." Three sample spectra are shown in Figure I.., Three sample spectra are shown in Figure \ref{fig:spectra}. Basic data for the cluster candidates are listed in Table 1.., Basic data for the cluster candidates are listed in Table \ref{tab:clusters}. . The V.7 photometry is from the HST data used in Larsenetal.(2001). while the A magnitudes are from the VET/ISAAC data in PO2.," The $V,I$ photometry is from the HST data used in \citet{lar01}, while the $K$ magnitudes are from the VLT/ISAAC data in P02." Badial velocities were determined by cross-correlating (he cluster spectra with those of the radial velocity standards. using the EXCOR task in the RV. package in IRAF.," Radial velocities were determined by cross-correlating the cluster spectra with those of the radial velocity standards, using the FXCOR task in the RV package in IRAF." The radial velocities listed in Table 1 are an average of the cross-correlation results [or each relerence star. where (he errors are estimates of the standard error on (he mean based on the (wo measurements.," The radial velocities listed in Table \ref{tab:clusters} are an average of the cross-correlation results for each reference star, where the errors are estimates of the standard error on the mean based on the two measurements." We note that there is a svstematic difference of about 100 kin/s between the radial velocity measurements for each of the two stars. suggesting that the eatalogued velocily of at least one of the stars is erroneous or (hat one star might have been misidentified.," We note that there is a systematic difference of about 100 km/s between the radial velocity measurements for each of the two stars, suggesting that the catalogued velocity of at least one of the stars is erroneous or that one star might have been misidentified." If this svstematic difference is taken into account. (he r.m.s.," If this systematic difference is taken into account, the r.m.s." difference between the two sets of mmeastvements is only about. 13 km/s. so the relative radial velocities are probably more accurate (han implied by (he errors listed in Table 1..," difference between the two sets of measurements is only about 13 km/s, so the relative radial velocities are probably more accurate than implied by the errors listed in Table \ref{tab:clusters}." For NGC! 4365 itself. (heRCS catalog (deVaucouleursetal.1991). lists a radial velocity of 1243£6 Καπ». Four objects turned oul to be either likely [oreground stars or have too low signal-to-noise to extract a useful spectrum.," For NGC 4365 itself, theRC3 catalog \citep{devau91} lists a radial velocity of $1243\pm6$ km/s. Four objects turned out to be either likely foreground stars or have too low signal-to-noise to extract a useful spectrum." This leaves us with 12 confirmed clusters. with a mean radial velocity of 11444τρ km/s and a dispersion of 279+67 km/s. In order to estimate ages and metallicities for (the GCs we emplov the Lick/IDS svstem of absorption indices (Worthevetal.1994).. including H94 and H54 from (1997).," This leaves us with 14 confirmed clusters, with a mean radial velocity of $1144\pm75$ km/s and a dispersion of $279\pm67$ km/s. In order to estimate ages and metallicities for the GCs we employ the Lick/IDS system of absorption indices \citep{wor94}, including $\delta_A$ and $\gamma_A$ from \citet{wo97}." .. After correcting for the radial velocities in Table L.. we re-measured the locations of several prominent features such as the Dalmer lines. G-band anclCa i T+]. lines and found the wavelength scales to be accurate to better than {," After correcting for the radial velocities in Table \ref{tab:clusters}, we re-measured the locations of several prominent features such as the Balmer lines, G-band andCa $+$ K lines and found the wavelength scales to be accurate to better than 1" We find that we are able to reproduce the results of IXhochfar Burkert when using only halo peculiar velocities in our calculations. ancl are able to reproduce our own results when the Llubble Low is included.,"We find that we are able to reproduce the results of Khochfar Burkert when using only halo peculiar velocities in our calculations, and are able to reproduce our own results when the Hubble flow is included." As a second check. we have taken the distribution of orbital circularities found. by Vormen(1997).. who used techniques similar to IxXhochfar&Burkert (2004).. and converted these into eccentricities using eqns. (8))," As a second check, we have taken the distribution of orbital circularities found by \scite{tormen97}, who used techniques similar to \scite{khochfar04}, and converted these into eccentricities using eqns. \ref{eq:fecc}) )" and (9)) (assuming f»= 1)., and \ref{eq:fcirc}) ) (assuming $f_2=1$ ). Correcting for the fact that orbits with c>] are not included in the distribution of Tormen.(1997) we find an eccentricity distribution as shown bv the crosses in Fie. 11.., Correcting for the fact that orbits with $e>1$ are not included in the distribution of \scite{tormen97} we find an eccentricity distribution as shown by the crosses in Fig. \ref{fig:ecccomp}. We conclude that. these two dilferent. approaches to determining distributions of halo orbital parameters produce consistent results. providing they attempt to measure the same quantities.," We conclude that these two different approaches to determining distributions of halo orbital parameters produce consistent results, providing they attempt to measure the same quantities." The differences between the distributions of eccentricities reported here ancl by IxXhochfar&(2004) v.l can be traced to the choice of whether to include the Hubble flow in particle velocities (as we did). or to use peculiar velocities. as did IxXhochfar&Burkert(2004)v.," The differences between the distributions of eccentricities reported here and by \scite{khochfar04} v.1 can be traced to the choice of whether to include the Hubble flow in particle velocities (as we did), or to use peculiar velocities, as did \scite{khochfar04} ." 1.. We can test for correlations between the infall directions of pairs of satellites merging into the same halo., We can test for correlations between the infall directions of pairs of satellites merging into the same halo. Figure 12 shows the distribution of angles ó between the radius vectors of pairs of satellites merging into the same host Note that we have summed the results from all simulation outputs to obtain this distribution., Figure \ref{fig:pair} shows the distribution of angles $\phi$ between the radius vectors of pairs of satellites merging into the same host Note that we have summed the results from all simulation outputs to obtain this distribution. This is. permissible as our ain here is to search for any deviation [rom uncorrelated infall directions., This is permissible as our aim here is to search for any deviation from uncorrelated infall directions. As such. it does not matter if the cillerent outputs are correlated in different wavswe would. still see a difference from the null hypothesis of no correlations.," As such, it does not matter if the different outputs are correlated in different ways—we would still see a difference from the null hypothesis of no correlations." Ehe distribution appears to cliller significantly from that expected. if there were no correlations between infall directions., The distribution appears to differ significantly from that expected if there were no correlations between infall directions. This correlation between infall. directions is qualitatively as expected if mergers tend to occur along filaments. Le. there is an enhancement in the number ofmergers at small angles. ς<30°.2 with a corresponding suppression of mergers with angles around 90," This correlation between infall directions is qualitatively as expected if mergers tend to occur along filaments, i.e. there is an enhancement in the number ofmergers at small angles, $\zeta \lsim\, 30^\circ$ , with a corresponding suppression of mergers with angles around $90^\circ$ ." ones: the slopes. the values and the behaviour of the break time as a function of angle (see Tab. 3)),"ones: the slopes, the values and the behaviour of the break time as a function of angle (see Tab. \ref{tabgau}) )" are consisten with what expected. for a NSE LJ seen within the cone (sce Tab. 11)., are consistent with what expected for a NSE HJ seen within the cone (see Tab. \ref{tab}) ). On the contrary the break does not. become smoother (3rd column. of Tab. 3)), On the contrary the break does not become smoother (3rd column of Tab. \ref{tabgau}) ) as the line of sieh approaches the edge. like in the LJ but its shape remains rather unaltered.," as the line of sight approaches the edge, like in the HJ but its shape remains rather unaltered." Finally. on average the Gaussian jet has a less sharp break in the lighteurve.," Finally, on average the Gaussian jet has a less sharp break in the lightcurve." This is in agreemen with previous calculations (Ciranot. Ixumar 2003)., This is in agreement with previous calculations (Granot Kumar 2003). " For 020, instead the pre-break slope becomes Latter ane Hatter and for ϐ>SNO, it becomes positive: in this latter case the lighteurve is actually dominated by. the emission coming from the core.", For $\theta>2\theta_c$ instead the pre-break slope becomes flatter and flatter and for $\theta\ge 8\theta_c$ it becomes positive; in this latter case the lightcurve is actually dominated by the emission coming from the core. The polarisation curves present intermeciate characteristics between the LLJ and the SJ ones (Fig 17))., The polarisation curves present intermediate characteristics between the HJ and the SJ ones (Fig \ref{fig:gau_po}) ). The absence of edges and the presence of a symmetric luminosity gracicnt with respect to the jet axis. produce (as in the case of a SJ} a one-peak curve with a constant polarisation angle.," The absence of edges and the presence of a symmetric luminosity gradient with respect to the jet axis, produce (as in the case of a SJ) a one-peak curve with a constant polarisation angle." On the other hand. the exponential decrease of Luminosity outside the core makes the relation between polarisation curve and lighteurve more close to the LLJ’s one: the peak is located after the break time in the total Dux.," On the other hand, the exponential decrease of luminosity outside the core makes the relation between polarisation curve and lightcurve more close to the HJ's one: the peak is located after the break time in the total flux." " As the viewing angle increases. especially lor 6,2@ the maximum in the lighteurve moves torwards /=ἐν. but eventually the core starts to dominate the lighteurve since early times because of the exponential luminosity distribution and the polarisation curves resembles that of an orphan afterglow."," As the viewing angle increases, especially for $\theta_o>\theta_{c}$ the maximum in the lightcurve moves torwards $t=t_b$, but eventually the core starts to dominate the lightcurve since early times because of the exponential luminosity distribution and the polarisation curves resembles that of an orphan afterglow." " The previous sections confirm what first claimed in ΠΕΟΣ: the lighteurves ofa 11. and o£SJ with a,=2 are very similar but their intrinsic features depend on the viewing angle for the SJ and on the opening angle for the LJ.", The previous sections confirm what first claimed in RLR02: the lightcurves of a HJ and of SJ with $\alpha_{\epsilon}=2$ are very similar but their intrinsic features depend on the viewing angle for the SJ and on the opening angle for the HJ. On the other hand the polarisation curves are completely dilferent., On the other hand the polarisation curves are completely different. These characteristics are the direct consequences of an energy distribution οxϐ the lighteurve is dominated. by the line of sight emission while (for any a.) the polarisation curve is dominated by the emission coming from an angle L/P with the line of sight., These characteristics are the direct consequences of an energy distribution $\epsilon\propto\theta^{-2}$: the lightcurve is dominated by the line of sight emission while (for any $\alpha_{\epsilon}$ ) the polarisation curve is dominated by the emission coming from an angle $1/\Gamma$ with the line of sight. This means that the total Lux we receive does not bear footprints of the jet. structure while the observed polarisation does., This means that the total flux we receive does not bear footprints of the jet structure while the observed polarisation does. In Fig., In Fig. " IS. we directly compare the lighteurves anc the polarisation curves [rom IJ and SJ with £75.06.)=Li. and θε=26,."," \ref{fig:inomcom} we directly compare the lightcurves and the polarisation curves from HJ and SJ with $E_{iso}(\theta_o)=E_{iso}$ and $\theta_{jet}=2\,\theta_o$." These are the parameters for which their lighteurves are more similar., These are the parameters for which their lightcurves are more similar. " We also show the lighteurve and. polarisation curve for à Gaussian jet with £5;.,(6,)=Lis, and 8.2OG611."," We also show the lightcurve and polarisation curve for a Gaussian jet with $E_{iso}(\theta_o)=E_{iso}$ and $\theta_{c}\simeq0.6\,\theta_{jet}$." lig., Fig. IS (upper panel) summarises the comparison ciscussed £4.1 and 85.2 «mong the characteristics of the lighteurves of the three jet structures., \ref{fig:inomcom} (upper panel) summarises the comparison discussed 4.1 and 5.2 among the characteristics of the lightcurves of the three jet structures. In particular it should be noticed the Ilattening before the break. present in the SJ lighteurve and the almost perfect match between the LJ and CJ lighteurves (the GJ liehteurve has been divided by a factor 2 or it would be overlaid don the LJ one).," In particular it should be noticed the flattening before the break, present in the SJ lightcurve and the almost perfect match between the HJ and GJ lightcurves (the GJ lightcurve has been divided by a factor 2 or it would be overlaid don the HJ one)." " The pre-break bump is actually the only sign of the underlving jet structure: when L/P~80, and the lighteurve breaks. the jet core is also visible and its contribution gives that [lux excess that we »ereeive as a Lattenine."," The pre-break bump is actually the only sign of the underlying jet structure: when $1/\Gamma\sim\theta_o$ and the lightcurve breaks, the jet core is also visible and its contribution gives that flux excess that we perceive as a flattening." The larger is the viewing angle the smaller is {εν and more prominently the core out-shines he line of sight Lux at the break., The larger is the viewing angle the smaller is $E_{iso}$ and more prominently the core out-shines the line of sight flux at the break. Some authors claimed (c.g. CGranot Ixumar 2003) that this feature can used o discriminate between the LLJ and the SJ., Some authors claimed (e.g. Granot Kumar 2003) that this feature can used to discriminate between the HJ and the SJ. However the shape and the intensity of the Πατομής depends on how the wines and the core join together ancl this is a free parameter (3)., However the shape and the intensity of the flattening depends on how the wings and the core join together and this is a free parameter $\beta_{\epsilon}$ ). Consequently. comparing the model with observations oovides a wav to fix the shape of the energy. distribution rut not a way to test the model itself, Consequently comparing the model with observations provides a way to fix the shape of the energy distribution but not a way to test the model itself. Besides the pre-break lattening the temporal behaviour of the lighteurves plotted in Fig., Besides the pre-break flattening the temporal behaviour of the lightcurves plotted in Fig. 15. is identical and for this reason the same cata can be fitted with anv of the three models (e.g Panaitescu Ixumar 2003. for SJs and 11.5).," \ref{fig:inomcom} is identical and for this reason the same data can be fitted with any of the three models (e.g Panaitescu Kumar 2003, for SJs and HJs)." The comparison in Fig., The comparison in Fig. IS. (lower panel) clearly shows the main differences between the polarisation curves of a SJ. of a CJ and of a LLJ:," \ref{fig:inomcom} (lower panel) clearly shows the main differences between the polarisation curves of a SJ, of a GJ and of a HJ:" As maw be seen. the distances of the Ser CMD features are similar to those of the Ser core and associated globular clusters.,"As may be seen, the distances of the Sgr CMD features are similar to those of the Sgr core and associated globular clusters." All of the Ser CMD background features show a slightly increased reddening compared to their respective loreground clusters of 0.02-0.05 magnitudes in E(D—V)., All of the Sgr CMD background features show a slightly increased reddening compared to their respective foreground clusters of 0.02-0.05 magnitudes in $E(B-V)$. On average. the Ser CMD features are best fit with 0.04 magnitude additional reddening before that of the foreground. cluster and 0.02 magnitudes more reddening than the values estimated Irom the τουεπας maps of Schlegel et al. (," On average, the Sgr CMD features are best fit with 0.04 magnitude additional reddening before that of the foreground cluster and 0.02 magnitudes more reddening than the values estimated from the reddening maps of Schlegel et al. (" 1998).,1998). The additional color shilt compared to the foreground cluster could reflect additional reddening along; the line of sight., The additional color shift compared to the foreground cluster could reflect additional reddening along the line of sight. The foreground clusters are all within 5-9 kpe of the Sun and all have Galactic Y and, The foreground clusters are all within 5-9 kpc of the Sun and all have Galactic $Y$ and Sect. ??..,Sect. \ref{Method}. In Sect., In Sect. ?? we investigate the shape of the correlation function for red sequence and blue cloud galaxies. and in Sect.," \ref{Results} we investigate the shape of the correlation function for red sequence and blue cloud galaxies, and in Sect." ?? the results are discussed., \ref{Discussion} the results are discussed. " We assume a cosmological geometry taken from the WMAP results (Spergeletal. 2006)) and the final 2dFGRS power spectrum results (Coleetal. 2005) a flat model with O,,=0.25."," We assume a cosmological geometry taken from the WMAP results \citealp{Spergel03,Spergel06}) ) and the final 2dFGRS power spectrum results \citealp{Cole05}) ): a flat model with $\Omega_m=0.25$." All lengths quoted are 1n comoving units., All lengths quoted are in comoving units. " Normally. we show explicit dependence on / (which denotes [Hy/LO0kins+Mpe| but for absolute magnitudes we suppress this dependence. so that 35 denotes Mp5log,h."," Normally, we show explicit dependence on $h$ (which denotes $H_0 / 100 \rm \,km\,s^{-1}\,Mpc^{-1}$ ); but for absolute magnitudes we suppress this dependence, so that $M_B$ denotes $M_B - 5 \log_{10}h$." To date. COMBO-17 (Classifying Objects with Medium Band Observations in 17filters) has surveyed three disjoint ~3I«30° southern equatorial fields (for their coordinates see Wolfetal. 2003)) to deep limits in 5 broad and 12 medium passbands. covering wavelengths from 100 to 930nnm.," To date, COMBO-17 lassifying bjects with edium and bservations in 17filters) has surveyed three disjoint $\sim 31'\times 30'$ southern equatorial fields (for their coordinates see \citealp{Wolf03}) ) to deep limits in $5$ broad and $12$ medium passbands, covering wavelengths from $400$ to $930$ nm." A detailed description of the survey along with filter curves can be found in Wolfetal.(2004)., A detailed description of the survey along with filter curves can be found in \citet{COMBOMain04}. . All observations were carried out using the Wide Field Imager at the MPG/ESO 2.2 m-telescope on La Silla. Chile.," All observations were carried out using the Wide Field Imager at the MPG/ESO 2.2 m-telescope on La Silla, Chile." In each filter. typically 10 to 20 individual exposures were taken (up to 50 for ultradeep R-band images totalling 20kks with seeing :5 005).," In each filter, typically $10$ to $20$ individual exposures were taken (up to $50$ for ultradeep $R$ -band images totalling $20$ ks with seeing $\la 0\farcs8$ )." Galaxies were detected on the deep AH-band images by using SExtractor (Bertin&Arnouts 1996)., Galaxies were detected on the deep $R$ -band images by using xtractor \citep{Bertin96}. The spectral energy distributions (SEDs) for &- detected objects were measured by performing seeing-adaptive. weighted-aperture photometry in all 17 frames at the position of the ?-band detected object.," The spectral energy distributions (SEDs) for $R$ -band detected objects were measured by performing seeing-adaptive, weighted-aperture photometry in all $17$ frames at the position of the $R$ -band detected object." All magnitudes are quoted with a Vega zero point., All magnitudes are quoted with a Vega zero point. Using the 17-band photometry. objects are classified using a scheme based on template spectral energy distributions (Wolfetal.2001b.a).," Using the 17-band photometry, objects are classified using a scheme based on template spectral energy distributions \citep{Wolf01a,Wolf01b}." . The classification algorithm basically compares the observed colours of each object with a colour library of known objects., The classification algorithm basically compares the observed colours of each object with a colour library of known objects. This colour library 1s assembled from observed and model spectra by synthetic. photometry performed using an accurate representation of the instrumental characteristics of COMBO-17., This colour library is assembled from observed and model spectra by synthetic photometry performed using an accurate representation of the instrumental characteristics of COMBO-17. For galaxy classification. we use PÉGGASE model spectra (see Ρίου&Rocea-Volmerange1997 for an earlier version of the model).," For galaxy classification, we use PÉGGASE model spectra (see \citealp{Pegase97} for an earlier version of the model)." The template spectra are à two-dimensional age/reddening sequence. in. which a fixed exponential star formation timescale 7= 1GGyr is assumed. ages vary between 50 MMyr and 15 GGyr. and the reddening £(2—V) can be as large as 0.5 mmag. adopting a Small Magellanic Cloud Bar extinction curve.," The template spectra are a two-dimensional age/reddening sequence, in which a fixed exponential star formation timescale $\tau = 1$ Gyr is assumed, ages vary between $50$ Myr and $15$ Gyr, and the reddening $E(B-V)$ can be as large as $0.5$ mag, adopting a Small Magellanic Cloud Bar extinction curve." Note that we do not apply any morphological star/galaxy separation or use other criteria., Note that we do not apply any morphological star/galaxy separation or use other criteria. Using a minimum variance estimator. each object 15 assigned a redshift (f it is not classified as a star).," Using a minimum variance estimator, each object is assigned a redshift (if it is not classified as a star)." The redshift errors in this process depend on magnitude and type of the object. and for galaxies can be approximated by The galaxy redshift estimate quality has been tested by comparison with spectroscopic redshifts for almost 1000 objects (see Wolfetal.2004)).," The redshift errors in this process depend on magnitude and type of the object, and for galaxies can be approximated by The galaxy redshift estimate quality has been tested by comparison with spectroscopic redshifts for almost 1000 objects (see \citealp{COMBOMain04}) )." At bright limits Ro<20. the redshifts are accurate to ao./(1|2)&0.01. and the error is dominated by mismatches between template and real galaxy spectra.," At bright limits $R < 20$, the redshifts are accurate to $\sigma_z/(1 + z) \simeq 0.01$ , and the error is dominated by mismatches between template and real galaxy spectra." This error can contain a systematic component that is dictated by the exact filter placement. but these ‘redshift focusing’ effects are of the order of magnitude of the random redshift errors for ~<1 and are unimportant for the current analysis.," This error can contain a systematic component that is dictated by the exact filter placement, but these `redshift focusing' effects are of the order of magnitude of the random redshift errors for $z<1$ and are unimportant for the current analysis." At the median apparent magnitude RoxO2 σαi)e0.02.," At the median apparent magnitude $R \simeq 23$, $\sigma_z/(1 + z) \sim 0.02$." For the faintest galaxies. the redshift accuracy approaches those achievable using traditional broadband photometric surveys. o./(1|:)20.05.," For the faintest galaxies, the redshift accuracy approaches those achievable using traditional broadband photometric surveys, $\sigma_z/(1 + z) \ga 0.05$." We thus restricted our analysis to galaxies with F<23., We thus restricted our analysis to galaxies with $I< 23$. Fig., Fig. 1. shows the redshift distribution of the 22310 COMBO-17 galaxies between +=0.2 and :=1.2 (with and Mp15).," \ref{zdistrib} shows the redshift distribution of the $22\,310$ COMBO-17 galaxies between $z = 0.2$ and $z = 1.2$ (with $I < 23$ and $M_B < -18$ )." The peak at +=0.733 in Fig., The peak at $z=0.733$ in Fig. | is due to areal structure in the Chandra Deep Field South. which has been spectroscopically confirmed (Gillietal.2003).," \ref{zdistrib} is due to a real structure in the Chandra Deep Field South, which has been spectroscopically confirmed \citep{Gilli03}." . In order to define a volume limited sample. we restrict our analysis to the redshift range 0.1<20.8 and galaxiesbrighter than lp—1s. which leaves us with 10360 galaxies for the analysis.," In order to define a volume limited sample, we restrict our analysis to the redshift range $0.4 < z < 0.8$ and galaxiesbrighter than $M_B= -18$, which leaves us with $10\,360$ galaxies for the analysis." Note that D-band luminosities can be determined directly without any A-correction uncertainty. based on the photometry in our 17 filters between 100 and 930 nnm and an interpolation of the corresponding template spectra.," Note that $B$ -band luminosities can be determined directly without any $K$ -correction uncertainty, based on the photometry in our 17 filters between $400$ and $930$ nm and an interpolation of the corresponding template spectra." We do not apply anyevolutionary corrections., We do not apply anyevolutionary corrections. The distribution of the redshift errors for all galaxies m our subsample with F< 23. Mp< sand Οι<2Οδ Is shown in Fig. 2..," The distribution of the redshift errors for all galaxies in our subsample with $I<23$ , $M_B < -18$ and $0.4 < z < 0.8$ is shown in Fig. \ref{relzerror}. ." We use the prescription of Belletal.(2004) to separate galaxies into the red-sequence component and the remaining blue cloud component:, We use the prescription of \citet{Bell03} to separate galaxies into the red-sequence component and the remaining blue cloud component: transfer is sienificanty clelaved or avoided. althogether due to rotational mixing (CaseMindeAlinketal.2009).,transfer is significanty delayed or avoided althogether due to rotational mixing \citep[Case M in][]{demink09}. Interestingly. tight binary systems with massive stars have been discovered. e.g. CQ Cop.," Interestingly, tight binary systems with massive stars have been discovered, e.g. CQ Cep." In this svstem the stellar masses are ΕΛ. and 30M.. and the orbital period is 1.6d.," In this system the stellar masses are $\msun$ and $\msun$, and the orbital period is 1.6d." One might therefore speculate whether Cygnus. N-1 is the result of such an evolutionary channel., One might therefore speculate whether Cygnus X-1 is the result of such an evolutionary channel. In the previous section we derived the. requirect parameters when the black hole was formed., In the previous section we derived the required parameters when the black hole was formed. At this time. the system consisted of a helium core of ~9 orbiting a stellar companion of 46 M.," At this time, the system consisted of a helium core of $\sim9$ orbiting a stellar companion of $\sim 46$ ." . The orbital separation was 15It.. and the orbital period. 0.95 days.," The orbital separation was $15\; \rsun$, and the orbital period 0.95 days." The separation can be compared to the Roche lobe of the donor. which was SJt...," The separation can be compared to the Roche lobe of the donor, which was $8\;\rsun$." This is somewhat smaller than the predicted. racius of a zero-age main sequence (ZAAIS) 46 AL. star (which is l0It. ). and comparable to the radius of a star in the lower end of our derived range.," This is somewhat smaller than the predicted radius of a zero-age main sequence (ZAMS) 46 $_{\odot}$ star (which is $\sim 10\;\rsun$ ), and comparable to the radius of a star in the lower end of our derived range." From these results it is clear that even at ZAAIS. the donor would have been too large.," From these results it is clear that even at ZAMS, the donor would have been too large." While rotational mixing may keep a star from expanding as it evolves. it does. not reduce the size at ZAMS and cannot be invoked as à means of enabling the tidal locking required.," While rotational mixing may keep a star from expanding as it evolves, it does not reduce the size at ZAMS and cannot be invoked as a means of enabling the tidal locking required." In order to allow for a wider orbit. and slightly less massive companion. one may investigate the results if a slightly more massive He core at tidal locking is assumed.," In order to allow for a wider orbit, and slightly less massive companion, one may investigate the results if a slightly more massive He core at tidal locking is assumed." The separation is à slow function. of mass. so the orbit. does not. widen much.," The separation is a slow function of mass, so the orbit does not widen much." Llowever. the Roche lobe radius is a slightly stronger function of mass so the Roche lobe radius of the companion actually shrinks slightlv even though the orbit widens.," However, the Roche lobe radius is a slightly stronger function of mass so the Roche lobe radius of the companion actually shrinks slightly even though the orbit widens." Lt is thereby clear that a more massive He core will not allow for tidal locking at the required frequency., It is thereby clear that a more massive He core will not allow for tidal locking at the required frequency. Another alternative to consider is that the svstem formis with two main sequence stars close in mass., Another alternative to consider is that the system forms with two main sequence stars close in mass. The svstem undergoes common envelope evolution. leading to two close lle stars at which point tidal locking occurs.," The system undergoes common envelope evolution, leading to two close He stars at which point tidal locking occurs." Winds then widen the binary to present parameters., Winds then widen the binary to present parameters. The scenario is attractive as the secondary does show chemical peculiarities and is enriched in Hle., The scenario is attractive as the secondary does show chemical peculiarities and is enriched in He. However. with a mass ratio close to unity the evolution of the two stars would be very similar. and by the time the primary becomes a black hole the secondary. would have lost too much mass to represent the current svstenm.," However, with a mass ratio close to unity the evolution of the two stars would be very similar, and by the time the primary becomes a black hole the secondary would have lost too much mass to represent the current system." So far we have neglected. any clleet of accreted mass and angular momentum on the evolution of the svstem. and assumed that the spin is solely determined by the system parameters at tidal locking.," So far we have neglected any effect of accreted mass and angular momentum on the evolution of the system, and assumed that the spin is solely determined by the system parameters at tidal locking." We can however estimate the possible change in spin contributed by aceretion onto the black hole., We can however estimate the possible change in spin contributed by accretion onto the black hole. " Phe current massloss rate from the donor has been estimated by Ciesetal.(2003). to AL,wg3slo” AL. vrd. Vrti", The current massloss rate from the donor has been estimated by \citet{gie03} to $\dot{M}_{wind} = 3 \times 10^{-6}$ $_{\odot}$ $^{-1}$. "leketαἱ.(2007). find a higher mass loss rate. Moa=Ὁ10"" M. ft."," \citet{vri07} find a higher mass loss rate, $\dot{M}_{wind} = 5 \times 10^{-6}$ $_{\odot}$ $^{-1}$." ‘Phe mass aceretion rate is clearly variable: however. following Vrtileketal.(2007).. we can estimate it for a relatively bright state (Lx=107 CLES 13.," The mass accretion rate is clearly variable; however, following \citet{vri07}, we can estimate it for a relatively bright state $L_X = 10^{38}$ ergs $^{-1}$ )." [n this case Lus.=Lxfec. where e=0.42 for a maximally rotating black hole.," In this case $\dot{M}_{capture} = L_X / e c^2$, where $e=0.42$ for a maximally rotating black hole \citep{st83}." " (Shapiro&Teukol-sky 1983).. This vielels AME510"" M. vet.", This yields $\dot{M}_{capture} \sim 5 \times 10^{-9}$ $_{\odot}$ $^{-1}$. For €vg Χα. a more realistic value is e.=0.1. giving IAM~10“AL. +.," For Cyg X-1, a more realistic value is $e=0.1$, giving $\dot{M}_{capture} \sim 10^{-8}$ $_{\odot}$ $^{-1}$." The age of the svstem is dillieult to determine. but Alirabel&Rodrigues(2003). estimated it to be 7LO? vears by comparing the relative velocity and distance between (νο X-1 and its assumed formation site in the CygnusOD3 association of massive stars.," The age of the system is difficult to determine, but \citet{mir03} estimated it to be $\sim7 \times 10^6$ years by comparing the relative velocity and distance between Cyg X-1 and its assumed formation site in the CygnusOB3 association of massive stars." The black hole mass could thus only have increased by ~0.1M. in the time since formation., The black hole mass could thus only have increased by $\sim0.1{\Msun}$ in the time since formation. In order to significantly change the spin. the black hole must have acereted =»1M.," In order to significantly change the spin, the black hole must have accreted $>1$." ".. For à 10. black hole. he Eddington aceretion rate is ~LO"" +."," For a 10 black hole, the Eddington accretion rate is $\sim 10^{-7}$ $^{-1}$." Thus. he black hole would. need to acerete at the Eddington rate or ~101 vears to significantly affect the spin.," Thus, the black hole would need to accrete at the Eddington rate for $\sim10^7$ years to significantly affect the spin." This is not a likely scenario., This is not a likely scenario. ln addition. the current aceretion rate is merely a few per cent of the Edcington rate.," In addition, the current accretion rate is merely a few per cent of the Eddington rate." Therefore. je acereted mass can be neglected to first order.," Therefore, the accreted mass can be neglected to first order." “Phe low mass accretion onto the black hole also means that the spin xvwameter cannot have been changed by mass transfer [rom )6 companion star., The low mass accretion onto the black hole also means that the spin parameter cannot have been changed by mass transfer from the companion star. " Aq,0.02 for an accreted. mass of hence the value measured now is the same as when 10 black hole was formed."," $\Delta a_* \leq 0.02$ for an accreted mass of, hence the value measured now is the same as when the black hole was formed." Elfects such as beaming may lead us to underestimate 10 luminosity. ancl thereby the accretion rate.," Effects such as beaming may lead us to underestimate the luminosity, and thereby the accretion rate." However. μαuclies of X-ray binaries show that the transition between 16 so-called. hard and. soft states tvpically occur around a ew per cent of the Eddington luminosity (Doneetal.2007).," However, studies of X-ray binaries show that the transition between the so-called hard and soft states typically occur around a few per cent of the Eddington luminosity \citep{done07}." . Spectral studies show that Cve N-1 is mostly observed in the nud state: thus. the accretion rate cannot be very high even if beaming leads us to underestimate it.," Spectral studies show that Cyg X-1 is mostly observed in the hard state; thus, the accretion rate cannot be very high even if beaming leads us to underestimate it." Another possibility which may [ead us to underestimate the aceretion rate is asvmmetric accretion., Another possibility which may lead us to underestimate the accretion rate is asymmetric accretion. In this case. the radiative ellicicncy can be much lower than during spherical accretion.," In this case, the radiative efficiency can be much lower than during spherical accretion." While such a scenario is unlikely at present. we cannot rule out tha the system has undergone a period of asvniumetric accretion in the past. and thereby accreted. more mass than the estimate above.," While such a scenario is unlikely at present, we cannot rule out that the system has undergone a period of asymmetric accretion in the past, and thereby accreted more mass than the estimate above." However. the accretion rate is still limitec by the capture rate of the stellar wind from the companion. and we find it unlikely that asymmetric acerction coulc have increased the accreted mass to the level required.," However, the accretion rate is still limited by the capture rate of the stellar wind from the companion, and we find it unlikely that asymmetric accretion could have increased the accreted mass to the level required." One possibility to clo so is to invoke a period of super-IEddington accretion after the black hole has formed., One possibility to do so is to invoke a period of super-Eddington accretion after the black hole has formed. Such a. perio would have to be very short. and the accretion rate therefore extremely high.," Such a period would have to be very short, and the accretion rate therefore extremely high." While this scenario cannot be ruled out. the feasibility of super-Ecelington accretion is still under debate.," While this scenario cannot be ruled out, the feasibility of super-Eddington accretion is still under debate." Lt is possible that the svstem underwent a period. of mass transfer before the creation of the black hole. and this mav have spun up the stellar core.," It is possible that the system underwent a period of mass transfer before the creation of the black hole, and this may have spun up the stellar core." We will therefore consider the case of mass accretion onto the helium core., We will therefore consider the case of mass accretion onto the helium core. Although mass transfer may have occurred. also at. earlier stages in the binary evolution. accretion at this stage will primarily spin up the envelope of the star. and it is unclear how much angular momentum is actually gained by the core.," Although mass transfer may have occurred also at earlier stages in the binary evolution, accretion at this stage will primarily spin up the envelope of the star, and it is unclear how much angular momentum is actually gained by the core." The maximum time during which the Le core can accrete matter is determined by its evolution. andis of the order of 10 vears.," The maximum time during which the He core can accrete matter is determined by its evolution, andis of the order of $10^6$ years." " In order to increase the rotational frequency sullicientl to change the spin parameter. by Aa.= 0.1. the core would have to accrete more than (assuming a raciius of Ao,=OSL. )."," In order to increase the rotational frequency sufficiently to change the spin parameter by $\Delta a_* = 0.1$ , the core would have to accrete more than (assuming a radius of $R_{\rm co}=0.8R_{\odot}$ )." The recent increased interest in the analysis of hydrodynamic dise flows is motivated. on one hand. by the study of turbulent processes. and. on the other. by the investigation of regular structure formation in protoplanetary dises.,"The recent increased interest in the analysis of hydrodynamic disc flows is motivated, on one hand, by the study of turbulent processes, and, on the other, by the investigation of regular structure formation in protoplanetary discs." Indeed. many astrophysical dises are thought to be neutral or having ionization rates too low to effectively couple with magnetic field.," Indeed, many astrophysical discs are thought to be neutral or having ionization rates too low to effectively couple with magnetic field." Among these are cool and dense areas of protoplanetary discs. discs around young stars. X-ray transient and dwarf nova systems in quiescence (see e.g. Gammie and Menou 1998. Sano et al.," Among these are cool and dense areas of protoplanetary discs, discs around young stars, X-ray transient and dwarf nova systems in quiescence (see e.g. Gammie and Menou 1998, Sano et al." 2000. Fromang. Terquem and Balbus 2002).," 2000, Fromang, Terquem and Balbus 2002)." Observational data shows that astrophysical discs often exhibit radial gradients of thermodynamic variables (see e.g. Sandin et al., Observational data shows that astrophysical discs often exhibit radial gradients of thermodynamic variables (see e.g. Sandin et al. 2008. Issela et al.," 2008, Issela et al." 2007)., 2007). To what extent hese inhomogeneities affect the processes occurring in the disc is still subject open to investigations., To what extent these inhomogeneities affect the processes occurring in the disc is still subject open to investigations. It has been found that strong ocal entropy gradients in the radial direction may drive the Rossby wave instability (Lovelace et al., It has been found that strong local entropy gradients in the radial direction may drive the Rossby wave instability (Lovelace et al. " 1999, Li et al."," 1999, Li et al." 2000) that transfers hermal to kinetic energy and leads to vortex formation., 2000) that transfers thermal to kinetic energy and leads to vortex formation. However. in astrophysical dises. radial stratification is more likely weak.," However, in astrophysical discs, radial stratification is more likely weak." In his case. the radial entropy (temperature) variation on the global scale leads to the existence of baroclinic perturbations over the barotropic equilibrium state.," In this case, the radial entropy (temperature) variation on the global scale leads to the existence of baroclinic perturbations over the barotropic equilibrium state." This more appropriate situation has recently become a subject of extensive study., This more appropriate situation has recently become a subject of extensive study. Klahr and Bodenheimer (2003) pointed out that the radial stratification in the dise can lead to the global baroclinic instability., Klahr and Bodenheimer (2003) pointed out that the radial stratification in the disc can lead to the global baroclinic instability. Numerical results show that the resulting state is highly chaotic and transports angular momentum outwards., Numerical results show that the resulting state is highly chaotic and transports angular momentum outwards. Later Klahr (2004) performed a local 2D linear stability analysis of a radially stratified flow with constant surface density and showed that baroclinic perturbations can grow transiently during a limited ime interval., Later Klahr (2004) performed a local 2D linear stability analysis of a radially stratified flow with constant surface density and showed that baroclinic perturbations can grow transiently during a limited time interval. Johnson and Gammie (2005) derived analytic solutions for 3D linear perturbations in a radially stratified disces in the Boussinesq approximation., Johnson and Gammie (2005) derived analytic solutions for 3D linear perturbations in a radially stratified discs in the Boussinesq approximation. They tind that leading and railing waves are characterized by positive and negative angular momentum flux. respectively.," They find that leading and trailing waves are characterized by positive and negative angular momentum flux, respectively." Later Johnson and Gammie (2006) yerformed numerical simulations. in the local shearing sheet model. to test the radial convective stability and the effects of baroclinic perturbations.," Later Johnson and Gammie (2006) performed numerical simulations, in the local shearing sheet model, to test the radial convective stability and the effects of baroclinic perturbations." They found no substantial instability due o the radial stratification., They found no substantial instability due to the radial stratification. This result reveals a controversy over he issue of baroclinic instability., This result reveals a controversy over the issue of baroclinic instability. Presently. it seems that nonlinear baroclinic instability is an unlikely development in the local dynamics of sub-Keplerian dises with weak radial stratification.," Presently, it seems that nonlinear baroclinic instability is an unlikely development in the local dynamics of sub-Keplerian discs with weak radial stratification." Potential vorticity production. and the formation and development of vortices in radially stratified dises have been studied by Petersen et al. (," Potential vorticity production, and the formation and development of vortices in radially stratified discs have been studied by Petersen et al. (" 2007a.b) by using pseudospectral simulations in the anelastic approximation.,"2007a,b) by using pseudospectral simulations in the anelastic approximation." They show that the existence of thermal perturbations in the radially stratified disc flows leads to the formation of vortices., They show that the existence of thermal perturbations in the radially stratified disc flows leads to the formation of vortices. Moreover. stronger vortices appear in discs with higher temperature perturbations or in simulations with higher Reynolds numbers. and the transport of angular momentum may be both outward and inward.," Moreover, stronger vortices appear in discs with higher temperature perturbations or in simulations with higher Reynolds numbers, and the transport of angular momentum may be both outward and inward." Keplerian differential rotation in the dise is characterized by a strong velocity shear in the radial direction., Keplerian differential rotation in the disc is characterized by a strong velocity shear in the radial direction. It is known tha shear flows are non-normal and exhibit a number of transien phenomena due to the non-orthogonal nature of the operators (see e.g. Trefethen et al., It is known that shear flows are non-normal and exhibit a number of transient phenomena due to the non-orthogonal nature of the operators (see e.g. Trefethen et al. 1993)., 1993). In fact. the studies described above did not take into account the possibility of mode coupling and energy transfer between different modes due to the shear flow induced mode conversion.," In fact, the studies described above did not take into account the possibility of mode coupling and energy transfer between different modes due to the shear flow induced mode conversion." Mode coupling is inherent to shear flows (cf., Mode coupling is inherent to shear flows (cf. Chagelishvili et al., Chagelishvili et al. 1995) and often. in many respects. defines the role of perturbation modes in the system dynamies and the further," 1995) and often, in many respects, defines the role of perturbation modes in the system dynamics and the further" aquillenicepasrochesster.edu. hubbardapas.rochestercdu Ever since the double-peaked nucleus of N31 was clearly resolved by IIubble Space Telescope (IST) imagine (Laueretal. 1993).. the morphology of this svstem has been a challenge to explain.,"ster.edu, hubbardpas.rochester.edu } } Ever since the double-peaked nucleus of M31 was clearly resolved by Hubble Space Telescope (HST) imaging \citep{lauer}, the morphology of this system has been a challenge to explain." The nost successful kinematic uodel is the ececeutric stellar disk proposed by Tremaine(1995) where stars in apsidally aligned elliptical. orbits about a massive black hole result in an over-deusity at heir apoapses. thus accounting for the brighter peak Pl.," The most successful kinematic model is the eccentric stellar disk proposed by \citet{tremaine} where stars in apsidally aligned elliptical orbits about a massive black hole result in an over-density at their apoapses, thus accounting for the brighter peak P1." The black hole itself resides near the fainter. more centrally located peak denoted P2.," The black hole itself resides near the fainter, more centrally located peak denoted P2." Though this model was been successful at matching the observed velocity aud uunmositv distribution (vormenudy&Bender1999:Statleretal.1999:Bacon2001:Samibhlus&Srichar 2002)). eccentric disk formation reniadus a nivsterv.," Though this model has been successful at matching the observed velocity and luminosity distribution \citealt{kormendy,statler,bacon,sambhus}) ), eccentric disk formation remains a mystery." Tota(2002) showed that a small fraction of counter rotating stars. possibly originating from an disrupted elobular cluster on a retrograde orbit. could cause a more nassive pre-existing stellar disk to develop a lopsided or om=1 instability.," \cite{touma} showed that a small fraction of counter rotating stars, possibly originating from an disrupted globular cluster on a retrograde orbit, could cause a more massive pre-existing stellar disk to develop a lopsided or $m=1$ instability." The self-cousisteunt ducmatic nodeling of Samblus&Sridhar (2002).. which requires a πια percentage of counter rotating stars. supports this scenario.," The self-consistent kinematic modeling of \citet{sambhus}, , which requires a small percentage of counter rotating stars, supports this scenario." Baconetal.(2001). proposed that a collision roni a passing molecular cloud or globular cluster could shock a pre-existiug stellar disk off-ceuter. resulting in a oue lived. precessing mode.," \cite{bacon} proposed that a collision from a passing molecular cloud or globular cluster could knock a pre-existing stellar disk off-center, resulting in a long lived, precessing mode." The N-body simmlations of Jacobs&Selhwood(1999):Taga(2002) have illustrated hat lopsided stellar disks could be long-lived.," The N-body simulations of \citet{jacobs,taga} have illustrated that lopsided stellar disks could be long-lived." The scenarios discussed by Sambhus&Sridhar(2002):Baconetal. (2001).. begin with an initially axisvunuetric stellar disk. which them becomes lopsided either because of a violent event (such as a collision with a elobular cluster) or the erowth of an instability.," The scenarios discussed by \citet{sambhus,touma,jacobs,taga,bacon}, begin with an initially axisymmetric stellar disk, which then becomes lopsided either because of a violent event (such as a collision with a globular cluster) or the growth of an instability." However Dekli(2000a) proposed that M31 eccentric disk could have been a result of a single disruptions event., However \citet{bekki} proposed that M31's eccentric disk could have been a result of a single disruption event. Te succeeded at producing an eccentric stellar disk by disrupting a elobular cluster near a niassive black hole iu aa N-body simulation. though an SPU simulation of the disruption of a massive eascous cloud did not vield an ecceutric disk (Dekli20005).," He succeeded at producing an eccentric stellar disk by disrupting a globular cluster near a massive black hole in an N-body simulation, though an SPH simulation of the disruption of a massive gaseous cloud did not yield an eccentric disk \citep{bekki2}." . The massive black hole iu iu M31 is moderate with aguams 30τν10AZ. (IKormieudy&Bender1999:Baconetal. 2001).," The massive black hole in in M31 is moderate with a mass $3 -7 \times 10^7 M_\odot$ \citep{kormendy,bacon}." . The eccentric disk itself is ucarly as massive as the black hole. ~3«LOTAL.. (Penge2002:Saubhus&Sridhar2002:Baconctal. 2001).. preseutius a problem for the elobular cluster disruption scenario proposed by Bekki(2000a}) which asstmed that the globular cluster was typical of Galactic globular clusters and of order a wullion solar masses.," The eccentric disk itself is nearly as massive as the black hole, $\sim 3 \times 10^7 M_\odot$ \citep{peng, sambhus, bacon}, presenting a problem for the globular cluster disruption scenario proposed by \citet{bekki} which assumed that the globular cluster was typical of Galactic globular clusters and of order a million solar masses." Tere we reconsider Dekkis proposal. that a single diszuption event could have produced the eccentric disk in M31.," Here we reconsider Bekki's proposal, that a single disruption event could have produced the eccentric disk in M31." The disruption event is likely to be complex so we focus on what final disks are capable ofsupporting lopsided a slow modes. drawing from the recent work of Tremaine(2001) who developed a formalisin for the purpose of predicting the precession rates and eccentricities of discrete modes for low mass. nearly Ixeplerian disks.," The disruption event is likely to be complex so we focus on what final disks are capable of supporting lopsided a slow modes, drawing from the recent work of \citet{tremaine2001} who developed a formalism for the purpose of predicting the precession rates and eccentricities of discrete modes for low mass, nearly Keplerian disks." We place limits ou the density aud core radius of progenitor clusters for eccentric disks uear massive black holes., We place limits on the density and core radius of progenitor clusters for eccentric disks near massive black holes. The resulting diagranà is useful toward predicting what types of galaxies are most likely to harbor eccentric disks. for predicting the probability that eccentric disk formation events occur and for euiding the initial conditions of N-body sinmlatious which may determine if aud how they fori.," The resulting diagram is useful toward predicting what types of galaxies are most likely to harbor eccentric disks, for predicting the probability that eccentric disk formation events occur and for guiding the initial conditions of N-body simulations which may determine if and how they form." The observed correlation between mass of a black hole and the bulee dispersion (Gebhardtctal.2000:Ferrarese allows us to relate theblack hole to the bulee of its host galaxy.," The observed correlation between mass of a black hole and the bulge dispersion \citep{gebhardt2000,ferrarese} allows us to relate theblack hole to the bulge of its host galaxy." where σ. is the stellar bulee dispersion. aud we adopt constants in the relation giveu by Tremaineetal. (2002)..," where $\sigma_*$ is the stellar bulge dispersion, and we adopt constants in the relation given by \citet{tremaine2002}. ." "using several telescopes separated by at least the diameter of the asteroid would increase the detection rate, but the cadence of OGLE-III at about five minutes would simply undersample and miss such an event.","using several telescopes separated by at least the diameter of the asteroid would increase the detection rate, but the cadence of OGLE-III at about five minutes would simply undersample and miss such an event." " OGLE-IV will provide both a higher sensitivity and a higher cadence, but probably not a rapid enough cadence to distinguish such an event."," OGLE-IV will provide both a higher sensitivity and a higher cadence, but probably not a rapid enough cadence to distinguish such an event." The best approach would be a difficult hybrid of the high cadence of observations such as ? on a large telescope and the monitoring of many stars as OGLE., The best approach would be a difficult hybrid of the high cadence of observations such as \citet{2006AJ....132..819R} on a large telescope and the monitoring of many stars as OGLE. " Because the goal is not small bodies as in ?,,"," Because the goal is not small bodies as in \citet{2006AJ....132..819R}," he X-ray analysis is included in that work. and only a brief summary is presented here.,"the X-ray analysis is included in that work, and only a brief summary is presented here." “Phe method of X-ray analysis ollows the multiphase technique emploved in the studies of ISS0745-191 and Abell 1835 by Allen (1996a.b).," The method of X-ray analysis follows the multiphase technique employed in the studies of PKS0745-191 and Abell 1835 by Allen (1996a,b)." A re-analvsis of both of these clusters. is included in the current work., A re-analysis of both of these clusters is included in the current work. For the purposes of this paper. clusters are classified into three categories: cooling Hows. non-cooling Lows and intermediate svstems.," For the purposes of this paper, clusters are classified into three categories; cooling flows, non-cooling flows and intermediate systems." The cooling Hows are those clusters with central cooling times «5.10 vr and for whieh the lux rom cooling gas is spectrally determined to account for z20 ver cent of the total X-ray luminosity., The cooling flows are those clusters with central cooling times $< 5 \times 10^{9}$ yr and for which the flux from cooling gas is spectrally determined to account for $\geq 20$ per cent of the total X-ray luminosity. Intermediate clusters are those svstems with central cooling times «107 vr and or which the cooling flows are spectrally determined to contribute «20 per cent of the total X-ray luminosity., Intermediate clusters are those systems with central cooling times $< 10^{10}$ yr and for which the cooling flows are spectrally determined to contribute $< 20$ per cent of the total X-ray luminosity. Non-cooling How systems are those clusters with central cooling : Lo . . ↓⊔↓∢⊾⊳∖↙⇁↓∪∙∖⇁↓⋅⊳⋜⋯∠⇂∖∖⊽↓∐≼⇍⇂↥⊳∖↓↥∪∖∖⊽⊔∪⊳∖↓≻⋯∼⇂↓⋅⋜↧⇂∢⊾∖⇁⊔⇂∢⋅⊔⊓⋅⇂∪↓⋅⋅ ≼∙∪∪↥⋠↓⊔⋏," Non-cooling flow systems are those clusters with central cooling times $> 10^{10}$ yr, and which show no spectral evidence for cooling flow emission." ↳≱↓∪∖∖⊽⋖⋅↓↕↓↕≻≻↕∢≱↓↕⊳↓⊲↸∪↓⋅⇂⋅⊔∐∠⇂∢⊾↿⋜↧⊀↓⊳∖≱∖∢⋅⋖⋅⇀∖∐∢⋅⊔↙∣∣∣∕⊽⊔≤⋗≤⋗⊤⋡ in preparation).," For full details see Allen (1997, in preparation)." Spectra were extracted fron all four ASCA detectors (except for PINSO0745-191. for which the S1 data were lost due to chip saturation problems) in circular regions. centred. on the X-ray. centroids. Clable 2).," Spectra were extracted from all four ASCA detectors (except for PKS0745-191, for which the S1 data were lost due to chip saturation problems) in circular regions, centred on the X-ray centroids (Table 2)." For the SIS data. the raclii of the regions were adjusted to minimize the number of chip bouncdaries crossed (thereby minimizing the systematic uncertainties introduced. by such crossings) whilst covering as large a region of the clusters as possible.," For the SIS data, the radii of the regions were adjusted to minimize the number of chip boundaries crossed (thereby minimizing the systematic uncertainties introduced by such crossings) whilst covering as large a region of the clusters as possible." Data from the regions between the chips were masked out anc excluded., Data from the regions between the chips were masked out and excluded. For the CUS data a constant extraction radius of 6 arcmin was Used., For the GIS data a constant extraction radius of 6 arcmin was used. " For the CLS observations. anc SIS observations of clusters in regions of low Galactic column clensity (Vg5.LOLu )). background subtraction was carried out using the ""blank sky observations of high Galactic [atitucle fields complied during the performance verification stage of the ASCA mission."," For the GIS observations, and SIS observations of clusters in regions of low Galactic column density $N_{\rm H} \approxlt 5 \times 10^{20}$ ), background subtraction was carried out using the `blank sky' observations of high Galactic latitude fields complied during the performance verification stage of the ASCA mission." For such data sets. the blank-sky observations provide a reasonable representation of the cosmic and instrumental backgrounds in the detectors.," For such data sets, the blank-sky observations provide a reasonable representation of the cosmic and instrumental backgrounds in the detectors." The background. data were screened. ancl grade selected in the, The background data were screened and grade selected in the "In order to make progress. we compute (he spatial dependence of the various mocles upstream in the WIKDJ approximation:7.e.. in the limit τὸx. and in particular /,|aL. the size of the upstream precursor.","In order to make progress, we compute the spatial dependence of the various modes upstream in the WKBJ approximation:, in the limit $k_y\rightarrow\infty$, and in particular $k_y^{-1}\ll L$, the size of the upstream precursor." I other words. we take all perturbed physical quantities to be of the form and all derivatives in the wr direction(I.e... perpendicular to the shock) are considered small when compared with terms proportional to Αγ.," In other words, we take all perturbed physical quantities to be of the form and all derivatives in the $x$ direction, perpendicular to the shock) are considered small when compared with terms proportional to $k_y$." " This is a perturbation analvsis in which the transverse wavenuniber 7, is assumed large and as a consequence the longitudinal wavenumber zzWoy is also large.", This is a perturbation analysis in which the transverse wavenumber $k_y$ is assumed large and as a consequence the longitudinal wavenumber $\approx W_X$ is also large. The presence of a non-constant amplitude Qy(Cr) is equivalent to keeping the first (vo ternis in an asymptotic expansion in the small parameter (kL)+., The presence of a non-constant amplitude $Q_X(x)$ is equivalent to keeping the first two terms in an asymptotic expansion in the small parameter $(k_yL)^{-1}$. This is often called the physical optics approximation (BenderandOrszag1978)., This is often called the physical optics approximation \citep{benderorszag1978}. This analvsis is quile standard. but the amusing thing is that we don't even need to carry it through.," This analysis is quite standard, but the amusing thing is that we don't even need to carry it through." In fact. we shall show later that the stability analvsis requires knowledge of the physical quantities immediately beforethe shock. while knowledge of the perturbations run with vr further from the shock is immaterial.," In fact, we shall show later that the stability analysis requires knowledge of the physical quantities immediately beforethe shock, while knowledge of the perturbations run with $x$ further from the shock is immaterial." We see from the above that all physical «quantiües close to the shock satisfy This is precisely the same form (hat holds in the homogeneous medium. so (hat eqs.," We see from the above that all physical quantities close to the shock satisfy This is precisely the same form that holds in the homogeneous medium, so that eqs." 34 and 17 still hold.," \ref{homogeneoussolution} and \ref{justahelp} still hold." Also. the space-time dependence of the d-mode for the hall-plane v>0 is derived in Appendix A.. assuming spatial homogeneity of the background solution: and (his. for the argument above. applies in the WIAXBJ limit also (ο (he upstream. fluid.," Also, the space-time dependence of the d-mode for the half-plane $x>0$ is derived in Appendix \ref{app:dmode}, assuming spatial homogeneity of the background solution; and this, for the argument above, applies in the WKBJ limit also to the upstream fluid." Let us also remark (hat. in this spatially homogeneous limit. vorticitv perturbations do nol couple to particles: in other words. spatial gradients are neelieibly small ancl thus vorlicily perturbations. which can only be Lie-advected from upstream infinity. must. vanish identically.," Let us also remark that, in this spatially homogeneous limit, vorticity perturbations do not couple to particles: in other words, spatial gradients are negligibly small, and thus vorticity perturbations, which can only be Lie-advected from upstream infinity, must vanish identically." This is the result we need: since we are using a WIXDJ approximation. we can (reat the upstream fluid as if it were homogeneous. wilh the values for the physical quantities taken to be those immediately before the shock: we call this the Homogeneous Approximation: il Clearly breaks down when the WIXBJ analysis does. which occurs lor ky!x L. the size of the upstream precursor.," This is the result we need: since we are using a WKBJ approximation, we can treat the upstream fluid as if it were homogeneous, with the values for the physical quantities taken to be those immediately before the shock: we call this the Homogeneous Approximation: it clearly breaks down when the WKBJ analysis does, which occurs for $k_y^{-1} \approx L$ , the size of the upstream precursor." Pop III stars could trigger collapsar gamma-ray bursts.,Pop III stars could trigger collapsar gamma-ray bursts. Observations of such energetic GRBs at very high redshifts will be a unique probe of the high-redshift Universe., Observations of such energetic GRBs at very high redshifts will be a unique probe of the high-redshift Universe. " With a semi-analytical approach we estimated the star formation rate for Pop IIL1 and IIL.2 stars including all relevant feedback effects: photo-dissociation, reionization, and metal enrichment."," With a semi-analytical approach we estimated the star formation rate for Pop III.1 and III.2 stars including all relevant feedback effects: photo-dissociation, reionization, and metal enrichment." Using radio transient sources we are able to derive constraints on the intrinsic rate of GRBs., Using radio transient sources we are able to derive constraints on the intrinsic rate of GRBs. " We estimated the predicted GRB rate for both Pop III.1 and Pop III.2 stars, and argued that the latter is more likely to be observed with future experiments."," We estimated the predicted GRB rate for both Pop III.1 and Pop III.2 stars, and argued that the latter is more likely to be observed with future experiments." We expect to observe maximum of N<20 GRBs per year integrated over at z>6 for Pop IIL2 and N<0.08 per year integrated over at z>10 for Pop IIL1 with EXIST., We expect to observe maximum of $N \lesssim 20$ GRBs per year integrated over at $z > 6$ for Pop III.2 and $N \lesssim 0.08$ per year integrated over at $z > 10$ for Pop III.1 with EXIST. " We also expect a larger number of radio afterglows than X-ray prompt emission because the radio afterglow is long-lived, for ~10? days above ~0.3 mJy from Fig. 7.."," We also expect a larger number of radio afterglows than X-ray prompt emission because the radio afterglow is long-lived, for $\sim 10^2$ days above $\sim 0.3$ mJy from Fig. \ref{fig:GRBafterglow}." " Combining with the intrinsic GRB rate and constraints from radio transients, we expect roughly ~10—104 radio afterglows above =0.3 mJy already on the sky."," Combining with the intrinsic GRB rate and constraints from radio transients, we expect roughly $\sim 10-10^4$ radio afterglows above $ \gtrsim 0.3$ mJy already on the sky." " They are indeed detectable by ALMA, EVLA, LOFAR,"," They are indeed detectable by ALMA, EVLA, LOFAR," A number of observational studies of GJ 1214b's atmosphere have already taken place. and here we attempt (o rectify our modeling efforts with (he available data.,"A number of observational studies of GJ 1214b's atmosphere have already taken place, and here we attempt to rectify our modeling efforts with the available data." To date. observations of GJ 1214b's atmosphere have been focused on Gransit measurements to determine {he planet's effective radius as a function of wavelength (Qransmission spectrum).," To date, observations of GJ 1214b's atmosphere have been focused on transit measurements to determine the planet's effective radius as a function of wavelength (transmission spectrum)." An alternative observing sirategv. would be to observe GJ. 1214b al secondary. eclipse to obtain. clay-sicle enission spectroscopy., An alternative observing strategy would be to observe GJ 1214b at secondary eclipse to obtain day-side emission spectroscopy. Unfortunately. the expected secondary eclipse depth for GJ 1214b at wavelengths shoriward of 5 jn is less than LOO ppm (?) and is therefore likely to remain bevond the reach of observational detection lor current instrumentation.," Unfortunately, the expected secondary eclipse depth for GJ 1214b at wavelengths shortward of 5 $\mu$ m is less than 100 ppm \citep{mil10} and is therefore likely to remain beyond the reach of observational detection for current instrumentation." In (he meantime. (ransiission spectroscopy has the added benefit of being highly sensitive to (he atmospheric mean molecular weight. which allows for a better understanding of the bulk composition of (he atmosphere.," In the meantime, transmission spectroscopy has the added benefit of being highly sensitive to the atmospheric mean molecular weight, which allows for a better understanding of the bulk composition of the atmosphere." The observational efforts to date are summarized as follows., The observational efforts to date are summarized as follows. The [Earth survey produced (he original measurement of GJ 1214b's transit depth using a broad-band optical/near-IB filler spanning ~G75-105-O0 nm (?).., The MEarth survey produced the original measurement of GJ 1214b's transit depth using a broad-band optical/near-IR filter spanning $\sim$ 675-1050 nm \citep{cha09}. These transi€ observations produced a transit depth of L.35%.. which was later refined by ? to 1.374. using additional epochs of MEarth observations along with transit observatiois from the VLT and FLWO 1.2-meter telescope.," These transit observations produced a transit depth of $1.35$, which was later refined by \citet{ber11} to $1.37$ using additional epochs of MEarth observations along with transit observations from the VLT and FLWO 1.2-meter telescope." " 7?| [uther extended the transit observatiois to shorter wavelengths at r--band. obtaining a (ransit depth of (R,/RP=0.01084+0.00056."," \citet{kun10} further extended the transit observations to shorter wavelengths at -band, obtaining a transit depth of $(R_{p}/R_{\star})^2 = 0.01084 \pm 0.00056$." ILowever. their r-band data is highly degenerate with limb darkening. and including the formal error bars on their limb darkening parameters leads(ο a much larger error bar in the transit depth.," However, their $r$ -band data is highly degenerate with limb darkening, and including the formal error bars on their limb darkening parameters leadsto a much larger error bar in the transit depth." ? produced (he first waveleneth-dependent Gransmission spectru nin the verv-near-IR. [rom 730 to 1000 nm. using ihe FORS2 instrument on the VLT.," \citet{bea10} produced the first wavelength-dependent transmission spectrum in the very-near-IR from 780 to 1000 nm, using the FORS2 instrument on the VLT." The resulting transmission spectrum is leatureless. as discussed in Section 1..," The resulting transmission spectrum is featureless, as discussed in Section \ref{intro}." ? provide (wo additional data points to the transmission spectrum ab longer wavelengths in the IR. using the two weum Spitzer IRAC channels., \citet{des11} provide two additional data points to the transmission spectrum at longer wavelengths in the IR using the two warm Spitzer IRAC channels. Their 3.6 and4.5 jan data continue (o reveal a flat transmission specirum at high significance., Their 3.6 and4.5 $\mu$ m data continue to reveal a flat transmission spectrum at high significance. ?— are the only authors to report a wavelength dependei m transit depth for GJ 1214b., \citet{cro11} are the only authors to report a wavelength dependent in transit depth for GJ 1214b. The J and Ks band data show a strong discrepancy. between the transit depths observed ab these (wo wavelengths at a level of several signa., Their J and Ks band data show a strong discrepancy between the transit depths observed at these two wavelengths at a level of several sigma. This is attributed to GJ 1214b having a hydrogen-vich atmosphere with a large scale heielit. which is the only way to produce such a large difference between the (transit depths observed at (wo separate wavelengths.," This is attributed to GJ 1214b having a hydrogen-rich atmosphere with a large scale height, which is the only way to produce such a large difference between the transit depths observed at two separate wavelengths." Ilere we attempt to fit all the available data with our modeled transmission spectra from section 2.2.., Here we attempt to fit all the available data with our modeled transmission spectra from Section \ref{tr_spec}. We compare each of our modeled spectra to the observed (transit depths from all of the data sets where multi-wavelength data was obtained. ancl we compute a (A7) parameter to assess how welleach model reproduces the data.," We compare each of our modeled spectra to the observed transit depths from all of the data sets where multi-wavelength data was obtained, and we compute a goodness-of-fit $\chi^2$ ) parameter to assess how welleach model reproduces the data." " We perform a comparison to the ensemble of multi-wavelength data from ον, 2.. aud. ?.."," We perform a comparison to the ensemble of multi-wavelength data from \citet{bea10}, , \citet{des11}, , and \citet{cro11}. ." We additionally, We additionally (CL) reduces to a weighted sum over the galaxies with luminosity L. but unlike 1/1 explicitly accounts for fluctuations in the galaxy density with redshift.,"$\Phi(L)$ reduces to a weighted sum over the galaxies with luminosity $L$, but unlike $1/\Vm$ explicitly accounts for fluctuations in the galaxy density with redshift." " As each observed galaxy contributes linearly to this estimated LF. this means that a random catalogue with a consistent LF can be generated by simply cloning galaxies from the observed catalogue. with a rate which we derive from a maximum likelihood analysis. and redistributing them uniformly over the volume in which they would satisfy the survey selection criteria,"," As each observed galaxy contributes linearly to this estimated LF, this means that a random catalogue with a consistent LF can be generated by simply cloning galaxies from the observed catalogue, with a rate which we derive from a maximum likelihood analysis, and redistributing them uniformly over the volume in which they would satisfy the survey selection criteria." As each galaxy in the random catalogue is a clone of an observed galaxy it carries with it all the measured properties of hat galaxy., As each galaxy in the random catalogue is a clone of an observed galaxy it carries with it all the measured properties of that galaxy. Hence. provided they can be moditied for the change in redshift (e.g. k-correcting luminosities). the resulting random catalogue has all the properties of the original and can be used ο study clustering as a function of any of those properties.," Hence, provided they can be modified for the change in redshift (e.g. k-correcting luminosities), the resulting random catalogue has all the properties of the original and can be used to study clustering as a function of any of those properties." This echnique should be particularly applicable to multi-wavelength surveys such as GAMA ο) and its overlapwith H-ATLAS (?).. 6dF (2).. zCOSMOS ¢?) and future redshift surveys designed to orobe galaxy evolution.," This technique should be particularly applicable to multi-wavelength surveys such as GAMA \citep{GAMA} and its overlapwith H-ATLAS \citep{HATLAS}, 6dF \citep{6dF}, zCOSMOS \citep{zCOSMOS} and future redshift surveys designed to probe galaxy evolution." In Section ?? we develop a joint maximum likelihood estimator for an assumed non-evolving LF and the| run of overdensity as a function of redshift., In Section \ref{sec:LF} we develop a joint maximum likelihood estimator for an assumed non-evolving LF and the run of overdensity as a function of redshift. We. also. show how the LF estimator relates to the standard 1/177 estimator.," We, also, show how the LF estimator relates to the standard $1/\Vm$ estimator." Section 2? extends this estimator to include galaxy evolution., Section \ref{sec:evol} extends this estimator to include galaxy evolution. In Section ?? we show how the estimator can be extended to provide a simple algorithm for generating a random galaxy catalogue., In Section \ref{sec:rancat} we show how the estimator can be extended to provide a simple algorithm for generating a random galaxy catalogue. The method is tested and illustrated with mock data in Section 22. and we conclude in Section ??..The commonly used STY (Sandage. Tammann Yahil 25) and EEP (Efstathiou. Ellis Peterson ?) maximum likelihood estimators of the galaxy luminosity function (LF) assume the probability of a galaxy having luminosity in the interval £4L/2 to L|dLf2 ina volume element dx centred at position x can be factorized as They then construct estimators that are independent of the density. p(x). by factoring out its dependence.," The method is tested and illustrated with mock data in Section \ref{sec:results} and we conclude in Section \ref{sec:conc}.The commonly used STY (Sandage, Tammann Yahil \citeyear{STY}) ) and EEP (Efstathiou, Ellis Peterson \citeyear{EEP}) ) maximum likelihood estimators of the galaxy luminosity function (LF) assume the probability of a galaxy having luminosity in the interval $L-dL/2$ to $L+dL/2$ in a volume element $d^3{\bf x}$ centred at position ${\bf x}$ can be factorized as They then construct estimators that are independent of the density, $\rho({\bf x})$, by factoring out its dependence." " Thus they start with the following probability that in an apparent magnitude limited catalogue a galaxy à at redshift z,, will have luminosity £L, The STY and EEP methods differ in that STY assume a parametric (Schechter function) form for the LF. while EEP simply adopt a stepwise (binned) description of the LF."," Thus they start with the following probability that in an apparent magnitude limited catalogue a galaxy $\alpha$ at redshift $z_\alpha$ will have luminosity $L_\alpha$ The STY and EEP methods differ in that STY assume a parametric (Schechter function) form for the LF, while EEP simply adopt a stepwise (binned) description of the LF." In both cases the derivation of the LF estimator follows by forming the likelihood. which is the total probability for the whole galaxy sample given the model parameters. and maximising this likelihood (or its logarithm) over the model parameters (bin values in the case of EEP).," In both cases the derivation of the LF estimator follows by forming the likelihood, which is the total probability for the whole galaxy sample given the model parameters, and maximising this likelihood (or its logarithm) over the model parameters (bin values in the case of EEP)." " If we are interested in estimating both the LF and the spherically averaged density field we can instead start with the probability of finding a galaxy at redshift z,, with luminosity £,, in an apparent magnitude limited sample.", If we are interested in estimating both the LF and the spherically averaged density field we can instead start with the probability of finding a galaxy at redshift $z_\alpha$ with luminosity $L_\alpha$ in an apparent magnitude limited sample. Here dV/dz is the differential of the survey volume with redshift and ;X(z) is the galaxy overdensity (averaged over a radial bin) at redshift z., Here ${dV}/{dz}$ is the differential of the survey volume with redshift and $\Delta(z)$ is the galaxy overdensity (averaged over a radial bin) at redshift $z$. Here we are assuming that there is no redshift evolution of the luminosity function and hence p(x) varies only due to density fluctuations., Here we are assuming that there is no redshift evolution of the luminosity function and hence $\rho({\bf x})$ varies only due to density fluctuations. " Adopting binned estimates of both the luminosity function ó; and overdensity A, we can write this probability as Here the sum over p (later also q) runs over redshift bins with V, being the volume and A, the galaxy overdensity of the bin.", Adopting binned estimates of both the luminosity function $\phi_i$ and overdensity $\Delta_p$ we can write this probability as Here the sum over $p$ (later also $q$ ) runs over redshift bins with $V_p$ being the volume and $\Delta_p$ the galaxy overdensity of the bin. The sum over ὁ (later also j) runs over the bins in the luminosity ‘unction with ó; being equal to o(L)dL for that bin.," The sum over $i$ (later also $j$ ) runs over the bins in the luminosity function with $\phi_i$ being equal to $\phi(L)\, dL$ for that bin." " The functions Os.fe, and YCL,,|L;) represent simple binning functions which are unity if galaxy a falls in the corresponding redshift and uminosity bin and zero otherwise.", The functions $D(z_\alpha \vert z_p)$ and $D(L_\alpha \vert L_i)$ represent simple binning functions which are unity if galaxy $\alpha$ falls in the corresponding redshift and luminosity bin and zero otherwise. " Similarly ο.) is a step-unction which is unity if the minimum luminosity £7°"" required or a galaxy to make it into the magnitude limited sample at the redshift of bin p is fainter than the luminosity £; of that bin.", Similarly $S(\Lm_p\vert L_i)$ is a step-function which is unity if the minimum luminosity $\Lm_p$ required for a galaxy to make it into the magnitude limited sample at the redshift of bin $p$ is fainter than the luminosity $L_i$ of that bin. " Using his notation we can write For the maximum likelihood solution. the derivatives of In£ with respect to bin values A,, and o; will be zero."," Using this notation we can write For the maximum likelihood solution, the derivatives of $\ln \Lik$ with respect to bin values $\Delta_q$ and $\phi_j$ will be zero." Hence we have ding The meaning of the various terms in these equations can be made more explicit by adopting the following notation., Hence we have and The meaning of the various terms in these equations can be made more explicit by adopting the following notation. " Let the estimate of the number of galaxies in the survey based on the values of ó; and 4X, be Let the number of galaxies falling in each luminosity and redshift bin be NV; and A’, respectively and let be the predicted mean galaxy number density in redshift bin q based on the estimated LF and assuming the mean density . i.e. A,= 1. Finally let"," Let the estimate of the number of galaxies in the survey based on the values of $\phi_i$ and $\Delta_p$ be Let the number of galaxies falling in each luminosity and redshift bin be $N_i$ and $N_p$ respectively and let be the predicted mean galaxy number density in redshift bin $q$ based on the estimated LF and assuming the mean density , i.e. $\Delta_q=1$ Finally let" actually fit their data to a model.,actually fit their data to a model. Iu this paper we offer alternate interpretations of these spectral features., In this paper we offer alternate interpretations of these spectral features. All our interpretations involve atomic transitions. mainiv in We-like ious of micd-Z clemenuts at B~lo? G. consistent with the B-field derived frou tle NS spin properties.," All our interpretations involve atomic transitions, mainly in He-like ions of mid-Z elements at $B\sim10^{12}$ G, consistent with the B-field derived from the NS spin properties." The most likely of these interpretations is that the NS atmosphere contains Oxvecn or Neon: ost noteworthy is thateH our models. whether cousideriug just the two strong features or including the third weal feature. demand mid-Z elemieuts for an acceptable solution.," The most likely of these interpretations is that the NS atmosphere contains Oxygen or Neon; most noteworthy is that our models, whether considering just the two strong features or including the third weak feature, demand mid-Z elements for an acceptable solution." Our model. combined with the aud data. casily rule out the Tron aud high-Z solutions of Moreghettietal.(2002).," Our model, combined with the and data, easily rule out the Iron and high-Z solutions of \citet{mereghetti02}." . Some conuuents are in order on our approach., Some comments are in order on our approach. The atomic spectroscopy data used in this analysis is based on a novel approach for obtaining fast aud accurate solutions to the Schroddinger equation for D-fields in the Landau regine (appropriate for all cases considered here)., The atomic spectroscopy data used in this analysis is based on a novel approach for obtaining fast and accurate solutions to the Schröddinger equation for B-fields in the Landau regime (appropriate for all cases considered here). " This approach. iuiulticoufigurational. perturbative. hybrid. Uartrec. Hartree-Fock theory, allows rapid computation of transition energies and oscillator strengths for arbitrary atom. don. excitation state and D-Beld (Mori&Tlai-ley (2002a).. hereafter MIIO2a)."," This approach, multiconfigurational, perturbative, hybrid, Hartree, Hartree-Fock theory, allows rapid computation of transition energies and oscillator strengths for arbitrary atom, ion, excitation state and B-field \citet{mori02}, hereafter MH02a)." This permits a complete search of all possible spectroscopic transitions consistent with the given line or cdge energies., This permits a complete search of all possible spectroscopic transitions consistent with the given line or edge energies. While it may appear that this approach produces an unmterestinelv large nuuber of potential solutions. we demonstrate in a companion paper (Mori&Ibulev (2002b).. hereafter MIIO2b) that this is not the case.," While it may appear that this approach produces an uninterestingly large number of potential solutions, we demonstrate in a companion paper \citet{mori02_2}, hereafter MH02b) that this is not the case." We show that the presence of two or more line or edge features provides a remarkable robustuess to a host of poorlyuuderstood atomic plysics effects and uniuubiguouslv restricts the atiuosphiere composition to mid-Z elemoeuts., We show that the presence of two or more line or edge features provides a remarkable robustness to a host of poorly-understood atomic physics effects and unambiguously restricts the atmosphere composition to mid-Z elements. We only briefly mention our data reduction here. as our approach closely follows that of SZPT.," We only briefly mention our data reduction here, as our approach closely follows that of SZPT." Iudeed. we cluphasize that none of our conclusions here would be modified if we simply used the spectral line parameters derived by SZPT.," Indeed, we emphasize that none of our conclusions here would be modified if we simply used the spectral line parameters derived by SZPT." Our analysis is described in more detail iu MIIO2b., Our analysis is described in more detail in MH02b. The results presented here are for phase-integrated spectra oulv., The results presented here are for phase-integrated spectra only. Subsequent work will consider phase-resolved data. which cau provide more formation ou the system eeonietry.," Subsequent work will consider phase-resolved data, which can provide more information on the system geometry." We ft the spectrum with two models: a blackbody with two absorption edees (edee model} aud a blackbody with two absorption lines (liue model}., We fit the spectrum with two models: a blackbody with two absorption edges (edge model) and a blackbody with two absorption lines (line model). As noted bv SZPT. these spectral features are required to get acceptable fits.," As noted by SZPT, these spectral features are required to get acceptable fits." " The fit parameters for our models are given in Table Ἐν,", The fit parameters for our models are given in Table \ref{tab_fit}. We show the raw spectrin in feure d overlaid with a blackbody to clearly indicate the presence of the absorption features., We show the raw spectrum in figure \ref{fig_bb} overlaid with a blackbody to clearly indicate the presence of the absorption features. Figures show the results of our best fit line aud edee models., Figures \ref{fig_lineedge} show the results of our best fit line and edge models. We briefly review the quantum numbers of bouud electrons in B-fields iu the Landau regime., We briefly review the quantum numbers of bound electrons in B-fields in the Landau regime. States are labeled by Ga.) where am is the magnetic quanti uunuber aud v is the longitudinal quantum uunber.," States are labeled by $(m,\nu)$ where $m$ is the magnetic quantum number and $\nu$ is the longitudinal quantum number." The v=(0 states have huger binding enerey than the ν>0 states., The $\nu=0$ states have larger binding energy than the $\nu>0$ states. Consistent with the terminology of MITO2a. we call the former tighth-bound states aud the latter states;," Consistent with the terminology of MH02a, we call the former tightly-bound states and the latter states." Conerally the eround state of au don is a tiehtlh-bounud state., Generally the ground state of an ion is a tightly-bound state. In the N-ray. baud transitions are mostly likely to be either plioto-absorption (tightl-bound state to continu) or absorption lines from tighth-bound to looselv-bouud state (tight-loose transition)., In the X-ray band transitions are mostly likely to be either photo-absorption (tightly-bound state to continuum) or absorption lines from tightly-bound to loosely-bound state (tight-loose transition). Tight-tight transitious appear in the optical baud., Tight-tight transitions appear in the optical band. Details of the transition selection rules are discussed clsewhere (ΠΟΡα.NITO2D).," Details of the transition selection rules are discussed elsewhere (MH02a,MH02b)." We first considered the two strongest features at ~0.7 keV and ~Ll keV and assume both features are due to atomic transitious in a single clement ar ionization state (Case A)., We first considered the two strongest features at $\sim0.7$ keV and $\sim1.4$ keV and assume both features are due to atomic transitions in a single element and ionization state (Case A). This effectively defines a solution for the dominant absorbing clement iu terms of Te-like ious., This effectively defines a solution for the dominant absorbing element in terms of He-like ions. Li-like ious and those iu lower ionization states are uot dominant absorbers under the expecte atmospheric conditions (MIIO2b)., Li-like ions and those in lower ionization states are not dominant absorbers under the expected atmospheric conditions (MH02b). . Te-like ious cauno be the dominant absorbers because this is grosslv inconuuensurate with the features relative widths am streugths even uuder conditions far removed from loca thermodynamic equilibrimm (MIIO25)., H-like ions cannot be the dominant absorbers because this is grossly incommensurate with the features' relative widths and strengths even under conditions far removed from local thermodynamic equilibrium (MH02b). ILlike ious can. however. be preseut since the relevant spectral features will be blended with the IHe-like features.," H-like ions can, however, be present since the relevant spectral features will be blended with the He-like features." In thle Ie-Iike ions. the electrons are making tight-loose transitions out of the (0.0)(1.0) evound state to the (0.111.11 excited states respectively. or to the continui.," In the He-like ions, the electrons are making tight-loose transitions out of the $(0,0)(1,0)$ ground state to the $(0,1)(1,1)$ excited states respectively, or to the continuum." Neither tighth-vound states at higher maguetie quantuni nuniber nor ron-adjaceut tighth-bound states are acceptable., Neither tightly-bound states at higher magnetic quantum number nor non-adjacent tightly-bound states are acceptable. In the ormer case the feature energy ratios cannot be produced and in the latter case unobserved features in the wand would be produced., In the former case the feature energy ratios cannot be produced and in the latter case unobserved features in the band would be produced. We searched for any combination of clement. redshitt and B-field which could give the observed positious of he spectral features.," We searched for any combination of element, redshift and B-field which could give the observed positions of the spectral features." Our D-field range was ~10H C o ~2«10H C. Tn the case of edee solutious we also omitted (sinall) pressure shifts (details in MITU2b)., Our B-field range was $\sim10^{11}$ G to $\sim2\times10^{14}$ G. In the case of edge solutions we also permitted (small) pressure shifts (details in MH02b). Line solutious are insensitive to pressure shifts., Line solutions are insensitive to pressure shifts. The propertics of the solutions including derived values of the B-field and redshift are shown in table 2.., The properties of the solutions including derived values of the B-field and redshift are shown in table \ref{tab_summary}. The first two solutions involve atomic line transitions in ΠοΗμκο Oxveen aud Neou and the third solution We-like Neon absorption edges., The first two solutions involve atomic line transitions in He-like Oxygen and Neon and the third solution He-like Neon absorption edges. A similar Oxvecn solution was rejected because its redshift was too low. violating causality and stability conditious or the NS interior (Lindblom198[:IHaeuseletal.1999).," A similar Oxygen solution was rejected because its redshift was too low, violating causality and stability conditions for the NS interior \citep{lindblom84, haensel99}." . For the Neou edge solution there is an electron cvelotron ine in the cucrey land but it was nade to overlap the higher euergv spectral feature wo oedutroducius a small pressure shift (~5090 eV)., For the Neon edge solution there is an electron cyclotron line in the energy band but it was made to overlap the higher energy spectral feature by introducing a small pressure shift $\sim50-90$ eV). Such pressure shifts slightly affect the euergy ratio of the wo edee features and serve to further coustrain otler elements aud conditions of the atinosphiere (MIIO25)., Such pressure shifts slightly affect the energy ratio of the two edge features and serve to further constrain other elements and conditions of the atmosphere (MH02b). The ine and edge widths are all consistent with expectations or Stark broadening aud nou-coustaut B-field broadening respectively (MITO2D])., The line and edge widths are all consistent with expectations for Stark broadening and non-constant B-field broadening respectively (MH02b). Our case D assumes that one spectral feature is an atomic transition aud the secoud is a cvelotrou liue., Our case B assumes that one spectral feature is an atomic transition and the second is a cyclotron line. " A l.l keV or 0.7 keV electron cvelotron line defines à B-field of L2«1011|:) Gor 6.6«οσα1:3 respectively,", A 1.4 keV or 0.7 keV electron cyclotron line defines a B-field of $1.2\times10^{11}(1+z)$ G or $0.6\times10^{11}(1+z)$ G respectively. Iu the former case solutions cau only be found for II-dike 1ος transitioning out of the (0.0) eround state to the," In the former case solutions can only be found for H-like ions transitioning out of the $(0,0)$ ground state to the" he unresolved turbulent pressure that is independent of he forcing.,the unresolved turbulent pressure that is independent of the forcing. Nevertheless. the global statistics of turbulent oressure varies with the forcing.," Nevertheless, the global statistics of turbulent pressure varies with the forcing." The physical conditions of he gas and the turbulence in the cosmological large-scale structure are obviously cilferent: here we are dealing mostly with subsonic or transonic [low., The physical conditions of the gas and the turbulence in the cosmological large-scale structure are obviously different: here we are dealing mostly with subsonic or transonic flow. As this study. shows. one needs the investigation of the role of turbulence forcing and turbulent support in this regime. and their appications to cosmological simulations. in order to better understand the eas civnamics in the IGM.," As this study shows, one needs the investigation of the role of turbulence forcing and turbulent support in this regime, and their applications to cosmological simulations, in order to better understand the gas dynamics in the IGM." The numerical simulations were carried out on the SCL Altix 4700HLRD-H. of the Leibniz Computing Centre in Garching (Germany)., The numerical simulations were carried out on the SGI Altix 4700 of the Leibniz Computing Centre in Garching (Germany). Phe code is developed. by the Laboratory for Computational Astrophysics at. the University of California in San Diego., The code is developed by the Laboratory for Computational Astrophysics at the University of California in San Diego. T1ο data analysis was performed using the toolkit. (?)., The data analysis was performed using the toolkit . . Thanks to Carlo Ciocoli for useful discussions. and to the anonymous referee for constructive comments. which improve the manuscript.," Thanks to Carlo Giocoli for useful discussions, and to the anonymous referee for constructive comments, which improved the manuscript." Al Al 3.2. , \ref{comparison-sgs} \ref{comparison-sgs} \ref{results} period calibrators examined (Table 1)).,period calibrators examined (Table \ref{table1}) ). " Additional observations for VY Pyx and V703 Sco were obtained via the AAVSO's Sonoita (SRO) and Bright Star Monitor (BSM) The SRO features an SBIG STL-1001E CCD (fov: 20’x20’) mounted upon a 35-cm telescope stationed near the town of Sonoita, Arizona."," Additional observations for VY Pyx and V703 Sco were obtained via the AAVSO's Sonoita (SRO) and Bright Star Monitor (BSM) The SRO features an SBIG STL-1001E CCD (fov: $\arcmin$ $\arcmin$ ) mounted upon a 35-cm telescope stationed near the town of Sonoita, Arizona." " The BSM features an SBIG ST8XME CCD (fov: 127'x84"") mounted upon a 6-cm wide-field telescope located at the Astrokolkhoz telescope facility near Cloudcroft, New Mexico."," The BSM features an SBIG ST8XME CCD (fov: $\arcmin$ $\arcmin$ ) mounted upon a 6-cm wide-field telescope located at the Astrokolkhoz telescope facility near Cloudcroft, New Mexico." The AAVSO observations are tied to photometric standards according to precepts outlined in2008)., The AAVSO observations are tied to photometric standards according to precepts outlined in. . The data for VZ Cnc were supplemented by observations taken at the Abbey Ridge Observatory2007)., The data for VZ Cnc were supplemented by observations taken at the Abbey Ridge Observatory. . photometry for Galactic classical Cepheid calibrators was obtained from the catalogue of(2000)., photometry for Galactic classical Cepheid calibrators was obtained from the catalogue of. . 'The phased light curves for several variables are presented in Fig. 1.., The phased light curves for several variables are presented in Fig. \ref{fig1}. " The relevant photometry (is) shall be available online via databases maintained by CDS, ASAS, TASS, and the AAVSO."," The relevant photometry (is) shall be available online via databases maintained by CDS, ASAS, TASS, and the AAVSO." " The pulsation periods employed to phase the data were adopted from the GCVS2009a), the AAVSO's VSX2010),, and the GEOS RR Lyr survey2007)."," The pulsation periods employed to phase the data were adopted from the GCVS, the AAVSO's VSX, and the GEOS RR Lyr survey." ". Several pulsators display pronounced amplitude variations and are discernably multiperiodic (e.g., AI Vel, V703 Sco, SX Phe, Figs."," Several pulsators display pronounced amplitude variations and are discernably multiperiodic (e.g., AI Vel, V703 Sco, SX Phe, Figs." " 1 and 2)), topics that shall be elaborated upon elsewhere."," \ref{fig1} and \ref{fig2}) ), topics that shall be elaborated upon elsewhere." 24 variables with parallaxes measured by Hipparcos and HST are employed to calibrate the Wesenheit diagram (Table 1))., 24 variables with parallaxes measured by Hipparcos and HST are employed to calibrate the Wesenheit diagram (Table \ref{table1}) ). " The sample consists of 8 SX Phoenicis and ó Scuti variables, 4 RR Lyrae variables, 2 type II Cepheids, and 10 classical Cepheids."," The sample consists of 8 SX Phoenicis and $\delta$ Scuti variables, 4 RR Lyrae variables, 2 type II Cepheids, and 10 classical Cepheids." " That sample is supplemented by 6 type II Cepheids detected by in their comprehensive survey of the galaxy M1062009b),, which features a precise geometric-based distance estimate1999)."," That sample is supplemented by 6 type II Cepheids detected by in their comprehensive survey of the galaxy M106, which features a precise geometric-based distance estimate." . It is perhaps ironic that stars 7.2 Mpc distant may be enlisted as calibrators because of an absence of viable parallaxes for nearby objects., It is perhaps ironic that stars $7.2$ Mpc distant may be enlisted as calibrators because of an absence of viable parallaxes for nearby objects. " Type II Cepheids within the inner region of M106 were not employed in the calibration because of the likelihood of photometric contamination via crowding and blending4,, see2010b)."," Type II Cepheids within the inner region of M106 were not employed in the calibration because of the likelihood of photometric contamination via crowding and blending, see." The stars employed were observed in the outer regions of M106 where the stellar, The stars employed were observed in the outer regions of M106 where the stellar function of quasars. they will not create a new MDII.,"function of quasars, they will not create a new MBH." The occupation fraction. of AIBIIs (see figure 3) is therefore largelyindependent of the accretion mechanism. and a true signature of the formation process., The occupation fraction of MBHs (see figure 3) is therefore largely of the accretion mechanism and a true signature of the formation process. To date. most theoretical models for the evolution of AIBUs in galaxies do not includehow MDIIS form.," To date, most theoretical models for the evolution of MBHs in galaxies do not include MBHs form." This work is a first analysis of the observational signatures of massive black hole formation mechanisms in the low redshift universe. complementary to the investigation by Sesana ct al. (," This work is a first analysis of the observational signatures of massive black hole formation mechanisms in the low redshift universe, complementary to the investigation by Sesana et al. (" 2007). where the focus was on detection. of seeds. at he very carly times where they form. via gravitational waves emitted. curing MDII mergers.,"2007), where the focus was on detection of seeds at the very early times where they form, via gravitational waves emitted during MBH mergers." We focus here on xossible dvnamical signatures that forming massive black role seeds carries over to the local Universe., We focus here on possible dynamical signatures that forming massive black hole seeds carries over to the local Universe. We believe hat the signatures of seed. formation mechanisms will be aw more clear if considered. jointly with the evolution of he spheroids that they host., We believe that the signatures of seed formation mechanisms will be far more clear if considered jointly with the evolution of the spheroids that they host. The mass. ancl especially he frequency. of the forming MID seeds is a necessary input when investigating how the feedback. [rom accretion onto MDIIs influences the host. galaxy. and is generally introduced in numerical models using extremely simplified.hoc prescriptions (e.g... 2?2?7?7??)).," The mass, and especially the frequency, of the forming MBH seeds is a necessary input when investigating how the feedback from accretion onto MBHs influences the host galaxy, and is generally introduced in numerical models using extremely simplified, prescriptions (e.g., \citealt{springel05,dimatteo05,hopkins06,croton05,cattaneo06,bower06}) )." Adopting more detailed models for black hole seed formation. as outlined here. can in principle strongly allect. such results.," Adopting more detailed models for black hole seed formation, as outlined here, can in principle strongly affect such results." For instance. ? find that AGN activity is typically confined to galaxies with Al>IMAL.," For instance, \citet{kauffmann04} find that AGN activity is typically confined to galaxies with $M>10^{10}\msun$." ££ we. consider the occupation fraction of AIBUs in such galaxies. we find that it dillers by a large [actor between models A and €. being of order in the low cllicieney model (at 2—1 4) and or higher in model C. Consequenthy. the possibility of ACN feedback and its elfect on the host would be selective in the former case. or widespread in the latter case.," If we consider the occupation fraction of MBHs in such galaxies, we find that it differs by a large factor between models A and C, being of order in the low efficiency model (at $z\sim 1-4$ ) and or higher in model C. Consequently, the possibility of AGN feedback and its effect on the host would be selective in the former case, or widespread in the latter case." Adopting sensible assumptions for the masses. ancl frequency of ALBIL seeds in. models of ealaxy formation is necessary if we want to understand the symbiotic growth of AIBITs and their hosts.," Adopting sensible assumptions for the masses, and frequency of MBH seeds in models of galaxy formation is necessary if we want to understand the symbiotic growth of MBHs and their hosts." If one assumes that the outflow is momentumdriven at all radii (ie. efficient shock cooling everywhere). the outflow would exert a thrust given. precisely by the weight [σα of the overlying gas of mass Ma.,"If one assumes that the outflow is momentum–driven at all radii (i.e. efficient shock cooling everywhere), the outflow would exert a thrust given precisely by the weight $4f_g\sigma^4/G$ of the overlying gas of mass $M_{\rm gas}$." Then the total work done by this thrust on the gas. assumed to extend to some radius Rois because the eas is in equilibrium with the isothermal dark matter halo.," Then the total work done by this thrust on the gas, assumed to extend to some radius $R$, is because the gas is in equilibrium with the isothermal dark matter halo." Therefore a purely momentumdriven outflow would [ail by a factor 2 to remove the overlying eas. which is essentially the result claimed by Silk&Nusser(2010)..," Therefore a purely momentum–driven outflow would fail by a factor 2 to remove the overlying gas, which is essentially the result claimed by \citet{2010ApJ...725..556S}." Llowever. cooling is inellective once the shock radius is ] kpe for a typical galaxy and so the outflow: becomes energy.driven.," However, cooling is ineffective once the shock radius is $\ga 1$ kpc for a typical galaxy and so the outflow becomes energy–driven." " This is because the shock is Compton cooled while it is close to the SMDII and the radius at which the Compton cooling time begins to exceed the shock Low time varies as 0.75034, kpc. where where we've assumed a wind velocity of 0.10."," This is because the shock is Compton cooled while it is close to the SMBH and the radius at which the Compton cooling time begins to exceed the shock flow time varies as $0.75 \sigma_{200}^3$ kpc, where where we've assumed a wind velocity of $0.1c$." H£ the shock is to cool radiatively. it must do so bv means of thermal bremsstrahlung because of the magnitude of the shock temperature (2=OP(pfeNoLOM for e= 0.10).," If the shock is to cool radiatively, it must do so by means of thermal bremsstrahlung because of the magnitude of the shock temperature $T \simeq 10^{12}(v/c)^2 K \sim 10^{10}\rm K$ for $v=0.1 c$ )." However. the free-free cooling time is long in this regime 5«107p.3 vears where n is the electron. number clensity— and it exceeds the shock [low time at all interesting radii.," However, the free-free cooling time is long in this regime – $\sim 5 \times 10^8 n^{-1}$ years where $n$ is the electron number density – and it exceeds the shock flow time at all interesting radii." For this reason. once the shell becomes energv-driven. it remains energy driven.," For this reason, once the shell becomes energy-driven, it remains energy driven." αἱ coronal heights where gradients are smaller and scale heights larger.,at coronal heights where gradients are smaller and scale heights larger. At this resolution ihe model has been run for roughly 1 hour solar time., At this resolution the model has been run for roughly 1 hour solar time. The initial model is seeded with magnetic field. which rapidly receives sullicient stress from photospheric motions to maintain coronal temperatures (777500000 IX) in the upper part of the computational domain. in the same manner as [ist accomplished by GudiksenNordlund(2004).," The initial model is seeded with magnetic field, which rapidly receives sufficient stress from photospheric motions to maintain coronal temperatures $T>500\,000$ K) in the upper part of the computational domain, in the same manner as first accomplished by \citet{Gudiksen+Nordlund2004}." . The initial fiekl was obtained by semi-randomlyw spreading 20—30 positive and negative patches of vertical field at the bottom boundary some 1.5 Mm below the photosphere. then calculating ancl inserting the potential field arising from (his distribution in (he remainder of the domain.," The initial field was obtained by semi-randomly spreading $20-30$ positive and negative patches of vertical field at the bottom boundary some $1.5$ Mm below the photosphere, then calculating and inserting the potential field arising from this distribution in the remainder of the domain." Stresses sufficient to maintain a minimal corona are built up by photospheric motions after roughly 20 minutes solar time., Stresses sufficient to maintain a minimal corona are built up by photospheric motions after roughly $20$ minutes solar time. The model has an average unsigned field in the photosphere of 160 G and is distributed in the photosphere in two bands ol vertical field centered around roughly 2=7 Mm andr =13 Mm., The model has an average unsigned field in the photosphere of $160$ G and is distributed in the photosphere in two bands of vertical field centered around roughly $x=7$ Mm and $x=13$ Mm. In the corona this results in loop-shaped structures that stretch between these bands ancl are mainly. oriented in the r-direction. as can be seen by following the red field lines shown in Fig. 1l..," In the corona this results in loop-shaped structures that stretch between these bands and are mainly oriented in the $x$ -direction, as can be seen by following the red field lines shown in Fig. \ref{fig:init}." Note that the lime (/=1850 8) shown in the figure was chosen to coincide with the ejection of the spicule of tvpe that is the subject of this paper., Note that the time $t=1850$ s) shown in the figure was chosen to coincide with the ejection of the spicule of type that is the subject of this paper. The jet is clearly visible in (lie isosurface that outlines (he position of the transition region near c—7 Man., The jet is clearly visible in the isosurface that outlines the position of the transition region near $x=7$ Mm. To start the events leading to the jets. we introduce a non-twisted magnetic [αν tube into the computational domain through its lower boundary. (hat lies some 1.5 Mani below the photosphere. as described in detail by Martinez-Sykoraοἱal. (2008).. section 3.2.," To start the events leading to the jets, we introduce a non-twisted magnetic flux tube into the computational domain through its lower boundary, that lies some $1.5$ Mm below the photosphere, as described in detail by \citet{paper1}, , section 3.2." Horizontal magnetic [lux of strength. 10* G is injected in a band of 1.5 Mm of diameter parallel (ο the y-axis aud centered al rv=8 Mm at the bottom boundary., Horizontal magnetic flux of strength $10^3$ G is injected in a band of $1.5$ Mm of diameter parallel to the $y$ -axis and centered at $x=8$ Mm at the bottom boundary. Hence. the injected magnetic field is nearly perpendicular to the orientation of tlie pre-existing ambient nagnetic field outlined by the coronal loops that are seen in Fig. 1..," Hence, the injected magnetic field is nearly perpendicular to the orientation of the pre-existing ambient magnetic field outlined by the coronal loops that are seen in Fig. \ref{fig:init}." The details of the input parameters of the simulation can be found in Martinez-Svkoraetal.(2009b).., The details of the input parameters of the simulation can be found in \citet{Martinez-Sykora:2009rw}. The simulation as. (herelore. on (the one hand. a pre-existing field which interacts with granular convection similar to Abbett(2007):Isobeetal.(2008).. and on the other hand. it has new emerging nagnetic [lux which is injected through the bottom boundary (Archontisetal.2004:Cheungelal.2007:Alartinez-Svkoraet2008) and interacts with the granular convection and the pre-existing magnetic field.," The simulation has, therefore, on the one hand, a pre-existing field which interacts with granular convection similar to \citet{abbett2007,Isobe:2008lr}, and on the other hand, it has new emerging magnetic flux which is injected through the bottom boundary \citep{archontis2004,cheung2007,paper1} and interacts with the granular convection and the pre-existing magnetic field." In the various simulations we have run. and in particular in (he simulation discussed here. a large numberof spicule-like structures are found.," In the various simulations we have run, and in particular in the simulation discussed here, a large numberof spicule-like structures are found." Most of these resemble spicules of, Most of these resemble spicules of ike IU 182030. in which there is leveliue-off of the QPO frequency aud thus evidence for the ISCO.,"like 4U 1820–30, in which there is leveling-off of the QPO frequency and thus evidence for the ISCO." The match of this asvinptotic frequency with the frequency xedieted from the eravitational mass and general relativity will provide us with uuprecedented quantitative tests of eeneral relativityin strong eravity., The match of this asymptotic frequency with the frequency predicted from the gravitational mass and general relativity will provide us with unprecedented quantitative tests of general relativity in strong gravity. Iu conclusion. herefore. the coutiuued qualitative aud quantitative agreement of the beat-frequeney nodel with observations of kilolhertz QPOs has not ouly vielded inportaut new constraints on the equation of state of the deuse matter in the core of neutron stars and. possibly. the first direct evidence for uustable orbits around neutron stars. a kev xediction of ecueral relativity.," In conclusion, therefore, the continued qualitative and quantitative agreement of the beat-frequency model with observations of kilohertz QPOs has not only yielded important new constraints on the equation of state of the dense matter in the core of neutron stars and, possibly, the first direct evidence for unstable orbits around neutron stars, a key prediction of general relativity." It also indicates strouely that future observations of hese sources. especially with bigh-arca tiniug missions. will allow us to coutiuue olnake qualitative leaps in our observational understanding of strong eravity aud dense matter.," It also indicates strongly that future observations of these sources, especially with high-area timing missions, will allow us to continue to make qualitative leaps in our observational understanding of strong gravity and dense matter." bubble size distribution and use this for calculating the 21-em yower spectrum.,bubble size distribution and use this for calculating the 21-cm power spectrum. Such models are very useful in predicting the signal quickly for a wide range of scales and investigating the urge parameter space., Such models are very useful in predicting the signal quickly for a wide range of scales and investigating the large parameter space. However. they cannot incorporate details of reionization and become less accurate when the bubbles start overlapping.," However, they cannot incorporate details of reionization and become less accurate when the bubbles start overlapping." Numerical simulations are probably the best way to orediet the expected 21-em signal., Numerical simulations are probably the best way to predict the expected 21-cm signal. Although challenging. there has been considerable progresses in simulating the large scale 21-cem signal during the entire EoR (Ilievetal.2006:Mellema200623:McQuinnetal.2007:Shin2008:Baek 2009).," Although challenging, there has been considerable progresses in simulating the large scale 21-cm signal during the entire EoR \citep{iliev06,mellema06,mcquinn07,shin08,baek09}." Tore approximate but much faster semi-numerical simulations of he structure and evolution of reionization and the 21-em signal ave also been developed (Zahnetal.2007:Mesinger&FurlanettoChoudhuryetal. 2009).," More approximate but much faster semi-numerical simulations of the structure and evolution of reionization and the 21-cm signal have also been developed \citep{zahn07,mesinger07,santos08,geil08,thomas09,choudhury09}." . These methods are capable of generating volumes with sizes as large as 1Gpc? (Alvarezetal.2009:Santosetal. 2010).," These methods are capable of generating volumes with sizes as large as $\sim 1 \rm {Gpc}^3$ \citep{alvarez09,santos10}." . Many aspects such as source properties. feed back effects. distribution and properties of sinks have also been investigated in detail (seeTrac&Gnedin2009.reionization simulations)..," Many aspects such as source properties, feed back effects, distribution and properties of sinks have also been investigated in detail \citep[see][ for a review on reionization simulations]{trac09}." One of the major goals of all first generation EoR telescopes is to measure the spherically averaged 3D 21-em power spectrum., One of the major goals of all first generation EoR telescopes is to measure the spherically averaged 3D 21-cm power spectrum. Measurements of the 21-em power spectrum will provide a wealth of information about the timing and duration of reionization. large scale distribution of H I and its evolution. source properties and clustering (Alietal.2005:SethiDatta2007:Lidzetal.2008:Barkana 2009).," Measurements of the 21-cm power spectrum will provide a wealth of information about the timing and duration of reionization, large scale distribution of H I and its evolution, source properties and clustering \citep{ali05,sethi05,datta07,lidz08,barkana09}." . To obtain the spherically averaged 3D power spectrum one needs to average over the 3D volume oroduced by the observations., To obtain the spherically averaged 3D power spectrum one needs to average over the 3D volume produced by the observations. Of this 3D volume one axis (the LOS axis) is along the frequency direction., Of this 3D volume one axis (the LOS axis) is along the frequency direction. Since light from the ower frequency side of the 3D volume takes a longer time to reach us than light from the high frequency side. the observer will see reionization in an earlier phase at the lower frequency side than at he higher frequency side.," Since light from the lower frequency side of the 3D volume takes a longer time to reach us than light from the high frequency side, the observer will see reionization in an earlier phase at the lower frequency side than at the higher frequency side." The statistics of 21-em fluctuations could herefore be changing over the observed volume., The statistics of 21-cm fluctuations could therefore be changing over the observed volume. As we will see in section 2 and 3. in some reionization scenarios the change could be substantial especially near the end of reionization.," As we will see in section 2 and 3, in some reionization scenarios the change could be substantial especially near the end of reionization." Almost all orevious studies calculate the 3D 21-em power spectrum without aking this effect into account., Almost all previous studies calculate the 3D 21-cm power spectrum without taking this effect into account. " In this paper we investigate the effect of LOS evolution or the so called ""light cone’ effect on the measured 21-em power spectrum. using numerical simulations to quantify it."," In this paper we investigate the effect of LOS evolution or the so called `light cone' effect on the measured 21-cm power spectrum, using numerical simulations to quantify it." Understanding the light cone effect is important because it will be present in the data and needs to be taken into account when interpreting the observed 21-cm power spectrum., Understanding the light cone effect is important because it will be present in the data and needs to be taken into account when interpreting the observed 21-cm power spectrum. Our aim is to understand under which conditions and at what scales this effect needs to be considered., Our aim is to understand under which conditions and at what scales this effect needs to be considered. The light cone effect is well known from studies of galaxy clustering (seee.g.Matsubaraetal.1997)., The light cone effect is well known from studies of galaxy clustering \citep[see e.g.][]{matsubara97}. . In the context of 21-em studies of reionization it was first considered by Barkana&Loeb (2006)., In the context of 21-cm studies of reionization it was first considered by \citet{barkana06}. . These authors studied analytically the anisotropic structure of the two point correlation function caused by the effect., These authors studied analytically the anisotropic structure of the two point correlation function caused by the effect. This appears to be only work that considered the effect of a changing source population., This appears to be only work that considered the effect of a changing source population. However. more work has been done on the light cone effect for a single bright source. such as a QSO.," However, more work has been done on the light cone effect for a single bright source, such as a QSO." For this case the effect will make the H II region appear to be teardrop- (Wyitheetal.2005:YuMajumdar2010)..," For this case the effect will make the H II region appear to be teardrop-shaped \citep{wyithe05, yu05, majumdar10}." The effects on the power spectrum and correlation function for this cause were investigated by Sethi&Haiman(2008)., The effects on the power spectrum and correlation function for this case were investigated by \citet{sethi08}. In addition. for very luminous sources the effect of relativistically expanding H II regions (Shapiroetal.2006) would have to be added to the one purelv due to evolution of the signal along the LOS.," In addition, for very luminous sources the effect of relativistically expanding H II regions \citep{shapiro06} would have to be added to the one purely due to evolution of the signal along the LOS." Bright QSOs are quite rare. so the more common form of the light cone effect will be due to the evolving source population and the growing H II regions around groups of sources.," Bright QSOs are quite rare, so the more common form of the light cone effect will be due to the evolving source population and the growing H II regions around groups of sources." Our aim is to study this version of the effect on the spherically averaged 3D and the ID LOS power spectra using realistio numerical simulations of reionization., Our aim is to study this version of the effect on the spherically averaged 3D and the 1D LOS power spectra using realistic numerical simulations of reionization. The paper is organized as follows., The paper is organized as follows. Section 2 briefly describes our simulations and the procedure used to generate light cone cubes., Section 2 briefly describes our simulations and the procedure used to generate light cone cubes. We present our results in Section 3., We present our results in Section 3. Section 4 describes two simple toy models which explain qualitatively the main features we see in the simulation results., Section 4 describes two simple toy models which explain qualitatively the main features we see in the simulation results. Section 5 investigates how the inclusion of peculiar velocities affect our results., Section 5 investigates how the inclusion of peculiar velocities affect our results. We summarize our results and conclusions in Section 6., We summarize our results and conclusions in Section 6. " The cosmological parameters we use throughout the paper are Q,,,=0.27.ο0.0),=0.044.0.7.n0.96 and ox=0.5. consistent with theWAYAP seven-year results (Komatsuetal.2011)."," The cosmological parameters we use throughout the paper are $\Omega_m=0.27, \Omega_k=0, \Omega_b=0.044, h=0.7, n=0.96$ and $\sigma_8=0.8$, consistent with the seven-year results \citep{komatsu11}." The 2l-cm radiation is emitted when neutral hydrogen atoms go through spin-flip transitions., The 21-cm radiation is emitted when neutral hydrogen atoms go through spin-flip transitions. The radiation can be decoupled from the cosmic microwave background (CMB) photons either through collisions with hydrogen atoms and free electrons (Purcell&Field1956:1959:Zygelman2005) or through Lya photon pumping (Wouthuysen1952:Field1959:Chen&Miralda-Escudé2004:Hirata2006:Chuzhoy&Shapiro 2006).," The radiation can be decoupled from the cosmic microwave background (CMB) photons either through collisions with hydrogen atoms and free electrons \citep{purcell56, field59, zygelman05} or through $\alpha$ photon pumping \citep{wouthuysen52, field59, chen04, hirata06, chuzhoy06}." . This makes 21-em radiation detectable either in emission or absorption against the CMB., This makes 21-cm radiation detectable either in emission or absorption against the CMB. " The differential brightness temperature with respect to the CMB is commonly written using the spin temperature 7. as OL), στ21.14 where μι and 9g are the mass averaged neutral fraction and the density fluctuations of hydrogen.", The differential brightness temperature with respect to the CMB is commonly written using the spin temperature $T_s$ as T_b 27.4 ( where ${x}_{\rm H I}$ and $\delta_\mathrm{H}$ are the mass averaged neutral fraction and the density fluctuations of hydrogen. " Note that the 21-em signal remains undetectable when the spin temperature 7, is coupled to the CMB temperature Zc315.", Note that the 21-cm signal remains undetectable when the spin temperature $T_s$ is coupled to the CMB temperature $T_{\rm{CMB}}$. During the EoR. 7% is expected to be coupled to the gas kinetic temperature through Lya photon coupling.," During the EoR, $T_s$ is expected to be coupled to the gas kinetic temperature through $\alpha$ photon coupling." In addition the gas kinetic temperature is expected to be much higher than the CMB temperature due to heating by shocks. X-rays and Ένα photons.," In addition the gas kinetic temperature is expected to be much higher than the CMB temperature due to heating by shocks, X-rays and $\alpha$ photons." This would make the redshifted 21-cm signal visible in emission., This would make the redshifted 21-cm signal visible in emission. We assume here that 75zTi.Tosipg Which makes the 21-em signal independent of the actual value of 74., We assume here that $T_s \approx T_{\rm{gas}}\gg T_{\rm{CMB}}$ which makes the 21-cm signal independent of the actual value of $T_s$. This is a reasonable assumption during the later stages of the EoR. During the initial stages of reionization. when there are few sources of radiation. this assumption might not hold (Baeketal.2010:Thomas&Zaroubi201 L).," This is a reasonable assumption during the later stages of the EoR. During the initial stages of reionization, when there are few sources of radiation, this assumption might not hold \citep{baek10,thomas10}." . The next subsection describes how we simulate the fluctuations in the H I density., The next subsection describes how we simulate the fluctuations in the H I density. Details about our simulation methodology (N-body simulation and the subsequent radiative transfer) have been presented in previous papers (Ilievetal.2006:Mellema2006a:Iliev2007. 2011.," Details about our simulation methodology (N-body simulation and the subsequent radiative transfer) have been presented in previous papers \citep{iliev06,mellema06,iliev07,iliev11}." Thevetal.011). described the simulations we use here in more detail., \cite{iliev11} described the simulations we use here in more detail. Here we only present a brief overview of the major features of these simulations., Here we only present a brief overview of the major features of these simulations. We start by simulating the evolution of the dark matter distribution using the CubePM N-body code in a comoving volume of (163cMpc) using 30727 particles and G144% cells.," We start by simulating the evolution of the dark matter distribution using the $^3$ M N-body code in a comoving volume of $(163 \, \rm{cMpc})^3$ using $3072^3$ particles and $6144^3$ cells." "Numinosity by factors not accounted for in the light-curve correction process, e.g. the properties of the host galaxy.","luminosity by factors not accounted for in the light-curve correction process, e.g. the properties of the host galaxy." " The effect of host galaxy properties on iis precisely the purpose of our study, so including the intrinsic scatter has the effect of weakening the strength of the measured correlations."," The effect of host galaxy properties on is precisely the purpose of our study, so including the intrinsic scatter has the effect of weakening the strength of the measured correlations." " If we perform the fit including the intrinsic uncertainty, we find our best-fit and only but the significances slopesof the non-zero interceptsslopesvary drop by slightly,about 0.20."," If we perform the fit including the intrinsic uncertainty, we find our best-fit slopes and intercepts vary only slightly, but the significances of the non-zero slopes drop by about $0.2 \sigma$." " In Figure 5,, we plot HR versus the mass-weighted average age of the host galaxy."," In Figure \ref{figHRvAge}, we plot HR versus the mass-weighted average age of the host galaxy." Figure 6 shows HR versus the stellar mass of the host galaxy., Figure \ref{figHRvMass} shows HR versus the stellar mass of the host galaxy. The lines are the best-fit model as determined fromoverplotted LINMIX., The overplotted lines are the best-fit model as determined from LINMIX. " In all our LINMIX analyses we use 100,000 MCMC realizations."," In all our LINMIX analyses we use 100,000 MCMC realizations." For the HR. trend with age we find the equation of the best-fit line to be The MCMC realizations in LINMIX are used to generate a sampling of the posterior distribution on the slope., For the HR trend with age we find the equation of the best-fit line to be The MCMC realizations in LINMIX are used to generate a sampling of the posterior distribution on the slope. " Of the MCMC realizations, have a slope greater than zero."," Of the MCMC realizations, have a slope greater than zero." Fitting a Gaussian to the posterior slope distribution yields a mean of —0.015 and a standard deviation of 0.008., Fitting a Gaussian to the posterior slope distribution yields a mean of $-0.015$ and a standard deviation of 0.008. " Based on this Gaussian fit, the mean slope differs from a slope of zero by 1.90."," Based on this Gaussian fit, the mean slope differs from a slope of zero by $1.9 \sigma$." " Thus, for the HR-age correlation we quote the significance of a zero slope as 1.9σ."," Thus, for the HR-age correlation we quote the significance of a non-zero slope as $1.9 \sigma$ ." " For the HR trend with mass the best- line is Of the MCMC realizations, have a slope greater than zero."," For the HR trend with mass the best-fit line is Of the MCMC realizations, have a slope greater than zero." This corresponds to a 3.00 significance of a non-zero slope., This corresponds to a $3.0 \sigma$ significance of a non-zero slope. " Our results indicate that after light-curve correction, there appears to be a deficit of underluminous in older, more massive galaxies."," Our results indicate that after light-curve correction, there appears to be a deficit of underluminous in older, more massive galaxies." " To test whether this result is due to incompleteness, we investigated the subsample of 40 ffor which iis complete (z€ 0.15)."," To test whether this result is due to incompleteness, we investigated the subsample of 40 for which is complete $z \leq 0.15$ )." Up to z=0.15 the survey is estimated to be ~ efficientfor, Up to $z = 0.15$ the survey is estimated to be $\sim$ efficientfor We attempted to describe the multi-wavelength SED of B2013+370 with the one-zone leptonic emission model described in and (2009).,We attempted to describe the multi-wavelength SED of B2013+370 with the one-zone leptonic emission model described in and . ". The model-predicted(2002) SEDs are shown in Figure 6,, and the assumed model parameters are summarized in Table 6.."," The model-predicted SEDs are shown in Figure \ref{2015-sed}, and the assumed model parameters are summarized in Table \ref{tab:2013-model}." The redshift of the source was assumed to be 0.1 throughout the modeling process., The redshift of the source was assumed to be 0.1 throughout the modeling process. " A pure synchrotron self-Compton model gives a poor description of the SED and requires a very low magnetic field, resulting in a strongly particle dominated jet (1.Η/1ο~ 10-9, with Lg and L, being the magnetic and particle power)."," A pure synchrotron self-Compton model gives a poor description of the SED and requires a very low magnetic field, resulting in a strongly particle dominated jet $L_B/L_e \sim 10^{-5}$ , with $L_B$ and $L_e$ being the magnetic and particle power)." " This is not surprising: SSC models typically fail to reproduce the high-energy component of Compton dominated blazars (LBLs, and specially FSRQs) unless the magnetic field is reduced to unphysically low values."," This is not surprising: SSC models typically fail to reproduce the high-energy component of Compton dominated blazars (LBLs, and specially FSRQs) unless the magnetic field is reduced to unphysically low values." This is addressed in external Compton models by adding a population of low energy photons external to the jet., This is addressed in external Compton models by adding a population of low energy photons external to the jet. FSRQs are often described with leptonic models where SSC is dominating in the X-ray band and EC explains the gamma-ray output2001)., FSRQs are often described with leptonic models where SSC is dominating in the X-ray band and EC explains the gamma-ray output. " We explore this scenario by adding an external radiation field with temperature Ti;= 1000KK. The resulting set of parameters (SSC+EC}) is closer to the typical values encountered in blazar SED modeling, but still needs low sub-equipartition magnetic fields and fails to reproduce the observed X-ray spectral slope."," We explore this scenario by adding an external radiation field with temperature $T_{ext}=1000$ K. The resulting set of parameters $_1$ ) is closer to the typical values encountered in blazar SED modeling, but still needs low sub-equipartition magnetic fields and fails to reproduce the observed X-ray spectral slope." The best fit (SSC+EC2) is achieved with both X-rays and gamma- being dominated by EC emission., The best fit $_2$ ) is achieved with both X-rays and gamma-rays being dominated by EC emission. " Parameters in exact equipartition (Lpg/L.= 1) can be achieved in this case, requiring a rather low temperature of the external radiation field (Τεν= 100KK) that could originate from cold dust."," Parameters in exact equipartition $L_B/L_e = 1$ ) can be achieved in this case, requiring a rather low temperature of the external radiation field $T_{ext}=100$ K) that could originate from cold dust." We note that the relatively low frequencies of the photons produced in the first-order SSC 10!7 HHz) make the second-order SSC (peaking at (~~10?? HHz) become efficient., We note that the relatively low frequencies of the photons produced in the first-order SSC $\sim 10^{17}$ Hz) make the second-order SSC (peaking at $\sim 10^{23}$ Hz) become efficient. " The lack of an E= 50GGeV detection, where the gamma-ray absorption by extragalactic background light is strongly redshift dependent, makes the assumed z—0.1 a non-critical model parameter."," The lack of an $E\gtrsim 50$ GeV detection, where the gamma-ray absorption by extragalactic background light is strongly redshift dependent, makes the assumed $z=0.1$ a non-critical model parameter." Similar best-fit solutions close to equipartition were found assuming z up to 1.5., Similar best-fit solutions close to equipartition were found assuming $z$ up to 1.5. A similar set of model parameters (assuming z—0.2 this time) can also describe the average and 2010 August states shown in Figure 6.., A similar set of model parameters (assuming $z=0.2$ this time) can also describe the average and 2010 August states shown in Figure \ref{2015-sed}. " The SED for B2023+336, shown in Figure 7,, shows the same blazar-like features discussed for B2013+370: two-component structure, hard X-ray spectrum, and dominant gamma-ray power."," The SED for B2023+336, shown in Figure \ref{2025-sed}, shows the same blazar-like features discussed for B2013+370: two-component structure, hard X-ray spectrum, and dominant gamma-ray power." " However, only archival non-contemporaneous optical and X-ray data are available."," However, only archival non-contemporaneous optical and X-ray data are available." " Given that B2023+336 is known to be variable at all frequencies, we don not attempt to model this source because of the lack of a simultaneous SED."," Given that B2023+336 is known to be variable at all frequencies, we don not attempt to model this source because of the lack of a simultaneous SED." " Spatial association and the observed variability in the gamma-ray and radio bands allow us to establish a firm association between B2013+370 and the previously unidentified gamma-ray source 3EG J2016+3657 (1FGL confirming the thesis of J2015.7+3708),and(2001)."," Spatial association and the observed variability in the gamma-ray and radio bands allow us to establish a firm association between B2013+370 and the previously unidentified gamma-ray source 3EG J2016+3657 (1FGL J2015.7+3708), confirming the thesis of and." ". A compiled SED, (2000)adding newly analyzed OVRO, Swif-XRT and Fermi-LAT data shows a two component structure that further supports the blazar association."," A compiled SED, adding newly analyzed OVRO, -XRT and -LAT data shows a two component structure that further supports the blazar association." The SED was successfully modeled with a leptonic one-zone model with both X-ray and gamma-ray power dominated by external Comptonization of a low-temperature external radiation field., The SED was successfully modeled with a leptonic one-zone model with both X-ray and gamma-ray power dominated by external Comptonization of a low-temperature external radiation field. " T'he gamma-ray dominated SED, hard X-ray spectrum, and preference for EC models point towards B2013+370 being an LBL or an FSRQ."," The gamma-ray dominated SED, hard X-ray spectrum, and preference for EC models point towards B2013+370 being an LBL or an FSRQ." " We also find strong evidence of gamma-ray emission from the blazar B20234-336, that was likely contributing to the unidentified gamma-ray source 3EG J2027--3429 (1FGL J2027.6+3335), as hypothesized by and(2004)."," We also find strong evidence of gamma-ray emission from the blazar B2023+336, that was likely contributing to the unidentified gamma-ray source 3EG J2027+3429 (1FGL J2027.6+3335), as hypothesized by and." Our analysis of the available Fermi-LAT data resolves two independent gamma-ray sources of very different character., Our analysis of the available -LAT data resolves two independent gamma-ray sources of very different character. J2025.1+3342 is spatially associated with the blazar B20234-336 and shows a hint of variability., J2025.1+3342 is spatially associated with the blazar B2023+336 and shows a hint of variability. " The tentative observation of an extreme scattering event in the radio light curve of B20234-336 further supports the hypothesis of it being extragalactic in origin, the flux decrease being caused by a cloud of plasma in the galactic interstellar medium crossing the line of sight."," The tentative observation of an extreme scattering event in the radio light curve of B2023+336 further supports the hypothesis of it being extragalactic in origin, the flux decrease being caused by a cloud of plasma in the galactic interstellar medium crossing the line of sight." " The other resolved component of 3EG J20274-3429 (J2028.34-3333) is characterized as a steady gamma-ray emitter with an exponentially cutoff energy spectrum, qualities which are typical of LAT detected pulsars."," The other resolved component of 3EG J2027+3429 (J2028.3+3333) is characterized as a steady gamma-ray emitter with an exponentially cutoff energy spectrum, qualities which are typical of LAT detected pulsars." " 'This result has recently been confirmed by(2011),, who report the discovery of nine previously unknown gamma-ray pulsars using a blind search method."," This result has recently been confirmed by, who report the discovery of nine previously unknown gamma-ray pulsars using a blind search method." " This discovery supports the hypothesis of and that a pulsar could be responsible for the gamma-ray excess 3EG J2027+3429, or at leastpart of it."," This discovery supports the hypothesis of and that a pulsar could be responsible for the gamma-ray excess 3EG J2027+3429, or at leastpart of it." Optical spectroscopy of the studied objects is complicated due to their low optical luminosity and the extreme dust absorption in the optical, Optical spectroscopy of the studied objects is complicated due to their low optical luminosity and the extreme dust absorption in the optical as a general monitor of the condition of the solar wind flux.,as a general monitor of the condition of the solar wind flux. " However. the delay between ACE and the Earth is approximately one hour,"," However, the delay between ACE and the Earth is approximately one hour." In this section we describe the steps taken in the initial data reduction and then continue to detail the method used to test for the presence of SWCX contamination., In this section we describe the steps taken in the initial data reduction and then continue to detail the method used to test for the presence of SWCX contamination. The objective when designing the method was to find the key indicators for SWCX-emission. namely short term variability in line emission from the solar wind ion species.," The objective when designing the method was to find the key indicators for SWCX-emission, namely short term variability in line emission from the solar wind ion species." Short term variations in the diffuse background indicate a local source. and the presence of line emission at certain energies expected from the solar wind is a diagnostic of SWCX-emission.," Short term variations in the diffuse background indicate a local source, and the presence of line emission at certain energies expected from the solar wind is a diagnostic of SWCX-emission." We grade the indicators and develop a procedure to automatically flag observations that may have experienced SWCX-enhancement throughout their exposure., We grade the indicators and develop a procedure to automatically flag observations that may have experienced SWCX-enhancement throughout their exposure. In this paper we consider single XMM-Newton pointings. but the future paper will explore multiple pointings of the same target to investigate variations between pointings.," In this paper we consider single XMM-Newton pointings, but the future paper will explore multiple pointings of the same target to investigate variations between pointings." The data used in this analysis were taken from the XSA. which can be found at:acecivsalindex.," The data used in this analysis were taken from the XSA, which can be found at:." shtinl.. We used publicly available software in this. project. accessible through the web pages of the XMM-Newton Background Working Group For each observation an Original Data File (ODF) was downloaded from the XSA.," We used publicly available software in this project, accessible through the web pages of the XMM-Newton Background Working Group For each observation an Original Data File (ODF) was downloaded from the XSA." The ODF files were processed using the XMM-Newton Extended Source Analysis Software (ESAS) software package (??).. found on the BGWG pages as mentioned above.," The ODF files were processed using the XMM-Newton Extended Source Analysis Software (ESAS) software package \citep{kuntz2008, snowden2008}, found on the BGWG pages as mentioned above." Table 1 lists the observations used in this preliminary analysis., Table \ref{tabobsused} lists the observations used in this preliminary analysis. We included several observations used by ο and with the aim to use these observations as control subjects for our method.," We included several observations used by \citet{kuntz2008} and \citet{snowden2004} with the aim to use these observations as control subjects for our method." The remainder of the observations were taken from a range of times of year and times 1n the mission. representive as much as possible of a random selection of observations throughout the XMM-Newton mission.," The remainder of the observations were taken from a range of times of year and times in the mission, representive as much as possible of a random selection of observations throughout the XMM-Newton mission." To undertake our analysis we created lighteurves from event files for each XMM-Newton observation., To undertake our analysis we created lightcurves from event files for each XMM-Newton observation. To do this we filtered the data files for soft proton and particle background contamination using ESAS and other software before commencing with the creation of the lightcurves., To do this we filtered the data files for soft proton and particle background contamination using ESAS and other software before commencing with the creation of the lightcurves. The ESAS software is currently only available for the MOS detectors (?) and therefore the analysis detailed here only concerns the MOS instruments., The ESAS software is currently only available for the MOS detectors \citep{turner} and therefore the analysis detailed here only concerns the MOS instruments. However. improvements to include the PN (?) camera are underway and are expected in an imminent release of the ESAS software.," However, improvements to include the PN \citep{struder} camera are underway and are expected in an imminent release of the ESAS software." In our future paper we aim to incorporate PN data into our analysis., In our future paper we aim to incorporate PN data into our analysis. Cleaned and calibrated event files were created from the ODF when using the ESAS tool/mos-filter., Cleaned and calibrated event files were created from the ODF when using the ESAS tool. . The task runs several XMM-Newton Science Analysis Software (SAS) tasks. including for the basic processing of the event files.," The task runs several XMM-Newton Science Analysis Software (SAS) tasks, including for the basic processing of the event files." It then created two lighteurves; one in the field of view and one outside of the field of view from the corners of the detectors for a band between kkeV and kkeV. Soft proton contamination will fall in the field of view (with the exception of extremely large flares where some soft protot contamination may be scattered into the out of field of view regions). whereas the out of field of view data are only affected by the particle-induced background.," It then created two lightcurves; one in the field of view and one outside of the field of view from the corners of the detectors for a band between keV and keV. Soft proton contamination will fall in the field of view (with the exception of extremely large flares where some soft proton contamination may be scattered into the out of field of view regions), whereas the out of field of view data are only affected by the particle-induced background." A count-rate histogram ts then created for the in field of view lighteurve. which should have a roughly Gaussian profile if the observation ts unaffected by soft-proton contamination (see the example in Figure 2)).," A count-rate histogram is then created for the in field of view lightcurve, which should have a roughly Gaussian profile if the observation is unaffected by soft-proton contamination (see the example in Figure \ref{figexphist}) )." Any large bumps or deviations from the roughly Gaussiat shape should be treated with caution as these indicate high levels of contamination., Any large bumps or deviations from the roughly Gaussian shape should be treated with caution as these indicate high levels of contamination. A Gaussian is fitted to the peak of the distribution and using a threshold of +1.5c this fit is used to create good-time-interval (GTI) periods for the data., A Gaussian is fitted to the peak of the distribution and using a threshold of ${\pm}$ $\sigma$ this fit is used to create good-time-interval (GTI) periods for the data. The blue vertical lines of Figure 2. show the range used for the Gaussian fit and the red vertical lines indicate the limits taker for the GTI periods., The blue vertical lines of Figure \ref{figexphist} show the range used for the Gaussian fit and the red vertical lines indicate the limits taken for the GTI periods. Further SAS tasks are used to filter the files using the GTI periods to create a cleaned event file., Further SAS tasks are used to filter the files using the GTI periods to create a cleaned event file. At important point to note Is that there may still be residual soft- contamination after undergoing these procedures (?).., An important point to note is that there may still be residual soft-proton contamination after undergoing these procedures \citep{deluca2004}. For each event file we removed sources in the field of view by utilising the source list from the 2XMM catalogue processing (see documentationfuhb/nodeH.htinl)) to ereate a region file and then extracting the sources from the event file withevselect., For each event file we removed sources in the field of view by utilising the source list from the 2XMM catalogue processing (see ) to create a region file and then extracting the sources from the event file with. . We initially used a source extraction radius of 35 areseconds. extending this to remove bright or extended sources If needed.," We initially used a source extraction radius of 35 arcseconds, extending this to remove bright or extended sources if needed." Checks were made of images created for each cleaned event file to ensure that residual sources were not present., Checks were made of images created for each cleaned event file to ensure that residual sources were not present. If residual sources remained the extraction radius was increased iteratively until an effectively source-free event file was obtained. although observations with exceptionally bright sources were removed from the sample.," If residual sources remained the extraction radius was increased iteratively until an effectively source-free event file was obtained, although observations with exceptionally bright sources were removed from the sample." The remaining useful observations are shown in Table |.., The remaining useful observations are shown in Table \ref{tabobsused}. After this procedure any residual emission from point sources should be negligible., After this procedure any residual emission from point sources should be negligible. Software for the automated removal of sources will be developed for part I of these articles., Software for the automated removal of sources will be developed for part II of these articles. We considered observations that use full-frame mode and rejected all other modes for this preliminary study., We considered observations that use full-frame mode and rejected all other modes for this preliminary study. We then created spectra and the associated response matrices. and auxiliary files for those observations which we wished to study further., We then created spectra and the associated response matrices and auxiliary files for those observations which we wished to study further. We used the ESAS tasks and to create the spectra. background spectra and instrument response and auxiliary files.," We used the ESAS tasks and to create the spectra, background spectra and instrument response and auxiliary files." We used à circular spectrum extraction radius of 17000 detector units to incorporate the in field of view region (pixel size of 0.05, We used a circular spectrum extraction radius of 17000 detector units to incorporate the in field of view region (pixel size of 0.05 X-ray observations to compute the energy stored in X-ray cavities and estimate the jet power.,X-ray observations to compute the energy stored in X-ray cavities and estimate the jet power. " They then use radio data to investigate the scaling between jet power and radio luminosity, and find a relation that has the same slope as that of Willott et al. ("," They then use radio data to investigate the scaling between jet power and radio luminosity, and find a relation that has the same slope as that of Willott et al. (" "1999), but where an f=1 gives a relation that is two orders of magnitude below their normalisation.","1999), but where an $f=1$ gives a relation that is two orders of magnitude below their normalisation." An f~20 seems thus more in agreement with these studies., An $f\sim 20$ seems thus more in agreement with these studies. Similarly Martinnez-Sansigre Rawlings (2010) find that a minimum of f=20 is required to fit the local radio luminosity function of galaxies., Similarly Martínnez-Sansigre Rawlings (2010) find that a minimum of $f=20$ is required to fit the local radio luminosity function of galaxies. " On the other hand, some studies (e.g. Croston et al."," On the other hand, some studies (e.g. Croston et al." " 2003, 2004) suggest that the value of f should be high for FRIs and low for FRIIs, f 10-20, and low for FRIIs, f~ 1-2."," 2003, 2004) suggest that the value of $f$ should be high for FRIs and low for FRIIs, $f\sim$ 10-20, and low for FRIIs, $f\sim$ 1-2." " The regime at which not all radio galaxies are powerful accretors occurs at a lower radio luminosity 1035WHz! sr!), as can be seen in Figure 1 of Ogleetal. (2006).."," The regime at which not all radio galaxies are powerful accretors occurs at a lower radio luminosity $<5\times 10^{26}\,\rm W\,Hz^{-1}\,sr^{-1}$ ), as can be seen in Figure 1 of \citet{2006ApJ...647..161O}." " Given that vLy12,m is a proxy for bolometric luminosity and hence accretion rate, and Ly151mHz traces the jet power produced by the SMBH, the very large scatter observed in the right panel of Figure 4 indicates that galaxies with similar accretion rates can produce powerful or weaker jets."," Given that $\nu L_{\nu \rm 12\mu m}$ is a proxy for bolometric luminosity and hence accretion rate, and $L_{\nu \rm 151MHz}$ traces the jet power produced by the SMBH, the very large scatter observed in the right panel of Figure \ref{fig:l151_l12} indicates that galaxies with similar accretion rates can produce powerful or weaker jets." Therefore the scatter is probably due to a continuous range of efficiencies with which AGN produce jets., Therefore the scatter is probably due to a continuous range of efficiencies with which AGN produce jets. " The factors that rule this efficiency are still unclear, but black hole spin might be a dominant mechanism (e.g. see Sikoraetal.2007 and references within)."," The factors that rule this efficiency are still unclear, but black hole spin might be a dominant mechanism (e.g. see \citealt{2007ApJ...658..815S} and references within)." " Spin is indeed an appealing mechanism for it allows nominal efficiencies =1, since some of the jet power originates from rotation of the black hole, rather than from the accreted (e.g. Rees 1984))."," Spin is indeed an appealing mechanism for it allows nominal efficiencies $\gtrsim 1$, since some of the jet power originates from rotation of the black hole, rather than from the accreted (e.g. \citealt{1984ARA&A..22..471R}) )." Raviοἱal.(2010).,\citet{rav10}. . The difference with the previous observations is the rotational phase of each peak. not the difference of phase between them.," The difference with the previous observations is the rotational phase of each peak, not the difference of phase between them." The variability of the pulse shape. as well as the amplitude. could be due to some instability of the emission region. as proposed by Ravietal.(2010).," The variability of the pulse shape, as well as the amplitude, could be due to some instability of the emission region, as proposed by \citet{rav10}." . Many. parameters enter in (he growth rate w of the evclotron maser (Muteletal.2007). such as electron density. velocity distribution (/) and its anisotropy (Of/Ov_). plasma frequency. (7/5) aid others.," Many parameters enter in the growth rate $\omega$ of the cyclotron maser \citep{mut07} such as electron density, velocity distribution $f$ ) and its anisotropy $(\partial f/\partial v_\bot)$, plasma frequency $\nu_{\mathrm p}$ ) and others." Since the growth rate is a non linear [unction of them. and the intensity of an unsaturated maser is {xexp(w). even a small variation of one of the above parameters can result in a significant. variation of the emereine Πας.," Since the growth rate is a non linear function of them, and the intensity of an unsaturated maser is $I\propto \exp(\omega)$, even a small variation of one of the above parameters can result in a significant variation of the emerging flux." An abrupt period change of 2.18 seconds. occurring probably in 1935. has been elaimed bv Pyperetal.(1998). [rom the analysis of photometric data: a new spin down of about 1 second has been inferred by CIrigilioetal.2008) from the phase shift of the coherent radio enission between 1998 and 1999.," An abrupt period change of 2.18 seconds, occurring probably in 1985, has been claimed by \cite{pyp98} from the analysis of photometric data; a new spin down of about 1 second has been inferred by \citep{tri08} from the phase shift of the coherent radio emission between 1998 and 1999." Now. with a new set ofpoints alter 12 vears. and with the inclusion of the Ravietal.(2010) results. the spin down is confirmed and (he increment of the rotational period AP is determined with great accuracy by fitting the midpoints of the (wo peaks (circles and line in Fig. 3)):," Now, with a new set ofpoints after 12 years, and with the inclusion of the \citet{rav10} results, the spin down is confirmed and the increment of the rotational period $\Delta P$ is determined with great accuracy by fitting the midpoints of the two peaks (circles and line in Fig. \ref{delay}) ):" AP=1.122:0.03 s. If we plot the phase of the peaks as a [function of the epoch (Fig. 3)).," $\Delta P=1.12 \pm 0.03$ s. If we plot the phase of the peaks as a function of the epoch (Fig. \ref{delay}) )," we see that they appear wilh a regularly. increasing delay. indicating that the rotational period of has changed.," we see that they appear with a regularly increasing delay, indicating that the rotational period of has changed." Assuming that the change of period occured close to the observations of 1993. we determine new ephemeris ofVir: for JD>2450966. nominally June 1993.," Assuming that the change of period occurred close to the observations of 1998, we determine new ephemeris of: for $JD>245 0966$, nominally June 1998." " It is worthwhile to stress that this method of period determination οἶνος a relative error of 7x 10"".", It is worthwhile to stress that this method of period determination gives a relative error of $7\times 10^{-7}$ . Ou curent hypothesis is that the galaxies and black holes observed today. originated over 13 Gyr ago. growing lrom seeds of primordial density perturbations.,"Our current hypothesis is that the galaxies and black holes observed today originated over 13 Gyr ago, growing from seeds of primordial density perturbations." One can test this hypothesis by studsyiug the star formation rate (SFR) history. Irom the Epoch of Reionizalion (EoR) at redshifts 6<2«12. through the peak era al z£22—3 (Ilopkins Deacon 2006) down to the present epoch.," One can test this hypothesis by studying the star formation rate (SFR) history, from the Epoch of Reionization (EoR) at redshifts $6 < z < 12$, through the peak era at $z \approx 2-3$ (Hopkins Beacom 2006) down to the present epoch." " The feedback of ionizing radiation. kinetic energy. and heavy elements leaves imprints on early stars. supernovae. and galaxies. providing a “Lossil record"" that can be detected through abunclanees in Galactic halo stars and the intergalactic medium (IGM) and in the distributions of mass. metallicity. and luminosity of galaxies."," The feedback of ionizing radiation, kinetic energy, and heavy elements leaves imprints on early stars, supernovae, and galaxies, providing a “fossil record"" that can be detected through abundances in Galactic halo stars and the intergalactic medium (IGM) and in the distributions of mass, metallicity, and luminosity of galaxies." Determining when and how the universe was reionized bv (hese early sources have been important questions for decades (Gunn Peterson 1965: Sunvaev LOTT: Robertson 22010)., Determining when and how the universe was reionized by these early sources have been important questions for decades (Gunn Peterson 1965; Sunyaev 1977; Robertson 2010). It has been suggested that IGM reionization was complete by z226.5 (Fan 22001: Gnedin Fan 2006: Fan 22006: Πα Cowie 2006). based on strong aabsorption from neutral hydrogen along lines of sight (ο QSOs at z>6.," It has been suggested that IGM reionization was complete by $z \approx 6.5$ (Fan 2001; Gnedin Fan 2006; Fan 2006; Hu Cowie 2006), based on strong absorption from neutral hydrogen along lines of sight to QSOs at $z > 6$." Decker ((2007) and Songaila (2004) used transmission of the ((and Ly2)) forest out to z=5.8 and 2=6.3. respectively. to suggest a smoothly decreasing ionization rate toward higher redshifts.," Becker (2007) and Songaila (2004) used transmission of the (and ) forest out to $z = 5.8$ and $z = 6.3$, respectively, to suggest a smoothly decreasing ionization rate toward higher redshifts." Recent survevs of high-redshift galaxies and eemitters (Douwens 2011a: Ouchi 0: INashikawa 2—6-—58, Recent surveys of high-redshift galaxies and emitters (Bouwens 2011a; Ouchi 2010; Kashikawa 2011; Ono 2012; Schenker 2012) infer an increasing IGM neutral fraction from the declining populations between $z = 6-8$. Further evidence for an increasing neutral fraction comes [rom the decreasing sizes of ionized “near zones” associated with quasars between z=5.7 and 2=6.4 (Crilli 22010) and from the ddamping wing in the transmission profile toward (he newly discovered quasar al 2=7.085 (Mortlock 22011).," Further evidence for an increasing neutral fraction comes from the decreasing sizes of ionized “near zones"" associated with quasars between $z = 5.7$ and $z = 6.4$ (Carilli 2010) and from the damping wing in the transmission profile toward the newly discovered quasar at $z = 7.085$ (Mortlock 2011)." These studies all suggest Chat the IGM is becoming increasingly neutral between 2=6-7. marking the end of cosmic relonization when ionized reeions overlap and percolate.," These studies all suggest that the IGM is becoming increasingly neutral between $z = 6-7$, marking the end of cosmic reionization when ionized regions overlap and percolate." The Soft Ganuna-Rayv Repeaters (SGRs: see IIurlev.2000. [or a recent. observational review) are a unique class of Galactic neutron stars that exhibit bright flaring activity in the,The Soft Gamma-Ray Repeaters (SGRs; see \citealt{h99} for a recent observational review) are a unique class of Galactic neutron stars that exhibit bright flaring activity in the We can relate the clustering parameter b to the variance of the counts-in-cells distribution through which allows us to describe the clustering of galaxies with the GQED in a self-consistent manner with no free parameters.,We can relate the clustering parameter $b$ to the variance of the counts-in-cells distribution through which allows us to describe the clustering of galaxies with the GQED in a self-consistent manner with no free parameters. This also allows us to relate b to the volume integral of the two-point correlation function such that which indicates that b depends on £4 andvaries with cell volume V., This also allows us to relate $b$ to the volume integral of the two-point correlation function such that which indicates that $b$ depends on $\overline{\xi}_2$ andvaries with cell volume $V$. " Although the derivation of equation by [Ahmad](2002) was done assuming that all8(8) galaxies have the same mass, theoretical work by |Ahmadetal.|(2006) showed that the statistical mechanical framework can be extended to take into account population components of differing masses."," Although the derivation of equation by \citet{2002ApJ...571..576A} was done assuming that all galaxies have the same mass, theoretical work by \citet{2006IJMPD..15.1267A} showed that the statistical mechanical framework can be extended to take into account population components of differing masses." " In addition, N-body simulations by also showed that the GQED for the case where galaxies are of the same mass is often a good fit to N-body simulations where galaxies are allowed to take a range of masses."," In addition, $N$ -body simulations by \citet{1993ApJ...403..476I} also showed that the GQED for the case where galaxies are of the same mass is often a good fit to $N$ -body simulations where galaxies are allowed to take a range of masses." This suggests that the GQED given in equation is a reasonable approximation to the counts-in-cells distribution., This suggests that the GQED given in equation is a reasonable approximation to the counts-in-cells distribution. "(18) Together with the physical motivation behind its derivation, the GQED can be used to gain further insights into the physics behind the counts-in-cells distribution."," Together with the physical motivation behind its derivation, the GQED can be used to gain further insights into the physics behind the counts-in-cells distribution." 'The negative binomial distribution was proposed in the cosmological context by |Carruthers&Minh|(1983) and subsequently derived by |Elizalde&Gaztanaga|(1992) by describing the distribution as statistical random process where N galaxies are introduceda in m spatially disconnected boxes., The negative binomial distribution was proposed in the cosmological context by \citet{1983PhLB..131..116C} and subsequently derived by \citet{1992MNRAS.254..247E} by describing the distribution as a statistical random process where $N$ galaxies are introduced in $m$ spatially disconnected boxes. " In this model, the probability that a galaxy is introduced in a particular box is proportional to the number of galaxies already inside the box."," In this model, the probability that a galaxy is introduced in a particular box is proportional to the number of galaxies already inside the box." The resulting distribution is where is a clustering parameter that depends on cell volume and Dl is the standard gamma function., The resulting distribution is where is a clustering parameter that depends on cell volume and $\Gamma$ is the standard gamma function. " Similar to the GQED, the NBD can also describe the counts-in-cells distribution self-consistently with no free parameters, and the clustering parameter g is just &."," Similar to the GQED, the NBD can also describe the counts-in-cells distribution self-consistently with no free parameters, and the clustering parameter $g$ is just $\overline{\xi}_2$." An alternative derivation of the NBD in the thermodynamicframework of is given by −−, An alternative derivation of the NBD in the thermodynamicframework of \citet{1984ApJ...276...13S} is given by \citet{1995MNRAS.274..213S}. " In this case, the equivalent of b is given by Although this form fulfils 0€6<1, it was found to violate the second law of thermodynamics by which suggests that the NBD is not physically motivated."," In this case, the equivalent of $b$ is given by Although this form fulfils $0 \leq b \leq 1$, it was found to violate the second law of thermodynamics by which suggests that the NBD is not physically motivated." A closer look at the statistical random process from which the NBD was derived suggests that the NBD assumes galaxies form where there is already a cluster of galaxies., A closer look at the statistical random process from which the NBD was derived suggests that the NBD assumes galaxies form where there is already a cluster of galaxies. " This process does not take infall into account, and hence the depletion of regions outside a cluster that occur in the process of infall is not taken into account."," This process does not take infall into account, and hence the depletion of regions outside a cluster that occur in the process of infall is not taken into account." From the derivation of the NBD by (1992). we note that the NBD can describe the case where galaxies form from the merger of less massive objects.," From the derivation of the NBD by \citet{1992MNRAS.254..247E}, we note that the NBD can describe the case where galaxies form from the merger of less massive objects." " In this description, the less massive objects can be expected to follow the GQED, but not all of them can be observed."," In this description, the less massive objects can be expected to follow the GQED, but not all of them can be observed." " These objects may merge to form objects bright enough to be observed, and their locations are likely to be in denser regions that contain a higher density of fainter objects."," These objects may merge to form objects bright enough to be observed, and their locations are likely to be in denser regions that contain a higher density of fainter objects." " N-body simulations by show that while the VPF for galaxies follows the NBD, the VPF for dark matter particles follows the GQED."," $N$ -body simulations by \citet{2005ApJ...635..990C} show that while the VPF for galaxies follows the NBD, the VPF for dark matter particles follows the GQED." " While this qualitative explanation may seem plausible, a detailed quantitative analysis will depend on the physics of the more complicated halo occupation distribution."," While this qualitative explanation may seem plausible, a detailed quantitative analysis will depend on the physics of the more complicated halo occupation distribution." " The New York University value-added galaxy catalog (NYU-VAGC, [2005)) is a composite catalog with the Sloan Digital Sky Survey (SDSS) data as its primary component."," The New York University value-added galaxy catalog (NYU-VAGC, \citealt{2005AJ....129.2562B}) ) is a composite catalog with the Sloan Digital Sky Survey (SDSS) data as its primary component." " It contains over 550,000 galaxies with their redshifts and positions on the sky."," It contains over 550,000 galaxies with their redshifts and positions on the sky." " The catalog also contains extinction corrected and K-corrected absolute magnitudes for 8 bands, of which the u, g, r, i and z bands come from the SDSS and the J, H and K, bands come from the 2-Micron All-Sky Survey (2MASS) although for this study we use only the data from the SDSS."," The catalog also contains extinction corrected and $K$ -corrected absolute magnitudes for 8 bands, of which the $u$, $g$, $r$, $i$ and $z$ bands come from the SDSS and the $J$, $H$ and $K_s$ bands come from the 2-Micron All-Sky Survey (2MASS) although for this study we use only the data from the SDSS." The galaxies in the catalog are also corrected for fiber collisions using the “nearest” method described in (2005).., The galaxies in the catalog are also corrected for fiber collisions using the “nearest” method described in \citet{2005AJ....129.2562B}. Less that 10% of the galaxies are affected by this correction which allows for a more complete sample in crowded regions., Less that $10\%$ of the galaxies are affected by this correction which allows for a more complete sample in crowded regions. " In addition to the galaxy catalog, the NYU-VAGC also contains a survey geometry catalog that describes the survey footprint in terms of spherical polygons (described in Blantonetαἱ "," In addition to the galaxy catalog, the NYU-VAGC also contains a survey geometry catalog that describes the survey footprint in terms of spherical polygons (described in \citealt{2005AJ....129.2562B}) )." "Since the SDSS is not an all-sky survey, the survey //2005)).footprint determines the positions of cells and allows us to lay down cells where there is valid data."," Since the SDSS is not an all-sky survey, the survey footprint determines the positions of cells and allows us to lay down cells where there is valid data." " For this work, we use the large scale structure samples in the version of the catalog corresponding to the seventh data release of the SDSS DR7).."," For this work, we use the large scale structure samples in the version of the catalog corresponding to the seventh data release of the SDSS \citep[DR7]{2009ApJS..182..543A}." We use the subsample with a flux limit of r<17.6 and perform further selection cuts based on the properties of the sample., We use the subsample with a flux limit of $r < 17.6$ and perform further selection cuts based on the properties of the sample. " In particular, we choose absolute magnitude cuts to obtain a complete sample within a given redshift range."," In particular, we choose absolute magnitude cuts to obtain a complete sample within a given redshift range." " We consider two redshift ranges in the g, r and { bands at 0.04€z<0.12 and 0.12€z< 0.20."," We consider two redshift ranges in the $g$ , $r$ and $i$ bands at $0.04 \leq z \leq 0.12$ and $0.12 \leq z \leq 0.20$ ." " The low redshift limit of z>0.04 ensures that the sample is within the Hubble flow, and excludes the Coma and Virgo clusters."," The low redshift limit of $z \geq 0.04$ ensures that the sample is within the Hubble flow, and excludes the Coma and Virgo clusters." " Since the SDSS “great wall"" spans a redshift range of 0.065From an R image, Chapelon et al. (" 1999) eive out to 16 arcsec for the bar.,1999) give out to 16 arcsec for the bar. This agrees with Fricdli et al. (, This agrees with Friedli et al. ( 1996) who show that bars are generally longer in I than in R. The J/IN color niage (Fie.,1996) who show that bars are generally longer in K than in R. The J/K' color image (Fig. 8d) shows a smooth structure. increasingly red towards the ceuter. aud a steep central eradieunt (Fig.," 8d) shows a smooth structure, increasingly red towards the center, and a steep central gradient (Fig." 8h)., 8h). The bar region also appears redder than the surouudiugs., The bar region also appears redder than the surroundings. The color map also shows clear hints of the existence of a smuiall. red. circunmuclear reelonu.," The color map also shows clear hints of the existence of a small, red circumnuclear region." During /«οobsbo (he observer receives also photons [from shells that are outer of the shell. which have higher observed temperature(han {ο,"During $t7Ty(clo/∩⋅⇀↱≻↕⇁⋡∣⊓∪∣∣∖⇀⋃⊽⊐1iv1/12pyliG. Ro) "," During this phase adiabatic cooling dictates \citep[e.g.,][]{Nakar10}, $T \propto t_{obs}^{-1/3}$ and $L \propto t_{obs}^{-4/3}$, implying The range of the low energy power-law in rather limited $T_{bo}>\nu>T_{bo}(c t_{th,0}/R_*)^{1/3}= 0.5 T_{bo} \g_0^{1/\3} \M^{-1/12} \R^{1/6}$ ." Noteκ- that equation⋅ 19 and the spectral range where the high⋅ and low energv power-laws are observed. do depend on the specilic clensitw profile ancl are given [or n--3.," Note that equation \ref{eq Fnu upper} and the spectral range where the high and low energy power-laws are observed, do depend on the specific density profile and are given for $n=3$." At 10 the observed. luminosity is still dominated by light emitted when the shell become transparent. ~νι.," At $t_s^{obs}$ the observed luminosity is still dominated by light emitted when the shell become transparent, $\sim t_{th,0}$." This emission [fades quickly until the emission lrom the spherical phase becomes dominant., This emission fades quickly until the emission from the spherical phase becomes dominant. The facing light curve can be easily derive in case (hat ro>Lo since then the observed luminosity is dominated by emission of the shell al large angles (> 1/555).," The fading light curve can be easily derive in case that $\g_{f,0} \gg 1$, since then the observed luminosity is dominated by emission of the shell at large angles $>1/\g_{f,0}$ )." " The luminosity decays then as £Lx/,;obs> and the temperature as TxLL Usumar&Panaitescu2000:NakarPiran2003).. until the emission from the spherical phase becomes dominant."," The luminosity decays then as $L \propto t_{obs}^{-2}$ and the temperature as $T \propto t_{obs}^{-1}$ \citep{Kumar00,NakarPiran03}, until the emission from the spherical phase becomes dominant." During the spherical phase (he radius of the expanding sphere is not constant auvuiore., During the spherical phase the radius of the expanding sphere is not constant anymore. Instead. (he radius of the shells is ¢oxοἱ and the luminosity is dominated by photons that are leaking from the shell that satisfies 7~c/c.," Instead, the radius of the shells is $r \propto v t$ and the luminosity is dominated by photons that are leaking from the shell that satisfies $\tau \sim c/v$." We refer to this shell as theshell ancl denote its properties with the superscript (see Nakar&Sari2010. [or a detailed discussion). such that. e.g.. the shell satisfies. by definition. 7?= c/v.," We refer to this shell as the and denote its properties with the superscript $~\widehat{ }~$ ' (see \citealt{Nakar10} for a detailed discussion), such that, e.g., the shell satisfies, by definition, $\tauh=c/\vh$ ." The evolutionduring (he spherical phase depends on whether the shell is relativistic or not and on the initial temperature of the shell., The evolutionduring the spherical phase depends on whether the shell is relativistic or not and on the initial temperature of the shell. As long as 5;>>1 the initial, As long as $\gfh \gg 1$ the initial Dust is associated with many astronomical objects. such as stars and galaxies.,"Dust is associated with many astronomical objects, such as stars and galaxies." Dust erains (wpically absorb radiation at short wavelengths. and since the dust grains are usually cooler than the radiation sources. thev reemit (he absorbed radiation at longer wavelengtlis.," Dust grains typically absorb radiation at short wavelengths, and since the dust grains are usually cooler than the radiation sources, they reemit the absorbed radiation at longer wavelengths." Consequently. the presence of dust is usually detected by a flux excess at infrared wavelengths.," Consequently, the presence of dust is usually detected by a flux excess at infrared wavelengths." The usual challenge is (o use the spectral enerey distribution (SED) of the object. to ex(ract information about the nature of the underlving Iuminous source aud (he properties of (he surrounding dust: i.e. ils spatial distribution. optical depth and intrinsic properties.," The usual challenge is to use the spectral energy distribution (SED) of the object, to extract information about the nature of the underlying luminous source and the properties of the surrounding dust; i.e., its spatial distribution, optical depth and intrinsic properties." The intrinsic properGes of (he dust grains are (heir chemical composition. condensation temperature. shape ancl size.," The intrinsic properties of the dust grains are their chemical composition, condensation temperature, shape and size." ]|xnowledge of the dust grain sizes present in circumstellar matter is desirable for many astrophysical situations., Knowledge of the dust grain sizes present in circumstellar matter is desirable for many astrophysical situations. For example. it is believed that about of the dust injected into the ISM originates [rom the winds of AGB stars (Gehrz1989).. so knowledge of the size of the dust grains present in (he winds of such stars is fundamental for understanding the properties of interstellar dust.," For example, it is believed that about of the dust injected into the ISM originates from the winds of AGB stars \citep{geh89}, so knowledge of the size of the dust grains present in the winds of such stars is fundamental for understanding the properties of interstellar dust." Similarly. grain size is important for understanding the details ol grain formation and mass loss mechanisms for cool stars.," Similarly, grain size is important for understanding the details of grain formation and mass loss mechanisms for cool stars." Η we assume that the source spectrum and the spatial distribution of the dust ave known for these objects. the question becomes to what extent is il possible to obtain the intrinsic properties of the dust [rom knowledge of the SED alone.," If we assume that the source spectrum and the spatial distribution of the dust are known for these objects, the question becomes to what extent is it possible to obtain the intrinsic properties of the dust from knowledge of the SED alone." In (his paper. we investigate how grain size affects the SED and to what extent (he SED can be used to constrain the grain sizes.," In this paper, we investigate how grain size affects the SED and to what extent the SED can be used to constrain the grain sizes." It is well known that models of the SED are not unique., It is well known that models of the SED are not unique. For this reason it is imperative to identify (he fundamental parameters controlling the SED., For this reason it is imperative to identify the fundamental parameters controlling the SED. Recently. (1997).. hereafter IE9T. investigated the scaling properties of the radiation transfer problem in spherically symmetric dust-envelopes.," Recently, \citet{ive97}, hereafter IE97, investigated the scaling properties of the radiation transfer problem in spherically symmetric dust-envelopes." Thev found that the radiation transfer problem in dustyv media depends only on the following quantities:, They found that the radiation transfer problem in dusty media depends only on the following quantities: weeks to mouths. so these can be ruled out as a source for the observed transitions between subclasses in162.,"weeks to months, so these can be ruled out as a source for the observed transitions between subclasses in." . Towever. a tilted precessing disk. such as thought to be present in. e.g.. (νο δν (Vrtileketal.1988). cau lead to changes in the viewiug eeouetiy on a time scale of weeks to mouths.," However, a tilted precessing disk, such as thought to be present in, e.g., Cyg X-2 \citep{vrswke1988}, can lead to changes in the viewing geometry on a time scale of weeks to months." Combined with the effects of anisotropies and/or varving amounts of obscuration this could lead to chanecs iu the morphology of CD/IIID tracks aud branches., Combined with the effects of anisotropies and/or varying amounts of obscuration this could lead to changes in the morphology of CD/HID tracks and branches. Towever. sich a model would require a complex evolution of the viewing angle o account for the observed sequence (in time) of the various sub-classes.," However, such a model would require a complex evolution of the viewing angle to account for the observed sequence (in time) of the various sub-classes." Moreover. it cannot account for he systematic disappearance of the various Z source xyanches as is observed during the transition from Z to atoll.," Moreover, it cannot account for the systematic disappearance of the various Z source branches as is observed during the transition from Z to atoll." We conclude that viewing anele is probably also rot respousible for the NSNB subclasses., We conclude that viewing angle is probably also not responsible for the NSXB subclasses. We note that xuameters such as neutrou star mass ad spin frequency should not change substantially during au outburst. as he amount of matter that is accreted is negligible iu conrparisou to the neutron star mass.," We note that parameters such as neutron star mass and spin frequency should not change substantially during an outburst, as the amount of matter that is accreted is negligible in comparison to the neutron star mass." Given the above. and takiug also iuto consideration the ransieut nature of162.. we conclude that ransitious between the NS-LAINB subclasses in ⋜↧⋜⋯∖↴≻↥⋅∪↴⋝⋜∏⋝↕∙↖⇁↸∖∐↑∐⋅↸∖↕⋅↖⇁≼⊔⋅↕↖⇁↸∖∐↴⋝∙," Given the above, and taking also into consideration the transient nature of, we conclude that transitions between the NS-LMXB subclasses in are probably entirely driven by changes in." ↖↽↸⊳∐⋜⋯∶↴∙⊾↸∖↴∖↴↕∐⋀∐∙∙ ⊀≚↕↑∐∪∏∶↴∙⊾∐↖↖⇁↸∖↸⊳⋜⋯∐∪↑↸⊳∪∐∏≻↕↸∖↑↸∖↕⋅↖↽↥⋅∏↕↸∖∪∏↑↑∐⋜↧↑↑∐↸∖ persisteut Z and atoll sources differ iu. e.g.. neutrou star lass/spin/maenetic field. or viewing angle. our results indicate that these parineters are relatively nunportaut to the phenomenology of162.. and by extension. to that of the Z and atoll sources.," Although we cannot completely rule out that the persistent Z and atoll sources differ in, e.g., neutron star mass/spin/magnetic field, or viewing angle, our results indicate that these parameters are relatively unimportant to the phenomenology of, and by extension, to that of the Z and atoll sources." Such parameters mna. however. explain some of the differences between tracks in the CD/IITDs of sources with similarM.," Such parameters may, however, explain some of the differences between tracks in the CD/HIDs of sources with similar." The discussion of the role of the various possible inflow/outflow componcuts of the accretion process i etermining NS-LAINB subclasses and motion. along the οΠΙΟ tracks is of course hampered by the lack of reliable independent measures of the relevant inflow/outflow rates. so it is difficult to draw firm conchisions. even frou the rich phenomenology observed in162.," The discussion of the role of the various possible inflow/outflow components of the accretion process in determining NS-LMXB subclasses and motion along the CD/HID tracks is of course hampered by the lack of reliable independent measures of the relevant inflow/outflow rates, so it is difficult to draw firm conclusions, even from the rich phenomenology observed in." . IHTowevoer. as we discussed above. for most of the outburst of tthe low-energev count rate appears to be a fairly good tracer of the tthat determines the changes in the CD/IIID tracks.," However, as we discussed above, for most of the outburst of the low-energy count rate appears to be a fairly good tracer of the that determines the changes in the CD/HID tracks." It is plausible that this sscales monotonically with some overall representative average PCU2 (260 keV) count rate level of he CD/IIID tracks aud their average bolometric ΠΠος (LRIIU9)., It is plausible that this scales monotonically with some overall representative average PCU2 $\sim$ 2–60 keV) count rate level of the CD/HID tracks and their average bolometric luminosities (LRH09). Under certain assunptious this would imply that Cve-like Z source behavior corresponds o the highest overall energy release aud perhaps vvalues. followed by Sco-like Z source behavior aud then atoll source behavior.," Under certain assumptions this would imply that Cyg-like Z source behavior corresponds to the highest overall energy release and perhaps values, followed by Sco-like Z source behavior and then atoll source behavior." The above also implies that the rorizoutal branch and its upturn are plienomena related ο the highest yvalues. although. as we discuss below. this does not jecessarilv mncan that along a sinele Z track these parts of the track represcut the highest values of the accretion rate relevant to motion along the Z. The above interpretation in which an level determines the type of CD/IIID track of NS LAINBs has implications for proposed models for the role of mass flow rates in motion (1.0. spectral evolution) along he Z tracks.," The above also implies that the horizontal branch and its upturn are phenomena related to the highest values, although, as we discuss below, this does not necessarily mean that along a single Z track these parts of the track represent the highest values of the accretion rate relevant to motion along the Z. The above interpretation in which an level determines the type of CD/HID track of NS LMXBs has implications for proposed models for the role of mass flow rates in motion (i.e. spectral evolution) along the Z tracks." Such a picture is obviously problematic for nodels in which the same level that determines the tvpe of CD/IIID also directly determines the position along the Z. with this ecither increasing monotonically from the horizoutal to he flariug brauch (ILasiuseretal.1990:19903... as is still often assumed. or with cchaugme in the opposite direction. as was recently xoposed bv Churchctal.(2006) and Jacksonotal.(20093.," Such a picture is obviously problematic for models in which the same level that determines the type of CD/HID also directly determines the position along the Z, with this either increasing monotonically from the horizontal to the flaring branch \citep{havaeb1990,vrraga1990}, as is still often assumed, or with changing in the opposite direction, as was recently proposed by \citet{chhaba2006} and \citet{jachba2009}." . Tlowever. we cannot rule out that the accretion rate through some part of the iuuer accretion flow changes monotonically aloug the Z. A sueeested solution in which changes in a mass flow rate can explain both the chanecs in the type of the CDAMD tracks as well as motion along the Z track was discussed in IHO07.," However, we cannot rule out that the accretion rate through some part of the inner accretion flow changes monotonically along the Z. A suggested solution in which changes in a mass flow rate can explain both the changes in the type of the CD/HID tracks as well as motion along the Z track was discussed in H07." " Their solution was based on a model o» vanderΊαν(2001) for the so-called “parallel tracks phenomenon in NS-LAINBs (see.οι,Méndezetal.1998.forfurtherinformationon this).. which assumes hat there exists both a prompt and a filtered response o changes in the mass accretion rate AL, through the inner edee of the acerction disk."," Their solution was based on a model by \citet{va2001} for the so-called `parallel tracks' phenomenon in NS-LMXBs \citep[see, e.g.,][for further information on this]{mevava1998a}, which assumes that there exists both a prompt and a filtered response to changes in the mass accretion rate $_d$ through the inner edge of the accretion disk." For a detailed discussion of the filtered response scenario aud how it relates to notion along the Z we refer to ITOT. but we point out an opportunity aud a problem here.," For a detailed discussion of the filtered response scenario and how it relates to motion along the Z we refer to H07, but we point out an opportunity and a problem here." The model predicts that ranches would be prefercutially suppressed if there is a xoloused monotonic decay inAZ. which is somewhat renünisceut of the systematic disappearance of the Z source horizontal and uormal brauches.," The model predicts that branches would be preferentially suppressed if there is a prolonged monotonic decay in, which is somewhat reminiscent of the systematic disappearance of the Z source horizontal and normal branches." However. the observed long terii modulation in 22.9 keV fux is not uonotonic. aud ifit can be identified with üt should altcrnatingly suppress the horizontal aud the daring brauch. which is not observed.," However, the observed long term modulation in 2–2.9 keV flux is not monotonic, and if it can be identified with it should alternatingly suppress the horizontal and the flaring branch, which is not observed." An alternative scenario. in which motion along the Z rack is not governed byAZ.. was sugeested by Tomanetal. (2002).," An alternative scenario, in which motion along the Z track is not governed by, was suggested by \citet{hovajo2002}." . Iu such a scenario the paramceter(s) responsible for spectral and variability properties. e.9.. he inner disk radius. varies (vary) independently fromM.," In such a scenario the parameter(s) responsible for spectral and variability properties, e.g., the inner disk radius, varies (vary) independently from." The spectral fits by LBIIOO sueeest that motion along the horizoutal brauch aud the Sco-like faring xanch is cousistent with occurring at a nearly coustautAL. although this is not as clear for the normal brauc[um and Cye-like flaring brauch.," The spectral fits by LRH09 suggest that motion along the horizontal branch and the Sco-like flaring branch is consistent with occurring at a nearly constant, although this is not as clear for the normal branch and Cyg-like flaring branch." In anv case. the spectral fity. sugecst that yvariatious aloug individual Z tracks are very πια].," In any case, the spectral fits suggest that variations along individual Z tracks are very small." Based on this. LRMOO sugecst that the different Z xauches may be the result of various instabilities iu the accretion flow. which could be related to an increase m he radiation pressure in differcut parts of the flow (inner disk. boundary laver).," Based on this, LRH09 suggest that the different Z branches may be the result of various instabilities in the accretion flow, which could be related to an increase in the radiation pressure in different parts of the flow (inner disk, boundary layer)." This scenario avoids the difficulties of ibaviug to explain both eradual changes in the shape of he Z tracks aud motion along the Z track at thle same ine., This scenario avoids the difficulties of having to explain both gradual changes in the shape of the Z tracks and motion along the Z track at the same time. The observations of requiro that the occurrence of the assumed (ane unknown) iustabilities themsclyes depeuds on the level G.e.. the instabilities resulting iu the horizontal and normal brauches ouly beiug preseut at the highest," The observations of require that the occurrence of the assumed (and unknown) instabilities themselves depends on the level (i.e., the instabilities resulting in the horizontal and normal branches only being present at the highest" thank Andreas Bauer and Volker Springel for kindly supplying the driving parameters used for the calculations.,thank Andreas Bauer and Volker Springel for kindly supplying the driving parameters used for the calculations. We also thank Chris Nixon. Jasmina Lazendic-Galloway. Duncan Galloway. Joe Monaghan. Jules Kajtar. Terry Trieco. Guillaume and Florence Laibe for useful discussion and comment.," We also thank Chris Nixon, Jasmina Lazendic-Galloway, Duncan Galloway, Joe Monaghan, Jules Kajtar, Terry Tricco, Guillaume and Florence Laibe for useful discussion and comment." Figures were made using (2) , Figures were made using \citep{splashpaper} formation (as already mentioned in Sec. ??)).,formation (as already mentioned in Sec. \ref{Sect:introduction}) ). " We use a periodical comoving boxsize of [νο=0.5h~*Mpc on a side with 2x64° gas and dark-matter particles (for a resulting spacial resolution of ~0.4kpc/h comoving), sampled at the initial redshift z=100."," We use a periodical comoving boxsize of $L_{\rm box} = 0.5 h^{-1} \rm Mpc$ on a side with $2 \times 64^3$ gas and dark-matter particles (for a resulting spacial resolution of $\sim 0.4\,\rm kpc/{\it h}$ comoving), sampled at the initial redshift $z=100$." " The runs include gravity, hydrodynamics, wind feedback, non-equilibrium chemistry, and radiative transfer."," The runs include gravity, hydrodynamics, wind feedback, non-equilibrium chemistry, and radiative transfer." Stars are taken to be sources of ionizing radiation., Stars are taken to be sources of ionizing radiation. " Since each star particle in the simulation represents a whole stellar population with a Salpeter distribution, about of its mass is in high-mass stars (2 10M) that are able to produce UV photons."," Since each star particle in the simulation represents a whole stellar population with a Salpeter distribution, about of its mass is in high-mass stars $\gtrsim 10\msun$ ) that are able to produce UV photons." " The frequency distribution is assumed to be a black-body spectrum with an effective temperature of 3x10*K, which corresponds to a luminosity of approximately 8x1045photonss! per high-mass star in the stellar population of the star particle."," The frequency distribution is assumed to be a black-body spectrum with an effective temperature of $3\times 10^4 \, \rm K$, which corresponds to a luminosity of approximately $8 \times 10^{48} \, \rm photons \, s^{-1}$ per high-mass star in the stellar population of the star particle." " We assume that gas particles are converted into stars once a critical density of —10cm? is reached, and the gas temperature is below ~10K to make sure that the gas is effectively cooling (seedetailsin?).."," We assume that gas particles are converted into stars once a critical density of $\sim 10\,\rm cm^{-3}$ is reached, and the gas temperature is below $\sim 10^4\rm K$ to make sure that the gas is effectively cooling \cite[see details in][]{Maio2009}." " Star forming particles also experience SN-explosion feedback, which heats the gas above ~10°K, and wind feedback, which expels gas with a typical velocity of ~500km/s (seealso?,andreferences therein)."," Star forming particles also experience SN-explosion feedback, which heats the gas above $\sim 10^5\,\rm K$, and wind feedback, which expels gas with a typical velocity of $\sim 500\,\rm km/s$ \cite[see also][and references therein]{Springel2005}." " A pictorial representation of the simulated box is given in Fig. 7,,"," A pictorial representation of the simulated box is given in Fig. \ref{fig:maps}," " where we show mass-weighted temperature slices through the simulation volume at redshift z—10.61 and z=6.14 for the full run, including, in particular, both non-equilibrium chemistry and RT."," where we show mass-weighted temperature slices through the simulation volume at redshift $z=10.61$ and $z=6.14$ for the full run, including, in particular, both non-equilibrium chemistry and RT." " 'The first sources are well visible close to the central part of the slice, and, while the structure growth proceeds, more sources are found in scattered places along the converging filaments."," The first sources are well visible close to the central part of the slice, and, while the structure growth proceeds, more sources are found in scattered places along the converging filaments." " Obviously, in a wider perspective (say on ~100Mpc scale), radiative sources would be much more uniformly distributed."," Obviously, in a wider perspective (say on $\sim 100\,\rm Mpc$ scale), radiative sources would be much more uniformly distributed." " However, there are currently serious computational limitations for performing simulations with such large box sides and, simultaneously, with resolution good enough to resolve chemical evolution and radiative transfer at the same time."," However, there are currently serious computational limitations for performing simulations with such large box sides and, simultaneously, with resolution good enough to resolve chemical evolution and radiative transfer at the same time." " In the maps, the filamentary cold structures led by early molecular gas are well visible at temperatures around hundreds Kelvin."," In the maps, the filamentary cold structures led by early molecular gas are well visible at temperatures around hundreds Kelvin." " In the densest regions, radiative effects from first stars heat the medium above 10*K already by redshift z>10."," In the densest regions, radiative effects from first stars heat the medium above $\sim 10^4\,\rm K$ already by redshift $z\gtrsim 10$." More and more star formation episodes appear at later stages and contribute to the cosmic reionization process down to redshift z~6., More and more star formation episodes appear at later stages and contribute to the cosmic reionization process down to redshift $z\simeq 6$. " Given the small size of our box, we can clearly focus on the infalling phases of the cold material in the intersection of primordial filamentary structures, and on the subsequent SN explosions, which heat the gas and push material into the lower-density, void regions."," Given the small size of our box, we can clearly focus on the infalling phases of the cold material in the intersection of primordial filamentary structures, and on the subsequent SN explosions, which heat the gas and push material into the lower-density, void regions." " This helps understanding the different role played by the various feedback mechanisms, on the other side, the lack of a very large box also leads to an insufficient number of stellar sources to fully complete reionization by z~ 6.In Fig."," This helps understanding the different role played by the various feedback mechanisms, on the other side, the lack of a very large box also leads to an insufficient number of stellar sources to fully complete reionization by $z\sim 6$ .In Fig." 8 we plot the phase diagrams (gas temperature vs. number density) for the simulations with and without, \ref{fig:phase} we plot the phase diagrams (gas temperature vs. number density) for the simulations with and without Cataclysmic Variables (CVs) are interacting binaries in which a white dwarf accretes material from a red. dwarl secondary star through Itoche lobe over-Dow.,Cataclysmic Variables (CVs) are interacting binaries in which a white dwarf accretes material from a red dwarf secondary star through Roche lobe over-flow. The majority of CVs acerete via an accretion disc. with the flow forming a strong shock at some height above the photosphere of the white. chvarl: ⋅⊀this results in. the emissiono. of vX-rays.," The majority of CVs accrete via an accretion disc, with the flow forming a strong shock at some height above the photosphere of the white dwarf: this results in the emission of X-rays." For. those white dwarks which have a magnetic field strength above 10 ALG (thepolars or stars). the field is strong enough to prevent the formation ofan accretion dise and the accretion How ects directed towards its magnetic poles.," For those white dwarfs which have a magnetic field strength above $\sim$ 10 MG (the or ), the field is strong enough to prevent the formation of an accretion disc and the accretion flow gets directed towards its magnetic poles." The high field also locks the rotation rate of the white να to the binary orbital period., The high field also locks the rotation rate of the white dwarf to the binary orbital period. For those svstems with a magnetic Ποια strength between 0.1LOAIG the aceretion disc gets disrupted at some distance from the white cwarl: these are called thePolars (LPs)., For those systems with a magnetic field strength between $\sim$ 0.1–10MG the accretion disc gets disrupted at some distance from the white dwarf: these are called the (IPs). " Patterson (1994) reviewed. the properties. of then known IPs and noted six which gave ""significant clues’ as to their LP nature.", Patterson (1994) reviewed the properties of then known IPs and noted six which gave `significant clues' as to their IP nature. " These include a stable modulation in the optical and X-ray light curves which is close to. or at. the spin period of the ‘accreting white dwarlADAE (P.,;,):spin: typicallyΣΜΕΑ Puspe<<..Dua: a side-band period which results from a beat between Pis and {οι and a hard N-ray spectrum which shows evidence of strong. (and. complex) absorption."," These include a stable modulation in the optical and X-ray light curves which is close to, or at, the spin period of the accreting white dwarf $P_{spin}$ ); typically $P_{spin}1. Z(Q)zz21/6—1/20 8/40. Ree-1/267—3/401. 15/40. Z-2CRz1/C-- 3/0.Equation (44)) thenbecomes,"For $|\zeta| \gg 1$, $Z\left(\zeta\right) \approx -1/\zeta-1/2\zeta^3 -3/4\zeta^5$ , $R \approx -1/2 \zeta^2- 3/4\zeta^4$, $1+2\zeta^2 R\approx -3/2 \zeta^2 - 15/4\zeta^4$ , $Z-2 \zeta R \approx 1/\zeta^3+3/\zeta^5$ .Equation \ref{eq:closure_perp}) ) thenbecomes" is ruled out based on the velocity dispersion among the family members.,is ruled out based on the velocity dispersion among the family members. " Although the angular momentum distribution in the catastrophic regime has not been extensively studied, we expect that angular momentum transfer to the largest remnant is inefficient."," Although the angular momentum distribution in the catastrophic regime has not been extensively studied, we expect that angular momentum transfer to the largest remnant is inefficient." " The largest remnant is a gravitationally reaccumulated body; hence, the angular momentum of the reaccumulated mass does not approach the spin instability limit."," The largest remnant is a gravitationally reaccumulated body; hence, the angular momentum of the reaccumulated mass does not approach the spin instability limit." Numerical simulations of catastrophic disruption that resolve the shape of the largest remnant produce spherical remnants not fast spinning elongated remnants (??)..," Numerical simulations of catastrophic disruption that resolve the shape of the largest remnant produce spherical remnants not fast spinning elongated remnants \citep{Leinhardt2000,Leinhardt2009}." " Thus, the analytic argument suggests that the most straightforward way to create a body with high angular momentum via a collision is in a grazing impact between two objects of similar size at a velocity close to the mutual escape speed."," Thus, the analytic argument suggests that the most straightforward way to create a body with high angular momentum via a collision is in a grazing impact between two objects of similar size at a velocity close to the mutual escape speed." " Note, however, that the analytic solution makes several assumptions."," Note, however, that the analytic solution makes several assumptions." " For example, mass that is lost from the system as a result of the collision is not taken into account."," For example, mass that is lost from the system as a result of the collision is not taken into account." The escaping mass carries away some energy and momentum., The escaping mass carries away some energy and momentum. " In addition, the energy and momentum conservation are approximated and do not include terms for energy lost in heat and fracturing of the target and projectile."," In addition, the energy and momentum conservation are approximated and do not include terms for energy lost in heat and fracturing of the target and projectile." " To examine the predictions of the idealized analytic solutions, we conducted a series of low-resolution simulations of impacts between gravitational aggregates (Table 1))."," To examine the predictions of the idealized analytic solutions, we conducted a series of low-resolution simulations of impacts between gravitational aggregates (Table \ref{tab:pkd}) )." " Because the encounter velocities are modest (X1.2 km the energy lost to shock deformation during the s~!),collision is minimal, and gravitational forces dominate."," Because the encounter velocities are modest $\le 1.2$ km $^{-1}$ ), the energy lost to shock deformation during the collision is minimal, and gravitational forces dominate." " Thus, for efficiency, the low-resolution simulations utilized the N-body gravity codepkdgrav,, which resolves inelastic particle-particle collisions (??7).."," Thus, for efficiency, the low-resolution simulations utilized the $N$ -body gravity code, which resolves inelastic particle–particle collisions \citep{Richardson2000,Leinhardt2000,Leinhardt2002}." " Particle collisions were modeled using a hard sphere model, where the unbreakable spherical particles are non-penetrating."," Particle collisions were modeled using a hard sphere model, where the unbreakable spherical particles are non-penetrating." " The outcome of each inelastic collision were governed by conservation of momentum and typical coefficients of restitution of 0.5 and 1.0 in the normal and tangential directions, respectively, for particles representing ice or rock (seediscussionin?).."," The outcome of each inelastic collision were governed by conservation of momentum and typical coefficients of restitution of 0.5 and 1.0 in the normal and tangential directions, respectively, for particles representing ice or rock \citep[see discussion in][]{Leinhardt2009}." " Each projectile and target was modeled as a rubble pile, à gravitationally bound aggregate of 955 particles with no tensile strength (??).."," Each projectile and target was modeled as a rubble pile, a gravitationally bound aggregate of 955 particles with no tensile strength \citep{Leinhardt2000,Leinhardt2002}." Previous simulations (?) show that a thousand particles is enough to resolve general shape features in a rubble pile., Previous simulations \citep{Leinhardt2000} show that a thousand particles is enough to resolve general shape features in a rubble pile. We assumed two internal configurations: homogeneous and differentiated bodies., We assumed two internal configurations: homogeneous and differentiated bodies. " In the differentiated cases, the colliding bodies had two layers: a 1.0 g cm? mantle representing ice and a 3.0 g cm-? core representing rock."," In the differentiated cases, the colliding bodies had two layers: a 1.0 g $^{-3}$ mantle representing ice and a 3.0 g $^{-3}$ core representing rock." " The mass ratio of the icy mantle to rocky core was also varied to reach the desired bulk density, which resulted in a range of initial radii from about 500 to 800 km."," The mass ratio of the icy mantle to rocky core was also varied to reach the desired bulk density, which resulted in a range of initial radii from about 500 to 800 km." " Based on the analytic solutions, the projectile-to-target mass ratio was assumed to be one in most cases with a subset of simulations considering Mp/My=0.5."," Based on the analytic solutions, the projectile-to-target mass ratio was assumed to be one in most cases with a subset of simulations considering $M_{\rm P} / M_{\rm T} = 0.5$ ." " The parameter space included initial bulk densities from 1.0 to 9.0 g cm?, impact velocities between 0.7 to 1.2 km s-l, impact parameters from 0.55 to 0.71, and total system masses of 4.5 to 8.2x10?! kg."," The parameter space included initial bulk densities from 1.0 to 3.0 g $^{-3}$, impact velocities between 0.7 to 1.2 km $^{-1}$, impact parameters from 0.55 to 0.71, and total system masses of $4.5$ to $8.2\times 10^{21}$ kg." " Due to the low resolution, each individual particle had relatively large mass, and it was difficult to strip material from the surface of the largest remnant."," Due to the low resolution, each individual particle had relatively large mass, and it was difficult to strip material from the surface of the largest remnant." " As a result, we use these simulations only to refine the impact parameters that reproduce the observed rotation period and approximate mass of Haumea."," As a result, we use these simulations only to refine the impact parameters that reproduce the observed rotation period and approximate mass of Haumea." " The calculated mass of the largest remnant will be biased slightly upward, and the family members will be completely unresolved."," The calculated mass of the largest remnant will be biased slightly upward, and the family members will be completely unresolved." " Based on the low-resolution simulation results, impact parameters were chosen for high-resolution calculations of the formation of Haumea and its family members (Table 2))."," Based on the low-resolution simulation results, impact parameters were chosen for high-resolution calculations of the formation of Haumea and its family members (Table \ref{tab:sims}) )." We used a hybrid hydrocode to N-body code technique similar to the method used in studies of catastrophic collisions in the asteroid belt and the outer solar system (eg.????)..," We used a hybrid hydrocode to $N$ -body code technique similar to the method used in studies of catastrophic collisions in the asteroid belt and the outer solar system \citep[eg.][]{Michel2003,Durda2004,Nesvorny2006,Leinhardt2009}." The hybrid technique captures the shock deformation during the early stage of the collision and follows the gravity-controlled evolution of the material to very late times., The hybrid technique captures the shock deformation during the early stage of the collision and follows the gravity-controlled evolution of the material to very late times. " We used GADGET (?), a smoothed particle hydrodynamics code (SPH) modified to use tabular equations of state (?),, for the hydrocode phase and for the gravity phase of the calculation."," We used GADGET \citep{Springel2005}, a smoothed particle hydrodynamics code (SPH) modified to use tabular equations of state \citep{Marcus2009}, for the hydrocode phase and for the gravity phase of the calculation." SPH is a Lagrangian technique for solving the hydrodynamic equations in which the mass distribution is represented by spherically symmetric overlapping particles that are evolved with time (??)..," SPH is a Lagrangian technique for solving the hydrodynamic equations in which the mass distribution is represented by spherically symmetric overlapping particles that are evolved with time \citep{Gingold1977, Lucy1977}." SPH has been used extensively to model impacts in the solar system from asteroid collisions and family forming events to the formation of the Pluto-Charon system (e.g. ??7)..," SPH has been used extensively to model impacts in the solar system from asteroid collisions and family forming events to the formation of the Pluto-Charon system \citep[e.g.][]{Asphaug1998,Michel2003,Canup2005}." Although GADGET includes self-gravity it is not practical to use a hydrocode for the entire integration of the collision as the timestep is limited by the Courant condition., Although GADGET includes self-gravity it is not practical to use a hydrocode for the entire integration of the collision as the timestep is limited by the Courant condition. Thetargets and impactors were differentiated bodies composed of an ice mantle over a rock core with a bulk, Thetargets and impactors were differentiated bodies composed of an ice mantle over a rock core with a bulk This paper extends the Cabl5 xsuupliue technique to polarized power spectruu estination.,This paper extends the Gibbs sampling technique to polarized power spectrum estimation. We lave detailed the necessary generalization steps relative to the original telperature-only descriptions eiven by Jewelletal. Wandeltetal.(2001). :uid Eviksenetal.(2001).. and have considered. computatiowl aspects of polarized. analysis.," We have detailed the necessary generalization steps relative to the original temperature-only descriptions given by \citet{jewell:2004}, , \citet{wandelt:2004} and \citet{eriksen:2004}, and have considered computational aspects of polarized analysis." The algorithm was demonstrated with two specific exanrples., The algorithm was demonstrated with two specific examples. First. cousidering a vossible CAIBPol type uissjon. we showed that the Cibbs sampler cleanly separates E- aud D-auodes. and no special care is required.," First, considering a possible CMBPol type mission, we showed that the Gibbs sampler cleanly separates E- and B-modes, and no special care is required." " This is in sharp ccontrast το approximate uethods such as so-called the seudo-C,. for which exeat care mnust be taken iu order for he larger E-1iodes. not ο colupromise the minute D-anodes."," This is in sharp contrast to approximate methods such as so-called the $C_{\ell}$, for which great care must be taken in order for the larger E-modes not to compromise the minute B-modes." Second. we analyzed a Plauck-sized data set. demonstrating that the aleoritlini ds useful for analyzing he quantity of data which wi] come from uear-future CXMB experiments.," Second, we analyzed a Planck-sized data set, demonstrating that the algorithm is useful for analyzing the quantity of data which will come from near-future CMB experiments." " The Cübbs sampling resuts presented. here use svuuuetrie beams and noise which is ""correlated between pixels.", The Gibbs sampling results presented here use symmetric beams and noise which is uncorrelated between pixels. However. the €dbbs sapling algoritlua has potential to analyze consierably more complicated data sets than these.," However, the Gibbs sampling algorithm has potential to analyze considerably more complicated data sets than these." For Plauck. the solution lies iu exploiting the very regular scanning strategy. which reduces the computational bucen of a time-ordered data analysis.," For Planck, the solution lies in exploiting the very regular scanning strategy, which reduces the computational burden of a time-ordered data analysis." For a future CAIBPol nission. the solution lies in the relatively large angilay scales required.," For a future CMBPol mission, the solution lies in the relatively large angular scales required." Since it is possible o invert the noise covariance matrix for multipoles up to several hundirecls. one nay pre-colpute the all-important ΑΝΤΑ τιatrix.," Since it is possible to invert the noise covariance matrix for multipoles up to several hundreds, one may pre-compute the all-important $\mathbf{A}^T \mathbf{N}^{-1}\mathbf{A}$ matrix." After paving this high one-time cost. efficient auc exact analysis is feasible using the methods deseribed iu this paper.," After paying this high one-time cost, efficient and exact analysis is feasible using the methods described in this paper." " Finally, we reeniphnasize twat the Cübbs sampler provides a direct route to the exact likelihood (aud to the Bayesian posterior). aud it is 1imcli mo0re reliable than approximate methods."," Finally, we re-emphasize that the Gibbs sampler provides a direct route to the exact likelihood (and to the Bayesian posterior), and it is much more reliable than approximate methods." " This isie has been demonstrated. explicitly through the analvsis of the threc-vear WALAP ata. where an approximate liselihood between (=13 and 30 caused a non-neelieilde bias in the spectral oeidex s, (Eriksenctal.2006)."," This issue has been demonstrated explicitly through the analysis of the three-year WMAP data, where an approximate likelihood between $\ell=13$ and 30 caused a non-negligible bias in the spectral index $n_{\textrm{s}}$ \citep{eriksen:2006}." . Using Cübbs sampling. y.uch worries are ereatly reduced.," Using Gibbs sampling, such worries are greatly reduced." Further. this paper demonstrates that the method is in fact capable of ualvzius the amount of data that will come from the Plauck mission with reasonable conrputational resources.," Further, this paper demonstrates that the method is in fact capable of analyzing the amount of data that will come from the Planck mission with reasonable computational resources." Tt therefore secs very likely tliat this method will plav a xenificaut role in the analysis of future Pauck data., It therefore seems very likely that this method will play a significant role in the analysis of future Planck data. Equations 5 and 6 have bee Lwritten as simply as possible. for clarity when describing the extension of our Gibbs sapling aleoriluu to polarization.," Equations \ref{sampleMean} and \ref{sampleFluctuation} have been written as simply as possible, for clarity when describing the extension of our Gibbs sampling algorithm to polarization." A more realistic treatiuent will iuvolve multiple chanuels. sviumetric beams. the pixel window finction. and a cttoff at some value of ἐν," A more realistic treatment will involve multiple channels, symmetric beams, the pixel window function, and a cutoff at some value of $\ell$." In this appendix we write out. for reference. the log likchhood forsaid the sampling equations that one derives from this.," In this appendix we write out, for reference, the log likelihood for $\Bs$ and the sampling equations that one derives from this." Let the index. Arun over clamnels., Let the index $i$ run over channels. Let B; be the beam smoothing function. aud W be the WEALPis pixel window funcion.," Let $\BB_i$ be the beam smoothing function, and $\BW$ be the HEALPix pixel window smoothing function." If all channels are at the same resolution. then there is only one pixel window function: otherwise W wil sinoothingneed au i index as wel.," If all channels are at the same resolution, then there is only one pixel window function; otherwise $\BW$ will need an $i$ index as well." Let P be a projection operator that removes all modes with € above some cutoff., Let $\proj$ be a projection operator that removes all modes with $\ell$ above some cutoff. Note trat P. W. aud B; all counmute. and P commutes with S.," Note that $\proj$, $\BW$, and $\BB_i$ all commute, and $\proj$ commutes with $\BS$." As before. ma; are the maps and s is the signal.," As before, $\Bm_i$ are the maps and $\Bs$ is the signal." For eeneraitv. we aso include a foreground component £j. which is not otherwise discussed in this paper.," For generality, we also include a foreground component $\Bf_i$, which is not otherwise discussed in this paper." From the above equation. it is clear that W cau be absorbed into B;. so we do this and drop W from the equations.," From the above equation, it is clear that $\BW$ can be absorbed into $\BB_i$, so we do this and drop $\BW$ from the equations." The equations for sampling s=x|y become: where now we lave several 1:ips v; of Gaussian uuit variates., The equations for sampling $\Bs = \Bx + \By$ become: where now we have several maps $\mathbf{\chi}_i$ of Gaussian unit variates. Recall that these equatious require the square root of Sto be svinmetric., Recall that these equations require the square root of $\BS$to be symmetric. For a given electron energy distribution (i.e.. the respective moments (5) and (57)).D? the electron energy density can be related to svnchrotron Iuminosity. of some radiating volume VW by IIence For a radiating region modeled either as a moving or steady source. one has the transformation io the observer [rame where the Doppler [actor of the jet emission is 0=1/T(1—1) and @=cos|yr is the jet viewing angle (see.e.g..Sikoraetal.1997).,"For a given electron energy distribution (i.e., the respective moments $\langle \gamma \rangle$ and $\langle \gamma^2 \rangle$ ), the electron energy density can be related to synchrotron luminosity of some radiating volume $V'$ by Hence For a radiating region modeled either as a moving or steady source, one has the transformation to the observer frame where the Doppler factor of the jet emission is $\delta \equiv 1 / \Gamma (1 - \beta \mu)$ and $\theta \equiv \cos^{-1} \mu$ is the jet viewing angle \citep[see, e.g.,][]{sik97}." . Note that. for small jet viewing angles (0~I). the Povuting flux and the bulk power of radiating electrons do not behave in opposite wavs wilh respect to P and D. because LyxE?D? while LexT|!B.7? 2001).," Note that, for small jet viewing angles $\delta \sim \Gamma$ ), the Poynting flux and the bulk power of radiating electrons do not behave in opposite ways with respect to $\Gamma$ and $B$, because $L_{\rm B} \propto \Gamma^2 \, B^2$ while $L_{\rm e} \propto \Gamma^{-1} \, B^{-2}$ \citep[cf.][]{ghi01}." ". Setting one can find that the magnetic field {σον minimizing L;,, is (he one for which Ly=LoL,.", Setting one can find that the magnetic field $B_{\rm cr}$ minimizing $L_{\rm tot}$ is the one for which $L_{\rm B} = L_{\rm e} + L_{\rm p}$. This value is given by Let us next consider a chumpy jet. consisting of N identical clumps of radiating matter with comoving volumes V/. which are present within the region of volume V.," This value is given by Let us next consider a clumpy jet, consisting of $N$ identical clumps of radiating matter with comoving volumes $V'_{\rm c}$, which are present within the region of volume $V'$." The chimp filling [actor ean be defined. as Assuming that the jet velocity is uniform within the jet region under consideration. the Povnting flux lor the radiating matter is then," The clump filling factor can be defined as Assuming that the jet velocity is uniform within the jet region under consideration, the Poynting flux for the radiating matter is then" leading edge of the outllow.,leading edge of the outflow. That the deceleration. raclius is comparable with the prompt emission radius is consistent with the subtraction of the back-extrapolated lorware-shock emission from the optical prompt flux done for Figures 2 and 4: in the triere Case. the power-law decay of the forward-shock emission would set in only after ως and the 0.12 day optical decay could. be extrapolated backwards only up to an epoch which is alter the burst.," That the deceleration radius is comparable with the prompt emission radius is consistent with the subtraction of the back-extrapolated forward-shock emission from the optical prompt flux done for Figures \ref{t30} and \ref{t30a}: in the $r_{dec} > r_\gamma$ case, the power-law decay of the forward-shock emission would set in only after $r_{dec}$ and the 0.1–2 day optical decay could be extrapolated backwards only up to an epoch which is after the burst." The underlsing assumption of this work. that the IROTSIE optical counterpart. of. GRB 990123 arose from the same mechanism as the burst. is motivated by the similarity of its timing and decay rate to those of the Last-clecay phase of Swift. X-ray afterglows.," The underlying assumption of this work, that the ROTSE optical counterpart of GRB 990123 arose from the same mechanism as the burst, is motivated by the similarity of its timing and decay rate to those of the fast-decay phase of Swift X-ray afterglows." As the latter can be identified with the large-angle emission. produced. during the burst. we attribute the ROWSE optical counterpart to the same mechanism.," As the latter can be identified with the large-angle emission produced during the burst, we attribute the ROTSE optical counterpart to the same mechanism." However. the optical emission. associated. with GRB 990123 must be a dillerent spectral component than the burst. because. the optical [lux lies well above the extrapolation of the burst spectrum.," However, the optical emission associated with GRB 990123 must be a different spectral component than the burst because the optical flux lies well above the extrapolation of the burst spectrum." In this way. we arrived at the svnchrotron self-Compton mocel for GRB 990128 and its optical counterpart.," In this way, we arrived at the synchrotron self-Compton model for GRB 990123 and its optical counterpart." The spectral slope of the optical counterpart of GRB 990123 was not measured., The spectral slope of the optical counterpart of GRB 990123 was not measured. Future observations of carly optical afterglows will provide a very simple test of the angle emission for GRB optical counterparts: their. power-law clecay index and spectral slope should satisfv. equation (1))., Future observations of early optical afterglows will provide a very simple test of the large-angle emission for GRB optical counterparts: their power-law decay index and spectral slope should satisfy equation \ref{alpha}) ). The svnchrotron. self-Compton interpretation of the optical and ~-ray emissions of GRB 990123 implies that the optical spectral slope must be equal to either the low-cncrey or the high-energv. burst spectral slope., The synchrotron self-Compton interpretation of the optical and $\gamma$ -ray emissions of GRB 990123 implies that the optical spectral slope must be equal to either the low-energy or the high-energy burst spectral slope. The decay. index of he optical emission of GRB 990123 and the slope of the )urst. continuum below its peak satisfy equation (1)). thus »oviding support to the larec-anele interpretation proposed or the optical counterpart.," The decay index of the optical emission of GRB 990123 and the slope of the burst continuum below its peak satisfy equation \ref{alpha}) ), thus providing support to the large-angle interpretation proposed for the optical counterpart." In the framework of the synchrotron self-C'ompton mocel. the ROVSE optical and BATS 5-rav observations or GRB 990123 allow us to determine that the radius at which the burst emission. was produced. is comparable to he outflow ceceleration radius. which in itself does not rule out any of the possible origins (internal. reverse-external. or orward-external shocks) of the burst emission. but. points o that. if the burst arises from internal shocks. then most of these shocks must have occurred. on the decelerating. eading front of the outllow. as proposed. by Fenimore Ramirez-Ruiz (1999).," In the framework of the synchrotron self-Compton model, the ROTSE optical and BATSE $\gamma$ -ray observations for GRB 990123 allow us to determine that the radius at which the burst emission was produced is comparable to the outflow deceleration radius, which in itself does not rule out any of the possible origins (internal, reverse-external, or forward-external shocks) of the burst emission, but points to that, if the burst arises from internal shocks, then most of these shocks must have occurred on the decelerating, leading front of the outflow, as proposed by Fenimore Ramirez-Ruiz (1999)." Alternatively. that the burst emission was produced at the deceleration radius gives support to he electromagnetic model of Lyutikoy DBlandford (2003). which predicted such a burst location.," Alternatively, that the burst emission was produced at the deceleration radius gives support to the electromagnetic model of Lyutikov Blandford (2003), which predicted such a burst location." The outflow: parameters derived. from the optical and s-ray properties of CIUD 990123 imply. an up-scattered selí-absorption frequency. of 60 keV. which is inconsistent with 3epposAX observations. showing an optically-thin burst spectrum above 2 keV. This cilliculty can be. overcome if the magnetic field. does not occupy. the entire. shocked eas.," The outflow parameters derived from the optical and $\gamma$ -ray properties of GRB 990123 imply an up-scattered self-absorption frequency of 60 keV, which is inconsistent with BeppoSAX observations, showing an optically-thin burst spectrum above 2 keV. This difficulty can be overcome if the magnetic field does not occupy the entire shocked gas." The magnetic field. decay. Iength-scale is upper-bound by the condition that the burst spectrum is optically thin above 2 keV and lower-bound by that the shell shock-crossing time should not be longer than the duration. of a GRB pulse and the magnetic field. energy. should. not exceed equipartition., The magnetic field decay length-scale is upper-bound by the condition that the burst spectrum is optically thin above 2 keV and lower-bound by that the shell shock-crossing time should not be longer than the duration of a GRB pulse and the magnetic field energy should not exceed equipartition. From these conditions. we find that the magnetic field must occupy 10510.7 of the shocked shell. which is equal to 10.—107 plasma skin-depths.," From these conditions, we find that the magnetic field must occupy $10^{-3}-10^{-2}$ of the shocked shell, which is equal to $10^6-10^7$ plasma skin-depths." Lt is rather xuzzling that the magnetic field. cecay-leneth is so much arger than the natural scale for magnetic field. generation. and vet does not. occupy the entire shell of shocked. gas.," It is rather puzzling that the magnetic field decay-length is so much larger than the natural scale for magnetic field generation, and yet does not occupy the entire shell of shocked gas." Whether such a Large magnetic field. decay leneth-scale is »xossible remains an open question which cannot be currently addressed by numerical models of (vo-stream instabilities (Moevedey Loeb 1999). due to the large computational cHort required. to. follow the evolution. of magnetic fields over such long scales.," Whether such a large magnetic field decay length-scale is possible remains an open question which cannot be currently addressed by numerical models of two-stream instabilities (Medvedev Loeb 1999), due to the large computational effort required to follow the evolution of magnetic fields over such long scales." We note that other researchers have obtained similar constraints on the magnetic field. decay length-scale:ὃν from energetico argumentsὃν related to the outflow parameters obtained through afterelow modelling. Rossi Rees (2003) have set a low limit of 107 on the fraction of shell. fillel by magnetic field. while Peer Zhang (2006) have inferred a decay Iength-scale smaller by a factor 10 iui our value. from the condition that. in internal-shocks svnehrotron-emiussion GRBs. electrons co not. cool significantly during the burst.," We note that other researchers have obtained similar constraints on the magnetic field decay length-scale: from energetic arguments related to the outflow parameters obtained through afterglow modelling, Rossi Rees (2003) have set a low limit of $10^{-2}$ on the fraction of shell filled by magnetic field, while Pe'er Zhang (2006) have inferred a decay length-scale smaller by a factor 10 than our value, from the condition that, in internal-shocks synchrotron-emission GRBs, electrons do not cool significantly during the burst." There are two other bursts whose accompanying optical emission has been measured., There are two other bursts whose accompanying optical emission has been measured. The optical ancl *5-rav. light-curves ofGRB 041219 (Vestrand 2005) are correlated ancl the post-hurst ecay of the optical counterpart exhibits variability (Blake 2005). both indicating that the counterpart is not the larec-angle emission released. during the burst.," The optical and $\gamma$ -ray light-curves of GRB 041219A (Vestrand 2005) are correlated and the post-burst decay of the optical counterpart exhibits variability (Blake 2005), both indicating that the counterpart is not the large-angle emission released during the burst." The optical and 5-ray emissions of GRB 050820 (Vestrand 2006. Cenko 2006) are not correlated. consistent with the larec-angle emission. scenario. but the [| post-burst decay of the optical afterglow is too slow for that interpretation: the burst spectrum. £5κOLLEOLT.and equation (1)) imply a steeper. /.7 decay for the bluge-angle emission.," The optical and $\gamma$ -ray emissions of GRB 050820A (Vestrand 2006, Cenko 2006) are not correlated, consistent with the large-angle emission scenario, but the $t^{-1}$ post-burst decay of the optical afterglow is too slow for that interpretation: the burst spectrum, $F_\nu \propto \nu^{-0.1\pm0.1}$, and equation \ref{alpha}) ) imply a steeper, $t^{-2}$ decay for the large-angle emission." Pherefore.. CRB 090123 is so [ar the only case exhibitingὃν a fast-decavingIn optical counterpart. uncorrelated with the burst emission. that can be interpreted as arising from the same mechanism as the burst.," Therefore, GRB 990123 is so far the only case exhibiting a fast-decaying optical counterpart, uncorrelated with the burst emission, that can be interpreted as arising from the same mechanism as the burst." MK06).,MK06). For the details of the spectrophotometric observations and analysis the interested readers are referred to MKO6 paper., For the details of the spectrophotometric observations and analysis the interested readers are referred to MK06 paper. The integrated emission-line fluxes relative to Ho... corrected for foreground Galactic extinction. and for underlying stellar absorption. as obtained by MKO6 are listed in Table 2..," The integrated emission-line fluxes relative to $\beta$, corrected for foreground Galactic extinction and for underlying stellar absorption, as obtained by MK06 are listed in Table \ref{tab:chemical}." " To correct the observed line ratios for reddening. the intrinsic case B Balmer line ratios were taken from Osterbrock (1989) assuming n.=100cm.? and Τ,=107 K. The value of the logarithmic extinction (or reddening coefficient) at H2. 7) was hence derived from the Ha/H:? ratio."," To correct the observed line ratios for reddening, the intrinsic case B Balmer line ratios were taken from Osterbrock (1989) assuming $_e=100 {\rm{cm}}^{-3}$ and $_e=10^4$ K. The value of the logarithmic extinction (or reddening coefficient) at $\beta$, $\beta$ ) was hence derived from the $\alpha$ $\beta$ ratio." The estimated reddening for NGC 3741 was found to be negligible (C(CH.2722.6 «10. i., The estimated reddening for NGC 3741 was found to be negligible $\beta$ )=2.6 $\times 10^{-3}$ ). No [OIII|A4363 was detected in NGC 3741. hence in the absence of the measurement of I([OIITJA4363). the oxygen abundance of the galaxy was estimated using the bright emission lines [OT] and [OIII]. using a grid) of photo-ionization models developed by MeGaugh (1991).," No $\lambda$ 4363 was detected in NGC 3741, hence in the absence of the measurement of $\lambda4363$ ), the oxygen abundance of the galaxy was estimated using the bright emission lines [OII] and [OIII], using a grid of photo-ionization models developed by McGaugh (1991)." In such models R2s-2[E 2) and [OITIT/[OTI] ratios are used to derived an empirical estimate of the oxygen abundance., In such models $_{23}$ $\beta$ ) and [OIII]/[OII] ratios are used to derived an empirical estimate of the oxygen abundance. " As Ro; is double valued. the degeneracy of the Re, relation was broken by inspecting the value of [NIT]/[OII] ratio (van Zee et al."," As $_{23}$ is double valued, the degeneracy of the $_{23}$ relation was broken by inspecting the value of [NII]/[OII] ratio (van Zee et al." 1998)., 1998). For NGC 3741 logt[NII/JOITD——1.5. hence the low-abundance branch of the model grid of the Re relation from MeGaugh (1991) was considered.," For NGC 3741 $\sim - 1.5$, hence the low-abundance branch of the model grid of the $_{23}$ relation from McGaugh (1991) was considered." The derived ratios for NGC 3741 are listed in Table 2.., The derived ratios for NGC 3741 are listed in Table \ref{tab:chemical}. The oxygen abundance derived using the bright line calibration was hence found to be 12+ logtO/H)-. 7.66+0.10., The oxygen abundance derived using the bright line calibration was hence found to be 12+ log(O/H)= $\pm$ 0.10. The uncertainty in this estimate also includes the uncertainty in the model calibrations of the semiemperical relation between line strength and elemental abundance for logO/H) (McGaugh 1991)., The uncertainty in this estimate also includes the uncertainty in the model calibrations of the semiemperical relation between line strength and elemental abundance for log(O/H) (McGaugh 1991). Figure 8. shows the absolute B. magnitude for NGC 3741. plotted against the derived oxygen abundance.," Figure \ref{fig:metal-lumin} shows the absolute B magnitude for NGC 3741, plotted against the derived oxygen abundance." The same quantity is also plotted for a sample of galaxies compiled from literature: the sample from which these galaxies have been drawn are listed in the figure caption., The same quantity is also plotted for a sample of galaxies compiled from literature; the sample from which these galaxies have been drawn are listed in the figure caption. The solid line with the slope and intercept of ( O.LISEO.01. 6.2440.16) respectively. shows the best fit to the data.," The solid line with the slope and intercept of ( $-$ $\pm$ 0.01, $\pm$ 0.16) respectively, shows the best fit to the data." As can be seen NGC 3741 follows the luminosity relation as defined by other dwarf galaxies., As can be seen NGC 3741 follows the metallicity-luminosity relation as defined by other dwarf galaxies. We will now compare the derived oxygen abundance and gas fraction of NGC 3741 with expectations from the closed-box chemical evolution in galaxies., We will now compare the derived oxygen abundance and gas fraction of NGC 3741 with expectations from the closed-box chemical evolution in galaxies. In a closed-box model the baryonic gus mass fraction j/ (the ratio of the gas mass to the total mass in gus and stars) and the gas-phase abundance (2) are related as where p is the elemental yield by mass., In a closed-box model the baryonic gas mass fraction $\mu$ (the ratio of the gas mass to the total mass in gas and stars) and the gas-phase abundance (Z) are related as where p is the elemental yield by mass. The effective yield. pur. is detined as the yield that would be deduced if the galaxy was assumed to be a simple closed-box.," The effective yield, $\rm{_{eff}}$, is defined as the yield that would be deduced if the galaxy was assumed to be a simple closed-box." In order to compute s+ for estimating por. we need to know the amount of gas that could participate in star formation.," In order to compute $\mu$ for estimating $\rm{_{eff}}$, we need to know the amount of gas that could participate in star formation." For galaxies with extended HI disks whether to compute s using the entire HI mass or just the HI mass within the optical disk is an important issue (Garnett 2002)., For galaxies with extended HI disks whether to compute $\mu$ using the entire HI mass or just the HI mass within the optical disk is an important issue (Garnett 2002). We computed pur for the two limiting cases Le. (1) using the entire HI mass and (ii) using only the HI mass within the optical disk., We computed $\rm{_{eff}}$ for the two limiting cases i.e. (i) using the entire HI mass and (ii) using only the HI mass within the optical disk. The effective yield of oxygen for NGC 3741. using the entire HI mass. is found to be pay=0.0069+0.0007. (derived using," The effective yield of oxygen for NGC 3741, using the entire HI mass, is found to be $\rm{_{eff}}=0.0069 \pm 0.0007$ (derived using" Assuming the overdensity lies in a cube of side MMpe. the co-moving of the overdensity is 1700 MMpe?.,"Assuming the overdensity lies in a cube of side Mpc, the co-moving of the overdensity is $\sim1700$ $^3$." Dark matter simulations of the early Universe show that matter collapses in filaments. and our selection method preferentially selects tilaments that are close to being perpendicular to the plane of the sky.," Dark matter simulations of the early Universe show that matter collapses in filaments, and our selection method preferentially selects filaments that are close to being perpendicular to the plane of the sky." Therefore this estimate of the volume is very uncertain., Therefore this estimate of the volume is very uncertain. The colour distribution of the statistical excess was derived by subtracting the colour distribution of the interloping ggalaxies (measured from the CF+ and normalised by area) from the colour distribution of galaxies within the 3 HzRGs in overdense fields., The colour distribution of the statistical excess was derived by subtracting the colour distribution of the interloping galaxies (measured from the CF+ and normalised by area) from the colour distribution of galaxies within the 3 HzRGs in overdense fields. Ideally the colours of all excess galaxies within the HzRG fields should be derived., Ideally the colours of all excess galaxies within the HzRG fields should be derived. However. the variance due to the interloper population is approximately. proportional to the field area.," However, the variance due to the interloper population is approximately proportional to the field area." " Therefore the colours of the statistical excess was only measured within 3.5 co-moving Mpe (2.1) of1425-148. παπάMRC2104—242.. where the number of excess galaxies is more than 4 times theuncertainty(see reftig:number,οxcess,al dthinR))."," Therefore the colours of the statistical excess was only measured within 3.5 co-moving Mpc ) of, and, where the number of excess galaxies is more than 4 times theuncertainty(see \\ref{fig:number_of_excess_gal_withinR}) )." " reftig:JH,clourdisplavsthecolourdist ributionofALL-JHK egalaxiesintheCE —.ealaxieswithin2.\' oofthe3overdenseH cRGs.andthederivedstatisticalealaxvercess."," \\ref{fig:JH_colour} displays the colour distribution of galaxies in the CF+, galaxies within of the 3 overdense HzRGs, and the derived statistical galaxy excess." T hecolourdistribut. Kolmogorov|Smirnov( KS)test.," The colour distribution of the statistical excess differs from the control field, which is quantified using a two-sided Kolmogorov-Smirnov (KS) test." The KS test requires continuous unbinned data. so a mock catalogue of galaxy colours was created by sampling random values whilst constraining the catalogue to match the observed colour distribution of the statistical excess.," The KS test requires continuous unbinned data, so a mock catalogue of galaxy colours was created by sampling random values whilst constraining the catalogue to match the observed colour distribution of the statistical excess." The KS test was performed 1000 times and in each test the colours of the excess galaxies were drawn from a different set of random values., The KS test was performed 1000 times and in each test the colours of the excess galaxies were drawn from a different set of random values. The probability. p. gives the significance level of the test (ranging between ϐ and 1) and is the median of all derived p. The KS test rejects the null hypothesis with p-0.001. so the colour distribution of the excess galaxies differs signiticantly from the colour distribution of galaxies in the CF+.," The probability, p, gives the significance level of the test (ranging between 0 and 1) and is the median of all derived p. The KS test rejects the null hypothesis with p=0.001, so the colour distribution of the excess galaxies differs significantly from the colour distribution of galaxies in the CF+." The excess galaxies in the 3 overdense fields are not drawn randomly from the control field population and are therefore unlikely to be caused by a chance line-of-sight alignment., The excess galaxies in the 3 overdense fields are not drawn randomly from the control field population and are therefore unlikely to be caused by a chance line-of-sight alignment. The colour distribution of UDS galaxies with photometric redshifts in the range 2.2Sppey<2.7 Gp. UDS sample: see Section 3.2.1)) is shown in« reftig:compare, The colour distribution of UDS galaxies with photometric redshifts in the range $2.21 (we adopt S,xv—ü. where S, is the flux density at the frequency v)."," Their radio spectra are steep, with spectral indices $\alpha>1$ (we adopt $S_{\nu} \propto \nu^{-\alpha}$, where $S_{\nu}$ is the flux density at the frequency $\nu$ )." Observations show that radio halos are not common in galaxy clusters., Observations show that radio halos are not common in galaxy clusters. Large halos are found in only .1/3 of the most massive and X-ray luminous clusters (e.g.. Giovannini et al.," Large halos are found in only $\sim 1/3$ of the most massive and X-ray luminous clusters (e.g., Giovannini et al." " 1999, Kempner Sarazin 2001. Venturi et al."," 1999, Kempner Sarazin 2001, Venturi et al." 2008. Cassano et al.," 2008, Cassano et al." 2008). and become even rarer in less massive systems.," 2008), and become even rarer in less massive systems." The rest of the clusters seems to form a distinct population of systems (Brunetti et al., The rest of the clusters seems to form a distinct population of systems (Brunetti et al. 2007. 2009).," 2007, 2009)." Clusters with and without a giant halo appear segregated in terms of their dynamical state: halos are located exclusively in merging systems. while clusters without radio halos are typically more relaxed (e.g.. Buote 2001. Cassano et al.," Clusters with and without a giant halo appear segregated in terms of their dynamical state: halos are located exclusively in merging systems, while clusters without radio halos are typically more relaxed (e.g., Buote 2001, Cassano et al." 2010. and references therein).," 2010, and references therein)." Few exceptions are known. where a merging system does not have a radio halo. typically with relatively low X-ray luminosity (Ly£8x1077 erg s': eg. Cassano et al.," Few exceptions are known, where a merging system does not have a radio halo, typically with relatively low X-ray luminosity $L_X \ltsim 8 \times 10^{44}$ erg $^{-1}$; e.g., Cassano et al." 2010. Russell et al.," 2010, Russell et al." 2011)., 2011). The halo-merger connection suggests that the energy necessary to generate radio halos — through acceleration. of particles and amplification of magnetic fields — is provided by cluster mergers., The halo-merger connection suggests that the energy necessary to generate radio halos – through acceleration of particles and amplification of magnetic fields – is provided by cluster mergers. Although the origin of radio halos is still debated (e.g.. Brunetti et al.," Although the origin of radio halos is still debated (e.g., Brunetti et al." 2008. Pfrommer et al.," 2008, Pfrommer et al." 2008. Donnert et al.," 2008, Donnert et al." " 2010. Keshet and Loeb 2010. Brown and Rudnick 2011. Jeltema and Profumo 2011). current observations (e.g.. Cassano 2009. and references therein) appear to favour models where the giant halos are caused by merger-driven turbulence. that reaccelerates relativistic particlesmodel, Petrosian 2001. Brunetti et al."," 2010, Keshet and Loeb 2010, Brown and Rudnick 2011, Jeltema and Profumo 2011), current observations (e.g., Cassano 2009, and references therein) appear to favour models where the giant halos are caused by merger-driven turbulence that reaccelerates relativistic particles; Petrosian 2001, Brunetti et al." 2001)., 2001). In line with present data. these models predict that halos are more probably found i massive clusters and become quite rare in systems with mass 210? M. (Le. Ly£7—8x107 erg sl) at intermediate redshift (z~0.2+0.5: Cassano et al.," In line with present data, these models predict that halos are more probably found in massive clusters and become quite rare in systems with mass $ \ltsim 10^{15}$ $_{\odot}$ (i.e., $L_X \ltsim 7-8 \times 10^{44}$ erg $^{-1}$ ) at intermediate redshift $z \sim 0.2 \div 0.5$; Cassano et al." 2008)., 2008). Here. we report the discovery of a giant radio halo in RXCJJI514.9-1523. a galaxy cluster at z=0.22 with a relatively low X-ray luminousity. ασο=7-2X103 erg ! (Bóhhringer et al.," Here, we report the discovery of a giant radio halo in J1514.9-1523, a galaxy cluster at z=0.22 with a relatively low X-ray luminousity, $L_{X \,[0.1-2.4 \rm \, kev]}=7.2 \times 10^{44}$ erg $^{-1}$ (Böhhringer et al." 2004)., 2004). " We adopt the ACDM cosmology with Hy=70 km s! Mpe!. OQ,=0.3 and Q4.=0.7."," We adopt the $\Lambda$ CDM cosmology with $_0$ =70 km $^{-1}$ $^{-1}$, $\Omega_m=0.3$ and $\Omega_{\Lambda}=0.7$." At the redshift of J1514.9-1523. this gives a scale of 1=3.59 kpe.," At the redshift of J1514.9-1523, this gives a scale of $1^{\prime \prime}=3.59$ kpc." JJ1514.9-1523 is in the cluster sample of the extended (GMRT) Radio Halo Survey. an ongoing project to expand the existing sample of galaxy clusters (Venturi et al.," J1514.9-1523 is in the cluster sample of the extended ) Radio Halo Survey, an ongoing project to expand the existing sample of galaxy clusters (Venturi et al." 2007 2008; see Cassano et al., 2007 2008; see Cassano et al. 2010 for details)., 2010 for details). In this work. we analyze archivalGMRT observations of RXCJJI514.9-1523 at 327 MHz and data at 1.4 GHz from the pointing containing the cluster. that we have reprocessed.," In this work, we analyze archival observations of J1514.9-1523 at 327 MHz and ) data at 1.4 GHz from the pointing containing the cluster, that we have reprocessed." We also observed the cluster with theGMRT at 235 MHz/610 MHz in August 2009. as part of the extendedGMRT Radio Halo Survey.," We also observed the cluster with the at 235 MHz/610 MHz in August 2009, as part of the extended Radio Halo Survey." Variable radio frequency interference was present for the whole observation. particularly on the shortest spacings.," Variable radio frequency interference was present for the whole observation, particularly on the shortest spacings." The subsequent editing left à sparse sampling at the short baselines. preventing the production of an image of the radio halo of any use.," The subsequent editing left a sparse sampling at the short baselines, preventing the production of an image of the radio halo of any use." A reobservation is currently planned., A reobservation is currently planned. It is prudent to check the convergence of computed results.,It is prudent to check the convergence of computed results. We have performed additional simmlations with 128* and 512* erid points., We have performed additional simulations with $128^3$ and $512^3$ grid points. We show in Figure (7)) an example of these convergence tests we have done., We show in Figure \ref{fig:converga}) ) an example of these convergence tests we have done. " We see that. while the difference between the 128* and 256° cases cani amount up (o tens of percent at late times (sav. {ο>5). the difference between the 256* and 512* cases is dramatically reduced and is at a level of a few percent even al very late (mes (///,,,> 10)."," We see that, while the difference between the $128^3$ and $256^3$ cases can amount up to tens of percent at late times (say, $t/t_{dyn}>5$), the difference between the $256^3$ and $512^3$ cases is dramatically reduced and is at a level of a few percent even at very late times $t/t_{dyn}>10$ )." It is instructive to notice that the tendency is to decrease the level of mixing as we Increase (he resolution., It is instructive to notice that the tendency is to decrease the level of mixing as we increase the resolution. So our results must be interpreted as an upper limit in the metal enrichment of minihalos by shockwaves. with an accuracy of a few percent.," So our results must be interpreted as an upper limit in the metal enrichment of minihalos by shockwaves, with an accuracy of a few percent." It is frequently assumed that (he metallicity of the intergalactic medium is (he primary determinant of the epoch of the transition from Pop-Lll to Pop-II stars., It is frequently assumed that the metallicity of the intergalactic medium is the primary determinant of the epoch of the transition from Pop-III to Pop-II stars. We wish to point oul a potentially laree difference between (he metallicity of the intergalactic medium ancl the metallicity of the gas in minihalos., We wish to point out a potentially large difference between the metallicity of the intergalactic medium and the metallicity of the gas in minihalos. Utilizing hvdrodyvnamie simulations of gas elouds in minihalos subject (o destructive processes associated with the encompassing intergalactic shocks carrving metal-enriched gas. we find that à large fraction of gas in virialized minihalos remains at a metallicity much lower than that of the intergalactic medium.," Utilizing hydrodynamic simulations of gas clouds in minihalos subject to destructive processes associated with the encompassing intergalactic shocks carrying metal-enriched gas, we find that a large fraction of gas in virialized minihalos remains at a metallicity much lower than that of the intergalactic medium." " For example. for realistic shocks of velocities of 10— 100km/s. more than (9054. 655.) of the high density gas with p>500p; inside a minihalo virialized at 2=10 of mass (10*.10)A. remains at a metallicity lower than of that of the intergalactic medium by redshift 2= 6. under the harsh condition that the minihalo is exposed (ο shockwaves continuously [rom 2=10 to ο,"," For example, for realistic shocks of velocities of $10-100$ km/s, more than $90\%,65\%$ ) of the high density gas with $\rho \ge 500\rho_b$ inside a minihalo virialized at $z=10$ of mass $(10^7,10^6)\msun$ remains at a metallicity lower than of that of the intergalactic medium by redshift $z=6$ , under the harsh condition that the minihalo is exposed to shockwaves continuously from $z=10$ to $z=6$." In the standard. cosmological model. if large halos with efficient. atomic cooling are responsible for producing most of the reionizing photons. smaller minihalos virialize before ihe universe is significantly reionized.," In the standard cosmological model, if large halos with efficient atomic cooling are responsible for producing most of the reionizing photons, smaller minihalos virialize before the universe is significantly reionized." Thus. gas in virialized minihalos may provide an abundant reservoir of primordial gas to possibly allow for the formation of metal-free stars (o extend (o much lower redshift (han expected otherwise based on the enrichment of intergalactic medium.," Thus, gas in virialized minihalos may provide an abundant reservoir of primordial gas to possibly allow for the formation of Population-III metal-free stars to extend to much lower redshift than expected otherwise based on the enrichment of intergalactic medium." A related issue that is not addressed here concerns the fate of the gas inside minihalos when exposed (o reionizing photons., A related issue that is not addressed here concerns the fate of the gas inside minihalos when exposed to reionizing photons. The situation is complicated because the timescale of the photo-evaporation of gas in minihalos (Darkana&Loeb2002:Hlievetal.2005:Ciardiοἱal.2006) max be ~ LOOMis (Shapiroetal.2004): the timescale may be still longer at higher redshifts (2> 10) and/or at lower ionizing [fluxes (han used in the work of Shapiroetal. (2004)..," The situation is complicated because the timescale of the photo-evaporation of gas in minihalos \citep{baretal02,ili05,cia06} may be $\sim 100$ Myrs \citep{sha04}; the timescale may be still longer at higher redshifts $z>10$ ) and/or at lower ionizing fluxes than used in the work of \cite{sha04}. ." It may be that a full understanding requires detailedcalculations that incorporate both radiative (ransfer ancl metal-enrichment processes., It may be that a full understanding requires detailedcalculations that incorporate both radiative transfer and metal-enrichment processes. model with 7.=3500 K and loge=0.0 that we used earlier.,model with $T_{\mathrm{eff}} = 3500$ K and $\log g = 0.0$ that we used earlier. The comparison is shown in Fig. 9.., The comparison is shown in Fig. \ref{fig:as_ng}. Now the differences are somewhat larger than in the previous comparisons. which is to be expected because the detailed calculations are nearly totally Independent.," Now the differences are somewhat larger than in the previous comparisons, which is to be expected because the detailed calculations are nearly totally independent." " Overall. however. the comparison Is very similar. showing that the two models have essentially the same structures. although we note that the NextGen model has a temperature bulge compared with our model in the pressure range —1«logygPea,+1.5."," Overall, however, the comparison is very similar, showing that the two models have essentially the same structures, although we note that the NextGen model has a temperature bulge compared with our model in the pressure range $-1 < \log_{10} P_{\mathrm{gas}} < + 1.5$." We have not observed this kind of feature in the comparisons we have made with the Kuruez models or between our spherical and plane-parallel models., We have not observed this kind of feature in the comparisons we have made with the Kurucz models or between our spherical and plane-parallel models. A note about the relative run times of the two codes: the time per iteration running on our single-processor desktop workstation is just of the time per iteration given in the header files of the NG-giant model., A note about the relative run times of the two codes: the time per iteration running on our single-processor desktop workstation is just of the time per iteration given in the header files of the NG-giant model. The program (?) is another well established code that has the ability to compute LTE. line-blanketed. spherical model atmospheres.," The program \citep{2008A&A...486..951G} is another well established code that has the ability to compute LTE, line-blanketed, spherical model atmospheres." From the MARCS web site (ittp:jmarcs.astro.uu.se/)) the model with parameters Το K. loge=0.0 and M=1Mo is closest the the examples we have been using.," From the MARCS web site ) the model with parameters $T_{\mathrm{eff}} = 4000$ K, $\log g = 0.0$ and $M = 1 \ M_{\sun}$ is closest the the examples we have been using." This model also has solar abundances and a microturbulent velocity of 2 km/s. The header lines in the model gives the spherical parameters L=6390Lo and R=1.1550x10em166Ro., This model also has solar abundances and a microturbulent velocity of 2 km/s. The header lines in the model gives the spherical parameters $L = 6390 \ L_{\sun}$ and $R = 1.1550 \times 10^{13} \ \textrm{cm} = 166 \ R_{\sun}$. MARCS defines the radius at τε=1.0. not at tp=2/3 that we use. but this is a small difference.," MARCS defines the radius at $\tau_{\mathrm{R}} = 1.0$, not at $\tau_{\mathrm{R}} = 2/3$ that we use, but this is a small difference." Therefore. we have started from the model with Toy=4000 K. logg=0.0 and microturbulence = 2 km/s in the same grid (/grids/gridp880dfnew/ap88k2odfnew.dat)) used earlier. and we have computed a spherical model with the luminosity. mass and radius of the MARCS model.," Therefore, we have started from the model with $T_{\mathrm{eff}} = 4000$ K, $\log g = 0.0$ and microturbulence = 2 km/s in the same grid ) used earlier, and we have computed a spherical model with the luminosity, mass and radius of the MARCS model." The comparison is shown in Fig 10.., The comparison is shown in Fig \ref{fig:as_m}. " The models agree very well in the range logyP,«1.5. where the NextGen model displayed a temperature bulge."," The models agree very well in the range $\log_{10} P_{\mathrm{gas}} < + 1.5$, where the NextGen model displayed a temperature bulge." But. the spherical MARCS model appears to have a pressure inversion at 7.>6500 K. something that is not present in the comparison. with the model.," But, the spherical MARCS model appears to have a pressure inversion at $T > 6500$ K, something that is not present in the comparison with the model." Overall. however. the structures are in substantial agreement.," Overall, however, the structures are in substantial agreement." We have modified the robust. open-source. plane-parallel model atmosphere program to treat spherically extended geometry.," We have modified the robust, open-source, plane-parallel model atmosphere program to treat spherically extended geometry." The resulting spherical code.SATLAs.. which ts available in both opacity distribution funetion and opacity sampling versions. was used to compute several test models.," The resulting spherical code, which is available in both opacity distribution function and opacity sampling versions, was used to compute several test models." At high surface gravity the spherical model structure is essentially identical to the plane-parallel model structure., At high surface gravity the spherical model structure is essentially identical to the plane-parallel model structure. At low surface gravity. the models agree very well with the spherical model structures computed by and byMARCS.," At low surface gravity, the models agree very well with the spherical model structures computed by and by." . The program. which runs easily on a desktop workstation. offers a viable alternative for modeling the atmospheres of low surface gravity stars.," The program, which runs easily on a desktop workstation, offers a viable alternative for modeling the atmospheres of low surface gravity stars." As an example of the utility ofSArLAs.. we have used it to compute more than 2500 models to create model cubes with fine parameter spacing covering the specific. L..," As an example of the utility of, we have used it to compute more than 2500 models to create model cubes with fine parameter spacing covering the specific $L_{\ast}$ ," On the Value of Job Migration inOnline Makespan Minimization Albers?,Makespan minimization on identical machines is a fundamental scheduling problem that has received considerable research interest over the last forty years. Matthias Hellwig” Susanne Abstract Makespan minimization on iderticalparallel machines," Let $\sigma = J_1, \ldots, J_n$ be a sequence of jobs that has to be scheduled non-preemptively on $m$ identical parallel machines." ts acl," Each job $J_i$ is specified by a processing time $p_i$, $1\leq i \leq n$ ." assical schedul," The goal is to minimize the makespan, the maximum completion time of any job in a schedule." ing problem. We consider, In the offline setting all jobs are known in advance. the online scenario wherea seq, In the online setting the jobs arrive one by one. uence of »Jobshasto bescheduled non-pre," Each job $J_i$ has to be scheduled immediately on one of the machines without knowledge of any future jobs $J_k$, $k>i$." emptively on #7machines so as t," An online algorithm $A$ is called $c$ -competitive if, for any job sequence, $A$ 's makespan is at most $c$ times the optimum makespan for that sequence \cite{ST}." o minimize the , Early work on makespan minimization studied the offline setting. maximumcompletion time," Already in 1966, Graham \cite{G} presented the scheduling algorithm that schedules each job on a least loaded machine." of any[1.58.job. 1.9201]., can be used as an offline and online strategy and achieves a performance ratio of $2-1/m$. The bestcompetitive ratio that, Hochbaum and Shmoys devised a famous polynomial time approximation scheme \cite{HS}. can beachieved by deterministic online," More recent research, published mostly in the 1990s, investigated the online setting." competitiveness algorithms ists1 known.1," The best competitive factor that can be attained by deterministic online algorithms is in the range $[1.88,1.9201]$." therangefor general Currently norandomized online algorithm withInathis," Due to this relatively high factor, compared to 's ratio of $2-1/m$, it is interesting to consider scenarios where an online scheduler has more flexibility to serve the job sequence." smallerpaperwe explorethe power ofjob migration., In this paper we investigate the impact of job migration. in. i.e.an onlinescheduler allowed to performa limited number ofjob reassignme," At any time an online algorithm may perform, a job already scheduled on a machine may be removed and transferred to another machine." ts. Migration isà common technique used in theory and practice, Process migration is a well-known and widely used technique to balance load in parallel and distributed systems. to balance loadin parallel processing e, It leads to improved processor utilization and reduced processing delays. nvironments., Migration policies have been analyzed extensively in theory and practice. Asour main r, It is natural to investigate makespan minimization with job migration. esult wesettle theperformance thatcan achieved deterministic online algorithms., In this paper we present a comprehensive study and develop tight upper and lower bounds on the competitive ratio that can be achieved by deterministic online algorithms. " We develop an algorithm that is«,,,-competitive. for any m O2."," It shows that even with a very limited number of migration operations, significantly improved performance guarantees are obtained." " where o, 1sthe solu", We review the most important results relevant to our work. tionof a certaine," As mentioned above, is $(2-1/m)$ -competitive." "quation. For =2.à» =L/3 and Iun, «s6,5"," Deterministic online algorithms with a smaller competitive ratio were presented in \cite{A,BFKV,FW,GW,KPT}." TV 4€ 1/62)/40|WWye 1/62))zm 1.1659. , The best algorithm currently known is 1.9201-competitive \cite{FW}. . HereTT 4isthe lowerbranch oftheLambert," Lower bounds on the performance of deterministic strategies were given in \cite{A,BKR,FKT,GRTW,R,RC}." TTfunction. Foribe> 11.," The best bound currently known is 1.88, for general $m$." the algorithmuses at most," Randomized online algorithms cannot achieve a competitive ratio smaller than $e/(e-1)\approx 1.58$ \cite{CVW,S}." 77»migration may performed.migrationsWe com," No randomized algorithm whose competitive ratio is provably below the deterministic lower bound is currently known, for general $m$ ." plementachieve competitivethisresultby rat," If job preemption is allowed, the best competitiveness of online strategies is equal to $e/( e-1)\approx 1.58$ \cite{CVW2}." ioa matchingsmaller, Makespan minimization with job migration was first addressed by Aggarwal et al. \cite{AMZ}. thanlower bound:We, They consider an offline setting. Nofinally onlinetrade," An algorithm is given a schedule, in which all jobs are already assigned, and a budget." algorithmperformance that use, The algorithm may perform job migrations up to the given budget. sfor o(n)migrations.job We givea family of algorith, The authors design strategies that perform well with respect to the best possible solution that can be constructed with the budget. ms that is ¢-co," Online makespan minimization on $m=2$ machines was considered in \cite{MLW,TY}." mpetitive., The best competitiveness is 4/3. forαμ., Sanders et al. any5/3 x 6< 2.Fore 5/3.the strategyuses at most li Job migrations.," \cite{SSS} study an online setting in which before the assignment of each job $J_i$, jobs up to a total processing volume of $\beta p_i$ may be migrated, for some constant $\beta$." For e= 1.75.at most 2.5/7migr," For $\beta=4/3$, they present a 1.5-competitive algorithm." ations areused. Department of albcrsüinctormnaczic.," They also show a $(1+\epsilon)$ -competitive algorithm, for any $\epsilon >0$, where $\beta$ depends exponentially on $1/\epsilon$." hu Computer bcrlin.ccScience.— Humboldt-Un, The algorithms are robust in that the stated competitive ratios hold after each job assignment. iversitit zuBerlin. Unterden Linden 6. 10099 Be," However in this framework, over time, $\Omega(n)$ migrations may be performed and jobs of total processing volume $\beta \sum_{i=1}^n p_i$ may be moved." rl, Englert et al. in. Department of ComputerScience. — Humboldt-Universitit zu Berlin., \cite{EOW} study online makespan minimization if analgorithm is given a buffer that may be used to partially reorder the job sequence. Unter den Linden 6. 10099Berlin.,In each step an algorithm assigns onejob from the buffer to the machines. lt is now well understood that the accretion disces in lowmass Xταν binarics (LAINBs) are strongly iracliated by he central X.ravs. and that this has a decisive ellect on heir thermal stability (van Paraclijs. 1996: Wing. νου διος. 1996).,"It is now well understood that the accretion discs in low--mass X–ray binaries (LMXBs) are strongly irradiated by the central X–rays, and that this has a decisive effect on their thermal stability (van Paradijs, 1996; King, Kolb Burderi, 1996)." Irraciation stabilizes LAINB clises compared with the otherwise similar ones in cataclysmic variables (CVs) bv removing their hydrogen ionization zones., Irradiation stabilizes LMXB discs compared with the otherwise similar ones in cataclysmic variables (CVs) by removing their hydrogen ionization zones. In CVs this instability causes cwarl nova outbursts. and in LAINBs it) produces. transient outbursts rather than »ersistent aceretion.," In CVs this instability causes dwarf nova outbursts, and in LMXBs it produces transient outbursts rather than persistent accretion." “Lhe irradiation cllect appears to. be weaker if the accretor is a black hole rather than a neutron star. possibly because of the lack of a hard surface (Nine. lxolb Szuszkiewiez. 1997).," The irradiation effect appears to be weaker if the accretor is a black hole rather than a neutron star, possibly because of the lack of a hard surface (King, Kolb Szuszkiewicz, 1997)." The result is that neutron LAINBs with short (~ hours) orbital periods tend to be persistent. while similar blackhole binaries are largely transient.," The result is that neutron--star LMXBs with short $\sim$ hours) orbital periods tend to be persistent, while similar black–hole binaries are largely transient." Both types of LAINBs must. be transient at sullicienthy long orbital periods. since a long period implies a larec clisc. so that a large N.ray luminosity would be needed to keep the dise edge ionized and thus suppress outbursts.," Both types of LMXBs must be transient at sufficiently long orbital periods, since a long period implies a large disc, so that a large X–ray luminosity would be needed to keep the disc edge ionized and thus suppress outbursts." We can write this stability requirement as where ALAS is the minimum: central accretion rate required to keep the disc stable. 2 is the outer cise radius. and 2 is the orbital period. and we have used Ixepler's law.," We can write this stability requirement as where $\dot M_{\rm crit}^{\rm irr}$ is the minimum central accretion rate required to keep the disc stable, $R_{\rm d}$ is the outer disc radius, and $P$ is the orbital period, and we have used Kepler's law." Thus for Large. {0. ApeSa WILL rise above any Likely steady accretion rate. making longperiod svstems transient.," Thus for large $P$, $\dot M_{\rm crit}^{\rm irr}$ will rise above any likely steady accretion rate, making long–period systems transient." This simple prediction (Ning. Frank. Ixolb Ritter. 1997) seems to be borne out by the available evidence.," This simple prediction (King, Frank, Kolb Ritter, 1997) seems to be borne out by the available evidence." The precise coefficient in (1)) depends on uncertainties in the vertical disc structure (see the discussion in Dubus. Lasota. ]lameury Charles. 1999).," The precise coefficient in \ref{crit}) ) depends on uncertainties in the vertical disc structure (see the discussion in Dubus, Lasota, Hameury Charles, 1999)." Here 1 adopt the form derived by Wine. Kolb Szuszkiewicz (1997).," Here I adopt the form derived by King, Kolb Szuszkiewicz (1997)." They argued that for a steady blackhole aceretor. the central irracliating source is likely to be the inner disc rather than a solid spherical surface. as [or a steady neutronstar accretor. (," They argued that for a steady black–hole accretor, the central irradiating source is likely to be the inner disc rather than a solid spherical surface, as for a steady neutron–star accretor. (" Note tha during an outburst of a/raensien! blackhole svstem such a spherical source may. be present. as the central aceretor may develop a corona.),"Note that during an outburst of a black–hole system such a spherical source may be present, as the central accretor may develop a corona.)" For a small source at the centre of the disc and Iving in its plane. the irradiation temperature Tui(22?) is given by (Fukuc. 1992).," For a small source at the centre of the disc and lying in its plane, the irradiation temperature $T_{\rm irr}(R)$ is given by (Fukue, 1992)." Here 5 is the ellicicney of rest.mass energy conversion into X.ray heating. 7 is the X.rav albedo. and (10 is the local disc scale. height.," Here $\eta$ is the efficiency of rest–mass energy conversion into X–ray heating, $\beta$ is the X–ray albedo, and $H(R)$ is the local disc scale height." Lhe minimum accretion rate required to keep the disc in the high state is eiven by setting Zi4(HI)=Tg. where is Py is the hydrogen ionization temperature.," The minimum accretion rate required to keep the disc in the high state is given by setting $T_{\rm irr}(R) = T_H$, where is $T_H$ is the hydrogen ionization temperature." Since Z always decreases with 0. the global minimum value A5 is given by conditions at the outer edge Ze of the disc.," Since $T$ always decreases with $R$, the global minimum value $\dot M_{\rm crit}^{\rm irr}$ is given by conditions at the outer edge $R_{\rm d}$ of the disc." For the parametrization adopted by Kine. Ixolb Szuszkiewiez (1997). and η= 0.2. this leads lo where ον is the disc filling fraction f£. (the ratio of Ly to the aceretor’s Roche lobe) in units of 0.7: ma.mo are the accretor and companion star mass in M.: and Equation (3)) is the same as eqn (12) of Wing. Ixolb Szuszkiewicz (1997) apart [rom the factors ος. there taken as unity.," For the parametrization adopted by King, Kolb Szuszkiewicz (1997), and $\eta = 0.2$ , this leads to where $f_{0.7}$ is the disc filling fraction $f$ (the ratio of $R_{\rm d}$ to the accretor's Roche lobe) in units of 0.7; $m_1, m_2$ are the accretor and companion star mass in $\msun$; and Equation \ref{crit2}) ) is the same as eqn (12) of King, Kolb Szuszkiewicz (1997) apart from the factors $f_{0.7}^2g$, there taken as unity." All of the uncertainties over disc thickness. warping. albedo ete are Iumped into the quantity g.," All of the uncertainties over disc thickness, warping, albedo etc are lumped into the quantity $g$." With gxforzl. equation (3)) appears to be largely successful in predicting that svstems with reasonably massive (5 TAL.) black holes and mainsequence companions should be transient.," With $g \simeq f_{0.7} \simeq 1$, equation \ref{crit2}) ) appears to be largely successful in predicting that systems with reasonably massive $5 - 7\msun$ ) black holes and main–sequence companions should be transient." By contrast. neutron star systems with main companions should be persistent. as the index of the ratio {ΗΕ in (2)) is unity. implyingmore elficient disc irradiation. (," By contrast, neutron star systems with main--sequence companions should be persistent, as the index of the ratio $H/R$ in \ref{eq3}) ) is unity, implyingmore efficient disc irradiation. (" equation (3)) also implies that lower black hole systems might be persistent.),Equation \ref{crit2}) ) also implies that lower--mass black hole systems might be persistent.) These results, These results "Introducing the central convergence. «,. a parameter that determinate the lensing properties of the Einasto profile. detined by: and use 1t to write o(1) in terms of &: For Einasto index with values a=I and w= with # integer. the last equation can be written as: The lens equation for the Einasto profile is then: which can be simplified to: for Einasto index with values a=I and a= with 7 integer.","Introducing the central convergence, $\kappa_{c}$, a parameter that determinate the lensing properties of the Einasto profile, defined by: and use it to write $\alpha\left(x\right)$ in terms of $\kappa_{c}$: For Einasto index with values $\alpha=\frac{1}{n}$ and $\alpha=\frac{2}{n}$ with $n$ integer, the last equation can be written as: The lens equation for the Einasto profile is then: which can be simplified to: for Einasto index with values $\alpha=\frac{1}{n}$ and $\alpha=\frac{2}{n}$ with $n$ integer." For a spherically symmetric lens being capable of forming multiple images of the source a sufficient condition is κο>| (?).., For a spherically symmetric lens being capable of forming multiple images of the source a sufficient condition is $\kappa_{c}>1$ \citep{1992grle.book.....S}. In the case x.€1 only one image of the source is formed., In the case $\kappa_{c}\leq1$ only one image of the source is formed. " In addition to the condition αι.>1 multiples images are produced only if|v|0."," In addition to the condition $\kappa_{c}>1$ multiples images are produced only if $\mid y\mid\leq y_{crit}$ \citep{2002ApJ...566..652L}, where $y_{crit}$ is the the maximum value of $y$ when $x<0$ or the minimum for $x>0$." " For singular profiles such as the NFW profile. the central convergence always is divergent. hence the condition 4,>| is always met. this implies that the NFW profile is capable of forming multiple images for any mass."," For singular profiles such as the NFW profile, the central convergence always is divergent, hence the condition $\kappa_{c}>1$ is always met, this implies that the NFW profile is capable of forming multiple images for any mass." Nonsingular profiles such as the Einasto profile are not capable of forming multiple images for any mass., Nonsingular profiles such as the Einasto profile are not capable of forming multiple images for any mass. Instead. the condition κ.>| sets a threshold for the lens mass required to form multiple images.," Instead, the condition $\kappa_{c}>1$ sets a threshold for the lens mass required to form multiple images." The deflection potential iCX) for spherically symmetric lens is given by: We see from equation (45)) that can find the lensing potential simply integrating the deflection angle:, The deflection potential $\psi\left(x\right)$ for spherically symmetric lens is given by: We see from equation \ref{eq:deflection_angle_potential}) ) that can find the lensing potential simply integrating the deflection angle: inversions iufered for many bot Jupiters (Hubenyetal.2003:Fortuey.2008:Spiegel2009:Zahuleetal.Ixuutsonet 2010).. the implication of a super-solar carbou-to-oxygeu alio luat leas one hot Jupiter (Macdhusudliaueal.2011).. the possible influeuce of magnetic drag on the atinospjeric Circulation (Pernaetal.2010a).. and a peculiar planet where cawu seems to be nuc1 hotter t]an noon (Crosslieldοἱal.2010).,"inversions inferred for many hot Jupiters \citep{Hubeny2003,Fortney2008,Spiegel2009,Zahnle2009,Knutson2010}, the implication of a super-solar carbon-to-oxygen ratio in at least one hot Jupiter \citep{Madhu2011}, the possible influence of magnetic drag on the atmospheric circulation \citep{Perna2010a}, and a peculiar planet where dawn seems to be much hotter than noon \citep{Crossfield2010}." . Iithe midst of a growing collection of oservatLous. some with unexpected or surprising resiIts. is tie continuing development of atinospleric moclels rviug to interoret and understand the 11easuleljenits.," In the midst of a growing collection of observations, some with unexpected or surprising results, is the continuing development of atmospheric models trying to interpret and understand the measurements." One set of atmospheric inodels are uuimerica oues that simulate the global circulatio1 patterns oncOse-in gas giants., One set of atmospheric models are numerical ones that simulate the global circulation patterns on close-in gas giants. With masses aud adii coiiparable to Jupiter. but subject to incident stellar [Iuxes 10.000 times stronger tlan what Jupiter 'eceives [rom tlie Sun. aud expected to be tidally locked into syuchronous orbits. hot Jupiers exls in an atiuospheric regime ulike anythinghi[un in our solar system. aud models of thei ratiospheric circulaοι are expanding iuto uncha‘tect territory.," With masses and radii comparable to Jupiter, but subject to incident stellar fluxes 10,000 times stronger than what Jupiter receives from the Sun, and expected to be tidally locked into synchronous orbits, hot Jupiters exist in an atmospheric regime unlike anything in our solar system, and models of their atmospheric circulation are expanding into uncharted territory." Iu order to try to understaud how atinosgheres work ii this new regime. the jodels that have been developed so Lar represent a ratee of comjxlexities. variois approaches. aud the use of difTerent sets of assuiptious.," In order to try to understand how atmospheres work in this new regime, the models that have been developed so far represent a range of complexities, various approaches, and the use of different sets of assumptions." Some of tlie simpest models solve the shaow water or ecquivalei barotropic equations ancl use various schenes to include the efTect of raciative heatiug (Choetal.2003.2008:Laughlin 2007).," Some of the simplest models solve the shallow water or equivalent barotropic equations and use various schemes to include the effect of radiative heating \citep{Cho2003,Cho2008,Langton2007}." . Others solve the primitive equatios of meeorology. either using a Newtonian relaxation sclele fo ‘the radiative forcing (Showman&Cuillot2002:CooyerShowman2005:Showmanet:il.2005Menou&Rauscher2000:RausererMNenou 2010).. a dual-band raciative transfer scherie (Heοetal.2011.similartotheouewepreset|here).. or more complex non-gray radiative tralsfer (Shownanetal.2009).," Others solve the primitive equations of meteorology, either using a Newtonian relaxation scheme for the radiative forcing \citep{Showman2002,Cooper2005,Showman2008,MR09,RM10}, a dual-band radiative transfer scheme \citep[][similar to the one we present here]{Heng2011}, or more complex non-gray radiative transfer \citep{Showman2009}." . Finally. the‘fe aeaso models that solve the full set of f[Iuid equations. using cdial-band [lus-limitecd diffusiou for the radiative transfer Liu2008:Dobbs-Dixoietal.201 Q).," Finally, there are also models that solve the full set of fluid equations, using dual-band flux-limited diffusion for the radiative transfer \citep{DobbsDixon2008,DobbsDixon2010}." ". Here we present an ipdatecl versiou of our previous general circulation mocel that now ineπο a ""double-gray"" radiative transfer scheme."," Here we present an updated version of our previous general circulation model that now includes a “double-gray"" radiative transfer scheme." Fuxes throughout the atinospliere are separaed into optical and iufrared coimyoneuts. each with its own absorption coefficient. which is coustau for the optical baud aud. can scale as a powerlaw with pressure for the infrared baud.," Fluxes throughout the atmosphere are separated into optical and infrared components, each with its own absorption coefficient, which is constant for the optical band and can scale as a powerlaw with pressure for the infrared band." We use salleard wo-stream radiative transfer eqlations to sove for the vertical fIuxes aud caleulate heati1 rates rom those., We use standard two-stream radiative transfer equations to solve for the vertical fluxes and calculate heating rates from those. In addition to prodicine self-coisistent radiative fluxes ald heating rates. itclicline he observable infrared. flux. eiue'eiug from tle top bouncary. this new code has the advalage of naintaitine only a moderate level of complexity.," In addition to producing self-consistent radiative fluxes and heating rates, including the observable infrared flux emerging from the top boundary, this new code has the advantage of maintaining only a moderate level of complexity." This facilitates comj»arison between sinuulated 'esults aid analytic profiles (Cuillot2010.seealsoHausen2008) all inakes it easier to clearM7 ideutify ie. effects due to changes in opacity., This facilitates comparison between simulated results and analytic profiles \citep[][see also Hansen 2008]{Guillot2010} and makes it easier to clearly identify the effects due to changes in opacity. Our jew code is described ii detail in Section 2.., Our new code is described in detail in Section \ref{sec:code}. " We demonstrate tie funetionality of our «οςe ""€ preseting a model of a generic hot Jupiter (Section 3)) aud we investigate Issues related tle atinospliere's behavior at deep p'essures (Section 3.1)).", We demonstrate the functionality of our code by presenting a model of a generic hot Jupiter (Section \ref{sec:models}) ) and we investigate issues related the atmosphere's behavior at deep pressures (Section \ref{sec:deep}) ). We then studs the effect of magnetic drag OL alinosj»herie circulation by applying a simplified drag scheme to our inodel. with drag strenetl ranging f'om weak to strong (Section L)).," We then study the effect of magnetic drag on atmospheric circulation by applying a simplified drag scheme to our model, with drag strengths ranging from weak to strong (Section \ref{sec:drag}) )." lu Section 5 we stummarize our results., In Section \ref{sec:conc} we summarize our results. table.,table. On December 14. there is insufficient low frequency. coverage {ο pul any constraints on component CI that had expanded so as to be optically thin far below 1.4 Gz and was apparently very weak at the lowest observed frequencies.," On December 14, there is insufficient low frequency coverage to put any constraints on component C1 that had expanded so as to be optically thin far below 1.4 GHz and was apparently very weak at the lowest observed frequencies." Figure 3 has four data points aud is fit with six parameters arising from the parametric form (defined in equation 3) for the SSA spectra of the components CL and C2., Figure 3 has four data points and is fit with six parameters arising from the parametric form (defined in equation 3) for the SSA spectra of the components C1 and C2. This is reduced to four free parameters by assuming that a is unchanged from December 6 (see the discussion above)., This is reduced to four free parameters by assuming that $\alpha$ is unchanged from December 6 (see the discussion above). In Figure 4. there are on6 data points that are fit bv the 6 [ree parameters associated with SSA spectral fits to the components C2 and C3.," In Figure 4, there are 6 data points that are fit by the 6 free parameters associated with SSA spectral fits to the components C2 and C3." The fits have the same values of à as they had on December 6., The fits have the same values of $\alpha$ as they had on December 6. Figures 1 (o 4 show the time evolution of the three components based on (he fits at the three epochs., Figures 1 to 4 show the time evolution of the three components based on the fits at the three epochs. Ouly component. C2. is adequately sampled so as to be resolved in all three epochs.," Only component, C2, is adequately sampled so as to be resolved in all three epochs." Figures 1 to 4 do not tell us very much about the evolution of component C1 since the spectral peak has evolved below the data sampling range by the second epoch., Figures 1 to 4 do not tell us very much about the evolution of component C1 since the spectral peak has evolved below the data sampling range by the second epoch. It is clear from Figures 1 to 4 that component C2 is not adiabatically expanding., It is clear from Figures 1 to 4 that component C2 is not adiabatically expanding. If that were true the spectral shape would merely migrate toward lower Irequency. wilh some decrease in the peak Πας (Aloffet1975)., If that were true the spectral shape would merely migrate toward lower frequency with some decrease in the peak flux \citep{mof75}. . To the contrary. (he peak flix density increased dramatically from December 6. 1993 to December 11. 1993.," To the contrary, the peak flux density increased dramatically from December 6, 1993 to December 11, 1993." This indicates that the plasmoid is evolving to a state of higher radiative efficiency., This indicates that the plasmoid is evolving to a state of higher radiative efficiency. The evolution between December 11 and December 14 is closer to adiabatic expansion as (he peak flux is approximately constant., The evolution between December 11 and December 14 is closer to adiabatic expansion as the peak flux is approximately constant. Thus. the rate al which the radiative elliciency is increasing slowed clown dramatically after December 11.," Thus, the rate at which the radiative efficiency is increasing slowed down dramatically after December 11." The hiehest radiative efficiency is in (he minimum energy configuration., The highest radiative efficiency is in the minimum energy configuration. So. Cae plasmoicl was [ar from the minimum enerev configuration on December 6. but appears to be evolving towards nuninnun energv alter December 11.," So, the plasmoid was far from the minimum energy configuration on December 6, but appears to be evolving towards minimum energy after December 11." By contrast. Figure 2 and 4 indicate that component C3 is shifüng in frequency ancl (he spectral peak is weakening after December 6.," By contrast, Figure 2 and 4 indicate that component C3 is shifting in frequency and the spectral peak is weakening after December 6." This tvpe of behavior is similar (o that of a component evolving very close to adiabatic expansion 1975)., This type of behavior is similar to that of a component evolving very close to adiabatic expansion \citep{mof75}. . Note that C3 is à much weaker component than Cl and C2., Note that C3 is a much weaker component than C1 and C2. The constant à. assumption is required to formally close (he set of equations as discussed above., The constant $\alpha$ assumption is required to formally close the set of equations as discussed above. In this subsection. the implications of this assumption in terms of spectral ageing ancl the generality of the model is discussed.," In this subsection, the implications of this assumption in terms of spectral ageing and the generality of the model is discussed." Note that the mathematical constraint of “constant a” translates physically to the notion that after December 6. the spectral ageing of the components is not dramatic.," Note that the mathematical constraint of ""constant $\alpha$ "" translates physically to the notion that after December 6, the spectral ageing of the components is not dramatic." This does not mean (hat there was not pronounced spectral ageing before December 6 aud modest spectral ageing alter December 6., This does not mean that there was not pronounced spectral ageing before December 6 and modest spectral ageing after December 6. There really is no direct information on the time history of the ejecta before December 6., There really is no direct information on the time history of the ejecta before December 6. For example. the dillerent spectral indices of the three," For example, the different spectral indices of the three" to the starburst.,to the starburst. Moreover. estimates of the host galaxy masses suggest that the growth of the black hole lags the growth of the spheroid (Borys et al.," Moreover, estimates of the host galaxy masses suggest that the growth of the black hole lags the growth of the spheroid (Borys et al." 2005: Alexander et al., 2005; Alexander et al. 2008: see also Coppin et al., 2008; see also Coppin et al. 2009)., 2009). While this may be the case for SMOs. analysis of massive galaxies selected on other criteria find evidence to the contrary. suggesting that more than one scenario is possible for the ormation of a massive galaxy and its SMBH.," While this may be the case for SMGs, analysis of massive galaxies selected on other criteria find evidence to the contrary, suggesting that more than one scenario is possible for the formation of a massive galaxy and its SMBH." For example. studies of powerful radio sources (McLure et al.," For example, studies of powerful radio sources (McLure et al." 2006) and luminous QSOs (Peng et al., 2006) and luminous QSOs (Peng et al. 2006) suggest that the black-hole mass to bulge uminosity ratio increases towards high redshifts thus indicating hat the black hole reaches its critical mass before the galaxy bulge is fully formed., 2006) suggest that the black-hole mass to bulge luminosity ratio increases towards high redshifts thus indicating that the black hole reaches its critical mass before the galaxy bulge is fully formed. The mid-infrared colours of our SMGs also argue against the oresenee of a powerful AGN in these objects unless they are very ughly obscured., The mid-infrared colours of our SMGs also argue against the presence of a powerful AGN in these objects unless they are very highly obscured. They are thus either intrinsically different objects o the QSO or they are caught at a different time in their evolution., They are thus either intrinsically different objects to the QSO or they are caught at a different time in their evolution. Page et al. (, Page et al. ( 2010. in prep.),"2010, in prep.)" argue that the X-ray absorption in he QSOs has its origin in an ionized absorber associated with a powerful wind capable of terminating the star formation., argue that the X-ray absorption in the QSOs has its origin in an ionized absorber associated with a powerful wind capable of terminating the star formation. Such eedback is a popular ingredient of models since it leads naturally to he relationship between SMBH mass and spheroid mass discussed above (e.g. Fabian 1999)., Such feedback is a popular ingredient of models since it leads naturally to the relationship between SMBH mass and spheroid mass discussed above (e.g. Fabian 1999). If the SMGs in the same field evolve to orm a cluster ellipticals then they would presumably go through a similar evolutionaryof sequence to the QSO but are caught at an earlier stage of their life cycle at |> 3) radio galaxies (HzRGs) concerns very bright SMGs in their fields., One difference worthy of note between the findings of this paper and those for high-redshift (typically $z>3$ ) radio galaxies (HzRGs) concerns very bright SMGs in their fields. Two of the seven HzRG fields imaged with SCUBA contain SMOs with Sas)2920 mJy (Stevens et al., Two of the seven HzRG fields imaged with SCUBA contain SMGs with $S_{850}>20$ mJy (Stevens et al. 2003) whereas the brightes object found around the QSOs has Sasso.~10 mJy., 2003) whereas the brightest object found around the QSOs has $S_{850}\sim10$ mJy. Although the samples are too small to give a statistically significant resul it appears that the SMGs detected around the lower redshift. less powerful. radio-quiet AGN have lower 5555.," Although the samples are too small to give a statistically significant result it appears that the SMGs detected around the lower redshift, less powerful, radio-quiet AGN have lower $S_{850}$." A direct comparison is not informative because the sources were extracted with differen signal-to-noise criteria and by different methods but comparing flux densities significantly above the catalogue cut-offs yields 5 SMGs with Sxso=6 mJy in the 7 HzRG fields while only 2 are detected around the 5 QSOs., A direct comparison is not informative because the sources were extracted with different signal-to-noise criteria and by different methods but comparing flux densities significantly above the catalogue cut-offs yields $8$ SMGs with $S_{850}\geq6$ mJy in the 7 HzRG fields while only $2$ are detected around the 5 QSOs. Given the effectively flat relationship between Sx-9 anc redshift for |<210 this difference in flux density leads to a proportional difference in star-formation rates (all. other things being equal)., Given the effectively flat relationship between $S_{850}$ and redshift for $12.5 (Archibald et al.," For example, in the case of HzRGs it was found that the detection rate increased dramatically at $z>2.5$ (Archibald et al." 2001: Reuland et al., 2001; Reuland et al. 2004) which is significantly higher than the average redshift of our QSO sample., 2004) which is significantly higher than the average redshift of our QSO sample. Another possibility is that the radio properties of the central AGN are in some way linked to environmental density (e.g. Kauffmann. Heckman Best 2008).," Another possibility is that the radio properties of the central AGN are in some way linked to environmental density (e.g. Kauffmann, Heckman Best 2008)." Indeed. recent work by Falder et al. (," Indeed, recent work by Falder et al. (" 2010) finds evidence for larger over-densities of galaxies around radio-loud objects (based on work carried out at 3.6 fam).,2010) finds evidence for larger over-densities of galaxies around radio-loud objects (based on work carried out at 3.6 $\mu$ m). Perhaps radio synchrotron luminosity is enhanced in regions where the inter-galactic medium is more dense., Perhaps radio synchrotron luminosity is enhanced in regions where the inter-galactic medium is more dense. An obvious next step will be to conduct a statistically meaningful survey of tields around AGN over the full range of redshifts in order to track star-formation activity as a function of cosmic time., An obvious next step will be to conduct a statistically meaningful survey of fields around AGN over the full range of redshifts in order to track star-formation activity as a function of cosmic time. The next generation bolometer camera on the JCMT (SCUBA-2) and SPIRE/PACS on-board the are instruments with good enough sensitivity to make such a campaign practical., The next generation bolometer camera on the JCMT (SCUBA-2) and SPIRE/PACS on-board the are instruments with good enough sensitivity to make such a campaign practical. It would also allow a bigger area to be mapped around each AGN. better matching the size of proto-cluster regions predicted by numerical simulations.," It would also allow a bigger area to be mapped around each AGN, better matching the size of proto-cluster regions predicted by numerical simulations." We thank Iun Smail for extensive comments on the draft manuscrip: and Mark Thompson for useful discussions., We thank Ian Smail for extensive comments on the draft manuscript and Mark Thompson for useful discussions. The James Clerk Maxwell Telescope is operated by The Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the United Kingdom. the Netherlands Organisation for Scientific Research. and the National Research Council of Canada.," The James Clerk Maxwell Telescope is operated by The Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the United Kingdom, the Netherlands Organisation for Scientific Research, and the National Research Council of Canada." JCMT data were taken under project IDs MOSAU46. MO3BU32 and MO4BUI4.," JCMT data were taken under project IDs M03AU46, M03BU32 and M04BU14." This work is based [in part] on observations made with the Spitzer Space Telescope. which is operated by the Je Propulsion Laboratory. California Institute of Technology under a contract with NASA.," This work is based [in part] on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA." Support for this work was provided by NASA through an award issued by JPL/Caltech., Support for this work was provided by NASA through an award issued by JPL/Caltech. J.A.S.. M.J.P. and Εις. acknowledge support from the Royal Society.," J.A.S., M.J.P. and F.J.C. acknowledge support from the Royal Society." Ε.Ο. acknowledges further support from the Spanish Ministerio de Educaciónn y Ciencia under project ESP2006-13608., F.J.C. acknowledges further support from the Spanish Ministerio de Educaciónn y Ciencia under project ESP2006-13608. "of spectral shape evolution with the rotational phase; in particular, no variation larger than the 1c error (kóT'~0.02 keV) was found in the blackbody temperatures at different phases.","of spectral shape evolution with the rotational phase; in particular, no variation larger than the $\sigma$ error $k\delta T\simeq0.02$ keV) was found in the blackbody temperatures at different phases." " To obtain flux measurements over the outburst, the Swift//XRT data were fit in the same way as the oones, simultaneously and with all parameters left free to vary, except for the absorption column density, that this time was fixed at the value measured withXMM-Newton."," To obtain flux measurements over the outburst, the /XRT data were fit in the same way as the ones, simultaneously and with all parameters left free to vary, except for the absorption column density, that this time was fixed at the value measured with." . This resulted in an acceptable fit (v2=1.01 for 602 dof) with spectral parameters similar to those reported in Table 2 (see Fig. 3))., This resulted in an acceptable fit $\chi^2_\nu=1.01$ for 602 dof) with spectral parameters similar to those reported in Table \ref{fits} (see Fig. \ref{history}) ). We plot the resulting long-term light curve in the top panel of Fig. 3.., We plot the resulting long-term light curve in the top panel of Fig. \ref{history}. " Although the available data do not allow us to perform an accurate modelling of the decay shape, because of the relatively high uncertainties on the fluxes and moderate time-span, we observe that similarly good fits can be obtained with either an exponential function or a broken power-law model."," Although the available data do not allow us to perform an accurate modelling of the decay shape, because of the relatively high uncertainties on the fluxes and moderate time-span, we observe that similarly good fits can be obtained with either an exponential function or a broken power-law model." " For an exponential function of the form F(t)= Aexp(—t/7), the fitting values (v2=0.84 for 23 dof) are A=(3.92+0.05)107? aand 7=(108+9) Adopting a broken power law for 22 dof;), the break occurs at (20+3) d, when the index changes from a;=—0.01+0.02 to ag=—0.54+0.09; the flux at the break time is (3.70.2)x10”1s~.."," For an exponential function of the form $F(t) = A \exp(-t/\tau)$ , the best-fitting values $\chi^2_\nu=0.84$ for 23 dof) are $A=(3.92\pm0.05)\times10^{-12}$ and $\tau=(108\pm9)$ Adopting a broken power law $\chi^2_\nu=0.73$ for 22 dof;), the break occurs at $(20\pm3)$ d, when the index changes from $\alpha_1=-0.01\pm0.02$ to $\alpha_2=-0.54\pm0.09$; the flux at the break time is $(3.7\pm0.2)\times10^{-12}$." In both cases we assumed as t=0 the time of the Swift//BAT trigger., In both cases we assumed as $t=0$ the time of the /BAT trigger. " From the broken power-law fit in particular, it is apparent that the source flux is consistent with a constant value for the first ~20 days."," From the broken power-law fit in particular, it is apparent that the source flux is consistent with a constant value for the first $\sim$$20$ days." The two models considered are plotted inFig. 3.., The two models considered are plotted inFig. \ref{history}. . Type Ia Superuovae (SNe) plav au important role iu Mocern astrophysics thanX o their ereat power in extragalactic distaice. determidations. which permitted he discovery of the cosnüc accoleration (27)...,"Type Ia Supernovae (SNe) play an important role in modern astrophysics thanks to their great power in extragalactic distance determinations, which permitted the discovery of the cosmic acceleration \citep{riess98, perl99}. ." Line-ofsieht extinction lias tobetasen iuto account to correct the distance estimate ο the SN lios ealaxy., Line-of-sight extinction has to be taken into account to correct the distance estimate of the SN host galaxy. Several enipirical nethods that make use of SN colors have bee1 developed or this purpose arc very differeit extinction laws from the Galactic law need to be invoked to reduce the dispersion iut1e calibration o “SNe Ta iu cosinological stidies (2??)..," Several empirical methods that make use of SN colors have been developed for this purpose and very different extinction laws from the Galactic law need to be invoked to reduce the dispersion in the calibration of SNe Ia in cosmological studies \citep{hicken09, folatelli10, wang09b}." Theoretical ancl observationa studies have shown evidence of an off-center ceflaeration as the mitial burning process iu SNe Ta (7777)..," Theoretical and observational studies have shown evidence of an off-center deflagration as the initial burning process in SNe Ia \citep{kasen09, maeda10a, maeda10c, maeda11}." Toslhow a relation etween the volocitv eradieut of the Si TT lines oserved near maxi heli and thenebular veocitv «hiTs measured from the [FeTI] A7155 and [NiTI] AT378 lines. which are t1ouehit trace the region where the initial deflagration occurs.," \citet{maeda10c} show a relation between the velocity gradient of the Si II lines observed near maximum light and thenebular velocity shifts measured from the $[{\rm Fe~II}]$ $\lambda 7155$ and $[{\rm Ni~II}]$ $\lambda 7378$ lines, which are thought to trace the region where the initial deflagration occurs." The off-center explosion mode of? expais the large diversi in velocity exadieuts near maxima liebt descrid in ?.. who classiBes as either hieh velocity eradient ΗΝ9) or low velocity eradicut (LV) SNe de»udiue on the veloci eracdieut o the SiLLA6355Γ line5 T. T7.," The off-center explosion model of \citet{maeda10c} explains the large diversity in velocity gradients near maximum light described in \citet{benetti05}, who classifies as either high velocity gradient (HVG) or low velocity gradient (LVG) SNe depending on the velocity gradient of the $Si~II~\lambda 6355$ line. \citet{kasen09}, \citet{maeda11}," aud 7? demonstrate both theoretically aud servatioally that the (BV) colors aud. Iuuünositv depend ou the asviunietry of the explosion aud the viewing iele., and \citet{foley11} demonstrate both theoretically and observationally that the $(B-V)$ colors and luminosity depend on the asymmetry of the explosion and the viewing angle. Here we present additional evidence that favors this new paraieni of asvnunetrie explosious in the form of strong correlations of (V L(VRyo and (By colors a very carly phases with the nebular velocity shifts at late epochs.," Here we present additional evidence that favors this new paradigm of asymmetric explosions in the form of strong correlations of $(V-I)$, $(V-R)$, and $(U-B)$ colors at very early phases with the nebular velocity shifts at late epochs." Tjese. correlations could be useful in improving SN color calibrations in future cosinological studies., These correlations could be useful in improving SN color calibrations in future cosmological studies. " Our sample cousists of 12 nearby SNe with a well-sampled helt curve. photometry from at least six davs before maxi lieht aud late-time spectroscopic observations. Le. at least 150 davs after πιαατα, to measure nebular velocity shits."," Our sample consists of 12 nearby SNe with a well-sampled light curve, photometry from at least six days before maximum light and late-time spectroscopic observations, i.e. at least 150 days after maximum, to measure nebular velocity shifts." In Table 1.. we sumunarize the decline rate (Am) and liw-ofsielt reddening values of our Type Ia SNe sample.," In Table \ref{Sample_tab}, we summarize the decline rate $\Delta m^{B}_{15}$ ) and line-of-sight reddening values of our Type Ia SNe sample." " We estiLate the epoch of maxiumui light for cach tL⋅∖⋅ter. ""Aunt. and the SN colors at different epochs using fifth order ]»»Ivuonial interpolated lieht curves."," We estimated the epoch of maximum light for each filter, $\Delta m^{B}_{15}$, and the SN colors at different epochs using fifth order polynomial interpolated light curves." We used Ix-correctec photometryAC for SN 200leo and S-corrected photometry whenever available in the literature., We used K-corrected photometry for SN 2004eo and S-corrected photometry whenever available in the literature. Given hat we are interested im assessing the rolatious between tical colors iux nebular velocity shifts arouud maxiumuu ight. we estimated host calaxy reddening using the Lira relation (?).. which is a method independent of SN colors i anima.," Given that we are interested in assessing the relations between optical colors and nebular velocity shifts around maximum light, we estimated host galaxy reddening using the Lira relation \citep{phillips99}, , which is a method independent of SN colors at maximum." To estimate Ctalacic extinction. we used the uaps of ? ;uxl the extinction law (I= 3.1) of ?.. which Is also useL for host galaxy reddening.," To estimate Galactic extinction, we used the maps of \citet{schlegel98} and the extinction law $R_V = 3.1$ ) of \citet{cardelli89}, which is also used for host galaxy reddening." The reddening estimates are shown in Table and the corresponding reddenine-corrected lieht curves are shown in Figure 1.., The reddening estimates are shown in Table \ref{Sample_tab} and the corresponding reddening-corrected light curves are shown in Figure \ref{ColorsMax_fig}. . " We adopted the nebular velocity shifts (1,,4,) from ? audstudied their relation with SN colors at differcut epochs.", We adopted the nebular velocity shifts $V_{\rm neb}$ ) from \citet{maeda11} andstudied their relation with SN colors at different epochs. Finally. we investigate the effect of Ca II lines.which," Finally, we investigate the effect of Ca II lines,which" LID 106506 and LID 171488).,HD 106506 and HD 171488). Fig., Fig. 6 plots this differential rotation against stellar convective zone depth fromSiess.Dufour&Forestini 2000)., \ref{Fig_czddr} plots this differential rotation against stellar convective zone depth \citep*[determined from][]{SiessL:2000}. . As can be seen in Fig., As can be seen in Fig. 6 the level of dillerential rotation does appear to increase slightly with decreasing convection zones depth (with some scatter) until the convective zone depth reaches ~0.2 (early-C stars) and then a dramatic increase in the level of surface dillerential rotation occurs., \ref{Fig_czddr} the level of differential rotation does appear to increase slightly with decreasing convection zones depth (with some scatter) until the convective zone depth reaches $\sim$ 0.2 (early-G stars) and then a dramatic increase in the level of surface differential rotation occurs. Why this should be is still not understood. but it appears that a change occurs in the rotation of the convective zone at this depth.," Why this should be is still not understood, but it appears that a change occurs in the rotation of the convective zone at this depth." As suggested by Jellers&Donati(2008).. for stars with thinner convective zones. such as HD. 141043. we niv be seeing closer to the base of the convective zone and this could. explain the higher levels of dilferential rotation seen on these stars.," As suggested by \citet{JeffersSV:2008}, for stars with thinner convective zones, such as HD 141943, we may be seeing closer to the base of the convective zone and this could explain the higher levels of differential rotation seen on these stars." Results from Donatietal.(20035) have shown wt for earbv-I& stars the differential rotation measured from magnetic features is higher than that measured. fron brightness features., Results from \citet{DonatiJF:2003b} have shown that for early-K stars the differential rotation measured from magnetic features is higher than that measured from brightness features. They. attribute this to the brightness and magnetic features being anchored at dilferent depths in 1e stellar convective zone and the convective zone having a racially varying cillerential rotation (unlike the Sun)., They attribute this to the brightness and magnetic features being anchored at different depths in the stellar convective zone and the convective zone having a radially varying differential rotation (unlike the Sun). Jellors&Donati(2008) ancl Jeffersctal.(2010). found. that rere is virtually no change (within errors) in the dillerential rotation measured from. brightness ancl magnetic features or the carly-G star HD. 171488 although the errors in the dilferential rotation measurements are. for the most. part. much larger than the errors for the carly-ly stars.," \citet{JeffersSV:2008} and \citet{JeffersSV:2010} found that there is virtually no change (within errors) in the differential rotation measured from brightness and magnetic features for the early-G star HD 171488 although the errors in the differential rotation measurements are, for the most part, much larger than the errors for the early-K stars." Although weir Stokes V. dillerential rotation measurements are for the most part higher than those measured from Stokes I. 11D 106506 (Waiteetal.2010). also shows only a small increase in the cilferential rotation from magnetic features over that from brightness features. but again the dilference is within 1e errors of the measurements.," Although their Stokes V differential rotation measurements are for the most part higher than those measured from Stokes I. HD 106506 \citep{WaiteIA:2010} also shows only a small increase in the differential rotation from magnetic features over that from brightness features, but again the difference is within the errors of the measurements." 1n contrast to this our 2010. results for LID 141943 show a large cillerence between the dillerential. rotation measured. from the brightness features compared. to that nmieasured. from the magnetic features. with the magnetic dillerential rotation being significantlv higher than that from the brightness features.," In contrast to this our 2010 results for HD 141943 show a large difference between the differential rotation measured from the brightness features compared to that measured from the magnetic features, with the magnetic differential rotation being significantly higher than that from the brightness features." One possible reason for this difference could. be the dillerent. latitude: distributions of the brightness and magnetic. features on HD. 141943., One possible reason for this difference could be the different latitude distributions of the brightness and magnetic features on HD 141943. In 2010 the spot. features of LID 1421943. are concentrated. in a minor polar spot and some lower Latitude features. while the magnetic features are more evenly distributed over the entire hemisphere (see Fie.," In 2010 the spot features of HD 141943 are concentrated in a minor polar spot and some lower latitude features, while the magnetic features are more evenly distributed over the entire hemisphere (see Fig." 5 in Paper D., 5 in Paper I). Such a dillerence in distribution may possibly lead to biases in the determination of the dillerential rotation. as the cilferential rotation is determined. over a smaller (or larger) latitude range.," Such a difference in distribution may possibly lead to biases in the determination of the differential rotation, as the differential rotation is determined over a smaller (or larger) latitude range." Both LID 106506 and LID 171488 have larger polar spots and less low-latitucle spot features than HD. 121943., Both HD 106506 and HD 171488 have larger polar spots and less low-latitude spot features than HD 141943. Thus. the two stars with more dominant. polar spots would be expected to more allected. by any bias in the latitude distribution between brightness and magnetic features. but neither star shows any significant cüsparity in cdillerential rotation.," Thus, the two stars with more dominant polar spots would be expected to more affected by any bias in the latitude distribution between brightness and magnetic features, but neither star shows any significant disparity in differential rotation." The mvason Why HD. 141943 alone shows a cdisparitv in the iferential rotation measurements between brightness and magnetic features remains unknown., The reason why HD 141943 alone shows a disparity in the differential rotation measurements between brightness and magnetic features remains unknown. A larger sample size is required to determine if HD. 141943 is just a unique case., A larger sample size is required to determine if HD 141943 is just a unique case. Unlike the results from earlv-Ix. stars (Donatictal. the earlv-G. star HD. 171488," Unlike the results from early-K stars \citep{DonatiJF:2003b, JeffersSV:2007} the early-G star HD 171488" average over angles between a constaut external acceleration gj and internal radial acceleration YMOND-,average over angles between a constant external acceleration $\bf{g}_{\rm ext}$ and internal radial acceleration $g_{\rm MOND}$. The fiction pr) can have different shapes., The function $\mu(x)$ can have different shapes. We tried the originallyproposed form (Mileroni.1983) phe)=fVL|r? but accepted aud used for all our analvsis the function poe)—c/(1|c). which eives slightly better results.," We tried theoriginally proposed form \citep{Milgrom} $\mu(x)=x/\sqrt{1+x^2}$, but accepted and used for all our analysis the function $\mu(x)=x/(1+x)$, which gives slightly better results." The function a(r]) is limited by the observations presented in Figure 1., The function $\alpha(r)$ is limited by the observations presented in Figure 1. The velocity anisotropy (r7) is a free function. but there are constraints.," The velocity anisotropy $\beta(r)$ is a free function, but there are constraints." Asviuptoticallv // &oes to zero at large distances where gravitational effect of the ceutral ealaxy diminishes., Asymptotically $\beta$ goes to zero at large distances where gravitational effect of the central galaxy diminishes. Ideally the velocity anisotropy at πα. distances also should be declining., Ideally the velocity anisotropy at small distances also should be declining. There aredifferent arguneuts why this should be the case. (, There are different arguments why this should be the case. ( 1) The tangential velocities of few satellites of the Malkv. Way. for which the proper motions are measured. strougly reject radial orbits (Ixallivavaliletal.2006:Piateketal. 2007).,"1) The tangential velocities of few satellites of the Milky Way, for which the proper motions are measured, strongly reject radial orbits \citep{Kallivayalil2006, Piatek2007}." . There is no reason to believe that our Galaxy should be special in this respect. (, There is no reason to believe that our Galaxy should be special in this respect. ( 2) Experience with eravitational dynaiuical svstenis diceate that in dynanucallv relaxed svstenis joc0.,2) Experience with gravitational dynamical systems indicate that in dynamically relaxed systems $\beta \approx 0$. Nunerous siunulatiouns of cosmological models illustrate this: 3 is simall in the ceutral region and increases to 0.2(0.3 at the viral radius (Cuestaetal.2007)., Numerous simulations of cosmological models illustrate this: $\beta$ is small in the central region and increases to $0.2-0.3$ at the viral radius \citep{Cuesta2007}. .. Note that we should distinguish the velocity anisotropy aud the orbital eccentricity., Note that we should distinguish the velocity anisotropy and the orbital eccentricity. For centrally concentrated: objects. which we are dealiug with here. already: isotropic velocities imply typical peri-fapoceuter ratios of 1:l-1:5.," For centrally concentrated objects, which we are dealing with here, already isotropic velocities imply typical peri-/apocenter ratios of 1:4-1:5." Tf eccentricity is Luger. a significant fraction of satellites comes too close to the ceutral LO kpc region where the satellites axe destroved by tidal forces.," If eccentricity is larger, a significant fraction of satellites comes too close to the central $\sim 10$ kpc region where the satellites are destroyed by tidal forces." The term ga in eq.(9)) describes the effect of external gravitational field., The term $\bf g_{\rm ext}$ in \ref{eq:gmond}) ) describes the effect of external gravitational field. It is specific for MOND., It is specific for MOND. In Newtonian dvuamics a homogeneous external eravity does not affect relative motions inside the object., In Newtonian dynamics a homogeneous external gravity does not affect relative motions inside the object. Because the MOND eravity is jionlinear. the iuterual force is affected by the external field (note that this is not the tidal orce).," Because the MOND gravity is nonlinear, the internal force is affected by the external field (note that this is not the tidal force)." This external effect is quite complicated., This external effect is quite complicated. The maguitude of the external force is substantial or the motion of the satellites., The magnitude of the external force is substantial for the motion of the satellites. Famaeyctal. point out that in MOND Muuerous sources aud effects generate about equal uaguitude of ga.," \citet{Fam2007,Wu2007} point out that in MOND numerous sources and effects generate about equal magnitude of $g_{\rm ext}$ ." For example. 600 Xii/s motion," For example, 600 km/s motion" , The idea to detect transits of exoplanets in the Epoch Photometry (ESA1997). trigerred several stuclics hat checked. the feasibility of such an attempt.,The idea to detect transits of exoplanets in the Epoch Photometry \citep{1997yCat.1239....0E} trigerred several studies that checked the feasibility of such an attempt. HébrardLecavelierDesEtanes(2006) concluded that 1hotometrv did not look like an ellicient tool for ransi detection. without using any prior information.," \cite{2006A&A...445..341H} concluded that photometry did not look like an efficient tool for transit detection, without using any prior information." Indeed. some teams have made detections of the transits of LID 209458 (Robichon&Arcnou2000:Castel-anoetal.2000:Socderhjelm 1999). and of LD189733 (Bouchy.E.etal.2005).. a detection that Liébrarc&Lecave-ierDesEtanes(2006) confirmed.," Indeed, some teams have made detections of the transits of HD 209458 \citep[][]{2000A&A...355..295R, 2000ApJ...532L..51C, 1999IBVS.4816....1S}, , and of HD189733 \citep{2005A&A...444L..15B}, a detection that \cite{2006A&A...445..341H} confirmed." Those teams used. the oeviouslv. available knowledge of the orbital elements. of he exoplanets (especially the period and the transit phase). in order to phase the data of those stars.," Those teams used the previously available knowledge of the orbital elements of the exoplanets (especially the period and the transit phase), in order to phase the data of those stars." Using he large time span that had elapsed: since the observations (for example. about S30. orbital periods tween. observations ancl the observations that Castellanoet.al.(2000) used for Η 209455). the teams managed to drastically reduce the uncertainties of the known »riods.," Using the large time span that had elapsed since the observations (for example, about 830 orbital periods between observations and the observations that \cite{2000ApJ...532L..51C} used for HD 209458), the teams managed to drastically reduce the uncertainties of the known periods." The posterior detections of both transits. prove hat information about the transits does exist in the data. although it is obviously futile to try to detect the transits in the natyvve Box Least Squares (BLS) approach (xovaesetal. 2002)..," The posterior detections of both transits prove that information about the transits does exist in the data, although it is obviously futile to try to detect the transits in the naïvve Box Least Squares (BLS) approach \citep{2002A&A...391..369K}." Thus the posterior detections motivated: us to re-examine Epoch Photometry data and to look for a way to utilize this survey ancl sipilar low-cadence photometric surveys. to detect exoplanets.," Thus the posterior detections motivated us to re-examine Epoch Photometry data and to look for a way to utilize this survey and similar low-cadence photometric surveys, to detect exoplanets." The approach we propose here is to use the data to maximize the chances to detect transits during hypothetical follow-up campaigns. Lc. instead of attempting to detect a transit. we use the data to schedule follow-up observations that together with the old data set may enable its detection.," The approach we propose here is to use the data to maximize the chances to detect transits during hypothetical follow-up campaigns, i.e., instead of attempting to detect a transit, we use the data to schedule follow-up observations that together with the old data set may enable its detection." In order to maximize the probability of sampling a transit in those surveys. and in order to predict the best possible future observing times. we chose to use Bayesian inference methods.," In order to maximize the probability of sampling a transit in those surveys, and in order to predict the best possible future observing times, we chose to use Bayesian inference methods." Bavesian analysis is based on Baves theorem and. can be written as: where pCH5;|D. is the posterior. probability of the Ηνpothesis 4/;. given 1}the prior information. £. and the data. D.," Bayesian analysis is based on Bayes theorem and can be written as: where $p(H_i|D,I)$ is the posterior probability of the Hypothesis $H_i$, given the prior information, $I$, and the data, $D$." pODLU2) is the probability of obtainingthe data D. eiven that //; and / are true.," $p(D|H_i,I)$ is the probability of obtainingthe data $D$, given that $H_i$ and $I$ are true." ois also known as the likelihood function L(41;)., It is also known as the likelihood function $L(H_i)$ . " PDL)=SM,pliο1) is a normalizationfactor that ensures that ST,put;|D.1)= 1."," $p(D|I)=\sum_i p(H_i|I)p(D|H_i,I)$ is a normalizationfactor that ensures that $\sum_i p(H_i|D,I)=1$ ." Ht is usually, It is usually exact number varvius somewhat with the details of the simulation (the vertical domain. iu particular. was a lianiting factor i mauv of the earliest simulations).,"exact number varying somewhat with the details of the simulation (the vertical domain, in particular, was a limiting factor in many of the earliest simulations)." As Shietal. (2010)... Cressel(20410). and Davisetal.(2010). discuss. the generic “buttertly” pattern can be attributed to the vertical riug of azimuthal feld due to the combinect effects of dvuame action near the disk uudplane aud the Parker instability at higher elevation.," As \citet{2010ApJ...708.1716S}, , \citet{2010MNRAS.405...41G}, , and \citet{2010ApJ...713...52D} discuss, the generic “butterfly” pattern can be attributed to the vertical rising of azimuthal field due to the combined effects of dynamo action near the disk midplane and the Parker instability at higher elevation." Until now. however. such features have not been reported in elobal simulations.," Until now, however, such features have not been reported in global simulations." Iu analogy to the results of local simulations. our global disk: simulation produces civnamo evcles with oscillation requenucies that are ten to tweuty times lower than he local orbital frequencies for a large rauge of radii.," In analogy to the results of local simulations, our global disk simulation produces dynamo cycles with oscillation frequencies that are ten to twenty times lower than the local orbital frequencies for a large range of radii." Furthennuore. the radial extent of our siumulatiou captures he sharing of dvnaimo power at peak frequencies across relatively huge radial ranges.," Furthermore, the radial extent of our simulation captures the sharing of dynamo power at peak frequencies across relatively large radial ranges." As such. dynamo cvcles xovide a tantalizing source of variability at frequencies conrparable to astronomically observed low-frequency quasi-periodic oscillations (LFQPOs) in multiple ealactic lack hole binary caucidates.," As such, dynamo cycles provide a tantalizing source of variability at frequencies comparable to astronomically observed low-frequency quasi-periodic oscillations (LFQPOs) in multiple galactic black hole binary candidates." We proceed with a discussion of our nunerical model (52). followed by a detailed description of the resulting dviuno cveles (53).," We proceed with a discussion of our numerical model $\S 2$ ), followed by a detailed description of the resulting dynamo cycles $\S 3$ )." We then compare our global siuulatioun to published local sinuulatious and discuss broader observational niplicatious (51). followed by our couchisions (55).," We then compare our global simulation to published local simulations and discuss broader observational implications $\S 4$ ), followed by our conclusions $\S 5$ )." Our fully three-dimensional maguctolbydrodvuamic (MIID) siuulation eniplovs a iodified version of the publicly available ZEUS-AIP (version 2) code. described in Stone&Norman(L992a).. Stone&Norman (1992)).. aud Πανοςetal.(2006)...," Our fully three-dimensional magnetohydrodynamic (MHD) simulation employs a modified version of the publicly available ZEUS-MP (version 2) code, described in \citet{1992ApJS...80..753S}, \citet{1992ApJS...80..791S}, and \citet{2006ApJS..165..188H}." ZEUS-AIP uses an Enlerian finite difference scheme accurate to second order in space to solve the equatious of ideal compressible MIID. where We emplov a eamuna-law (5= 5/3) gas equation of state.," ZEUS-MP uses an Eulerian finite difference scheme accurate to second order in space to solve the equations of ideal compressible MHD, where We employ a gamma-law $\gamma=5/3$ ) gas equation of state." Timesteps are set by the usual Couraut condition. and a protection routine prevents the density and pressure frou reaching artificially small audor negative values.," Timesteps are set by the usual Courant condition, and a protection routine prevents the density and pressure from reaching artificially small and/or negative values." The onlv adjustincuts we lave made to the fundamental ZEUS-AIP aleorithin involve this protection routine and. as described below. the introduction of modified eravity and the gas cooling function. A.," The only adjustments we have made to the fundamental ZEUS-MP algorithm involve this protection routine and, as described below, the introduction of modified gravity and the gas cooling function, $\Lambda$." Ciravitv is modified in our simulation to emulate the relevant effects of general relativity through a pseudo-Newtoman potential (Paczvuski&Wiita1980). of the form: This approach accurately captures for a Sclavarzsclild spacetime the position of the imucrimost stable circular orbit (ISCO) at r=Gry. the period of which is Ty3-61.6CAL/e? in this potential.," Gravity is modified in our simulation to emulate the relevant effects of general relativity through a pseudo-Newtonian potential \citep{1980A&A....88...23P} of the form: This approach accurately captures for a Schwarzschild spacetime the position of the innermost stable circular orbit (ISCO) at $r = 6 r_{\rm g}$ , the period of which is $\tau _{\rm ISCO} \approx 61.6~{\rm GM/c}^3$ in this potential." We initialize our computational exid usiug spherical coordinates (10ο). that span RoCαν.000c[0.052.0.95z].o0CἸθπό].," We initialize our computational grid using spherical coordinates $R,\theta,\phi$ ) that span $R \in [4 {\rm r_g},400 {\rm r_g}], \theta \in [0.05\pi,0.95\pi], \phi \in [0,\pi/4)$ ." The grid is non-uniform. logarithmically increasing in AR with a maxinan & resolution of AR=0.025 xr. at the inner οσο of the exid.," The grid is non-uniform, logarithmically increasing in $R$ with a maximum $R$ resolution of $\Delta R = 0.025$ $_{\rm g}$ at the inner edge of the grid." The zone aspect ratio is approximately AR:RAO:RAo=3:1:6 evervwhere within seven scale heights abovebelow the disk mudplane at 0=7/2). aud cach scale height is resolved with 25 computational zones in this reeion.," The zone aspect ratio is approximately $\Delta R: R\Delta \theta: R\Delta \phi = 3:1:6$ everywhere within seven scale heights above/below the disk midplane at $\theta = \pi/2$ ), and each scale height is resolved with $25$ computational zones in this region." Outside of this region. the @ resolution logarithmically increases outward.," Outside of this region, the $\theta$ resolution logarithmically increases outward." The total erid size is Neo.NoΑγ=512«381«GL1.2610° zones., The total grid size is $N_R \times N_\theta \times N_\phi = 512 \times 384 \times 64 = 1.26 \times 10^7$ zones. Standard ZEUS-AIP boundary treatments are cluploved. with a restreted boundary condition that permits outflow only iu the 4A directions.," Standard ZEUS-MP boundary treatments are employed, with a restricted boundary condition that permits outflow only in the $\pm R$ directions." Reflecting conditions are used near the coordinate pole iu 0 (as in DeVillers&Hawley2003.. for example). aud periodic conditions are applied ii o.," Reflecting conditions are used near the coordinate pole in $\theta$ (as in \citealt{2003ApJ...592.1060D}, for example), and periodic conditions are applied in $\phi$." The initial couditious correspond to a thin. axisviunietrie disk of constant iidplane deusitv and racially decreasing pressure:= and where py is the initial density in the disk midplane and fois the effective scale height.," The initial conditions correspond to a thin, axisymmetric disk of constant midplane density and radially decreasing pressure: and where $\rho_{\rm 0}$ is the initial density in the disk midplane and $h$ is the effective scale height." " The disk aspect ratio is iitialized to ές=0.05 evervwhere. aud a cooling fraction A is implemented to maintain this aspect ratio with a cooling time (7,4) that is related to the local orbital period (7,54) using an approach similar to that described in Nobleetal.(2009).."," The disk aspect ratio is initialized to $h/r=0.05$ everywhere, and a cooling function $\Lambda$ is implemented to maintain this aspect ratio with a cooling time $\tau_{\rm cool}$ ) that is related to the local orbital period $\tau_{\rm orb}$ ) using an approach similar to that described in \citet{2009ApJ...692..411N}." " The exact formu, of the cooling function is A=flrCrare)/Teool: where f=0οered| is a threshold function that enables cooliugle Grae!only whend] the internal cherey ο ds greater than the target energv Crare (uud which is equal to zero when ¢rarec ©)."," The exact form of the cooling function is $\Lambda = f(e-e_{\rm targ})/ \tau_{\rm cool}$, where $f = 0.5 [(e-e_{\rm targ})/|e-e_{\rm targ}|+1]$ is a threshold function that enables cooling only when the internal energy $e$ is greater than the target energy $e_{\rm targ}$ (and which is equal to zero when $e_{\rm targ} > e$ )." " The target enerev is chosen so that eisXpcr)?. which comes from the assumption that e;~(P/r)e,, in thin disks."," The target energy is chosen so that $e_{\rm targ} \propto \rho v_{\phi}^2 (h/r)^2$, which comes from the assumption that $c_s \sim (h/r) v_{\phi}$ in thin disks." Estimating the cooling time as the thermal timescale of the disk. we choose TegelΤι=τιν. which corresponds to a Shakura&Suuyaev(1973) alpha disk with a=0.1.," Estimating the cooling time as the thermal timescale of the disk, we choose $\tau_{\rm cool}=\tau_{\rm orb}/\alpha = 10 \tau_{\rm orb}$, which corresponds to a \citet{1973A&A....24..337S} alpha disk with $\alpha=0.1$." While the true effective alpha parameter varies spatially and iu time over the evolution of au AMID disk. this choice provides an adequate order-of-magnitude estimate for the implementation of cooling.," While the true effective alpha parameter varies spatially and in time over the evolution of an MHD disk, this choice provides an adequate order-of-magnitude estimate for the implementation of cooling." Additionally. we ran a short test simulation that revealed that the frequency range of the cdyvnamo cycle signal discussed in the following section was iuseusitive to the presence or absence of cooling. although the signal itself Was more pronounced in the case withcooling.," Additionally, we ran a short test simulation that revealed that the frequency range of the dynamo cycle signal discussed in the following section was insensitive to the presence or absence of cooling, although the signal itself was more pronounced in the case withcooling." The initial velocity profile is cutirely azimuthal and is set such that the effective centrifugal force balances the eravity of the central object iu the disk midplane., The initial velocity profile is entirely azimuthal and is set such that the effective centrifugal force balances the gravity of the central object in the disk midplane. The initial maenetic Ποια is completely poloidal in orientation and consists of a series of maguetie feld loopsthat,The initial magnetic field is completely poloidal in orientation and consists of a series of magnetic field loopsthat The results shown in Fig.,The results shown in Fig. 4 suggest. at the same time. more naturally the following scheme of formation and assembly.," 4 suggest, at the same time, more naturally the following scheme of formation and assembly." Assuming that dissipative gas-rich merger is the mechanism of spheroids formation. compact ΕΤΟΣ would be a natural consequence of this mechanism when most of the gas at disposal is burned in the central starburst. as discussed above.," Assuming that dissipative gas-rich merger is the mechanism of spheroids formation, compact ETGs would be a natural consequence of this mechanism when most of the gas at disposal is burned in the central starburst, as discussed above." To this end. the gas involved in the merger has to be suthciently cold to collapse oward the center and then ignite the main starburst produeing he compact remnant.," To this end, the gas involved in the merger has to be sufficiently cold to collapse toward the center and then ignite the main starburst producing the compact remnant." However. we could suppose that the gas in some of the progenitors is not so cold and homogeneous to allow he rapid central collapse deseribed above and that. consequently. he resulting starburst is not short and intense but much longer and possibly composed of many subsequents starbursts.," However, we could suppose that the gas in some of the progenitors is not so cold and homogeneous to allow the rapid central collapse described above and that, consequently, the resulting starburst is not short and intense but much longer and possibly composed of many subsequents starbursts." The rate at which the starburst(s) would be ignited or stoked could be modulated by the cooling time of the different gas clouds composing the gas reservoir and by their orbital and dynamica yarameters., The rate at which the starburst(s) would be ignited or stoked could be modulated by the cooling time of the different gas clouds composing the gas reservoir and by their orbital and dynamical parameters. In this case the remnant would not be compact and he mean age of the resulting stellar population would be much younger than the one produced in a single and short burst., In this case the remnant would not be compact and the mean age of the resulting stellar population would be much younger than the one produced in a single and short burst. This qualitative scenario would explain the co-existence of normal and compact ETGs observed at (2)=1.5 in spite of the same stellar mass. the lack of normal ETGs with high ορ and the absence of any correlation between compactness. stellar mass and formation redshift.," This qualitative scenario would explain the co-existence of normal and compact ETGs observed at $\langle z\rangle\simeq1.5$ in spite of the same stellar mass, the lack of normal ETGs with high $z_{form}$ and the absence of any correlation between compactness, stellar mass and formation redshift." The study of the spatial distribution of the stellar componen of ETGs at z>| can provide fundamental information on their past star formation and assembly histories., The study of the spatial distribution of the stellar component of ETGs at $z>1$ can provide fundamental information on their past star formation and assembly histories. In this regard. we believe that the study of the color gradient of high-z ETGs (Gargiulo et al.," In this regard, we believe that the study of the color gradient of high-z ETGs (Gargiulo et al." 2010) may represent a powerful probe of the early phases of ETGs formation., 2010) may represent a powerful probe of the early phases of ETGs formation. On the basis of the results discussed above and of the data we have at hand we have tried to put constraints on the number density of compact spheroids assembled in the very early Universe and on the resulting contribution to the SFR density., On the basis of the results discussed above and of the data we have at hand we have tried to put constraints on the number density of compact spheroids assembled in the very early Universe and on the resulting contribution to the SFR density. " The compact ETGs with Spun,>$5 have stellar masses Af,=[1—5]x10"" M, (Fig.", The compact ETGs with $z_{form}>5$ have stellar masses $\mathcal{M}_*=[1-5]\times10^{11}$ $_\odot$ (Fig. 4+. middle-right panel).," 4, middle-right panel)." " Considering a typical stellar mass of about |—2x10! M,. according to the gas-rich merger scheme. at least 50 per cent of this mass €»6xLO! M.) should form in about | Gyr during the merging at zu>$.as derived above."," Considering a typical stellar mass of about $1-2\times10^{11}$ $_\odot$, according to the gas-rich merger scheme, at least 50 per cent of this mass $\gae6\times10^{10}$ $_\odot$ ) should form in about 1 Gyr during the merging at $z_{assembly}>5$, as derived above." " This implies a mean star formation rate associated to the compact remnant (SFR)=60 M, | at z>5.", This implies a mean star formation rate associated to the compact remnant $\langle SFR\rangle\simeq60$ $_\odot$ $^{-1}$ at $z>5$. " The two progenitors. with masses (gas+stars) ~6x10 M. each. cannot have already formed more than 3xLO"" M. (50 per cent of mass) of stars each at the epoch of the merging."," The two progenitors, with masses (gas+stars) $\sim6\times10^{10}$ $_\odot$ each, cannot have already formed more than $3\times10^{10}$ $_\odot$ (50 per cent of mass) of stars each at the epoch of the merging." Since they formed these stellar masses before the merging. that is in about 0.5 Gyr. the required mean SFR is -60 M. vr' also in this case.," Since they formed these stellar masses before the merging, that is in about 0.5 Gyr, the required mean SFR is $\sim60$ $_\odot$ $^{-1}$ also in this case." These trelatively low) values agree with those derived for the star-forming galaxies observed at z>5 (e.g. Hickey et al., These (relatively low) values agree with those derived for the star-forming galaxies observed at $z>5$ (e.g. Hickey et al. 2010: Wilkins et al., 2010; Wilkins et al. " 2010) and with the detection of massive galaxies (>10 Mo at z>6 with age 200-700Myr and SFR~30 M, yr! (e.g. Eyles et al.", 2010) and with the detection of massive galaxies $>10^{10}$ $_\odot$ ) at $z>6$ with age 200-700Myr and $\sim30$ $_\odot$ $^{-1}$ (e.g. Eyles et al. 2005: 2007)., 2005; 2007). The possible (expected) intense phase of star formation (of some hundreds of /yr or more) experienced during the dissipative merger would last for very short times., The possible (expected) intense phase of star formation (of some hundreds of $_\odot$ /yr or more) experienced during the dissipative merger would last for very short times. Indeed. in an exponentially declining star formation history with e-folding time τ=0.1 Gyr. the star formation rate would drop by a factor ~3 in 0.1 Gyr and almost by a factor 10 in 0.2 Gyr.," Indeed, in an exponentially declining star formation history with e-folding time $\tau\simeq0.1$ Gyr, the star formation rate would drop by a factor $\sim3$ in $0.1$ Gyr and almost by a factor 10 in 0.2 Gyr." Since | Gyr is needed to form most of the stars (see Sec., Since 1 Gyr is needed to form most of the stars (see Sec. 3.1). the frequency with which we would observe a dissipative merger during the intense star formation phase would be less than 1:10.," 3.1), the frequency with which we would observe a dissipative merger during the intense star formation phase would be less than 1:10." This agrees with the apparent lack of strong bursting galaxies at very high-z and with the SFRs derived for high- spheroidal galaxies observed at ς>2 (see also Cava et al., This agrees with the apparent lack of strong star-bursting galaxies at very high-z and with the SFRs derived for high-mass spheroidal galaxies observed at $z>2$ (see also Cava et al. 2010 for very recent results)., 2010 for very recent results). We also tried to derive a lower limit to the number density of early compact spheroids at z>5 and to their contribution to the star formation rate density at that redshift., We also tried to derive a lower limit to the number density of early compact spheroids at $z>5$ and to their contribution to the star formation rate density at that redshift. Out of the 13 compact ETGs with Spo23. 3 belong to the ACS sample (Saraeco et.," Out of the 13 compact ETGs with $z_{form}>5$, 3 belong to the ACS sample (Saracco et." al 2010) on the GOODS-South field (143 aremin?) and 5 to the sample of massive ETGs selected on the ΕΙ field (150 aremin?) (Saracco et al., al 2010) on the GOODS-South field (143 $^2$ ) and 5 to the sample of massive ETGs selected on the S2F1 field (150 $^2$ ) (Saracco et al. 2005: Longhetti et al., 2005; Longhetti et al. 2007)., 2007). are 1.51x10° Mpe? and 1.634Χ10° Mpce? respectively., are $1.51\times10^6$ $^{3}$ and $1.64\times10^6$ $^{3}$ respectively. " Thus. the expected number densities of compact spheroids at z»5 derived by these two small samples are -2xl0 ? and n=3xI0 . from two times lower than the number density G2=4—5x10 4) of compact ETGs more massive than 10! M, observed at <<)~1.5 (Saracco et al."," Thus, the expected number densities of compact spheroids at $z>5$ derived by these two small samples are $n=2\times10^{-6}$ $^{-3}$ and $n=3\times10^{-6}$ $^{-3}$, from two times lower than the number density $n=4-5\times10^{-6}$ $^{-3}$ ) of compact ETGs more massive than $10^{11}$ $_\odot$ observed at $\langle z\rangle\simeq1.5$ (Saracco et al." 2010) and at z=O (Valentinuzzi et al., 2010) and at $z=0$ (Valentinuzzi et al. 201040)2009)., 2010a). " The contribution to the co-moving stellar mass density of these early compact spheroids is ~οκ10° M. . to be compared with 2.5x40* M, +. the lower limit to the co-moving stellar masx density at z>6 (Eyles et al."," The contribution to the co-moving stellar mass density of these early compact spheroids is $\sim6\times10^5$ $_\odot$ $^{-3}$, to be compared with $2.5\times10^6$ $_\odot$ $^{-3}$, the lower limit to the co-moving stellar mass density at $z\gae6$ (Eyles et al." 2007)., 2007). " Finally. their contribution teο the star formation rate density (SFRD). averaged over | Gyr at D S.isSFRD~6x 10+M, ! *. an order of magnitude lower than the total SFRD density estimated at z6 (Bouwens et al."," Finally, their contribution to the star formation rate density (SFRD), averaged over 1 Gyr at $z>5$, is $SFRD\simeq6\times10^{-4}$ $_\odot$ $^{-1}$ $^{-3}$, an order of magnitude lower than the total SFRD density estimated at $z\lae6$ (Bouwens et al." 2006: Stark et al., 2006; Stark et al. 2007)., 2007). Thus. all these quantities are well within those derived from the observations of the very high redshift galaxy population.," Thus, all these quantities are well within those derived from the observations of the very high redshift galaxy population." By the way. these latter observations provide supports in favour of the very early formation of compact spheroids whose contribution in terms of stellar mass and star formation rate densities can be significant.," By the way, these latter observations provide supports in favour of the very early formation of compact spheroids whose contribution in terms of stellar mass and star formation rate densities can be significant." " We used a sample of 62 ΕΤΟΣ at 0.9«zj,,2 to probe the star formation history and the mass assembly history of early-type galaxies at z>2.", We used a sample of 62 ETGs at $0.92$. Using the local size-mass relation as reference we, Using the local size-mass relation as reference we NGCA431: The quite strong bar preseut iu this galaxy is the most striking discovery and clearly reveals the disk nature of this dwarf again nicelv confined by its measured rotation (Simicu Pruguicl 2002).,: The quite strong bar present in this galaxy is the most striking discovery and clearly reveals the disk nature of this dwarf – again nicely confirmed by its measured rotation (Simien Prugniel 2002). Besides the bar we clearly note trailing arius and two dense reeious ou the leadiug side of the bar., Besides the bar we clearly note trailing arms and two dense regions on the leading side of the bar. This so-called T-structure js vorv similar to the results of a simulation preseuted by Patsis Athanassoula (2000)., This so-called T-structure is very similar to the results of a simulation presented by Patsis Athanassoula (2000). A nore fitting type for this “ASO” ealaxy would be dSBO/a.IC3468: Iu the very center of this dwarf elliptical we either observe a rather short bar ina nearly face-ou disk. or a small disk seen edge-on in a spheroid.," A more fitting type for this “dS0” galaxy would be dSB0/a.: In the very center of this dwarf elliptical we either observe a rather short bar in a nearly face-on disk, or a small disk seen edge-on in a spheroid." Surprisingly. Simicun Pruguicl (2002) found esseutially zero rotation along the position angle of this structure. which renders a clear interpretation of what we see impossible at prescut.," Surprisingly, Simien Prugniel (2002) found essentially zero rotation along the position angle of this structure, which renders a clear interpretation of what we see impossible at present." We cinphasize that none of these objects is comparable to IC3328., We emphasize that none of these objects is comparable to IC3328. The weak aud wniformiy wound spiral structure in this galaxw seenis to be truly unique. constituting a particular class ofdwarf galaxies: at least we did not fiud an additional example.," The weak and uniformly wound spiral structure in this galaxy seems to be truly unique, constituting a particular class of dwarf galaxies; at least we did not find an additional example." Our findines confirm previous sugeestions that a sizeable fraction of all bright early-type dwarts iu the VireoOo cluster ave disk Oogalaxies., Our findings confirm previous suggestions that a sizeable fraction of all bright early-type dwarfs in the Virgo cluster are disk galaxies. In a possible scenario for heir evolution they are former late-type disk galaxies which have been transformed to the svstems we observe odav during their iufall to the cluster., In a possible scenario for their evolution they are former late-type disk galaxies which have been transformed to the systems we observe today during their infall to the cluster. The discovery of more objects of this kind in the Virgo cluster. but also in other clusters. could therefore further constraiu )ossible nodels for the formation aud evolution of ype galaxies in general.," The discovery of more objects of this kind in the Virgo cluster, but also in other clusters, could therefore further constrain possible models for the formation and evolution of early-type galaxies in general." Primorcial Uuctuations generated acoustic waves in the carly universe. photon-xuwvon plasma.,Primordial fluctuations generated acoustic waves in the early universe photon-baryon plasma. Those waves were frozen at decoupling. 2~1100. then barvon acoustic oscillations (BAO) were imprinted in the cosmic microwave background. (CMD) at he sound horizon scale. as à series of peaks in the power spectrum or a single peak in the 2- correlation function (see eg Peebles anc Yu. 1970 and Ixomasu et al 2010 for t10 latest measurements bv WALAD).," Those waves were frozen at decoupling, $z\sim1100$, then baryon acoustic oscillations (BAO) were imprinted in the cosmic microwave background (CMB) at the sound horizon scale, as a series of peaks in the power spectrum or a single peak in the 2-point correlation function (see eg Peebles and Yu, 1970 and Komatsu et al 2010 for the latest measurements by WMAP)." LAO can also be seen at the present in matter power specrum. and its position. rgo can be used as a standard cosmological ruler.," BAO can also be seen at the present in matter power spectrum, and its position, $r_{BAO}$ can be used as a standard cosmological ruler." Measurements in the radial (redshift direction)) Ads. can be used to estimate the Llubble rate as ἐς)=cNzírgao. while angular measurements. AG. can be used to estimate the angular diameter distance: D(z)rergfA@ ," Measurements in the radial (redshift direction), $\Delta z$, can be used to estimate the Hubble rate as $H(z) =c\Delta z/ r_{BAO}$, while angular measurements, $\Delta \theta$, can be used to estimate the angular diameter distance: $D_A(z) =r_{BAO}/ \Delta \theta$." Baryon acoustic oscillations in the ealaxy correlations of the Sloan Digital Sky Survey (SDSS) luminous red galaxy (LI) sample have been used to constrain cosmological parameters (eg Eisenstein et al 2005. llutsi et al 2006. Sanchez et al 2009. Percival ct al 2010. Reid et al 2010. Ixazin et al 2010a and references therein).," Baryon acoustic oscillations in the galaxy correlations of the Sloan Digital Sky Survey (SDSS) luminous red galaxy (LRG) sample have been used to constrain cosmological parameters (eg Eisenstein et al 2005, Hutsi et al 2006, Sanchez et al 2009, Percival et al 2010, Reid et al 2010, Kazin et al 2010a and references therein)." Dillerent stuclies use dillerent wavs to extract the BAQO signal and quantify the significance of the measurements (see Sanchez ct al 2008)., Different studies use different ways to extract the BAO signal and quantify the significance of the measurements (see Sanchez et al 2008). For example. Eisenstein οἱ al 2005 and Sanchez et al 2009 used the full shape of the 2-point correlation to wCDAL class of modes and found constraints to the combination distance D2.(2)=(DAHy to the galaxy. sample mean redshift based. on a global 4? fitting. while Percival et al 2010 used a fit to the oscillatory components in the power spectrum to find constraints on Dis).," For example, Eisenstein et al 2005 and Sanchez et al 2009 used the full shape of the 2-point correlation to $\omega$ CDM class of models and found constraints to the combination distance $D_v(z)=(D_A^2/H)^{1/3}$ to the galaxy sample mean redshift based on a global $\chi^2$ fitting, while Percival et al 2010 used a fit to the oscillatory components in the power spectrum to find constraints on $D_v(z)$." These previous analysis used the monopole componen of the correlation function. where all pairs are averaged with independence of their orientation.," These previous analysis used the monopole component of the correlation function, where all pairs are averaged with independence of their orientation." Okumura et al 2008 did a separate analysis of pairs as a function of orientation bu avoiding the radial direction., Okumura et al 2008 did a separate analysis of pairs as a function of orientation but avoiding the radial direction. Gaztanaga. Cabré ancl Lui (2009. GCL hereafter) presented constraints to £/(2) base on the radial correlation. which uses only those pairs alignec with the redshift. direction.," Gaztanaga, Cabré and Hui (2009, GCH hereafter) presented constraints to $H(z)$ based on the radial correlation, which uses only those pairs aligned with the redshift direction." This reduces the number of observational data but boost the contrast on the BAO peak because of redshift space distortions., This reduces the number of observational data but boost the contrast on the BAO peak because of redshift space distortions. At intermediate scales.," At intermediate scales," X-ray emission is found virtually everywhere among the population of the main-sequence stars.,X-ray emission is found virtually everywhere among the population of the main-sequence stars. " The X-ray generating mechanisms differ however for ""hot. O and early-B stars. anc ‘cool’. late-A to M-type stars."," The X-ray generating mechanisms differ however for 'hot' O and early-B stars, and 'cool', late-A to M-type stars." In hot stars the correlatior between X-ray and bolometric luminosity at logLy/Li4j=—7 (2) is explained by X-ray emission arising from shocks 1 instabilities in their radiatively driven winds., In hot stars the correlation between X-ray and bolometric luminosity at $\log L_{\rm X}/L_{\rm bol} \approx -7$ \citep{berg97} is explained by X-ray emission arising from shocks in instabilities in their radiatively driven winds. In cool stars. X-ray emission originates in magnetic structures generatec by dynamo processes. powered by an interplay of convective motions in the outer layers and stellar rotation.," In cool stars, X-ray emission originates in magnetic structures generated by dynamo processes, powered by an interplay of convective motions in the outer layers and stellar rotation." " The observec activity levels range from logLx/Lpo=—-7..—3 ο). whereas an activity-rotation relation is present until the ""Sνamo saturates (foranoverviewonstellarcoronaesee?).."," The observed activity levels range from $\log L_{\rm X}/L_{\rm bol} \approx -7~...-3$ \citep{schmitt97}, whereas an activity-rotation relation is present until the dynamo saturates \citep[for an overview on stellar coronae see][]{gue04}." In intermediate mass stars. around spectral type late-A. the outer convection zone becomes increasingly thinner and the dynamo efficiency declines strongly.," In intermediate mass stars, around spectral type late-A, the outer convection zone becomes increasingly thinner and the dynamo efficiency declines strongly." A prominent example is the A7 star Altair. one of the hottest magnetically active stars detected in X-rays (?)..," A prominent example is the A7 star Altair, one of the hottest magnetically active stars detected in X-rays \citep{rob09a}." Thus one expects a virtually X-ray dark population at spectral types mid-B to mid-A. where stars neither possess an outer convection zone nor drive strong stellar winds.," Thus one expects a virtually X-ray dark population at spectral types mid-B to mid-A, where stars neither possess an outer convection zone nor drive strong stellar winds." The overall X-ray detection rate among those stars is with 10 surprisingly X-ray emission was detected from several of these stars (?).., The overall X-ray detection rate among those stars is with $\sim 10$ surprisingly X-ray emission was detected from several of these stars \citep{schroeder07}. Consequently. low-mass stars hidden in the vicinity of their optically bright primaries have been often proposed as the true origin of the X-ray emission.," Consequently, low-mass stars hidden in the vicinity of their optically bright primaries have been often proposed as the true origin of the X-ray emission." Unresolved companions are a likely explanation for the X-ray emission from “normal” main-sequence stars at these spectral types and in some cases they even can be shown to be responsible for the X-ray emission. e.g. in the eclipsing binary systems like aCCrB (?)..," Unresolved companions are a likely explanation for the X-ray emission from 'normal' main-sequence stars at these spectral types and in some cases they even can be shown to be responsible for the X-ray emission, e.g. in the eclipsing binary systems like $\alpha$ CrB \citep{schmitt93}." However. especially peculiar Ap/Bp stars and young Herbig AeBe stars are prime candidates for being intrinsic X-ray emitters (e.g.22)..," However, especially peculiar Ap/Bp stars and young Herbig AeBe stars are prime candidates for being intrinsic X-ray emitters \citep[e.g.][]{bab97,ste09}." In the here discussed Ap/Bp stars an interplay between stellar winds and large scale magnetic fields is thought to play the major role in the X-ray generation., In the here discussed Ap/Bp stars an interplay between stellar winds and large scale magnetic fields is thought to play the major role in the X-ray generation. Ap/Bp stars are magnetic. chemically peculiar (CP) stars that have completed an often significant fraction of their main sequence lifetime. 1.e. they are not especially young.," Ap/Bp stars are magnetic, chemically peculiar (CP) stars that have completed an often significant fraction of their main sequence lifetime, i.e. they are not especially young." Only a small fraction of about these stars typically exhibit various chemical peculiarities and a rather slow rotation compared to non-magnetic stars of similar spectral type., Only a small fraction of about these stars typically exhibit various chemical peculiarities and a rather slow rotation compared to non-magnetic stars of similar spectral type. The origin of their magnetic field is debated. but often thought to be of fossil origin. consistent with the finding that only a small fraction is magnetic and that field strength and rotation are independent.," The origin of their magnetic field is debated, but often thought to be of fossil origin, consistent with the finding that only a small fraction is magnetic and that field strength and rotation are independent." The magnetic field geometry in Ap/Bp stars is dominated by rather simple. large scale structures like a dipole and hence it is fundamentally different from the complex field geometry of magnetically active type stars (seee.g.theoverviewby?)," The magnetic field geometry in Ap/Bp stars is dominated by rather simple, large scale structures like a dipole and hence it is fundamentally different from the complex field geometry of magnetically active late-type stars \citep[see e.g. the overview by][]{lan92}." The prototypical case for a presumably single. magnetic Ap star with detected X-ray emission is IQ Aur.," The prototypical case for a presumably single, magnetic Ap star with detected X-ray emission is IQ Aur." In a 10 ks pointed observation withROSAT PSPC. IQ Aur was shown to be an X-ray source with a high X-ray luminosity of Lx1077 ss7! and a quite soft spectrum with Tx=0.3 keV (2. BM?97).," In a 10 ks pointed observation with PSPC, IQ Aur was shown to be an X-ray source with a high X-ray luminosity of $L_{\rm X}= 4 \times 10^{29}$ $^{-1}$ and a quite soft spectrum with $T_{\rm X}=0.3$ keV \citep[][BM97]{bab97}." . Thus a hypothetical late-type companion was a rather unlikely explanation., Thus a hypothetical late-type companion was a rather unlikely explanation. In order to explain the X-ray emission from IQ Aur and. more generally of Ap/Bp stars. BM97 introduced the “magnetically confined. wind-shock model (MCWS).," In order to explain the X-ray emission from IQ Aur and, more generally of Ap/Bp stars, BM97 introduced the 'magnetically confined wind-shock model' (MCWS)." In the MCWS model the radiatively driven wind components from both hemispheres of the star are magnetically confined and forced to collide in the vicinity of its equatorial plane., In the MCWS model the radiatively driven wind components from both hemispheres of the star are magnetically confined and forced to collide in the vicinity of its equatorial plane. As a consequence. strong shocks form and give rise to very efficient X-ray production from kinetic wind energy.," As a consequence, strong shocks form and give rise to very efficient X-ray production from kinetic wind energy." Although some fine-tuning Is required to obtain a rather high mass loss rate. the X-ray emission of IQ Aur can actually be accounted for with reasonable assumptions on the wind parameters: specifically BM97 assumed a stellar wind with Va=800 kmss! and a mass loss rate of Μο=107!—107!M yyr," Although some fine-tuning is required to obtain a rather high mass loss rate, the X-ray emission of IQ Aur can actually be accounted for with reasonable assumptions on the wind parameters; specifically BM97 assumed a stellar wind with $V_{\infty}=800$ $^{-1}$ and a mass loss rate of $\dot M_{\odot}=10^{-10} -10^{-11} M_{\odot}$ $^{-1}$." Notable advancements of the static BM97 model were achieved by magnetohydrodynamic simulations of magnetically channelled line-driven stellar winds (2)., Notable advancements of the static BM97 model were achieved by magnetohydrodynamic simulations of magnetically channelled line-driven stellar winds \citep{dou02}. . In a further study. these MHD simulations investigate an extended parameter space and include stellar rotation in the modeling (?)..," In a further study, these MHD simulations investigate an extended parameter space and include stellar rotation in the modeling \citep{dou08}." Dynamic variants of the MCWS model were successfully applied to Herbig AeBe and O-type stars and may actually extend to a whole class of magnetic early-type stars., Dynamic variants of the MCWS model were successfully applied to Herbig AeBe and O-type stars and may actually extend to a whole class of magnetic early-type stars. In this respect it can be considered as a ‘standard’ model that is invoked to explain a variety of phenomena like X-ray overluminosity. hard spectral components. flares or rotational," In this respect it can be considered as a 'standard' model that is invoked to explain a variety of phenomena like X-ray overluminosity, hard spectral components, flares or rotational" The problems associated with DEM interpolation and with the definition of Τε do not affect the Markov-Chain Monte Carlo (MCMC) technique developed by Kashyap Drake (1998).,The problems associated with DEM interpolation and with the definition of $T_{eff}$ do not affect the Markov-Chain Monte Carlo (MCMC) technique developed by Kashyap Drake (1998). This technique is based on a Bayesian statistical formalism that allows the determination of the most probable DEM curve that reproduces the observed line intensities., This technique is based on a Bayesian statistical formalism that allows the determination of the most probable DEM curve that reproduces the observed line intensities. " The heart of this technique relies on the application of the Bayes theorem to line intensities. stating that the probability PCY.F) of obtaining a set of observed line intensities F=(Fy.Fo.....F,) from a DEM characterized by a set of parameters X=CXj.Xs...X,) is given by where P(F) is a normalization factor. P(X) is an probability of the set of parameters X. and P(X.F;) is the probability of obtaining the observed intensity F; with the set of parameters X and has been defined by Kashyap Drake (1998) às where Fh is the intensity of line { caleulated with the DEM described by the set of parameters X. and cr is the uncertainty of the observed intensity F;."," The heart of this technique relies on the application of the Bayes theorem to line intensities, stating that the probability $P{\left({X,F}\right)}$ of obtaining a set of observed line intensities $F={\left({F_1,F_2,...,F_n}\right)}$ from a DEM characterized by a set of parameters $X={\left({X_1,X_2,...,X_m}\right)}$ is given by where $P{\left({F}\right)}$ is a normalization factor, $P{\left({X}\right)}$ is an probability of the set of parameters $X$, and $P{\left({X,F_i}\right)}$ is the probability of obtaining the observed intensity $F_i$ with the set of parameters $X$ and has been defined by Kashyap Drake (1998) as where $F_i^{th}$ is the intensity of line $i$ calculated with the DEM described by the set of parameters $X$, and $\sigma_i$ is the uncertainty of the observed intensity $F_i$." This method is implemented by choosing a grid of N temperature bins and assuming that within each bin the plasma is isothermal and can be described by an emission measure value £M;., This method is implemented by choosing a grid of $N$ temperature bins and assuming that within each bin the plasma is isothermal and can be described by an emission measure value $EM_i$ . Once the bin size 1s chosen. the set of parameters that describe the DEM is thus .... (EM.EMy).," Once the bin size is chosen, the set of parameters that describe the DEM is thus $X={\left({EM_1,...,EM_N}\right)}$ ." In order to determine the set of parameters X that provide the maximum probability PCX.F). Kashyap Drake (1998) adopted a Markov-Chain Monte Carlo approach.," In order to determine the set of parameters $X$ that provide the maximum probability $P{\left({X,F}\right)}$, Kashyap Drake (1998) adopted a Markov-Chain Monte Carlo approach." In this approach. the set of parameters X that describes an initial trial DEM is varied step by step: in each step only one of the parameters in the set X (1e. one EM; value only) is varied and the others are left unchanged: the change introduced to the varied parameter only depends on the set of parameters X. of the previous step.," In this approach, the set of parameters $X$ that describes an initial trial DEM is varied step by step; in each step only one of the parameters in the set $X$ (i.e. one $EM_i$ value only) is varied and the others are left unchanged; the change introduced to the varied parameter only depends on the set of parameters $X$ of the previous step." The new set of parameters X' has a different probability P(X’.F) from the previous one. and is accepted or rejected according to the Metropolis algorithm (Metropolis 1953). based on the change of probability P.," The new set of parameters $X'$ has a different probability $P{\left({X',F}\right)}$ from the previous one, and is accepted or rejected according to the Metropolis algorithm (Metropolis 1953), based on the change of probability $P$." This algorithm consists of generating a random number i. such that 0ηςI. and a function ACY.X) defined as The new set of parameters is accepted η0 and only in special cases with restricted. phase space does one find oscillatory modes. (3)=0 lo evaluate the coellicients. as a function. of time. we perform the inverse Laplace transform. deforming the contour to the Ws)sox: Assuming that the background is stable with no oscillatory modes. P+!""(Cs) has no poles in the hall plane js)=0."," For the general stable spherical stellar system, there will be no modes for $\Re(s)\ge0$ and only in special cases with restricted phase space does one find oscillatory modes, $\Re(s)=0$ To evaluate the coefficients as a function of time, we perform the inverse Laplace transform, deforming the contour to the $\Re(s)\rightarrow-\infty$: Assuming that the background is stable with no oscillatory modes, ${\bf{\cal D}}^{-1\,lm}(s)$ has no poles in the half plane $\Re(s)\ge0$." The final term gives a pole at s=e., The final term gives a pole at $s=i\omega$. Although there may be poles in the half plane Wis)<0. these will vanish for (=x relative to the pure imaginary contribution.," Although there may be poles in the half plane $\Re(s)<0$, these will vanish for $t\rightarrow\infty$ relative to the pure imaginary contribution." To perform the integral. one may take the s integration into the phase-space integral for the elements of ο(8).," To perform the integral, one may take the $s$ integration into the phase-space integral for the elements of ${\cal R}^{lm}(s)$." " In addition to D.1""(s). the s« ependence is in two simple poles and one finds an integral of the form For large values of /. this expression oscillates rapidly and we mav extract the dominant coherent: contribution."," In addition to ${\bf{\cal D}}^{-1\,lm}(s)$, the $s$ -dependence is in two simple poles and one finds an integral of the form For large values of $t$, this expression oscillates rapidly and we may extract the dominant coherent contribution." There are two cases: without and. with a resonance in the phase space., There are two cases: without and with a resonance in the phase space. The existence of a resonance in. phase space is defined by w|1.QU)=0 for f(T)z0.," The existence of a resonance in phase space is defined by $\omega + {\bf l}\cdot{\bf\Omega}({\bf I})=0$ for $f({\bf I})\not=0$." For the non-resonant case. the integrand has no singularity ancl we can consider cach term separately.," For the non-resonant case, the integrand has no singularity and we can consider each term separately." The first term: vields a contribution in phase with the perturbation while the second term in the brackets oscillates incoherently and makes no net contribution., The first term yields a contribution in phase with the perturbation while the second term in the brackets oscillates incoherently and makes no net contribution. The second. term. therefore. can be ignored.," The second term, therefore, can be ignored." For the resonant case. the contribution at large / has a sharp peak about w|retaining1Q(1) m =Oast+ x.," For the resonant case, the contribution at large $t$ has a sharp peak about $\omega + {\bf l}\cdot{\bf\Omega}({\bf I})=0$ as $t\rightarrow\infty$ ." Expanding Dblnjay about ζω and dominant ternis. one finds the contribution near the resonance is We will adopt the latter asymptotic form here anc sec in the final computation that the exp(iw) will cancel leaving," Expanding ${\bf{\cal D}}^{-1\,lm}(i\omega)$ about $i\omega$ and retaining only dominant terms, one finds the contribution near the resonance is We will adopt the latter asymptotic form here and see in the final computation that the $\exp(i\omega t)$ will cancel leaving" "The right-hand side of equation (10)) is the shearing time scale for an Alfvénnie. velocity fluctuation at Kj,κι with rms amplitude d1y,.",The right-hand side of equation \ref{eq:tcasc0}) ) is the shearing time scale for an Alfvénnic velocity fluctuation at $k_\perp = k_i$ with rms amplitude $\delta v_{k_i}$. This is a lower-limit on ἐς because in incompressible MHD. the anti-Sunward waves are sheared by waves propagating towards the Sun (Iroshnikov. 1963; Kraichnan 1965). as summarized in 2..," This is a lower-limit on $t_{\rm c}$ because in incompressible MHD, the anti-Sunward waves are sheared by waves propagating towards the Sun (Iroshnikov 1963; Kraichnan 1965), as summarized in \ref{sec:pred}." " Thus. if the Sunward waves are much less energetic than the anti-Sunward waves at &,=κι. the time required for Sunward waves to shear and substantially distort anti-Sunward waves is much greater than (δν) (Lithwick. Goldreich. Sridhar 2007: Beresnyak Lazarian 2005: Chandran 200823)="," Thus, if the Sunward waves are much less energetic than the anti-Sunward waves at $k_\perp = k_i$, the time required for Sunward waves to shear and substantially distort anti-Sunward waves is much greater than $(k_i \delta v_{k_i})^{-1}$ (Lithwick, Goldreich, Sridhar 2007; Beresnyak Lazarian 2008; Chandran 2008a)." The— cascade power— in low-frequency Alfvénn-wave turbulence at r=5R.. denoted £ is roughly ovt..," The cascade power in low-frequency Alfvénn-wave turbulence at $r=5 R_{\sun}$, denoted $\epsilon$ is roughly $\rho v_{ki}^2/ t_{\rm c}$." Given equation (10)). we can write where cy&0.25 in strong incompressible MHD turbulence with equal fluxes of Alfvénn waves propagating parallel and anti-parallel to the background magnetic field (Howes et al.," Given equation \ref{eq:tcasc0}) ), we can write where $c_0 \simeq 0.25$ in strong incompressible MHD turbulence with equal fluxes of Alfvénn waves propagating parallel and anti-parallel to the background magnetic field (Howes et al." 2008a)., 2008a). Substituting equation (9)) into equation (11)). we find This upper limit can be compared with the parameterized heating rates employed in empirical models of the fast solar wind.," Substituting equation \ref{eq:deltav2}) ) into equation \ref{eq:epsmax}) ), we find This upper limit can be compared with the parameterized heating rates employed in empirical models of the fast solar wind." Allen et al (1998) constructed a series of two-fluid models with heating rates chosen to match. measurements of the fast wind at | AU as well as the coronal-hole density profile inferred from the brightness profile of electron-scattered. polarized white light (Fisher Guhathakurta 1995).," Allen et al (1998) constructed a series of two-fluid models with heating rates chosen to match measurements of the fast wind at 1 AU as well as the coronal-hole density profile inferred from the brightness profile of electron-scattered, polarized white light (Fisher Guhathakurta 1995)." In these models. denoted SW2. SW3. and SW4. the total (electron plus proton) heating rates at r—SR. were 3.1«107?ereem ΕΛ. and 6.8«107?ergem7*s7!. respectively.," In these models, denoted SW2, SW3, and SW4, the total (electron plus proton) heating rates at $r=5 R_{\sun}$ were $3.1 \times 10^{-9}\mbox{ erg}\, \mbox{cm}^{-3} \, \mbox{s}^{-1}$, $1.4 \times 10^{-8} \mbox{ erg}\, \mbox{cm}^{-3} \, \mbox{s}^{-1}$, and $6.8 \times 10^{-9} \mbox{ erg}\, \mbox{cm}^{-3} \, \mbox{s}^{-1}$, respectively." Esser et al (1997) constructed similar models with higher temperatures at the coronal base and lower heating rates., Esser et al (1997) constructed similar models with higher temperatures at the coronal base and lower heating rates. The value of ε at r—SR. was 2«107?ergem7?s7! in their model A and 8«10779ergem74s7! in their model Since these models (by construction) provide a reasonable fit to the observed properties of the fast wind. we take the actual heating rate in coronal holes at r=5R. to be in the range spanned by these models. i.e.. between 2«107?ereem? and L4<107? ergem7*s7!.," The value of $\epsilon$ at $r=5 R_{\sun}$ was $2\times 10^{-10} \mbox{ erg}\, \mbox{cm}^{-3} \, \mbox{s}^{-1}$ in their model A and $8\times 10^{-10} \mbox{ erg}\, \mbox{cm}^{-3} \, \mbox{s}^{-1}$ in their model Since these models (by construction) provide a reasonable fit to the observed properties of the fast wind, we take the actual heating rate in coronal holes at $r=5 R_{\sun}$ to be in the range spanned by these models, i.e., between $2 \times 10^{-10} \mbox{ erg}\, \mbox{cm}^{-3} \, \mbox{s}^{-1}$ and $1.4 \times 10^{-8} \mbox{ erg}\, \mbox{cm}^{-3} \, \mbox{s}^{-1}$ ." Since the upper limit in equations! (12)) is above this range. we conclude that a model in which the fast wind is accelerated by heating from low-frequency Alfvénnic turbulence is consistent with the radio observations.," Since the upper limit in equation \ref{eq:epsmax2}) ) is above this range, we conclude that a model in which the fast wind is accelerated by heating from low-frequency Alfvénnic turbulence is consistent with the radio observations." " Future investigations could provide tighter constraints on the fraction of that arises directly from KAWs as well as the ratio of Sunward64, to anti-Sunward wave energy atk)—Kj. which could in principle lower the upper limit on € that is implied by the density fluctuation measurements."," Future investigations could provide tighter constraints on the fraction of $\delta n_{k_i}$ that arises directly from KAWs as well as the ratio of Sunward to anti-Sunward wave energy at $k_\perp = k_i$, which could in principle lower the upper limit on $\epsilon$ that is implied by the density fluctuation measurements." Measurements of density fluctuations in the solar wind at ~| AU have been carried out by a variety of methods (e.g.. Celnikier et al.," Measurements of density fluctuations in the solar wind at $\sim 1$ AU have been carried out by a variety of methods (e.g., Celnikier et al." 1983. 1987: Hnat et al.," 1983, 1987; Hnat et al." 2005: Kellogg Horbury 2005): these allow us to caleulate an upper limit on the heating by low-frequency Alfvénnic turbulence analogous to that derived in the previous section., 2005; Kellogg Horbury 2005); these allow us to calculate an upper limit on the heating by low-frequency Alfvénnic turbulence analogous to that derived in the previous section. For concreteness. we use Celnikier et al. (," For concreteness, we use Celnikier et al. (" 1987)'s period II to find an upper limit to the KAW contribution to the density fluctuations. but similar results are obtained from other measurements.,"1987)'s period II to find an upper limit to the KAW contribution to the density fluctuations, but similar results are obtained from other measurements." " From their Figure 7. we infer that Syο<1077 at Kip;c0.3.7. where Bc1.5«1077 G. ny=Wem. T,=1.5«10 K. pp—2«105 em. 77 km sc. vingc460 km s7!. and B~0.43 in this epoch of data."," From their Figure 7, we infer that $\delta n_k/n_0 \lesssim 10^{-2}$ at $k_\perp \rho_i \simeq 0.3$ where $B \simeq 1.5 \times 10^{-4}$ G, $n_0 \simeq 18$ $^{-3}$, $T_p \simeq 1.5 \times 10^5$ K, $\rho_p \simeq 2 \times 10^{6}$ cm, $v_A \simeq 77$ km $^{-1}$, $v_{\rm wind} \simeq 460$ km $^{-1}$, and $\beta \simeq 0.43$ in this epoch of data." Unlike in the observations of the solar corona described in $3.1.. there is no clear evidence for an inner scale to the density fluctuations at | AU.," Unlike in the observations of the solar corona described in \ref{sec:corona}, there is no clear evidence for an inner scale to the density fluctuations at 1 AU." " Given the lack of a preferred scale. we evaluate the density fluctuations at kp;~0.3 as a compromise between the scales where the KAW density fluctuations peak (kp;I) and the scales where incompressible MHD is a reasonable model for the cascade (&,p;«&1): our conclusions are. however. insensitive to reasonable variations about this choice."," Given the lack of a preferred scale, we evaluate the density fluctuations at $k_\perp \rho_i \simeq 0.3$ as a compromise between the scales where the KAW density fluctuations peak $k_\perp \rho_i \sim 1$ ) and the scales where incompressible MHD is a reasonable model for the cascade $k_\perp \rho_i \ll 1)$; our conclusions are, however, insensitive to reasonable variations about this choice." " A limit on the density fluctuations due to KAWs. of Syο1077 at kjp;~0.3 corresponds to a limit on the velocity fluctuations of 6v,/v4τς107 at the same scale (i.e. v,XDL km s) and thus to a limit on the heating rate due to low-frequency Alfvénnie turbulence of At ~|] AU. the heating rate in the solar wind can be directly measured from the non-adiabatic temperature profile of the protons and electrons. using €—pv,Tds/dr. For example. using the proton data from Voyager 2 (e.g.. Matthaeus et al."," A limit on the density fluctuations due to KAWs of $\delta n_k/n_0 \lesssim 10^{-2}$ at $k_\perp \rho_i \simeq 0.3$ corresponds to a limit on the velocity fluctuations of $\delta v_k/v_A \lesssim 10^{-2}$ at the same scale (i.e., $\delta v_k \lesssim 1$ km $^{-1}$ ) and thus to a limit on the heating rate due to low-frequency Alfvénnic turbulence of At $\sim 1$ AU, the heating rate in the solar wind can be directly measured from the non-adiabatic temperature profile of the protons and electrons, using $\epsilon \simeq \rho v_r Tds/dr.$ For example, using the proton data from Voyager 2 (e.g., Matthaeus et al." " 1999), we infer that £—34«107ereems!|is required to explain the non-adiabaticity of the solar wind at 1 The close correspondence between this measured heating rate at | AU and the upper limit in equation (13)) implies that. if low frequency Alfvénnic turbulence contributes to heating the solar wind at ~| AU. direct density fluctuations due to compressive KAWs must contribute significantly to the measured density fluctuations at Kjp;I."," 1999), we infer that $\epsilon \simeq 3 \times 10^{-16} \, \mbox{ erg}\, \mbox{cm}^{-3} \, \mbox{s}^{-1}$is required to explain the non-adiabaticity of the solar wind at 1 The close correspondence between this measured heating rate at 1 AU and the upper limit in equation \ref{eq:epsmaxEarth}) ) implies that, if low frequency Alfvénnic turbulence contributes to heating the solar wind at $\sim 1$ AU, direct density fluctuations due to compressive KAWs must contribute significantly to the measured density fluctuations at $k_\perp \rho_i \sim 1$." In this context. we note that Kellogg and Horbury (2005) have argued for an Ion-acoustic or KAW origin for the small-scale density fluctuations in the solar wind at 1. AU. using completely independent arguments.," In this context, we note that Kellogg and Horbury (2005) have argued for an ion-acoustic or KAW origin for the small-scale density fluctuations in the solar wind at 1 AU using completely independent arguments." It is also Important to note that the Celnikier et al., It is also important to note that the Celnikier et al. measurements are in the relatively slow solar wind (=450 km s7! ). in which the turbulence is observed to be fairly balanced (Grappin 1990).," measurements are in the relatively slow solar wind $v \simeq 450$ km $^{-1}$ ), in which the turbulence is observed to be fairly balanced (Grappin 1990)." Thus the cascade time is likely comparable to the lower limit in equation (10)). in which case the cascade power can also be comparable to the upper limit in equation (13)).," Thus the cascade time is likely comparable to the lower limit in equation \ref{eq:tcasc0}) ), in which case the cascade power can also be comparable to the upper limit in equation \ref{eq:epsmaxEarth}) )." The density fluctuation measurements of Celnikier et al. (, The density fluctuation measurements of Celnikier et al. ( 1987) show a break from a Kolmogorov spectrum at low k to a flatter spectrum at high k. This is qualitatively consistent with the expectations from Figure {.,1987) show a break from a Kolmogorov spectrum at low k to a flatter spectrum at high k. This is qualitatively consistent with the expectations from Figure \ref{fig:dn_sw}. .The observed break happens at a rest frame frequency of ~0.1 Hz (Celnikier et al., .The observed break happens at a rest frame frequency of $\simeq 0.1$ Hz (Celnikier et al. 1987). which corresponds to k7!~7«107 em >>pi.d;~ em using the Taylor hypothesis.," 1987), which corresponds to $k^{-1} \simeq 7 \times 10^{7}$ cm $\gg \rho_i, d_i \sim 3 \times 10^6$ cm using the Taylor hypothesis." " This suggests that f <1. οι, that the passive scalar contribution to the density fluctuations is small compared to the KAW contribution. so that the latter begins to dominate at kp;<| (see Fig. 1))."," This suggests that $f \ll 1$ , i.e., that the passive scalar contribution to the density fluctuations is small compared to the KAW contribution, so that the latter begins to dominate at $k_\perp \rho_i \ll 1$ (see Fig. \ref{fig:dn_sw}) )." Amonest the first results of extragalactic mid-LHt astronomy was the discovery of small number of galaxies that emit the bulk of their bolometrica luminosity in the infrared (Low Ixleinmann LOGS. Wheinmann Low 1970a.b).,"Amongst the first results of extragalactic mid-IR astronomy was the discovery of a small number of galaxies that emit the bulk of their bolometric luminosity in the infrared (Low Kleinmann 1968, Kleinmann Low 1970a,b)." The Infralted Astronomical Satellite. URAS. detected. large numbers of rese ultraluminous infrared. galaxies (ULIRGSs) (Soifer οἱ al.," The InfraRed Astronomical Satellite, IRAS, detected large numbers of these ultraluminous infrared galaxies (ULIRGs) (Soifer et al." 1984. Joseph Wright 1985. and Soifer. Neugebauer Llouck 1987) with cquasar-like luminosities of Lin(8 10060αι).>107?L..," 1984, Joseph Wright 1985, and Soifer, Neugebauer Houck 1987) with quasar-like luminosities of $\rm L_{IR}~(8$ $\rm 1000\,\mu m)~> 10^{12}\,L_\odot$." Phere is still debate as to the nature of the [ar-LE power source in these galaxies: is the inamense thermal energy driven by a dominant starburst. à dominant AGN or some combination of the two?," There is still debate as to the nature of the far-IR power source in these galaxies: is the immense thermal energy driven by a dominant starburst, a dominant AGN or some combination of the two?" " ""These Iow-recdshift IUCAS-selected. ULIBCGSs are expected to be the counterparts to the high redshift (22 1) SCUBA sources (see. e.g. Smail et al."," These low-redshift IRAS-selected ULIRGs are expected to be the counterparts to the high redshift $z >1$ ) SCUBA sources (see, e.g., Smail et al." 1998. Blain et al.," 1998, Blain et al." 2002. Webb ct al.," 2002, Webb et al." 2003. Chapman et al.," 2003, Chapman et al." 2003)., 2003). Most ULIRG systems have been shown to be disturbed. interacting or merging in some wav when the separation of nuclei is less than LOkpe (Sanders et al.," Most ULIRG systems have been shown to be disturbed, interacting or merging in some way when the separation of nuclei is less than 10kpc (Sanders et al." 1988. Clements et al.," 1988, Clements et al." 19060. Murphy. et al.," 1996, Murphy et al." 1996. Farrah ct al.," 1996, Farrah et al." 2001)., 2001). " The nature of widely separated ULERG systems 1s less clear (Dinh-V-""Prune et al.", The nature of widely separated ULIRG systems is less clear (Dinh-V-Trung et al. 2001. Meusinger et al.," 2001, Meusinger et al." 2001): are the 'omponents of the ULIBG. (supposedly the end. phase of 1e galactic interaction) beginning another merger or is the ULIRG a result of a multiple merger event (Borne et al., 2001): are the components of the ULIRG (supposedly the end phase of the galactic interaction) beginning another merger or is the ULIRG a result of a multiple merger event (Borne et al. 2000)?, 2000)? ‘This latter scenario is possible in widely separated ULIRGs with resolved double nuclei but might not apply to the ULIBG svstem IRAS09111.1007. which consisμα of two widely spaced. but. interacting Luminous infrarec ealaxies (LIItCis). each with a single nucleus.," This latter scenario is possible in widely separated ULIRGs with resolved double nuclei but might not apply to the ULIRG system $\rm IRAS~09111-1007$, which consists of two widely spaced but interacting luminous infrared galaxies (LIRGs), each with a single nucleus." Phe two LIRGs have a projected. separation of hhzf kpe and a velocity difference of 425kms.+ (Duc. Mirabel Maza. 1997).," The two LIRGs have a projected separation of $_{71}^{-1}\,$ kpc and a velocity difference of $\rm 425\,km\,s^{-1}$ (Duc, Mirabel Maza 1997)." 1n this letter we present jin resolved images and [luxes for IRAS091111007.," In this letter we present $\,\mu$ m resolved images and fluxes for $\rm IRAS~09111-1007$." We model the far-LIX clust emission t(« constrain the nature of the interaction., We model the far-IR dust emission to constrain the nature of the interaction. The data were taken using. the Second Generation Submillimeter High Angular Resolution Camera (SLIARC LL) at the Caltech Submillimeter Observatory on Mauna οi. in January ancl March 2004.," The data were taken using the Second Generation Submillimeter High Angular Resolution Camera (SHARC II) at the Caltech Submillimeter Observatory on Mauna Kea, Hawai'i, in January and March 2004." SILARC LL is a ysem-optiniused camera (Dowell et al.," SHARC II is a $\,\mu$ m-optimised camera (Dowell et al." 2003) built around a 1232 element. close-packecl bolometer array (Moseley. ct al., 2003) built around a $12\times 32$ element close-packed bolometer array (Moseley et al. 2004)., 2004). 1t achieves a point-source sensitivity of ανHzb? in good weather.," It achieves a point-source sensitivity of $\rm \sim 1\,Jy~Hz^{-1/2}$ in good weather." The 384 pixels of the SLUARC LL array image a region of around. 1.0ο.2.5., The 384 pixels of the SHARC II array image a region of around $1.0' \times 2.5'$. Lts filled absorber array provides instantaneous imaging of the entire field of view. samplec at roughly 2.5 pixels per," Its filled absorber array provides instantaneous imaging of the entire field of view, sampled at roughly 2.5 pixels per" ⋅⋅⋅⋅⋅ J=3-2intensityisweakerintheOrionBN/K ⋅ ⋅ LregionthanatOrionS 186 outhandtheno&tRi/fSN|€KL.,$J=3-2$ intensity is weaker in the Orion BN/KL region than at Orion South and the north of BN/KL. "D Tunaherefore, thelowerCOcolumndensityderived, ""NM J=3-2t0CO J=3-2ratiotowardOrionBN/KLmaybemisleading."," Therefore, the lower CO column density derived from the lower $J=3-2$ to $J=3-2$ ratio toward Orion BN/KL may be misleading." Eventhoughthe™C J=3-2lineiso pticallythickandmaybesel ∫∶∍−⊋↨⇧↕∍∁⊙ J=3-2ratioinsteadof alowerratioinOrionBN]K L.," Even though the $J=3-2$ line is optically thick and may be self-absorbed, this will result in a higher $J=3-2$ to $J=3-2$ ratio instead of a lower ratio in Orion BN/KL." "AsGoldsmithetadcol88it) poderetout, dracolinandestimetadculasediedoptong— 106150 llines is accurate except for the temperature >150 K, which is the case in the OMC-1 core."," As \citet{Goldsmith1997} pointed out, the column density calculated using $J$ lines is accurate except for the temperature $\geq150$ K, which is the case in the OMC-1 core." " Hence, higher-J CO observations are critical to determine the CO column density in the OMC-1 core region."," Hence, $J$ CO observations are critical to determine the CO column density in the OMC-1 core region." " In addition, already shown in Figure 6,, the low J=3-2toJ=6-5ratiosindicatethattheC'8O J-6-5intensityisstronglyenhancedtowardtheOrionBN |KL,S outh"," In addition, already shown in Figure \ref{ratio1}, the low $J=3-2$ to $J=6-5$ ratios indicate that the $J=6-5$ intensity is strongly enhanced toward the Orion BN/KL, South, and Bar regions, and is likely due to their PDR nature." ", and Ba The ∫−⊖−≤∠⋯∠↿∁↕⊰⊙ "," Nevertheless, shocks/outflows may also play an important role in the Orion BN/KL and South regions, leading to an extra heating in the cloud." J-6-5dataareusedheretoderivethegasexcitationtemperatureanddensityo Icore., The $J=6-5$ and $J=6-5$ data are used here to derive the gas excitation temperature and density of the OMC-1 core. "InthesubmillimeterregimewheretheRayleigh -Jeansapproximationiso ftennotvalid, theobservedradiationtemperaturei where Τεκ is the excitation temperature and 7, is the optical depth at a specific molecular line transition."," In the submillimeter regime where the Rayleigh-Jeans approximation is often not valid, the observed radiation temperature in local thermodynamic equilibrium (LTE) can be expressed as where $T_{\rm ex}$ is the excitation temperature and $\tau_{\nu}$ is the optical depth at a specific molecular line transition." " The background brightness temperature Ty, includes the cosmic background radiation of 2.73 K and the radiation from warm dust, ranging from about 5 K for less dense gas to about 26 K for the Orion Hor Core (Goldsmithetal.,1997)."," The background brightness temperature $T_{\rm bg}$ includes the cosmic background radiation of 2.73 K and the radiation from warm dust, ranging from about 5 K for less dense gas to about 26 K for the Orion Hor Core \citep{Goldsmith1997}." . The second term inside the brackets can be neglected since it only contributes <2% of TR., The second term inside the brackets can be neglected since it only contributes $\lesssim2\%$ of $T^{*}_{\rm R}$. " By making the assumption of the same excitation temperature for aand J=6-5, theopticaldepthso f? aand J=6-5canbedetermined fromtherelation Since the optical depth of J=6-5> 1, the optical depth of J=6-Scanbedirectlyobtained(~ 0.08) by assuming that the optical depth ratio is approximated to the isotopologic abundance ratio, and here we adopted [CO]V/[C50]] of 490 (Boreiko&Betz,1996;WilsonMatteucci,1992) and a beam filling factor of unity (T?= Twp)."," By making the assumption of the same excitation temperature for and $J=6-5$, the optical depths of and $J=6-5$ can be determined from the relation Since the optical depth of $J=6-5 \gg 1$ , the optical depth of $J=6-5$ can be directly obtained $\sim 0.08$ ) by assuming that the optical depth ratio is approximated to the isotopologic abundance ratio, and here we adopted ] of 490 \citep[][]{Boreiko1996,Wilson1992} and a beam filling factor of unity $T^{*}_{\rm R}=T_{\rm MB}$ )." The excitation temperatures of aand J-6-5canbeestimatedvia Then the total ccolumn density can be derived from where Eyp is 110.6 K for the J-6-5transitionandQ;o is the rotational partition function., The excitation temperatures of and $J=6-5$ can be estimated via Then the total column density can be derived from where $E_{\rm up}$ is 110.6 K for the $J=6-5$ transition and $Q_{\rm rot}$ is the rotational partition function. " In the end, the a [CO]]/[C!3O]] abundance ration of 490and a aabundance of 8x10? (Wilson&Matteucci, 1992).."," In the end, the column density can be estimated by adopting a ] abundance ration of 490and a abundance of $8\times10^{-5}$ \citep{Wilson1992}. ." analysis of the WALADP data should use only clata outside a mask. tthe WKOs5 (Yyr) or WOTS (Yvr) mask.,"analysis of the WMAP data should use only data outside a mask, the KQ85 (7yr) or KQ75 (7yr) mask." The Planck satellite measures the sky at more dilferent frequencies than the WALAP satellite., The Planck satellite measures the sky at more different frequencies than the WMAP satellite. Phis should. allow a more secure reduction of the foreground in the CMD map., This should allow a more secure reduction of the foreground in the CMB map. Lt is expected that the masked. region in the Planck data is significantly smaller., It is expected that the masked region in the Planck data is significantly smaller. lt might. be small enough in order to allow an acceptable reconstruction of the CMD within the mask which could provide a 2-point correlation function uscable at large scales., It might be small enough in order to allow an acceptable reconstruction of the CMB within the mask which could provide a 2-point correlation function useable at large scales. (?2) ," \citep{Gorski_Hivon_Banday_Wandelt_Hansen_Reinecke_Bartelmann_2005} " where # is the racial thickness of the torus. which we consider to be of the order of the distance to the SMDBII.,"where $R$ is the radial thickness of the torus, which we consider to be of the order of the distance to the SMBH." " We notethat IN,»1 or else. due to Poisson statistics. a sizable fraction of the lines of sight would contain no dust. grains at all."," We notethat $N_a \gg 1$ or else, due to Poisson statistics, a sizable fraction of the lines of sight would contain no dust grains at all." This would contracict the strong absorption of the broad lines in the type 2 AGN (Antonucci&Miller1985)., This would contradict the strong absorption of the broad lines in the type 2 AGN \citep{Antonucci85}. . Individual grains with size e<(0%1000 imi are optically thin to X-ravs with energv of a few keV (X-ravs with this characteristic energy typically determine the absorption column depth. in. observations)., Individual grains with size $a < a_0\simlt 1000\; \mu$ m are optically thin to X-rays with energy of a few keV (X-rays with this characteristic energy typically determine the absorption column depth in observations). Therefore. in contrast to the optical frequencies. absorption of the primary AGN continuum in the X-ravs measures the total column depth of the grains on the line of sight.," Therefore, in contrast to the optical frequencies, absorption of the primary AGN continuum in the X-rays measures the total column depth of the grains on the line of sight." This column depth can be related to the total mass of the small grains. [or a given size of the torus., This column depth can be related to the total mass of the small grains for a given size of the torus. " I£ the. volume of the torus is Ἐν&2zd4U/3. then the total mass of the grains in the torus is where p, is the material density ofa grain."," If the volume of the torus is $V_t \approx 2\pi R^3/3$, then the total mass of the grains in the torus is where $\rho_a$ is the material density of a grain." " Phe column depth of the grains on a line of sight is The required. surface density of metals in. ACN absorbers can be deduced from the ""hydrogen. column? [Ng reported. in. X-ray surveys (e.g.Sazonov&Revnivt-sev2004:Sazonovetal.2007:Cuainazziοἱ 2005)."," The column depth of the grains on a line of sight is The required surface density of metals in AGN absorbers can be deduced from the “hydrogen column” $N_H$ reported in X-ray surveys \citep[e.g.,][]{Sazonov04,SazonovEtal07,Guainazzi05}." . These assume that the metal-to-gas mass ratio is Ὅμω=0.02 as appropriate to the gas of Solar composition., These assume that the metal-to-gas mass ratio is $\zeta_{\rm met} = 0.02$ as appropriate to the gas of Solar composition. " Our model then ought to satisfy M,—CueNara. where mg is the mass of hydrogen atom."," Our model then ought to satisfy $\Sigma_a = \zeta_{\rm met} N_H m_H$, where $m_H$ is the mass of hydrogen atom." " This gives a constraint on the product in cm. where we set p,—2 g and Ng=Nox1077 7."," This gives a constraint on the product in cm, where we set $\rho_a = 2$ g $^{-3}$ and $N_H = N_{23} 10^{23}$ $^{-2}$." " The total mass of the grains (equation 10)). required to fulfill the X-ray constraints. becomes For a given number of grains on the line of sight. IN, the grain size can be estimated:Note that if NV291 then eX lym for No;=1."," The total mass of the grains (equation \ref{Ma}) ), required to fulfill the X-ray constraints, becomes For a given number of grains on the line of sight, $N_a$, the grain size can be estimated:Note that if $N_a \gg 1$ then $a\simlt 1\mu$ m for $N_{23}=1$." In contrast to debris disc svstems where gas is presumed to be absent (Wyatt2008).. the AGN torii cannot be totally cdevoid of eas because AGN is Fed by accretion of gas.," In contrast to debris disc systems where gas is presumed to be absent \citep{Wyatt08}, the AGN torii cannot be totally devoid of gas because AGN is fed by accretion of gas." " We can estimate the minimum column density of eas in the torus. Ny=phlt. where p js gas density in the torus via the mass continuity for eas accreting through the torus: where AM—Al(0:01vr) is the dimensionless gas accretion rate onto the AGN. A,=ΕΕ1ρο. and (20Mi,Ryle=2hFry is 1ο free-fall velocity."," We can estimate the minimum column density of gas in the torus, $\Sigma_g = \rho R$, where $\rho$ is gas density in the torus via the mass continuity for gas accreting through the torus: where $\dot M_{-2} = \dot M/(0.01 \msun/$ yr) is the dimensionless gas accretion rate onto the AGN, $R_{pc} = R/(1$ pc), and $v_{\rm ff} = (2G\mbh/R)^{1/2} = 2^{1/2} v_K$ is the free-fall velocity." Acrodyvnamic crag force. on the grains. due to the presence of eas is likely to be significant., Aerodynamic drag force on the grains due to the presence of gas is likely to be significant. " For supersonic erain: speeds. e. the drag force⋅ is""m £42(1/2).a7ο...per (Weeencr&Ashkenas1961)."," For supersonic grain speeds, $v$, the drag force is $F_d \approx (1/2) \pi a^2 \rho v^2$ \citep{WA61}." . The stopping time of the grain. Eu.," The stopping time of the grain, $t_s = (4\pi/3)\rho_a a^3 v/F_d$ ." Comparing this to dynamical time. fy= Rieg. we have [f|bass(S/3)apo/M.," Comparing this to dynamical time, $t_{\rm dyn} = R/v_K$ , we have $t_s/t_{\rm dyn} = (8/3) a\rho_a /\Sigma_g$." " πας grains of micron size will be stopped by the aerodynamic friction in a dynamical time even at the minimum X, caleulated above.", Thus grains of micron size will be stopped by the aerodynamic friction in a dynamical time even at the minimum $\Sigma_g$ calculated above. Grains of ~ cm sizes will be stronely allectec by the gas after a sullicienthy long time., Grains of $\sim$ cm sizes will be strongly affected by the gas after a sufficiently long time. " ‘This demonstrates that small grains that are crucial to the obseuration schemes of ACN are ""frozen in” with the gas.", This demonstrates that small grains that are crucial to the obscuration schemes of AGN are “frozen in” with the gas. Therefore. the issue of the vertical pressure support for the torus support must be addressed in this model even if the origin of the small grains is à vertically extended. collisional cascade.," Therefore, the issue of the vertical pressure support for the torus support must be addressed in this model even if the origin of the small grains is a vertically extended collisional cascade." ltadiation pressure of the ACN can blow out the grains away if the bolometric luminosity. Lig=fiaéead. is largeenough.," Radiation pressure of the AGN can blow out the grains away if the bolometric luminosity, $L_{\rm bol} = l_{\rm bol} \ledd$, is largeenough." " Here Ley,=4rOAyeας is the Ecelington luminosity of the black hole. 5; is the electron. scattering opacity."," Here $L_{\rm Edd} = 4\pi G \mbh c/\kappa_{\rm e}$ is the Eddington luminosity of the black hole, $\kappa_{\rm e}$ is the electron scattering opacity." In the case of an optically thin torus. (1993) find that erains smaller than are blown out by the radiation field.," In the case of an optically thin torus, \cite{LaorDraine93} find that grains smaller than are blown out by the radiation field." " Clearly. except for very dim sources where dia,«101. [i sized. erains are expected: to be driven out quickly if the torus is optically thin."," Clearly, except for very dim sources where $l_{\rm bol} < 10^{-4}$, $\mu$ m sized grains are expected to be driven out quickly if the torus is optically thin." However. the absorber we are interested in is optically thick to most of the AGN radiation (dominated by the UV bump).," However, the absorber we are interested in is optically thick to most of the AGN radiation (dominated by the UV bump)." We expect the radiation. pressure incident on the AGN-facecl side of the absorber to be ~Li4/2e. where 1/2 comes from the fact that roughly a half of the ACN radiation is intersectecd by the torus.," We expect the radiation pressure incident on the AGN-faced side of the absorber to be $\sim L_{\rm bol}/2c$, where $1/2$ comes from the fact that roughly a half of the AGN radiation is intersected by the torus." This factor. should be reduced: further if CIN. radiation is beamec in the direction. perpendicular to the absorber's svmmetry. plane., This factor should be reduced further if AGN radiation is beamed in the direction perpendicular to the absorber's symmetry plane. " The absorber's weight is 6MiM;I7. where M, is the total torus mass. consisting of the small erains mass. AZ. and the eas mass. Ad,"," The absorber's weight is $G\mbh M_t/R^2$, where $M_t$ is the total torus mass, consisting of the small grains mass, $M_a$, and the gas mass, $M_g$." Requiring that the torus weight is greater than the radiation pressure on it. we find that where foo=μμ0.01.," Requiring that the torus weight is greater than the radiation pressure on it, we find that where $l_{-2} = l_{\rm bol}/0.01$." " Since AL,=(Srο)7p,aN,,. we get a radius independent constraint on the product eN,: where we introduced the dust mass fraction in the torus. fa=AL(AL,|M) for brevity."," Since $M_a = (8\pi/9)R^2 \rho_a a N_a$, we get a radius independent constraint on the product $a N_a$ : where we introduced the dust mass fraction in the torus, $f_d \equiv M_a/(M_g + M_a)$ for brevity." LE the torus is composed of gas with the usual dust-to-gas abundance then fy= 0.01., If the torus is composed of gas with the usual dust-to-gas abundance then $f_d = 0.01$ . If the torus is dust free. like a classical debris disc around a star. then fj= I.," If the torus is dust free, like a classical debris disc around a star, then $f_d = 1$ ." Interestingly. equation 12. now requires that. the hydrogen column depth of the absorber exceeds," Interestingly, equation \ref{a_N_a} now requires that the hydrogen column depth of the absorber exceeds" "section we would like to demonstrate, how the symmetry of the Galaxy image in @ direction can determine the properties of the D(@,¢ map.","section we would like to demonstrate, how the symmetry of the Galaxy image in $\phi$ direction can determine the properties of the $D(\theta,\phi$ map." For that we rotate the band map by 20° along the pole axis and produce the same estimation of d? as is done for the Galactic reference system.," For that we rotate the W-band map by $20^\circ$ along the pole axis and produce the same estimation of $d^{\Delta}_{\l,m}$, as is done for the Galactic reference system." The result of estimation is shown in Fig.8.., The result of estimation is shown in \ref{rot}. " For comparison, in this Figurewe plot the difference and sum between D(0,9) maps before and after rotation."," For comparison, in this Figurewe plot the difference and sum between $D(\theta,\phi)$ maps before and after rotation." " From these Figures, these new symmetry of the W band map after rotation simply increase the amplitude of signal in Galactic plane zone, especially in the the central part of it."," From these Figures, these new symmetry of the W band map after rotation simply increase the amplitude of signal in Galactic plane zone, especially in the the central part of it." " At the end of this section, we summarize the main results of investigation of the given models of the GF signal."," At the end of this section, we summarize the main results of investigation of the given models of the GF signal." " In this section we apply the proposed d? estimator to the maps for Q, V and W band foregrounds (which are sum of synchrotron, free-free and dust emission)."," In this section we apply the proposed $d^{\Delta}_{\l,m}$ estimator to the maps for Q, V and W band foregrounds (which are sum of synchrotron, free-free and dust emission)." We then transform them by the d? estimator.," We then transform them by the $d^{\Delta}_{\l,m}$ estimator." " These foreground maps do not contain the CMB signal and instrumental noise, therefore they allow us to estimate the properties of the GF in details."," These foreground maps do not contain the CMB signal and instrumental noise, therefore they allow us to estimate the properties of the GF in details." " In Fig.9 we plot the D(0,Φ) maps for Q, V and W band foregrounds (A= 4) for the multipole range @<46."," In \ref{fgd} we plot the $D(\theta,\phi)$ maps for Q, V and W band foregrounds $\Delta=4$ ) for the multipole range $\l\le 46$." This range is determined by the resolution of the foregrounds maps (¢< 50)., This range is determined by the resolution of the foregrounds maps $\l\le 50$ ). " As one can see from these maps, the GF perfectly follows to 4n multipole correlation, which remove the brightest part of the signal down to the level + 50 mK for the Q band, —0.19,0.50 mK for the V band, —0.09,0.29 mK for the W band and —0.1,0.1 mK for the D(6,¢) map, the difference between V and W foregrounds."," As one can see from these maps, the GF perfectly follows to $4n$ multipole correlation, which remove the brightest part of the signal down to the level $\pm$ 50 mK for the Q band, $-0.19,0.50$ mK for the V band, $-0.09,0.29$ mK for the W band and $-0.1,0.1$ mK for the $D(\theta,\phi)$ map, the difference between V and W foregrounds." " Note that these limits are related with the brightest positive and negative spots (point sources) in the maps, while diffuse components have significantly smaller amplitudes."," Note that these limits are related with the brightest positive and negative spots (point sources) in the maps, while diffuse components have significantly smaller amplitudes." " To show the high resolution D(6,¢) map which characterizes the properties of the foregrounds in V and W band, in Fig.10 we plot the map of difference V—W bands, and the corresponding D(@,¢) map for £< 250."," To show the high resolution $D(\theta,\phi)$ map which characterizes the properties of the foregrounds in V and W band, in \ref{pow} we plot the map of difference $V-W$ bands, and the corresponding $D(\theta,\phi)$ map for $\l\le 250$ ." " Note that V—W map does not contain the CMB signal, but for high £ the properties of the signal are determined by the instrumental"," Note that $V-W $ map does not contain the CMB signal, but for high $\l$ the properties of the signal are determined by the instrumental" lüpt A cramatic event in the radio pulses received. from. the Crab Pulsar was observed in October LOOT. during routine observations at Green Bank and at Jodrell Bank (Backer et al.,"10pt A dramatic event in the radio pulses received from the Crab Pulsar was observed in October 1997, during routine observations at Green Bank and at Jodrell Bank (Backer et al." 2000: Smith ancl Lyne ikzmarkmainBocyCitationstart36., 2000; Smith and Lyne . . Ao prominent part of he event was an echo. folowing both the main pulse and the interpulse. which was attributed to multi-path propagation involving an ionised clouc ata large distance from the pulsar out. within the Crab Nel)ula.," A prominent part of the event was an echo, following both the main pulse and the interpulse, which was attributed to multi-path propagation involving an ionised cloud at a large distance from the pulsar but within the Crab Nebula." As the cloud had: crossed. the ine of sight. a large recuction of intensity was observed. ollowed by an increase in dispersion measure.," As the cloud had crossed the line of sight, a large reduction of intensity was observed, followed by an increase in dispersion measure." Backer οἱ al., Backer et al. describe the event in detail., describe the event in detail. Γον propose a model describing he cloud as a prism. attributing the echo to a rav. path hrough the main body of the prism. and the reduction in intensity to a lensing ellect as the thick base of the prism crossed. the line of sight.," They propose a model describing the cloud as a prism, attributing the echo to a ray path through the main body of the prism, and the reduction in intensity to a lensing effect as the thick base of the prism crossed the line of sight." Our paper is a revision of this niocel., Our paper is a revision of this model. The echo observed. on this occasion. and on several others (Lyne ct al. 2001))," The echo observed on this occasion, and on several others (Lyne et al. )," . had. two components. the first with reducing delay followed after several weeks by a second with increasing delay.," had two components, the first with reducing delay followed after several weeks by a second with increasing delay." It now seems that a more appropriate model would be an essentially symmetric model. involving refraction at the two edges of a cloud rather than within the main body of the cloud.," It now seems that a more appropriate model would be an essentially symmetric model, involving refraction at the two edges of a cloud rather than within the main body of the cloud." Phe lensing elfect is then the cause of both the delaved rav. path and t10 reduction in intensity., The lensing effect is then the cause of both the delayed ray path and the reduction in intensity. We suggest that the cloud is in the orm of a filament. which crosses the line of sight due to the known proper motion of the pulsar.," We suggest that the cloud is in the form of a filament, which crosses the line of sight due to the known proper motion of the pulsar." A similar analvsis has been aopplied. hy Crossley et al to echoes of giant. pulses from the Crab pulsar: these echoes had. much shorter delews. and were attributed to structure in the inner region of he Crab nebula.," A similar analysis has been applied by Crossley et al to echoes of giant pulses from the Crab pulsar; these echoes had much shorter delays, and were attributed to structure in the inner region of the Crab nebula." The sequence of events is shown in Figure. laa. which shows the evolution of the pulse profile as observed at 610. MIIZ curing 260 clays starting at ALJD 50620.," The sequence of events is shown in Figure \ref{picture}a a, which shows the evolution of the pulse profile as observed at 610 MHz during 260 days starting at MJD 50620." Data from the daily monitoring of the Crab pulsar (Lyne et al., Data from the daily monitoring of the Crab pulsar (Lyne et al. 1993) have been used to provide a single high signal-to-noise profile of the pulse cach day., 1993) have been used to provide a single high signal-to-noise profile of the pulse each day. Each observation is tvpically an integration over 12 h. obtained by adding the intensity svnchronously at the pulse period (approximately 33 ms).," Each observation is typically an integration over 12 h, obtained by adding the intensity synchronously at the pulse period (approximately 33 ms)." The pulse profile is presented as a grev-scale of intensity on a vertical line in the ligure (this is the only available format for this observation)., The pulse profile is presented as a grey-scale of intensity on a vertical line in the figure (this is the only available format for this observation). The full rotation period of 33 milliseconds is displaved. anc a constant. value of slowdown rate 7 is used throughout.," The full rotation period of 33 milliseconds is displayed, and a constant value of slowdown rate $\dot\nu$ is used throughout." The time-scale is adjusted to an ephemoeris determined [rom the pulse arrival times over a period of one month near the middle of the sequence: a vertical track of the pulses in the figure would. indicate rotation with normal slowdown., The time-scale is adjusted to an ephemeris determined from the pulse arrival times over a period of one month near the middle of the sequence; a vertical track of the pulses in the figure would indicate rotation with normal slowdown. The main pulse is preceded by the much weaker precursor, The main pulse is preceded by the much weaker precursor "Stephens 1986)) accept the null hypothesis of the distribution being drawn from a normal distribution at confidence, but this must be taken with caution as the number of objects is small.","Stephens \cite{dag86}) ) accept the null hypothesis of the distribution being drawn from a normal distribution at confidence, but this must be taken with caution as the number of objects is small." The X-ray emission is slightly elongated and there is no evidence of substructure., The X-ray emission is slightly elongated and there is no evidence of substructure. " The brightest cluster galaxy coincides with the X-ray emission peak and is at rest with respect to the cluster mean (zgcg= 0.8382, Av=65 km sl)."," The brightest cluster galaxy coincides with the X-ray emission peak and is at rest with respect to the cluster mean $z_{BCG}=0.8382$ , $\Delta v=65$ km $^{-1}$)." Since the detection of the first exoplanet orbiting à. solar-type star. more than 400 exoplanets have been detected.,"Since the detection of the first exoplanet orbiting a solar-type star, more than 400 exoplanets have been detected." The existence of most of these planets was established by monitoring radial velocity (RV) variations of the host star. originating from the gravitational pull of the unseen planetary companion.," The existence of most of these planets was established by monitoring radial velocity (RV) variations of the host star, originating from the gravitational pull of the unseen planetary companion." So-called hot Jupiters are giant planets only a few solar radii away from their host stars that provide the opportunity to attempt the detection of starlight reflected from these planets., So-called hot Jupiters are giant planets only a few solar radii away from their host stars that provide the opportunity to attempt the detection of starlight reflected from these planets. Five extended campaigns for the search for refected light by using high-resolution spectroscopy were completed by different groups (Charbonneau et al., Five extended campaigns for the search for refected light by using high-resolution spectroscopy were completed by different groups (Charbonneau et al. " 1999, Collier Cameron et al."," 1999, Collier Cameron et al." 1999. Collier Cameron et al.," 1999, Collier Cameron et al." 2002. Leigh et al.," 2002, Leigh et al." 2003a..," 2003a.," Leigh et al., Leigh et al. 2003b. Rodler et al.," 2003b, Rodler et al." 2008)., 2008). Apart from Collier Cameron et al. (, Apart from Collier Cameron et al. ( "1999), who claimed a detection of reflected starlight. which was later withdrawn (Collier Cameron et al.","1999), who claimed a detection of reflected starlight, which was later withdrawn (Collier Cameron et al." 2000). all campaigns resulted in a detection of reflected starlight. and upper limits to the planet-to-star flux ratio and to the geometric albedo of these planets were established: to date. the tightest confidence upper limits on the geoemtric albedos of the hot Jupiters 7 Boo b. HD 75289b and v And b are 0.39 (Leigh et al.," 2000), all campaigns resulted in a non-detection of reflected starlight, and upper limits to the planet-to-star flux ratio and to the geometric albedo of these planets were established: to date, the tightest confidence upper limits on the geoemtric albedos of the hot Jupiters $\tau$ Boo b, HD 75289b and $\upsilon$ And b are $0.39$ (Leigh et al." 2003a). 0.46 (Rodler et al.," 2003a), $0.46$ (Rodler et al." 2008). and 0.42 (Collier Cameron et al.," 2008), and $0.42$ (Collier Cameron et al." 2002). respectively.," 2002), respectively." These results provided important constraints on models of the planetary atmospheres such as those by Sudarsky et al. (, These results provided important constraints on models of the planetary atmospheres such as those by Sudarsky et al. ( 2000. 2003).,"2000, 2003)." As a result. models that predicted a high reflectivity for the planetary atmosphere could be ruled out for some of the studied planets.," As a result, models that predicted a high reflectivity for the planetary atmosphere could be ruled out for some of the studied planets." More recently. the albedos of several transiting hot Jupiters at visual wavelengths could be further constrained from measurements of the secondary transit events.," More recently, the albedos of several transiting hot Jupiters at visual wavelengths could be further constrained from measurements of the secondary transit events." For the transiting hot Jupiter HD 209458b. Rowe et al. (," For the transiting hot Jupiter HD 209458b, Rowe et al. (" 2008) placed a very stringent 3c upper limit on the geometric albedo of 0.17 in the wavelength regime of 400-700 nm.,2008) placed a very stringent $3\sigma$ upper limit on the geometric albedo of 0.17 in the wavelength regime of 400-700 nm. Using data of the CoRot-satellite of the transiting hot Jupiter CoRot-Db. Snellen et al. (," Using data of the CoRot-satellite of the transiting hot Jupiter CoRot-1b, Snellen et al. (" 2009) measured a phase-dependency of the planetary flux and reported an upper limit on the geometric albedo of 0.2 in the wavelength range of 400-1000 nm.,2009) measured a phase-dependency of the planetary flux and reported an upper limit on the geometric albedo of 0.2 in the wavelength range of 400-1000 nm. This upper limit of the geometric albedo of CoRot-Ib was confirmed by an independent analysis by Alonso et al. (, This upper limit of the geometric albedo of CoRot-1b was confirmed by an independent analysis by Alonso et al. ( 20092).,2009a). Using the same data set for the same target. Rogers et al. (," Using the same data set for the same target, Rogers et al. (" 2009) reports an estimate of the planetary geometric albedo to be 0.05.,2009) reports an estimate of the planetary geometric albedo to be 0.05. Alonso et al. (, Alonso et al. ( 2009b) placed a very stringent upper limit on the geometric albedo of 0.06 of the hot Jupiter CoRot-2b in the wavelength range 400-1000 nm.,2009b) placed a very stringent upper limit on the geometric albedo of 0.06 of the hot Jupiter CoRot-2b in the wavelength range 400-1000 nm. The analysis of measurements of the secondary eclipse of the hot Jupiter HAT-P-7b with the EPOXI spacecraft and the Kepler-satellite led to an estimate of the geoemtric albedo of 0.13 at 650 nm (Christiansen et al., The analysis of measurements of the secondary eclipse of the hot Jupiter HAT-P-7b with the EPOXI spacecraft and the Kepler-satellite led to an estimate of the geoemtric albedo of 0.13 at 650 nm (Christiansen et al. 2009)., 2009). Measurements of the secondary transit of the planet Ogle-Tr-56 in the z'-band indicate a low geometric albedo less than 0.15 (Sing Morales 2009)., Measurements of the secondary transit of the planet Ogle-Tr-56 in the $z'$ -band indicate a low geometric albedo less than 0.15 (Sing Morales 2009). For a general summary of the secondary transit measurements we refer to Cowan Agol (2010)., For a general summary of the secondary transit measurements we refer to Cowan Agol (2010). r Boóttis (HD 120136A) is a main-sequence star of spectral type F7. located at a distance of 15.6 pe from our Solar System.," $\tau$ Boöttis (HD 120136A) is a main-sequence star of spectral type F7, located at a distance of 15.6 pc from our Solar System." Butler et al. (, Butler et al. ( 1997) detected a massive hot Jupiter orbiting τ Boo via RV measurements; we note that this star is one of the brightest stars in the sky harboring a planet.,1997) detected a massive hot Jupiter orbiting $\tau$ Boo via RV measurements; we note that this star is one of the brightest stars in the sky harboring a planet. Shortly after the discovery of the planetary companion. two research groups started campaigns for the search for reflected light by way of high-precision spectroscopy. which finally resulted in non-detections.," Shortly after the discovery of the planetary companion, two research groups started campaigns for the search for reflected light by way of high-precision spectroscopy, which finally resulted in non-detections." The tightest published 99.9% confidence upper limit to the geometrical albedo is p.«0.39 under the assumption that the planetary radius Ry=1.2Κι. orbital inclination values />36° and grey albedo (Leigh et al.," The tightest published $99.9\%$ confidence upper limit to the geometrical albedo is $p<0.39$ under the assumption that the planetary radius $R_{\rm p}=1.2~R_{\rm Jup}$, orbital inclination values $i \geq 36^{\circ}$ and grey albedo (Leigh et al." 2003a)., 2003a). " These authors report the detection of a candidate signal of marginal significance with a projected orbital RV semi-amplitude K,=97kmsl. which corresponds to an orbital inclination ¢=407."," These authors report the detection of a candidate signal of marginal significance with a projected orbital RV semi-amplitude $K_{\rm p}=97~{\rm km~s^{-1}}$, which corresponds to an orbital inclination $i\approx 40^{\circ}$." Here. we present our analysis of new observations of the planetary system of r Boo taken with the UV-Visual Echelle Spectrograph (UVES) mounted on the VLT/UT2 at Cerro Paranal in Chile.," Here, we present our analysis of new observations of the planetary system of $\tau$ Boo taken with the UV-Visual Echelle Spectrograph (UVES) mounted on the VLT/UT2 at Cerro Paranal in Chile." Section 2 describes the basic ideas of the search for reflected light., Section 2 describes the basic ideas of the search for reflected light. Section 3 provides an overview over the planetary system. while Section 4 outlines the acquisition and reduction of the high-resolution spectra.," Section 3 provides an overview over the planetary system, while Section 4 outlines the acquisition and reduction of the high-resolution spectra." Section 5 provides a detailed description of the data analysis with a data modeling, Section 5 provides a detailed description of the data analysis with a data modeling al least up to 2R.,at least up to 2. ... Four main plumes are present within +£14° from the North pole. as the QO VI 1032 image shows in Figure 1.," Four main plumes are present within $\pm$ $^{\circ}$ from the North pole, as the O VI 1032 image shows in Figure 1." Thev appear as bright broad features. dimming with heliocdistance.," They appear as bright broad features, dimming with heliodistance." Since the observation time to scan the corona out to 2 ods 1.4 days. plumes are either fairly stable or (hev tend to form again in almost the same position.," Since the observation time to scan the corona out to 2 is 1.4 days, plumes are either fairly stable or they tend to form again in almost the same position." In 1.4 davs the displacement of the plumes due to solar rotation is negligible., In 1.4 days the displacement of the plumes due to solar rotation is negligible. Their width at 1.7 is roughly 5x10? 10! em., Their width at 1.7 is roughly $\times$ $^9$ $^{10}$ cm. Outside the central region. >|&LE|. plumes are weaker and fewer as shown by the intensity along the heliocentric circumference with radius 1.7 (Figure 1).," Outside the central region, $\ge\vert\pm 14^{\circ}\vert$, plumes are weaker and fewer as shown by the intensity along the heliocentric circumference with radius 1.7 (Figure 1)." Aim of the analvsis is to determine the solar wind velocity in plumes and surrounding regions. including interplume lanes and darker areas of lower plume population. outside 1. that is. background coronal hole regions. with the intent of identilving the source of the hiehspeed wind.," Aim of the analysis is to determine the solar wind velocity in plumes and surrounding regions, including inter–plume lanes and darker areas of lower plume population, outside $\pm$ $^{\circ}$, that is, background coronal hole regions, with the intent of identifying the source of the high–speed wind." Therelore the different regions are studied αἱ a height 1.7Ro... where plumes are still well identified and the wind has acquired on the average a sufficientlv hieh velocity. > 100 (Strachanetal.1993:Antonucciοἱ1997a.b:νο]1997a.andDodero 1999)..," Therefore the different regions are studied at a height 1.7, where plumes are still well identified and the wind has acquired on the average a sufficiently high velocity, $\geq$ 100 \citep{str93,ant97a,ant97b,koh97a,koh98,gio99}. ." The plume emission is averaged over the brightest peaks within 414° identified as dark segments in Figure 2. and the lane emission is averaged over the cimmest regions (dashed segmentis in Figure 2).," The plume emission is averaged over the brightest peaks within $\pm$ $^{\circ}$ identified as dark segments in Figure 2, and the lane emission is averaged over the dimmest regions (dashed segments in Figure 2)." The emission of dark background regions is averaged outside the interval X14., The emission of dark background regions is averaged outside the interval $\pm$ $^{\circ}$. The background average heliodistance. 1.82Ri... is hieher than that of plumes and interplume lanes. 1.72I.," The background average heliodistance, 1.82, is higher than that of plumes and inter–plume lanes, 1.72." .. The solar wind velocity relative to the three different regimes that have been identified. plume. interplume lanes aud dark background. is (hen measured by determining (he outflow velocily of the oxveen ions through (he ratio of the Doppler dimmed O VI A 1032 and À 1037 resonance lines (Noci.IXohlandWithbroe1987:Doderoetal.1998:Li1998).," The solar wind velocity relative to the three different regimes that have been identified, plume, inter–plume lanes and dark background, is then measured by determining the outflow velocity of the oxygen ions through the ratio of the Doppler dimmed O VI $\lambda$ 1032 and $\lambda$ 1037 resonance lines \citep{noc87,dod98,li98}." .. In (he outer corona these lines are emitted both via collisional excitation of (he coronal ions and via resonant scattering of photons coming from the transition region., In the outer corona these lines are emitted both via collisional excitation of the coronal ions and via resonant scattering of photons coming from the transition region. The second process is of increasing importance as (he corona becomes more rarefied., The second process is of increasing importance as the corona becomes more rarefied. In the [rame of relerence of the expanding solar wind the relative wavelength shift of incident photons and coronal absorbing profiles. causes a cdimmimg of the resonantemission that is a function of the," In the frame of reference of the expanding solar wind the relative wavelength shift of incident photons and coronal absorbing profiles, causes a dimming of the resonantemission that is a function of the" Monte Carlo simulations aud by applying it to the wavelet source-detection analysis of a ACIS image.,Monte Carlo simulations and by applying it to the wavelet source-detection analysis of a ACIS image. Here we describe a simple aud yet general procedure that allows for the calculation of the redistribution matrix without resorting to the ray-traciug., Here we describe a simple and yet general procedure that allows for the calculation of the redistribution matrix without resorting to the ray-tracing. To illustrate this procedure. we present the analysis of X-ray sources detected in two observations.," To illustrate this procedure, we present the analysis of X-ray sources detected in two observations." The first is an observation of Abell 2125 (Fie., The first is an observation of Abell 2125 (Fig. 1). a complex of galaxies aud diffuse hot eas al 2=0.2147.," 1), a complex of galaxies and diffuse hot gas at $z = 0.247$." This 82 ksec observation has the FoV of 17x 17’ (including only the 2x2 ACIS-I CCD array)., This 82 ksec observation has the FoV of $^\prime \times$ $^\prime$ (including only the $\times$ 2 ACIS-I CCD array). Wang. Owen. Ledlow (2001) Lave presented the main results from the observation. which are based partly ou the analysis discussed here.," Wang, Owen, Ledlow (2004) have presented the main results from the observation, which are based partly on the analysis discussed here." The second observation is an 18.5 ksec exposure of NGC 1591 (Sombrero). a uearly edge-0u Sa galaxy at a distance of 8.9 Mpc (Fig.," The second observation is an 18.5 ksec ACIS-S exposure of NGC 4594 (Sombrero), a nearly edge-on Sa galaxy at a distance of 8.9 Mpc (Fig." 2)., 2). Only the data [rom the on-axis 7) back-illuminated chip with a ΕΟΝ of 8/1Lx 8114 are include., Only the data from the on-axis 7) back-illuminated chip with a FoV of $\times$ 4 are included. A study of the discrete X-ray sources detected with the same data bas been reported by Di Stefano et al. (, A study of the discrete X-ray sources detected with the same data has been reported by Di Stefano et al. ( 2003) and is compared in the present. work.,2003) and is compared in the present work. Our study does not account for all potential instrumental effects., Our study does not account for all potential instrumental effects. In particular. multiple sources of small angular separatious may produce a single detection. affecting not only the source unuuber couutiug but also the shape of the uumber-Dux relation (Hasiuger et al.," In particular, multiple sources of small angular separations may produce a single detection, affecting not only the source number counting but also the shape of the number-flux relation (Hasinger et al." 1993)., 1993). Fortunately. with the superb spatial resolution of au imaging instrument such as Chandra. the effect is typically uot important (E a few percent).," Fortunately, with the superb spatial resolution of an imaging instrument such as , the effect is typically not important $\lesssim $ a few percent)." For the observatious analyzed here. we use the position-depeucent enerey-encireled radius as the detection aperture (EER: Jerius et al.," For the observations analyzed here, we use the position-dependent energy-encircled radius as the detection aperture (EER; Jerius et al." 2000). which is a factor of 2 smaller than the source removal racius shown in Figs.," 2000), which is a factor of 2 smaller than the source removal radius shown in Figs." 1 aud 2b., 1 and 2b. Clearly. few sources are alIectecd by overlapping detection apertures.," Clearly, few sources are affected by overlapping detection apertures." Here we consider the detection of point-like X-ray sources based ou au event couut image (e.g. Figs.," Here we consider the detection of point-like X-ray sources based on an event count image (e.g., Figs." E aud 2b)., 1 and 2b). Couuts iu such au image can be divided approximately iuto two compouents: oue from iudividual X-ray sources and the other from a smoothly-distributed background. consistiug of X-ray photous aud charged particle-induced events.," Counts in such an image can be divided approximately into two components: one from individual X-ray sources and the other from a smoothly-distributed background, consisting of X-ray photons and charged particle-induced events." This background varies across the image. but typically ou scales substantially greater thau the size ofthe PSF (Jerius et al.," This background varies across the image, but typically on scales substantially greater than the size of the PSF (Jerius et al." 2000)., 2000). Various source detection aud analysis schemes (wavelet. sliding-box. aud muaximuin likelihood centroid fitting) have been used iu previous studies ιο. Freeman et al.," Various source detection and analysis schemes (wavelet, sliding-box, and maximum likelihood centroid fitting) have been used in previous studies (e.g., Freeman et al." 2002: Haruclen et al., 2002; Harnden et al. 1981: Cruddace et αἱ., 1984; Cruddace et al. 1988)., 1988). Applications of these schemes to imagine data have been described in Wang et al. (, Applications of these schemes to imaging data have been described in Wang et al. ( 2003: 2001).,2003; 2004). To detect a source is to linc a significant count. iuuber deviation from the expected statistical backgrouud fluctuation: the total count number ny withiu a certain detection aperture is compared with the expected contribution from the background 55 (e.g... Fig.," To detect a source is to find a significant count number deviation from the expected statistical background fluctuation: the total count number $n_c$ within a certain detection aperture is compared with the expected contribution from the background $n_b$ (e.g., Fig." 3a). accounting for the statistical [uctuation.," 3a), accounting for the statistical fluctuation." " iy, is typically estimated from the diffuse X-ray intensity in the regione surroundingOm the detection aperture.", $n_b$ is typically estimated from the diffuse X-ray intensity in the region surrounding the detection aperture. Specilically. we first remove source candidates identified in the wavelet detection with a reduced threshold (S/N~ 2) aud thet simooth the remaining image with a Caussian keruel adjustedadaptively to achieve a spatially uniform," Specifically, we first remove source candidates identified in the wavelet detection with a reduced threshold $S/N \sim 2$ ) and then smooth the remaining image with a Gaussian kernel adjustedadaptively to achieve a spatially uniform" communications during the compilation phase.,communications during the compilation phase. In some cases (CGheller et al 1998b) this guarantees. good [Ioad-balance and acceptable elficieney., In some cases (Gheller et al 1998b) this guarantees good load-balance and acceptable efficiency. However the easy implementation hiddens the real role of communications (Sigurdsson ct al 1997). which unfortunately are crucial in a Trec-SPLIE code.," However the easy implementation hiddens the real role of communications (Sigurdsson et al 1997), which unfortunately are crucial in a Tree-SPH code." The lack of any communication. control would. lead to a strong code degradation. since the amount of computation is mostly remote. the code would. spend most. of the time communicating and the speed-up would be almost negligible.," The lack of any communication control would lead to a strong code degradation, since the amount of computation is mostly remote, the code would spend most of the time communicating and the speed-up would be almost negligible." A suitable data and work distribution must. be implemented. and this is the topic of the next two sections.," A suitable data and work distribution must be implemented, and this is the topic of the next two sections." To handle communication we decided to use. the SUALENI libraries. which are advantageous in a number of wavs.," To handle communication we decided to use the SHMEM libraries, which are advantageous in a number of ways." They have been released. by the former Cray to make the best use of the PSE hard-ware communication svstem., They have been released by the former Cray to make the best use of the T3E hard-ware communication system. Therefore these libraries intrinsically ensure fast communications., Therefore these libraries intrinsically ensure fast communications. Moreover they allow the use of an asvnchronous communication scheme. that is to say two cpus which want to exchange information. do not have to be necessarily synchronized.," Moreover they allow the use of an asynchronous communication scheme, that is to say two cpus which want to exchange information, do not have to be necessarily synchronized." This for instance permits to a cpu to perform some computation in the meantime it waits for some data to arrive. provided these data are not necessary to proceed. further.," This for instance permits to a cpu to perform some computation in the meantime it waits for some data to arrive, provided these data are not necessary to proceed further." As discussed above a crucial step in parallel coding is to work out a suitable data cistribution scheme., As discussed above a crucial step in parallel coding is to work out a suitable data distribution scheme. Dubinski(1997) and Dave et al (1997) algorithm stands on the Salmon (1991) tecursive Orthogonal Bisection Rectangular Domains Decomposition scheme., Dubinski(1997) and Davè et al (1997) algorithm stands on the Salmon (1991) Recursive Orthogonal Bisection Rectangular Domains Decomposition scheme. Any epu handles a portion of the overall volume. whose size is weighted on the amount of ocal work.," Any cpu handles a portion of the overall volume, whose size is weighted on the amount of local work." Briellv. the idea is to keep track of the particles computational work (work-load). and to distribute. the xuwiicles in domains with roughly the same amount of computational load.," Briefly, the idea is to keep track of the particles computational work (work-load), and to distribute the particles in domains with roughly the same amount of computational load." This does not necessarily mean that he sizes of the domains are equal. neither that the number of particles inside any cpu is the The work load can be estimated in several wavs. and the guiding criterion must be decided looking at those parts of the code which actually tend to suller more casily from unbalancing problems.," This does not necessarily mean that the sizes of the domains are equal, neither that the number of particles inside any cpu is the The work load can be estimated in several ways, and the guiding criterion must be decided looking at those parts of the code which actually tend to suffer more easily from unbalancing problems." In a “Lree-SPLE code the number of interactions is a function of the particles density. so an obvious solution would be to estimate the work-Ioad as the inverse of the time-step.," In a Tree-SPH code the number of interactions is a function of the particles density, so an obvious solution would be to estimate the work-load as the inverse of the time-step." For instance we obtained acceptable results using the following recipe: where const is a user-defined. parameter. ancl /; is the elobal particle time-step.," For instance we obtained acceptable results using the following recipe: where $const$ is a user-defined parameter, and $t_i$ is the global particle time-step." However better results can be obtained replacing the total time-step with the time spent to compute the gravitational force acting on a particle. in a manner similar to Dave et al Going into some details. we firstly. compute for any epu the bary-center of the particles work-load.," However better results can be obtained replacing the total time-step with the time spent to compute the gravitational force acting on a particle, in a manner similar to Davè et al Going into some details, we firstly compute for any cpu the bary-center of the particles work-load." Then the entire system work-load barvcenter is estimated., Then the entire system work-load barycenter is estimated. Axis by axis the simulation volume is recursively cut along a direction passing through the global barveenter ancl orthogonal to the ANIS., Axis by axis the simulation volume is recursively cut along a direction passing through the global barycenter and orthogonal to the axis. The computation of the >gravitational potential. as discussed above. procecds through three steps:," The computation of the gravitational potential, as discussed above, proceeds through three steps:" The data are resolved. line-of-sight velocity measurements of the solar surface taken bv (he Michelson Doppler Imager (MDI) on board the (SOLQO) spacecraft (Scherrerοἱal.1995).,The data are resolved line-of-sight velocity measurements of the solar surface taken by the Michelson Doppler Imager (MDI) on board the (SOHO) spacecraft \citep{MDI}. ". Ringe diagrams are constructed from small. 16""x16° patches of the solar disk. tracked to move with the solar differential rotation."," Ring diagrams are constructed from small, $16^\circ \times 16^\circ$ patches of the solar disk, tracked to move with the solar differential rotation." The regions are tracked across (he solar disk center., The regions are tracked across the solar disk center. The observation cadence is 1 minute. and the patches are tracked lor 8192 minutes.," The observation cadence is 1 minute, and the patches are tracked for 8192 minutes." They are projected onto a rectangular grid using Postel's projection and corrected for the distortion in the MDI optics., They are projected onto a rectangular grid using Postel's projection and corrected for the distortion in the MDI optics. The Doppler cubes are then Fourier transformed to obtain a three dimensional power spectrum., The Doppler cubes are then Fourier transformed to obtain a three dimensional power spectrum. A more detailed discussion of the construction of ring diagrams can be found in Patronetal.(1997). and Basuοἱal.(1999).," A more detailed discussion of the construction of ring diagrams can be found in \citet{Patron1997} and \citet{BAT99}." . The spectra are fit in the same way as Basuetal.(2004)., The spectra are fit in the same way as \citet{Basuetal2004}. . The funcüonal form is from Basuetal.(1999): it is an asymmetric Lorentzian profile with terms for advection in both transverse directions and for azimuthally asymmetric power distribution., The functional form is from \citet{BAT99}; it is an asymmetric Lorentzian profile with terms for advection in both transverse directions and for azimuthally asymmetric power distribution. Fits are done at constant frequency. so Chat (o interpret these measurements as discrete normal modes. we interpolate along; each ridge to integer values of the degree (," Fits are done at constant frequency, so that to interpret these measurements as discrete normal modes, we interpolate along each ridge to integer values of the degree $\ell$." Errors are treated in (he szune wav as (Basuetal.2004)., Errors are treated in the same way as \citep{Basuetal2004}. . Target active regions are selected from the NOAA active region catalog., Target active regions are selected from the NOAA active region catalog. Ring diagrams require higher resolution Dopplergrams (han the usual ALDI mecium-C data that are collected continuously., Ring diagrams require higher resolution Dopplergrams than the usual MDI $\ell$ ' data that are collected continuously. We use [full-disk Dopplereram data which are one of MDIs high rate’ data products. produced mainly during vearly (wo to three month dynamics run campaigns.," We use full-disk Dopplergram data which are one of MDI's `high rate' data products, produced mainly during yearly two to three month dynamics run campaigns." We require a data coverage of greater than80'%., We require a data coverage of greater than. . The NOAA active region catalog includes sunspol classifications according to the Mt. Wilson scheme., The NOAA active region catalog includes sunspot classifications according to the Mt. Wilson scheme. The Mt. Wilson classifications wea. 2. 5. and 9. and combinations of these.," The Mt. Wilson classifications are $\alpha$, $\beta$, $\gamma$, and $\delta$, and combinations of these." The NOAA catalog lists active regions for each dav that thev are visible. and in the case where the classification changes. we take the classification closest to center disk crossing.," The NOAA catalog lists active regions for each day that they are visible, and in the case where the classification changes, we take the classification closest to center disk crossing." In our sample. of the active regions are classified as either à. which are unipolar groups. or 2. which are simple bipolar groups.," In our sample, of the active regions are classified as either $\alpha$, which are unipolar groups, or $\beta$, which are simple bipolar groups." Ring diagrams suffer from a number of svstematic effects., Ring diagrams suffer from a number of systematic effects. These arise primarily [rom foreshortening when away from disk center. and secular changes in the characteristics of the MDI instrument.," These arise primarily from foreshortening when away from disk center, and secular changes in the characteristics of the MDI instrument." These effects can be minimized by studying the mode parameters of an aclive region relative to a quiet Sun region. tracked al (he same latitude and as near in time as possible.," These effects can be minimized by studying the mode parameters of an active region relative to a quiet Sun region, tracked at the same latitude and as near in time as possible." For (his sample. (wo «quiet regions were chosen for each active region. one on either side of the active region.," For this sample, two quiet regions were chosen for each active region, one on either side of the active region." In order to characterize the level of activity in our rings. we use a measure of the total unsigned line-ol-sight magnetic flux.," In order to characterize the level of activity in our rings, we use a measure of the total unsigned line-of-sight magnetic flux." This measure is the Magnetic Activity Index (MAI).," This measure is the Magnetic Activity Index (MAI)," selt-cousisteutlv from the jump conditions.,self-consistently from the jump conditions. Furthermore. either the forward or reverse shocked flow can be assumed to dominate emission. or enissiou frou both regions cau be included.," Furthermore, either the forward or reverse shocked flow can be assumed to dominate emission, or emission from both regions can be included." A kinematic model for an oblique shock is difficult to construct. because by its very nature. an oblique shock deflects the flow.," A kinematic model for an oblique shock is difficult to construct, because by its very nature, an oblique shock deflects the flow." Indeed. they have lone Όσοι invoked o imodel flow curvature in radio jets (Simith19s1)..," Indeed, they have long been invoked to model flow curvature in radio jets \citep{smi84}." Deflection of the flow would appear to be inconsistent with the simple. static. conical flow boundary assumed rere.," Deflection of the flow would appear to be inconsistent with the simple, static, conical flow boundary assumed here." However. cousider BL Lac as an example source: Denn.Mutel&AMarscher(2000) present extensive nonitoring by VLBI which reveals knots with linear volarization behavior stronglv suggestive of oblique shocks.," However, consider BL Lac as an example source: \citet{dmm00} present extensive monitoring by VLBI which reveals knots with linear polarization behavior strongly suggestive of oblique shocks." While these authors stress the curvature of the snot trajectories. and difference between the kinematics of the four componcuts studied. an overlay of the rajectories (as defined by the data. rather than the ielical flow model) for components ST and $9 exposes a remarkable similuity. while the trajectories of S9 and SLO differ significantly only at the last epoch of the later. auc in that SLO may be followed closer to the core.," While these authors stress the curvature of the knot trajectories, and difference between the kinematics of the four components studied, an overlay of the trajectories (as defined by the data, rather than the helical flow model) for components S7 and S9 exposes a remarkable similarity, while the trajectories of S9 and S10 differ significantly only at the last epoch of the later, and in that S10 may be followed closer to the core." While component S& docs follow a distinctly different. and nore curved. trajectory. the general Ποσο is of a well-defined channel with modest curvature amplified im xojection. that can support the propagation of multiple oblique structures.," While component S8 does follow a distinctly different, and more curved, trajectory, the general impression is of a well-defined channel with modest curvature amplified in projection, that can support the propagation of multiple oblique structures." Furthermore. studies such as that bv Ilughes(2005). show that oblique shocks (which may © transient features) can form aud propagate. filling the cross section of a flow. while that flow maintains a simple jet-like. rectilinear fori.," Furthermore, studies such as that by \citet{hug05} show that oblique shocks (which may be transient features) can form and propagate, filling the cross section of a flow, while that flow maintains a simple jet-like, rectilinear form." Au oblique «hock is this taken to be a plane spanning he jet. of obliquity 4. measured with respect to the direction of the upstream flow. which is approximated as being in the sense of the jet axis. ignoring the siuall divergence of the stream lines.," An oblique shock is thus taken to be a plane spanning the jet, of obliquity $\eta$, measured with respect to the direction of the upstream flow, which is approximated as being in the sense of the jet axis, ignoring the small divergence of the stream lines." 4=907 corresponds to a transverse shock. aud the orientation of the shock i:4. specified by the azimuthal direction of the shock ποια]. c.," $\eta=90\arcdeg$ corresponds to a transverse shock, and the orientation of the shock is specified by the azimuthal direction of the shock normal, $\psi$." The shocked flow is a volume extending from thi4. aueto a parallel plane. a distance vw along the flow axis.," The shocked flow is a volume extending from this planeto a parallel plane, a distance $w$ along the flow axis." The linut of the shocked flow is fixed: it is ou ie core. side of the shock plane for à “forward” shoc- noving faster than the underline jet flow). aud on ιο other side for a “reverse” shock (being overtaken bv ie jet flow).," The limit of the shocked flow is fixed; it is on the `core' side of the shock plane for a “forward” shock (moving faster than the underlying jet flow), and on the other side for a “reverse” shock (being overtaken by the jet flow)." The shocked flow iav be terminated bv diabatic expansion of the shocked material. radiative osses Within the flow. or simply reflect the distauce ιο downstream flow has extended since formation.," The shocked flow may be terminated by adiabatic expansion of the shocked material, radiative losses within the flow, or simply reflect the distance the downstream flow has extended since formation." Adiabatic expansion is not relevant in this context in the current model. as by coustruction. the flow is constrained ο lie within the quiescent jet boundary.," Adiabatic expansion is not relevant in this context in the current model, as by construction, the flow is constrained to lie within the quiescent jet boundary." Radiation losses could have imposed a frequeucv-depeudeut length on he downstream flow (\larscher&Cear1985). prior to evolution through the modeled domain. but as explained πι reftrausfer.. the UMRAO observing frequencies are close {being separated by ~ V3). and the leugth determined bv radiation losses goes as Vv1/2. so little. frequencydependence of the structure is expected.," Radiation losses could have imposed a frequency-dependent length on the downstream flow \citep{mar85} prior to evolution through the modeled domain, but as explained in \\ref{transfer}, , the UMRAO observing frequencies are close (being separated by $\sim\sqrt{3}$ ), and the length determined by radiation losses goes as $\nu^{-1/2}$, so little frequency-dependence of the structure is expected." For the sake of definitiveness. if is assumed that the length of shocked flow is simply the evolved extent of the downstream flow. which changes little diving the brief propagation through the modeled domain.," For the sake of definitiveness, it is assumed that the length of shocked flow is simply the evolved extent of the downstream flow, which changes little during the brief propagation through the modeled domain." " The shocked flow is characterized bv a compression κἘν and following Cawthorue&Cobb(1990).. the upstream flow speed in the rest frame of the shock. 3, is computec: From Lind&Blandford(1985) it follows that the downstreaiu flow speed (also in the shock frame) is given by and the flow is deflected by angle à given by The flow direction within the shocked region is modified bv ¢. the shock speed. ἐν is computed frou the assumed quiesceut flow speed (3%) aud the wpstreais speed in the shock frame (37). and the dowustream flow speed 3, is transformed iuto the observer's franc. Hs."," The shocked flow is characterized by a compression $\kappa<1$ , and following \citet{cc90}, the upstream flow speed in the rest frame of the shock, $\beta^{'}_u$ is computed: From \citet{lb85} it follows that the downstream flow speed (also in the shock frame) is given by and the flow is deflected by angle $\zeta$ given by The flow direction within the shocked region is modified by $\zeta$, the shock speed, $\beta_s$, is computed from the assumed quiescent flow speed $\beta_f$ ) and the upstream speed in the shock frame $\beta{'}_u$ ), and the downstream flow speed $\beta^{'}_d$ is transformed into the observer's frame, $\beta_d$." Within the shocked region of the jet. the particle ≼∐∖∐↴∖↴↕↑⋅↖⇁↕↴∖↴↕∐↸⊳↥⋅↸∖⋜↧↴∖↴↸∖≺∏⋝∙↖↽∕⋅⊳⊔↖−⋝⋟∙⋜⋯≼↧↑∐↸∖↕⊔⋜↧∶↴∙∐↸∖↑↕↸⊳∏↸∖↕≼↧: : 5123/3 .: ⋅ ↸⊳∪∐∏≻∪∐↸∖∐↑↴∖↴↻↥⋅∪⋅↿↾↸∖↸⊳↑↸∖≼↧∪∐↑∐↸∖↴∖↴∐∪↸⊳↨↘↽↻↕⋜⋯↸∖⋜∐⋅↸∖↕∐↸⊳↥⋅↸∖⋜↧↴∖↴↸∖≼↧ by the compression factor.," Within the shocked region of the jet, the particle density is increased by $\kappa^{-\left(\delta+2\right)/3}$, and the magnetic field components projected on the shock plane are increased by the compression factor." " As noted in refquiescent.. evidence for the acceleration or deceleration of flows is ambiguous. aud— comes primarily— from the observed deviations from simple rectilinear motion displaved by oa umber of superbluuinal conrponeuts,"," As noted in \\ref{quiescent}, evidence for the acceleration or deceleration of flows is ambiguous, and comes primarily from the observed deviations from simple rectilinear motion displayed by a number of superluminal components." It is difficult to distinguish between an acceleration or deceleration of the bulk fow. aud that of shock waves ou the flow. in addition to which acceleration or deceleration müght be im direction only. due to a (1iodest) curvature of the jet (sceforexampleAbuscher 2006)..," It is difficult to distinguish between an acceleration or deceleration of the bulk flow, and that of shock waves on the flow, in addition to which acceleration or deceleration might be in direction only, due to a (modest) curvature of the jet \citep[see for example][]{mar06}. ." Tn the abseuce of compelling evidence for shock acceleration or deceleration. the propagation of the shock is modeled by a simple constant displacement of the shocked region discussed in refoblique: radiation transfer is performed for the quiescent flow at the first time step. and then over the remaining NOL~10 time steps the center of the shocked reeion traverses the flow so that the shocked domain les just within the inflow jet volume at the second time step. and would have left the jet volume after the last time step.," In the absence of compelling evidence for shock acceleration or deceleration, the propagation of the shock is modeled by a simple constant displacement of the shocked region discussed in \\ref{oblique}; radiation transfer is performed for the quiescent flow at the first time step, and then over the remaining $N-1\sim10$ time steps the center of the shocked region traverses the flow so that the shocked domain lies just within the inflow jet volume at the second time step, and would have left the jet volume after the last time step." The corresponding physical time will be determined x the shock speed (3.). computed as described in refoblique.. audthe physical leugthof the flow: as he latter is subject to an arbitrary scaling. the time evolution is arbitrarily scaled to match typical outburst xeriodsseen in the UAIRAO data.," The corresponding physical time will be determined by the shock speed $\beta_s$ ), computed as described in \\ref{oblique}, , andthe physical lengthof the flow; as the latter is subject to an arbitrary scaling, the time evolution is arbitrarily scaled to match typical outburst periodsseen in the UMRAO data." according to: 1) pixels per resolution element (RE): 2) spectral resolution: 3) uumber of fringes along slit. By(7.j).,"according to: 1) pixels per resolution element (RE); 2) spectral resolution; 3) number of fringes along slit. $B_0(i,j)$," which is a uoise-Iree template. is then calculated.," which is a noise-free template, is then calculated." B(7.j) is a [rame taken at a different time with a tiny Doppler shift.," $B(i,j)$ is a frame taken at a different time with a tiny Doppler shift." 7 is the pixel number along the dispersion direction. and j is the pixel number along the slit direction.," $i$ is the pixel number along the dispersion direction, and $j$ is the pixel number along the slit direction." The observable inteusity change at a given pixel (7.j) in DEDI is expressed by: The Doppler shift is measured by monitoring the inteusity change at a given pixel in the equation: Frame By is assumed to be a noise-Dree template aud the noise of [rame B is the quadratic sum of the photou noise aud the detector noise ap: Equation (11)) is approximated under photon-limited conditions as B0.)=wvBG.J).," The observable intensity change at a given pixel $(i,j)$ in DFDI is expressed by: The Doppler shift is measured by monitoring the intensity change at a given pixel in the equation: Frame $B_0$ is assumed to be a noise-free template and the noise of frame $B$ is the quadratic sum of the photon noise and the detector noise $\sigma_D$: Equation \ref{eq:noise_2d}) ) is approximated under photon-limited conditions as $B_{rms}(i,j)=\sqrt{B(i,j)}$." Therefore. the RV uncertainty at pixel (2.j) is given by: The overall RV uncertainty for tle entire spectral range is given by: where," Therefore, the RV uncertainty at pixel $(i,j)$ is given by: The overall RV uncertainty for the entire spectral range is given by: where" The pulsar is very weak with a lux density of only 0.15 mJy in our 3 hour observation.,The pulsar is very weak with a flux density of only 0.15 mJy in our 3 hour observation. The pulsar is significantly scatter-broadened at this frequency and the peak Dux is only 1.5 mJy., The pulsar is significantly scatter-broadened at this frequency and the peak flux is only 1.5 mJy. We subcdivided the pulse period into 128 phase bins and examined each of the 2150000. pulses., We subdivided the pulse period into 128 phase bins and examined each of the $\sim$ 150000 pulses. No single phase bin of any pulse was in excess of 400 mJy or the noise level., No single phase bin of any pulse was in excess of 400 mJy or $\times$ the noise level. This is consistent with Ixaspi et al., This is consistent with Kaspi et al. who also reported a lack of giant pulses from this pulsar., \nocite{kcm+98} who also reported a lack of giant pulses from this pulsar. This pulsar was observed twice. cach observation was 1.5 hr in length.," This pulsar was observed twice, each observation was 1.5 hr in length." The integrated Dux densities were 8.63 ancl 7.70 mJy in the two observations., The integrated flux densities were 8.63 and 7.70 mJy in the two observations. Fhis pulsar has a profile which consists ofa single component with a peak flux of 100 m.Jv., This pulsar has a profile which consists of a single component with a peak flux of $\sim$ 100 mJy. Analvsis of cach SOfés sample revealed. that many strong samples were detected in a small phase window located. far into the wings of the trailing edge of the profile., Analysis of each $\mu$ s sample revealed that many strong samples were detected in a small phase window located far into the wings of the trailing edge of the profile. No such samples were detected on the leading edge and only a few at the peak of the pulse profile., No such samples were detected on the leading edge and only a few at the peak of the pulse profile. Ht was clear that the large pulses were resolved. on this timescale., It was clear that the large pulses were resolved on this timescale. We then divided the pulse period into 256 phase bins and the 746000 single pulses from. each observation were examined., We then divided the pulse period into 256 phase bins and the $\sim$ 46000 single pulses from each observation were examined. The rms per bin is 92 ms., The rms per bin is 92 mJy. Fieure 3 shows the pulse with the largest peak flux density., Figure 3 shows the pulse with the largest peak flux density. The Hux density in this phase bin is 500. the Dux density in the integrated. profile at this phase. but the integrated Dux is only 4 times that of the integrated profile (ic. it would not be classified as a true giant. pulse).," The flux density in this phase bin is $500\times$ the flux density in the integrated profile at this phase, but the integrated flux is only 4 times that of the integrated profile (i.e. it would not be classified as a true giant pulse)." “Phe pulse is clearly resolved with a half width of —1 ms., The pulse is clearly resolved with a half width of $\sim$ 1 ms. This width must be intrinsic: the DM smearing is only 120 yrs and the scattering ime at this frequency is negligible (2).., This width must be intrinsic; the DM smearing is only 120 $\mu$ s and the scattering time at this frequency is negligible \cite{jnk98}. Of the «93000 pulses collected. 52 had a peak Ilux density in excess of 50. the integrated Dux density at a given phase.," Of the $\sim$ 93000 pulses collected, 52 had a peak flux density in excess of $50\times$ the integrated flux density at a given phase." All these pulses are ocated between phases 0.06 and 0.095., All these pulses are located between phases 0.06 and 0.095. Figure th shows the cumulative probability distribution of the intensities at phase 0.079., Figure 4b shows the cumulative probability distribution of the intensities at phase 0.079. The mean Dux density at his phase is 4 mv. therefore only pulses with intensities &reater than SO« this can be detected. at the 3-0. level.," The mean flux density at this phase is 4 mJy, therefore only pulses with intensities greater than $80\times$ this can be detected at the $\sigma$ level." The distribution clearly deviates from that expected. from eaussian noise and at hieh Dux levels can best be described with a power lav with index 2.7., The distribution clearly deviates from that expected from gaussian noise and at high flux levels can best be described with a power law with index –2.7. This power Law index is very similar to that seen in the Crab pulsar and. PSI 131937|21., This power law index is very similar to that seen in the Crab pulsar and PSR B1937+21. In contrast Figure 4a shows intensities for a bin on the rising edge of the profile with the same integrated lux density as for phase 0.079., In contrast Figure 4a shows intensities for a bin on the rising edge of the profile with the same integrated flux density as for phase 0.079. No Large intensities are seen and the distribution is consistent with noise., No large intensities are seen and the distribution is consistent with noise. There are no true giant pulses seen in our data set for SR. DIT0644., There are no true giant pulses seen in our data set for PSR B1706–44. Phe maximum Lux density of anv single oulse was only ~4. the mean integrated Dux density., The maximum flux density of any single pulse was only $\sim$ $\times$ the mean integrated flux density. Figure 5 garows the distribution of fluxes summing over all phase xns., Figure 5 shows the distribution of fluxes summing over all phase bins. Phe lluxes have been normalised to take into account he elfects of interstellar scintillation., The fluxes have been normalised to take into account the effects of interstellar scintillation. The width of the distribution is essentially determined by the receiver noise., The width of the distribution is essentially determined by the receiver noise. However. there is an excess of counts at high Duxes - there are TS2 pulses with llux densities greater than 2.4. the mean Hux density but only 490 pulses with Dux densities less than the mean.," However, there is an excess of counts at high fluxes - there are 782 pulses with flux densities greater than $\times$ the mean flux density but only 490 pulses with flux densities less than $\times$ the mean." This indicates the pulsar flux is likely log-normally distributed., This indicates the pulsar flux is likely log-normally distributed. ]t is our belief that the power-law distribution shown in Figure 3b is indicative of giant pulse behaviour., It is our belief that the power-law distribution shown in Figure 3b is indicative of giant pulse behaviour. " Hf this power law continues to larger fluxes. then 3.7.10"" rotations are needed before reaching a pulse with 20 times the mean Lux density."," If this power law continues to larger fluxes, then $3.7\times 10^6$ rotations are needed before reaching a pulse with 20 times the mean flux density." This number of rotations is within a factor of 10 of the giant pulse rate in both PSR D1937|21 and DIS2124 but significantly: higher than that of the Crab., This number of rotations is within a factor of 10 of the giant pulse rate in both PSR B1937+21 and B1821–24 but significantly higher than that of the Crab. In the Vela pulsar. log-normal statistics are adequate to fit the distribution of Lux across the bulk of the pulse profile (Ixramoer et al.," In the Vela pulsar, log-normal statistics are adequate to fit the distribution of flux across the bulk of the pulse profile (Kramer et al." 2001. Cairns οἱ al.," 2001, Cairns et al." but the width of the distribution is significantly larger at the edge of the profile than in the middle.," \nocite{kjv01,cjd01} but the width of the distribution is significantly larger at the edge of the profile than in the middle." In addition to this. there are giant micro-pulses which occur well before the main pulse phase.," In addition to this, there are giant micro-pulses which occur well before the main pulse phase." These eint micro-pulses have a half-width of ~200 yrs. ancl are not at a fixed phase. but have an inherent jitter’ of about 1 ms (7)...," These giant micro-pulses have a half-width of $\sim$ 200 $\mu$ s, and are not at a fixed phase, but have an inherent `jitter' of about 1 ms \cite{jvkb01}." heir distribution is best described by a power-law (Ixramer et al. 2001)., Their distribution is best described by a power-law (Kramer et al. \nocite{kjv01}. . We have found new examples of both hese phenomena in our current survey., We have found new examples of both these phenomena in our current survey. PSR. DI7T0644 shows an additional example of giant micro-pulses., PSR B1706–44 shows an additional example of giant micro-pulses. Εις time. however. the giant micro-pulses are ocated on the trailing edge of the pulse. and are somewhat wider then in Vela with a half-width close to 1 ms.," This time, however, the giant micro-pulses are located on the trailing edge of the pulse, and are somewhat wider then in Vela with a half-width close to 1 ms." Again here is some phase jitter as to the location of the pulse maximum., Again there is some phase jitter as to the location of the pulse maximum. For this pulsar also. the distribution of Huxes is clearly power-law at high amplitudes.," For this pulsar also, the distribution of fluxes is clearly power-law at high amplitudes." 1n PSR BIO4658 we clearly see large amplitude pulses on both the leading and trailing edges of the integrated pulse prolile., In PSR B1046–58 we clearly see large amplitude pulses on both the leading and trailing edges of the integrated pulse profile. The intensity distribution at these phases. however. is adequately. described by a log-normal distribution with moderate width.," The intensity distribution at these phases, however, is adequately described by a log-normal distribution with moderate width." Phe peak fluxes achieved are in excess of 20. the mean llux density but there is no evidence for a power-law tail to the distribution., The peak fluxes achieved are in excess of $\times$ the mean flux density but there is no evidence for a power-law tail to the distribution. In this regard they are similar to the fluctuations seen on the rising eclee of the Vela pulsar., In this regard they are similar to the fluctuations seen on the rising edge of the Vela pulsar. No giant micro-pulses are detectable in PSRs J11056107. J1420GO4S. 13150958 or J16175055.," No giant micro-pulses are detectable in PSRs J1105--6107, J1420–6048, B1509–58 or J1617–5055." However. the sensitivitv to giant micro-pulses in these pulsars is not. as good as for PSR DI170644 or 101058.," However, the sensitivity to giant micro-pulses in these pulsars is not as good as for PSR B1706–44 or B1046–58." To demonstrate this. leUs assume that any giant pulses would be similar to those seen in PSR DI70644: Le. they would have an intrinsic. width of 0.5 ms. a power-law index of 9.0 and occur every 107 rotations.," To demonstrate this, let's assume that any giant pulses would be similar to those seen in PSR B1706–44; i.e. they would have an intrinsic width of 0.5 ms, a power-law index of –3.0 and occur every $10^7$ rotations." The brightest giant pulse in the observing time for PSRs J1105.6107. 11420.6048. BI5095s and JIGLIT5055 would therefore be less than 500 mv. (in 0.5 ms) ancl not detectable in the noise.," The brightest giant pulse in the observing time for PSRs J1105–6107, J1420–6048, B1509–58 and J1617–5055 would therefore be less than 500 mJy (in 0.5 ms) and not detectable in the noise." Giant pulses could only be detected in these pulsars if they were intrinsically very narrow. and/or occured much more frequently than in either Vela or PSR. DITOG44.," Giant pulses could only be detected in these pulsars if they were intrinsically very narrow, and/or occured much more frequently than in either Vela or PSR B1706–44." We find. as in previous studies (e.g. Tavlor et al. 1975)).," We find, as in previous studies (e.g. Taylor et al. \nocite{tmh75}) )," that the modulation of pulse. intensitv is larger in the, that the modulation of pulse intensity is larger in the are willing to accept.,are willing to accept. We find this very concept (the precision) very clillicult to evaluate., We find this very concept (the ) very difficult to evaluate. Lt is uncomfortable for any scientist to talk about the accuracy of a measurement whenever a confidence interval has not been assigned to it. ancl as has been exposed above. that is precisely the problem with spectroscopy of faint sources.," It is uncomfortable for any scientist to talk about the accuracy of a measurement whenever a confidence interval has not been assigned to it, and as has been exposed above, that is precisely the problem with spectroscopy of faint sources." In a previous paper (SOL) we showed that our particular technique is able to measure recshilts of [aint objects with a reliability which is comparable (Gf not superior) to that of the traditional spectroscopic method., In a previous paper (FS01) we showed that our particular technique is able to measure redshifts of faint objects with a reliability which is comparable (if not superior) to that of the traditional spectroscopic method. We present in this work a simple method that allows for the calculation of accurate confidence intervals around photometric redshift’ measurements., We present in this work a simple method that allows for the calculation of accurate confidence intervals around photometric redshift measurements. The use of these confidence intervals should. solve the problem. of the so-called errors; when the photometric technique gives results that are very different from the spectroscopic ones.," The use of these confidence intervals should solve the problem of the so-called , when the photometric technique gives results that are very different from the spectroscopic ones." We intend to show that in those apparently discordant cases. either. the values are in [act consistent (when the photometric value is actually compatible with the spectroscopic one within an acceptable probability level) or the problem. is serious enough to call for a revision ofbolh valueswhen they are incompatible to a Large degree of confidence.," We intend to show that in those apparently discordant cases, either the values are in fact consistent (when the photometric value is actually compatible with the spectroscopic one within an acceptable probability level) or the problem is serious enough to call for a revision of values–when they are incompatible to a large degree of confidence." We further suggest. that the photometric redshifts together with their associated probability Dunctions.must be used in the calculation of any quantity which is derived from the redshifts. in order to perform an adequate error assessment of the results.," We further suggest that the photometric redshifts together with their associated probability functions, be used in the calculation of any quantity which is derived from the redshifts, in order to perform an adequate error assessment of the results." The structure of this paper is as follows: in Section 2 we present the catalogues of photomoetric/spectroscopic redshifts over which our technique is tested., The structure of this paper is as follows: in Section \ref{seccat} we present the catalogues of photometric/spectroscopic redshifts over which our technique is tested. Section 3 contains the description. and. measurement of the sources of error. (photometric and. systematic) present in the photometric redshift determination., Section \ref{secerr} contains the description and measurement of the sources of error (photometric and systematic) present in the photometric redshift determination. We present ancl apply the technique to estimate errors in Section 4. and. discuss the results in Section 5..," We present and apply the technique to estimate errors in Section \ref{sectec}, and discuss the results in Section \ref{secdis}." Our conclusions are resumed in Section 6 We will use the catalogue presented by FSOL (vchich in turn is based on the spectroscopic catalogue by Cohen et al.," Our conclusions are resumed in Section \ref{seccon} We will use the catalogue presented by FS01 (which in turn is based on the spectroscopic catalogue by Cohen et al." 2000. COO hereafter). as a basis to calibrate the errors in. our photometric measurements.," 2000, C00 hereafter), as a basis to calibrate the errors in our photometric measurements." The photometric data used in the analysis include space images (Llubble Space Telescope optical observations through the filters E300. FASOW. 1606. ancl ESIAW). and grouncd-based observations taken at Witt Peak in the J. df. and A bands.," The photometric data used in the analysis include space images (Hubble Space Telescope optical observations through the filters F300W, F450W, F606W and F814W), and ground-based observations taken at Kitt Peak in the $J$, $H$, and $K$ bands." A few changes have been done. as follows: The total list. of. photometric/spectroscopie redshift pairs is now composed of 153 values.," A few changes have been done, as follows: The total list of photometric/spectroscopic redshift pairs is now composed of 153 values." As was presented in previous papers (Lanzetta. Fernánndez-Soto Χαμ 1998hereafter LEYOS.. ELY99. YOO. FSOL). the sources of error in the photometric redshift measurements are twolold.," As was presented in previous papers (Lanzetta, Fern\'anndez-Soto Yahil 1998–hereafter LFY98, FLY99, Y00, FS01), the sources of error in the photometric redshift measurements are twofold." Phere is an obvious uncertainty in the redshift which is associated to the uncertainty in the photometrie measurements. and this is taken into account in our calculation of the redshift likelihood function: where the product extends to the number of observed filters. -liàs a normalization constant. f; and e; are the flux. and associated error of the source measured in the 7-th band. and οι27) ave the model Duxes for a galaxy of type {αἱ recshift z in the ;-th band.," There is an obvious uncertainty in the redshift which is associated to the uncertainty in the photometric measurements, and this is taken into account in our calculation of the redshift likelihood function: where the product extends to the number of observed filters, $A$ is a normalization constant, $f_i$ and $\sigma_i$ are the flux and associated error of the source measured in the $i$ -th band, and $F_i(z,T)$ are the model fluxes for a galaxy of type $T$ at redshift $z$ in the $i$ -th band." In principle the Likelihood function determined. this wav should. allow us to calculate confidence limits in the parameters of interest (in our case the errors associated to 2)., In principle the likelihood function determined this way should allow us to calculate confidence limits in the parameters of interest (in our case the errors associated to $z$ ). But this only applies to the cases in whichdala., But this only applies to the cases in which. Vhis is not the case of our technique., This is not the case of our technique. Phe reason for this is that the discrete number of templates used to produce the model [uxes (six in our case) cannot be realistically expected: to reproduce the spectral energy. clistributions of all galaxies., The reason for this is that the discrete number of templates used to produce the model fluxes (six in our case) cannot be realistically expected to reproduce the spectral energy distributions of all galaxies. This fact will be particularly notorious For bright galaxies. where the —=igh-quality photometry will amplify any dillerence between the model and the observations. hence producing two ellects:," This fact will be particularly notorious for bright galaxies, where the high-quality photometry will amplify any difference between the model and the observations, hence producing two effects:" observed in this WLF.,observed in this WLF. lt is seen from Figure 4 that FP D exhibits a significant continuum enhancement in the impulsive phase that reaches a peak of ~8% at around 06:36:35 UT., It is seen from Figure 4 that FP B exhibits a significant continuum enhancement in the impulsive phase that reaches a peak of $\sim 8$ at around 06:36:35 UT. Moreover. the temporal evolution of the continuum enhancement shows a fairly well correlation with the 2550 keV TINK emission.," Moreover, the temporal evolution of the continuum enhancement shows a fairly well correlation with the 25–50 keV HXR emission." This fact indicates that the continuum enhancement is most probably related to the precipitation of non-thermal electrons into the chromosphere., This fact indicates that the continuum enhancement is most probably related to the precipitation of non-thermal electrons into the chromosphere. Ii comparison. the continuum enhancement at FP A is less significant. while the INR emission there seems stronger than that at FP D. To get a «quantitative view between the continuum emission ancl non-thermal electrons. we have further derived the energy content of the electron beams at the (wo FPs (see 833.1).," In comparison, the continuum enhancement at FP A is less significant while the HXR emission there seems stronger than that at FP B. To get a quantitative view between the continuum emission and non-thermal electrons, we have further derived the energy content of the electron beams at the two FPs (see 3.1)." The results show that in the impulsive phase. the enerev [lux οἱ non-thermal electrons precipitating al FP D is slightly less than that at FP A. Therefore. {here arises an interesting question: why a stronger electron beam at FP A results in a weaker continuum enhancement?," The results show that in the impulsive phase, the energy flux of non-thermal electrons precipitating at FP B is slightly less than that at FP A. Therefore, there arises an interesting question: why a stronger electron beam at FP A results in a weaker continuum enhancement?" To answer (he question about the different responses of the continuum enission to the 10n-thermal electrons at the two FPs. we need to check carefully the sspeclral signatures that provide a clue to the atmospheric heating (here.," To answer the question about the different responses of the continuum emission to the non-thermal electrons at the two FPs, we need to check carefully the spectral signatures that provide a clue to the atmospheric heating there." Generally speaking. the line emission can be affected by (three different mechanisms: beam precipitation of energetic electrons. thermal conduction. aid enhanced coronal pressure.," Generally speaking, the line emission can be affected by three different mechanisms: beam precipitation of energetic electrons, thermal conduction, and enhanced coronal pressure." In some cases. specific heating nuechanisms may be identified unambiguouslv from (he spectral signatures of the line profile (Canlfield et al.," In some cases, specific heating mechanisms may be identified unambiguously from the spectral signatures of the line profile (Canfield et al." 1984)., 1984). Figure 5 plots the line profiles for the two FPs at 06:36:16 UT., Figure 5 plots the line profiles for the two FPs at 06:36:16 UT. The figure shows that the line intensity αἱ FP A is much stronger than that at FP D at the start of ground-based observations. which means that the chromosphere at FP A has already. been heated to a considerable extent before observations.," The figure shows that the line intensity at FP A is much stronger than that at FP B at the start of ground-based observations, which means that the chromosphere at FP A has already been heated to a considerable extent before observations." The continuum emission shows a different behavior: il increases rapidly at the relatively cool FP D in rough coincidence with the ΗΝ emission. while it varies slowly at the relatively hot FP A. as shown in Figure 4.," The continuum emission shows a different behavior: it increases rapidly at the relatively cool FP B in rough coincidence with the HXR emission, while it varies slowly at the relatively hot FP A, as shown in Figure 4." As shown in Figure 5. the pprofile at FP A is relatively strong ancl broad without a visible reversal. while that at FP D is relatively weak and shows an appreciable central reversal.," As shown in Figure 5, the profile at FP A is relatively strong and broad without a visible reversal, while that at FP B is relatively weak and shows an appreciable central reversal." According to Canfield et al. (, According to Canfield et al. ( 1984). only a hieh coronal pressure can produce strong emission profiles without a central reversal. which fits the situation of FP A. Thus. the less sienificant continuum enhancement,"1984), only a high coronal pressure can produce strong emission profiles without a central reversal, which fits the situation of FP A. Thus, the less significant continuum enhancement" dust-to-gas mass ratio.,dust-to-gas mass ratio. In the MW the dust-to-gas mass ratio is 0.5x107? in the diffuse ISM 2009) and 0.9x107? in molecular clouds (Pollacketal.1994)., In the MW the dust-to-gas mass ratio is $0.5\times10^{-2}$ in the diffuse ISM \citep{Dra09} and $0.9\times10^{-2}$ in molecular clouds \citep{Pol94}. ". The molecular fraction, fg,, is very important, since it determines SFR and controls galaxy evolution."," The molecular fraction, $f_{{\rm H}_2}$, is very important, since it determines SFR and controls galaxy evolution." " The molecular fraction reaches fy,~1x107? around t~10*yr.", The molecular fraction reaches $f_{{\rm H}_{2}}\sim1\times10^{-3}$ around $t\sim10^{7}\ {\rm yr}$. " This results is robust for all models, since in this stage Πο formation in the gas phase is dominant over that on dust grains (Tegmarketal.1997;Hirashita&Ferrara2002)."," This results is robust for all models, since in this stage ${\rm H}_{2}$ formation in the gas phase is dominant over that on dust grains \citep{Teg97, Hir02}." . The gas temperature rapidly drops below 200K before 107yr., The gas temperature rapidly drops below $200\ {\rm K}$ before $10^{7}\ {\rm yr}$. " Then, the molecular fraction rapidly increases from t~10?yr and reaches ~0.83 at the galaxy age of ~0.8Gyr (z= 5)."," Then, the molecular fraction rapidly increases from $t\sim10^{8}\ {\rm yr}$ and reaches $\sim0.83$ at the galaxy age of $\sim0.8\ {\rm Gyr}$ $z=5$ )." " This is due to the enhancement of Hj formation on dust grains by increase of a4,9o."," This is due to the enhancement of ${\rm H}_{2}$ formation on dust grains by increase of $\sigma_{{\rm d},-20}$." " For t=3x107yr, σα,ορ21.1x107 and [dfn,/dt],,.., exceeds [dfu,/dt],,,.."," For $t\gtrsim\ 3\times10^{7}\ {\rm yr}$, $\sigma_{{\rm d},-20}\gtrsim1.1\times10^{-4}$ and $\left[{\rm d}f_{{\rm H}_{2}}/{\rm d}t\right]_{\rm dust}$ exceeds $\left[{\rm d}f_{{\rm H}_{2}}/{\rm d}t\right]_{\rm star}$." " For oa,52920.001, the increase of molecular fraction enhances the star formation."," For $\sigma_{{\rm d},-20}\gtrsim0.001$, the increase of molecular fraction enhances the star formation." " The cycle of the H2 formation on dust, the star formation and the dust formation bySNe, significantly accelerates galaxy evolution, such as rapid increase of the stellar mass fraction, Mstar/(Mgas+Mstar)."," The cycle of the ${\rm H}_{2}$ formation on dust, the star formation and the dust formation bySNe, significantly accelerates galaxy evolution, such as rapid increase of the stellar mass fraction, $M_{\rm star}/(M_{\rm gas}+M_{\rm star})$." " At the galaxy age ~0.8x10?yr, the stellar mass fraction goes up to Matar/(Mgas+Matar)~0.60."," At the galaxy age $\sim0.8\times10^{9}\ {\rm yr}$, the stellar mass fraction goes up to $M_{\rm star}/(M_{\rm gas}+M_{\rm star})\sim0.60$." " The SFR, W(t), decreases from the time when Mstar/(Mgas+Mstar)~0.45, since gas mass decreasessignificantly."," The SFR, $\Psi(t)$, decreases from the time when $M_{\rm star}/(M_{\rm gas}+M_{\rm star})\sim0.45$, since gas mass decreasessignificantly." The active star formation causes the formation of dust grains and metals., The active star formation causes the formation of dust grains and metals. " At t~0.8Gyr, the total dust cross-section, 24,20, goes up to 2.3 and the metallicity, Z, goes up to 3.3x1071 Zo."," At $t\sim0.8\ {\rm Gyr}$, the total dust cross-section, $\sigma_{{\rm d},-20}$, goes up to $2.3$ and the metallicity, $Z$, goes up to $3.3\times10^{-1}\ Z_{\odot}$ ." Figure 6 shows the results of the galaxy model with the dustdestruction by only the forward shocks (model B1m9) to illustrate the effects of dust destruction by forward shocks on the galaxy evolution., Figure \ref{0_6_1} shows the results of the galaxy model with the dustdestruction by only the forward shocks (model B1m9) to illustrate the effects of dust destruction by forward shocks on the galaxy evolution. In this model ng=1.0cm-?., In this model $n_{\rm SN}=1.0\ {\rm cm^{-3}}$. " The dust destruction by forward shocks slightly affects the dust-to-gas mass ratio, Da, after the galaxy age of ~5x105yr."," The dust destruction by forward shocks slightly affects the dust-to-gas mass ratio, $D_{{\rm d},-2}$, after the galaxy age of $\sim5\times10^{8}\ {\rm yr}$." " This is because.», the destruction by forward shocks is roughly proportional to the dust-to-gas mass ratio (see Equation (9))), and dust grains are destroyed significantly for Da,20.1 in this case."," This is because the destruction by forward shocks is roughly proportional to the dust-to-gas mass ratio (see Equation \ref{dustformulation}) )), and dust grains are destroyed significantly for $D_{{\rm d},-2}\gtrsim0.1$ in this case." The SFR decreases from the time when Mstar/(Mgas+Mstar)~0.4., The SFR decreases from the time when $M_{\rm star}/(M_{\rm gas}+M_{\rm star})\sim0.4$. " At ~0.8 Gyr, the molecular fraction reaches fy,~0.51 and the stellar mass fraction reaches Mstar/(MgasMaas)~ 0.47."," At $\sim0.8\ {\rm Gyr}$ , the molecular fraction reaches $f_{{\rm H}_{2}}\sim0.51$ and the stellar mass fraction reaches $M_{\rm star}/(M_{\rm gas}+M_{\rm star})\sim0.47$ ." " In Figure 7,, we show the results of our fiducial model Alm9 in which we include the dust destruction by both reverse and forward shocks in the case of ng=1 cm?."," In Figure \ref{0_5_1}, we show the results of our fiducial model A1m9 in which we include the dust destruction by both reverse and forward shocks in the case of $n_{\rm SN}=1\ {\rm cm^{-3}}$ ." " The molecular fraction reaches to fg,~1x107? around t~107yr.", The molecular fraction reaches to $f_{{\rm H}_{2}}\sim1\times10^{-3}$ around $t\sim10^{7}\ {\rm yr}$. " This is similar to Clm9 and B1m9. Aftert>10” yr, the molecular fraction evolution is quite different from models C1m9 and B1m9."," This is similar to C1m9 and B1m9.After $t\gtrsim10^{7}\ {\rm yr}$ , the molecular fraction evolution is quite different from models C1m9 and B1m9." The molecular fraction, The molecular fraction Spectral classification of Be stars in the SMC is. particularly ditheult.,Spectral classification of Be stars in the SMC is particularly difficult. Classification of Be stars in the Galaxy relies on using the ratios of many metal lines (Walborn&Fitzpatrick1990).. unfortunately the metallicity of SMC stars is lower than those in the Galaxy and so these metal lines appear extremely weak and are often not present.," Classification of Be stars in the Galaxy relies on using the ratios of many metal lines \citep{wal90}, unfortunately the metallicity of SMC stars is lower than those in the Galaxy and so these metal lines appear extremely weak and are often not present." There is also the added ditfieulty that the Balmer lines in particular will be rotationally broadened and hence obscure any comparisons to neighbouring lines., There is also the added difficulty that the Balmer lines in particular will be rotationally broadened and hence obscure any comparisons to neighbouring lines. Other dithculties are added when we consider the ettect of the circumstellar disk., Other difficulties are added when we consider the effect of the circumstellar disk. We often get Ha emission originating from the circumstellar disk but we can also see the circumstellar disks etfect on the higher order balmer lines though in-filling., We often get $\alpha$ emission originating from the circumstellar disk but we can also see the circumstellar disks effect on the higher order balmer lines though in-filling. As a result we use the classification criteria and methods as set out by Lennon(1997). and Evansetal.(2004)., As a result we use the classification criteria and methods as set out by \citet{len97} and \citet{eva04}. For the luminosity classification we have adopted the classification method set out in Walborn&Fitzpatrick(1990). however since this method relies on line ratios we face al the same diffieulties. as previously mentioned.," For the luminosity classification we have adopted the classification method set out in \citet{wal90}, however since this method relies on line ratios we face all the same difficulties as previously mentioned." We have also performed a check on this luminosity classification by comparing the absolute magnitude of the source in the V-band with the spectra classification obtained., We have also performed a check on this luminosity classification by comparing the absolute magnitude of the source in the V-band with the spectral classification obtained. Here we have adopted a distance modulus for the SMC of 18.9 (Harriesetal.2003) and we use the relevan tables in Wegner(2006)., Here we have adopted a distance modulus for the SMC of 18.9 \citep{{har03}} and we use the relevant tables in \citet{weg06}. . These tables are based on absolute magnitudes from HIPPARCOS data., These tables are based on absolute magnitudes from HIPPARCOS data. Although the luminosities of Be stars in the SMC may ditter somewhat to those in the Milky Way we have adopted this method as a check and recognise that in some cases the results obtained may be uncertain., Although the luminosities of Be stars in the SMC may differ somewhat to those in the Milky Way we have adopted this method as a check and recognise that in some cases the results obtained may be uncertain. This source was detected by both ROSAT (RX JOOS7.3-7325) and (AX10057.4-7325:Kahabkaetal.1999:Torii2000).," This source was detected by both ROSAT (RX J0057.3-7325) and \citep[AX J0057.4-7325;][]{kah99,tor00}." Coherent pulsations were first detected in the data at a period of 101.4540.07 ss. The resultant overlapping error circles allowed for some counterparts to be tentatively assigned (Edge&Coe 2003).., Coherent pulsations were first detected in the data at a period of $101.45\pm0.07$ s. The resultant overlapping error circles allowed for some counterparts to be tentatively assigned \citep{edg03}. . The detection of pulsations at 101.16+ 0.26ss in the data (McGowanetal.2007) has allowed the counterpart to be clearly identified as the source previously labelled E in Figure 3 of Edge&Coe(2003).. MACS 10057734 10 (Tucholkeetal. 1996).," The detection of pulsations at $101.16\pm0.26$ s in the data \citep{mcg07} has allowed the counterpart to be clearly identified as the source previously labelled E in Figure 3 of \citet{edg03}, MACS J0057-734 10 \citep{tuc96}." This source had first been identified as a possible counterpart in January 2000 due to its r-Ha colour revealing an excess of Ha., This source had first been identified as a possible counterpart in January 2000 due to its $\alpha$ colour revealing an excess of $\alpha$. Subsequently this source was observed 4+ years later in 2004 using the 1.9m SAAO telescope. two spectra taken on the night have been co-added and are shown inFigure |..," Subsequently this source was observed 4 years later in 2004 using the 1.9m SAAO telescope, two spectra taken on the night have been co-added and are shown inFigure \ref{fi101ha}. ." We can, We can The “standard model” of GRBs aud alterglows postulates magnetic feld auc accelerated particles in rough equipartition with the quasi-thermal btIk of the shocked plasina.,The “standard model” of GRBs and afterglows postulates magnetic field and accelerated particles in rough equipartition with the quasi-thermal bulk of the shocked plasma. Such magnetic fields must be generated in aud by the blast wave — simpe colupression of tle pre-existing field is iusulficieut by many orders of magituce., Such magnetic fields must be generated in and by the blast wave – simple compression of the pre-existing field is insufficient by many orders of magnitude. If the blast wave manages to eenerate the field somehow. particle acceleration must occur (Fermi 1919) giving the observed eijlssiou by a combination of svuchrotrou aud Comptou (Meszaros Rees 1f)93). and. possibly eiviug the observed ultra-high-euergy. cosinic rays (Waxinan 1995).," If the blast wave manages to generate the field somehow, particle acceleration must occur (Fermi 1949) giving the observed emission by a combination of synchrotron and Compton (Meszaros Rees 1993), and possibly giving the observed ultra-high-energy cosmic rays (Waxman 1995)." WerpFOPOsec that kinetic (colisiouless) plasma instabilities are important for the magnetic field gene‘ation (Cruzinov Waxiian 1999)., We proposed that kinetic (collisionless) plasma instabilities are important for the magnetic field generation (Gruzinov Waxman 1999). " But this “collisionless cynamo"" scenario lias a severe problem.", But this “collisionless dynamo” scenario has a severe problem. Weibel iustability generaes the fields ou small scales. roughly of order plasina skin.," Weibel instability generates the fields on small scales, roughly of order plasma skin." The fields can1Ol SULrive on siuall seales. non-linear Landau damping should kill them.," The fields cannot survive on small scales, non-linear Landau damping should kill them." We thereforespeculated that tte leneth scale of he liekl grows somerow (Cruginov 2001)., We therefore that the length scale of the field grows somehow (Gruzinov 2001). Receuly. a utumerical simulaticin of a 2D strong relativistic collisioness shock lias beeu repored (Spitkovssy 2008. ]xeshet et al 2008).," Recently, a numerical simulation of a 2D strong relativistic collisionless shock has been reported (Spitkovsky 2008, Keshet et al 2008)." The authors see t1e growth of the arge-scale field aud particle acceleration., The authors see the growth of the large-scale field and particle acceleration. Tha Olle Ca1 do such a thing from first principles is truly a great achievement., That one can do such a thing from first principles is truly a great achievement. There are just particles plus Maxwell iu the nunerical simulation — no asstinptious like MHD or postulaed scattering of the accelerated particles., There are just particles plus Maxwell in the numerical simulation – no assumptions like MHD or postulated scattering of the accelerated particles. But we argue (82) that magnetic fields cannot be geierated in 2D. even in collisioness plasma.," But we argue 2) that magnetic fields cannot be generated in 2D, even in collisionless plasma." We believe that the current numerical results are not final — au even better and lounger, We believe that the current numerical results are not final – an even better and longer "Westpfah 1995)) shows a peak at the position: S 19"" 28], | TO!lee [5 19"" (J2000). which is about 27 West of the position (see Fie. 1)).","Westpfahl \cite{Ton95}) ) shows a peak at the position: $^{h}$ $^{m}$ $^{2}$, $+$ $^{\deg}$ $^{\prime}$ $^{\prime\prime}$ (J2000), which is about $^{\prime\prime}$ West of the position (see Fig. \ref{FOV}) )." " However. due to the low avenlar resolution of the data (~ 15"") the radio position 15 not precise enought to exclude a coincidence with the N-ray source."," However, due to the low angular resolution of the data $\sim15^{\prime\prime}$ ) the radio position is not precise enought to exclude a coincidence with the X-ray source." While the steep radio spectral iudex of Ape=L.0:E0.2 (between the 6 and 20 em wavelength bands) favours supernova reninauts (SNR) as the source of the radio emission. the optical cmission line ratios sugeest that the region of the radio cussion is instead a IT IT regiou.," While the steep radio spectral index of $\alpha_{LC}=-1.0\pm0.2$ (between the 6 and 20 cm wavelength bands) favours supernova remnants (SNR) as the source of the radio emission, the optical emission line ratios suggest that the region of the radio emission is instead a H II region." " The MIPFS line ratio maps of 10 III], A5007 7 and 5 Π) AG717/Io in Fig.", The MPFS line ratio maps of [O III] $\lambda5007$ $\beta$ and [S II] $\lambda6717$ $\alpha$ in Fig. 9. show uo large variation over the IT TT region., \ref{flux_ratio} show no large variation over the H II region. Inside the ACIS-S error circle, Inside the ACIS-S error circle and such measurable quantities as darkanuatter fraction aud the shape of the low-mass eud of the stellar IME.,and such measurable quantities as dark-matter fraction and the shape of the low-mass end of the stellar IMF. Further progress will be determined by observational tests of these predictions. as well as mnore sophisticated οποιοςνασα. modeling of ETC formation.," Further progress will be determined by observational tests of these predictions, as well as more sophisticated chemodynamical modeling of ETG formation." Past studies sugecst that Ca does not behave like Me. with |Ca/Fe]| being possibly solar (or lower) aud not correlated with σ.," Past studies suggest that Ca does not behave like Mg, with [Ca/Fe] being possibly solar (or lower) and not correlated with $\sigma$." Trager (1998) found the Lick/IDS Cal227 index to be essentially independent of e;, Trager (1998) found the Lick/IDS Ca4227 index to be essentially independent of $\sigma$. Accordingly. Thomas (2003) concluded that [Ca/Fo] iu their sunuple ealaxics was also essentially constant with e.," Accordingly, Thomas (2003) concluded that [Ca/Fe] in their sample galaxies was also essentially constant with $\sigma$." Saelia (2002). on the other haud. ound the Ca ID triplet (CaT. 819. 855. 8G2 un) to be mildly decreasing with c6.," Saglia (2002), on the other hand, found the Ca II triplet (CaT, 849, 855, 862 nm) to be mildly decreasing with $\sigma$." Vazdekis (2003)x and Cenarro (2001) compared jew single stellar population svuthesis models for he CaT with data for field and Coma galaxies. again findingo very low [Ca/Fe].," Vazdekis (2003) and Cenarro (2004) compared new single stellar population synthesis models for the CaT with data for field and Coma galaxies, again finding very low [Ca/Fe]." While difficult o understand. eiven that both Ca and Ale are a clemeuts manufactured in similar (though not identical) uucleosvuthetic sites. the implications of these results are potentially important. eiviug theorists ample room for a wide range of speculations.," While difficult to understand, given that both Ca and Mg are $\alpha$ elements manufactured in similar (though not identical) nucleosynthetic sites, the implications of these results are potentially important, giving theorists ample room for a wide range of speculations." The unexpected behavior of Ca secs to be lustead inost Likely caused by clifficulties im the interpretation of the measurements. particularly because the two Ca iudices cmploved in these studies do not respond to Ca abundance variations in a clean fashion.," The unexpected behavior of Ca seems to be instead most likely caused by difficulties in the interpretation of the measurements, particularly because the two Ca indices employed in these studies do not respond to Ca abundance variations in a clean fashion." Prochaska (2005) showed that the Ca1227 index is severely affected by a CN bancheacd which contaminates the blue pseudocontiunuuu of the index. making it lower.," Prochaska (2005) showed that the Ca4227 index is severely affected by a CN bandhead which contaminates the blue pseudocontinuum of the index, making it lower." Because CN is strongly correlated with 0 (Trager 1998). the effect is stronger for hieher σ galaxies. offsetting any dependence of the Ca line streneth itself ono. thus making the iudex a-indepeudent.," Because CN is strongly correlated with $\sigma$ (Trager 1998), the effect is stronger for higher $\sigma$ galaxies, offsetting any dependence of the Ca line strength itself on $\sigma$, thus making the index $\sigma$ -independent." " Prochaska demonstrated this by defining a new iudex. 1227,.. which is less affected by CN contamination."," Prochaska demonstrated this by defining a new index, $_r$, which is less affected by CN contamination." " They showed that 1227, is as strongly correlated with 6 as Me hb.", They showed that $_r$ is as strongly correlated with $\sigma$ as Mg $b$. While the issue of the slope of the Ca1227-60 relation is sccmunely resolved. models that account for the effect of CN on the Cal227 iudex still indicate [Ca/Fo] ~ 0 in massive ETCs (Schiavon 2007. Craves 2007).," While the issue of the slope of the $\sigma$ relation is seemingly resolved, models that account for the effect of CN on the Ca4227 index still indicate [Ca/Fe] $\sim$ 0 in massive ETGs (Schiavon 2007, Graves 2007)." At face value. this confirms the abundance ratios found. by previous studies;," At face value, this confirms the abundance ratios found by previous studies." However. there iav be non-negleible systematics in the Ca abundances derived hy application of the Schiavon (2007) models.," However, there may be non-negligible systematics in the Ca abundances derived by application of the Schiavon (2007) models." They are affected by uncertainties in age. and in the abundances of Fe. €. and N. Thev are also affected by uncertainties in the wav models account for the contamination of Cal227 bv CN.," They are affected by uncertainties in age, and in the abundances of Fe, C, and N. They are also affected by uncertainties in the way models account for the contamination of Ca4227 by CN." So the matter should be considered far from settled., So the matter should be considered far from settled. Regarding the results based ou CaT. one should bear iu iiud that the integrated spectra of nietal-rich stellar populations iu the CaT region is dominated by M eiauts (Schiavon Darbuxy 1999). and that fact has implications for both the zero point and the slope of the [Ca/Fe|-7 relatio-," Regarding the results based on CaT, one should bear in mind that the integrated spectra of metal-rich stellar populations in the CaT region is dominated by M giants (Schiavon Barbuy 1999), and that fact has implications for both the zero point and the slope of the $\sigma$ relation." First let us consider the zero poiut., First let us consider the zero point. The stellar libraries emploved in the models used to analyze CaT data iu the past coutain hardly auyv M eiauts with kuown metallicity. let alone known [Ca/Fe (Cenarro 200La).," The stellar libraries employed in the models used to analyze CaT data in the past contain hardly any M giants with known metallicity, let alone known [Ca/Fe] (Cenarro 2001a)." Therefore. [CaΤα in the nodels themselves is uncertain. which obviously nakes it very hard for one to infer reliable [Ca/Fe roni colparison of those models with the data.," Therefore, [Ca/Fe] in the models themselves is uncertain, which obviously makes it very hard for one to infer reliable [Ca/Fe] from comparison of those models with the data." As reeards the slope of the 0 relation. we recal hat the CaT lines are located in a region where opacity in the spectra of M. eiauts is dominate w TiO lines.," As regards the slope of the $\sigma$ relation, we recall that the CaT lines are located in a region where opacity in the spectra of M giants is dominated by TiO lines." Wlile the definition of the CaT* index emploved iu these studies is partly iicaut to account for TiO contamination (Cenuarro 2001b). the iudex has not been shown to be inunue to variations iu which may bo imuportant. eiven that there is evidence that Ti is chhanced in ETC (Milone 2000).," While the definition of the $^\star$ index employed in these studies is partly meant to account for TiO contamination (Cenarro 2001b), the index has not been shown to be immune to variations in which may be important, given that there is evidence that Ti is enhanced in ETGs (Milone 2000)." Regarding the negative slope of the CaT ~ 6 relation. that could be due to the effect of TiO opacity on the pseudocoutinuunm. because: 1) TiO is well correlated with o (Trager 1998). and 2) TiO lines are more sensitive to netallicity than CaT lines (Schiavon 2000. Schiavon Barbuy 1999. Joregcuscu 1992).," Regarding the negative slope of the $^\star$ $\sim$ $\sigma$ relation, that could be due to the effect of TiO opacity on the pseudocontinuum, because: 1) TiO is well correlated with $\sigma$ (Trager 1998), and 2) TiO lines are more sensitive to metallicity than CaT lines (Schiavon 2000, Schiavon Barbuy 1999, rgensen 1992)." Finally. CN coutamination of the CaT iudices nay also be important (Exdelvi-Meudes Darbuy 1991).," Finally, CN contamination of the CaT indices may also be important (Erdelyi-Mendes Barbuy 1991)." Iu suunnuary. woe sugeest that Ca abundanuces are far from well known in ETCs. aud there is 10 compelling motivation to resort to extreme," In summary, we suggest that Ca abundances are far from well known in ETGs, and there is no compelling motivation to resort to extreme" Most striking. however. is the correlation shown in Fig. LO..,"Most striking, however, is the correlation shown in Fig. \ref{fig:pmz}," " between the total 1""adio power aud thedetected dust nasses.", between the total radio power and the dust masses. A linear reeression between logP aud logAL/AL: eives a slope of 0.61+0.16., A linear regression between $\log P$ and $\log M/M_{\sun}$ gives a slope of $0.61\pm 0.16$. We can reject (using f1ο reci]2ο eiven in e.g. Talcy Buuyou 1973)) the hypothesis hat radio power aud ¢ust mass are uncorrelated at f 99.9 level., We can reject (using the recipe given in e.g. Haber Runyon \cite{haber73}) ) the hypothesis that radio power and dust mass are uncorrelated at the 99.9 level. Ilowever. it is known that radio pow aud redshift are correlated iu flux limited samples: usi he test discussed by Aacklin (1982)). we can reject t ivpothesis that the appareut correlation between power aud dust mass is due exclusively to a correlation between Po and z aud M and z. at the level of [.36.," However, it is known that radio power and redshift are correlated in flux limited samples; using the test discussed by Macklin \cite{macklin82}) ), we can reject the hypothesis that the apparent correlation between power and dust mass is due exclusively to a correlation between P and z and M and z, at the level of $4.3 \sigma$." We παν illustrate this strong correlation Gudepeudent of redshift}. w dividing our sample in foira redsbüft iutervals (2<0.02. 02;<0.05. 0.05 Q8).," We may illustrate this strong correlation (independent of redshift), by dividing our sample in four redshift intervals $z<0.02$, $0.020.08$ )." The correlation remains in three of the forr redshüft iuterva (sce Fig. 10)):, The correlation remains in three of the four redshift interval (see Fig. \ref{fig:pmz}) ); " althoueh itis ornalls 1(t significant in the owest redshift biu Wiha) the correlalon Is very ποιος indeed in the other redshift bius. evel raf the number of objects involved is «valy of he order of 7 or 8 per biu: he significance leves are 3,Ἐν [3 ane 1.9 σ in order of increasing redshüft."," although it is formally not significant in the lowest redshift bin $0.45 \sigma$ ) the correlation is very strong indeed in the other redshift bins, even if the number of objects involved is only of the order of 7 or 8 per bin: the significance levels are 3.1, 4.3 and 4.9 $\sigma$ in order of increasing redshift." The location of t1ο upper nuits iu Fig., The location of the upper limits in Fig. 10 strongly suggests hat the «listribution iu the ogP?logM plane is bimodal. that is. if there is dus," \ref{fig:pmz} strongly suggests that the distribution in the $\log P - \log M$ plane is bimodal, that is, if there is dust" alic enabled he stucly of stellar variability. with amplitudes of a few percent (e.g. D.,and enabled the study of stellar variability with amplitudes of a few percent (e.g. \citealt{bruntt03}) ). With tlje number of transit surveys erowing steadily. 1ailliniagnitude photometry las become rouire.," With the number of transit surveys growing steadily, millimagnitude photometry has become routine." Pusline below 0.154.. 10wever. las oven dificult.," Pushing below $0.1$, however, has proven difficult." ‘To our kuowledege. Gillilandetal.(1993). holds he record for tle most precise (per exposre) grounc-basecd photonjetry. that has bee1 reported.," To our knowledge, \citet{gilliland93} holds the record for the most precise (per exposure) ground-based photometry that has been reported." Trey achieved a precsion as good as 250 pi lag gel Exposure Or a grp of ||2 starsd NI6T that tev monitored for solar-like oscillations., They achieved a precision as good as 250 $\mu$ mag per exposure for a group of 12 stars in M67 that they monitored for solar-like oscillations. P‘ior ο that. Cillileuid&“OWLL(1992) achieved a precision of τοῦ µ nage per exposure.," Prior to that, \citet{gilliland92} achieved a precision of 750 $\mu$ mag per exposure." Iu. bot of ese (uses OLv a haul «cof xight isolated stars we'e monitored., In both of these cases only a handful of bright isolated stars were monitored. -Sitce these projects were aljecl at searching [or shor ónme-scale. solar-like oscillations. the auhoSs applied high-pass filters lo eir light curves. thereN relloving any long tije-scale systematic (tretids together with any long lme-scale variability.," Since these projects were aimed at searching for short time-scale, solar-like oscillations, the authors applied high-pass filters to their light curves, thereby removing any long time-scale systematic trends together with any long time-scale variability." CFOUL-basec|l. subalillimaguituce per exJOSULEL photometry has also been plained for itdividual wieght objects (e.g. Jhaeal.2000 who obtaived an RMS of 800 µιας for e transiting system HD2¢91558 rng a plolometer: also see Wtrizetal.2005)).," Ground-based, sub-millimagnitude per exposure photometry has also been obtained for individual bright objects (e.g. \citealt{jha00} who obtained an RMS of 800 $\mu$ mag for the transiting system HD209458 using a photometer; also see \citealt{kurtz05}) )." Despite tte difficulties tu perOruiugsi bauilimagnitude photometry from the grouud for large jiunbers of st:us. the possible science rew:uds a'e compelliug.," Despite the difficulties in performing sub-millimagnitude photometry from the ground for large numbers of stars, the possible science rewards are compelling." Luproviug the precision of transit surveys by a [actor of teu woulc allow for the detection of 0.1% transits due to Neptuue-sized dlanets orbiting solar-type stars., Improving the precision of transit surveys by a factor of ten would allow for the detection of $0.1$ transits due to Neptune-sized planets orbiting solar-type stars. It would also allow the exploration of a new regime of stellar variability., It would also allow the exploration of a new regime of stellar variability. As discussed in the next section. theÀegacain iustrument on the NMT telescope is an ideal setup for achieving sub-anilimagnitide phoomery from the ground.," As discussed in the next section, the Megacam instrument on the MMT telescope is an ideal setup for achieving sub-millimagnitude photometry from the ground." Motivated by the »ossibili ol opening a uew regime to groud-based. tile-series Calupaigus. we set out to denolistra photometry for a large uuiaber of stars wih a per-exposure precision as good as a few parts 10.000 by conducting a shor time-se‘Tes stucv of he open cluster NGC 6791 using MAT/legacat," Motivated by the possibility of opening a new regime to ground-based, time-series campaigns, we set out to demonstrate photometry for a large number of stars with a per-exposure precision as good as a few parts in 10,000 by conducting a short time-series study of the open cluster NGC 6791 using MMT/Megacam." Iu the following section we clesTibe our observatious., In the following section we describe our observations. We follow with a discussion o“our cata reduction steps iu S3: in 81 we descriye tlie photouetric precision we have achieved: iu 85 we present new variable stars that we lave fouxl in tis field: aud we finish with a discussion of ow results. including the possibility of a search for trausitiug Neptune-sized plauets iu 86.," We follow with a discussion of our data reduction steps in 3; in 4 we describe the photometric precision we have achieved; in 5 we present new variable stars that we have found in this field; and we finish with a discussion of our results, including the possibility of a search for transiting Neptune-sized planets in 6." The data for tus project were obtained ou the ueghts of October μα. 9th aud 20th of 2001 uxing tlie Megacaui CCD inosaic (McLeodetal.2000 mounted ou the IMT 6.51 telescope.," The data for this project were obtained on the nights of October 4th, 9th and 20th of 2004 using the Megacam CCD mosaic \citep{mcleod00} mounted on the MMT 6.5m telescope." The Megacanm iustruime wis a 21 x 21 mosaic consisting of 36 2kx Ik. thinneck. backside-illumiuated CCDs that are eacl read out by two amplifiers.," The Megacam instrument is a $24\arcmin$ x $24\arcmin$ mosaic consisting of 36 $\times$ 4k, thinned, backside-illuminated CCDs that are each read out by two amplifiers." " The 1josale has a pixel scale of 0.08"" which allows for a well sampled poiut-spread-Duuction (PSF) even uunder the best seeit& concditious.", The mosaic has a pixel scale of $0.08\arcsec$ which allows for a well sampled point-spread-function (PSF) even under the best seeing conditions. The result is that in 1” seeing οἱe can collect as many as 2x10! piotous [rom a single star prior to saturation. setting the photon limit for the precision in a single exposure at 0.25 imnag.," The result is that in $1\arcsec$ seeing one can collect as many as $2 \times 10^{7}$ photons from a single star prior to saturation, setting the photon limit for the precision in a single exposure at 0.25 mmag." between the RGS. and previous CCD ratios within the inner 10 kpe radius. with some discrepancy for Si/Fe and Ni/Fe.,"between the RGS, and previous CCD ratios within the inner 10 kpc radius, with some discrepancy for Si/Fe and Ni/Fe." These results indicate that the CCD-derived metallicity ratios in ?. are robust., These results indicate that the CCD-derived metallicity ratios in \cite{SandersEnrich06} are robust. If the coolest gas is examined separately from the hotter gas. it appears to have Kkwer Fe and O metallicity. confirming the central abundance drop in the spatially resolved CCD measurements.," If the coolest gas is examined separately from the hotter gas, it appears to have lower Fe and O metallicity, confirming the central abundance drop in the spatially resolved CCD measurements." Fig., Fig. 17 showstqe best-fitting values of the cooler gas are only around 60 per cent of the metallicity of the hotter gas., \ref{fig:mdotcont} shows the best-fitting values of the cooler gas are only around 60 per cent of the metallicity of the hotter gas. It is possible that the metallicity variations are with temperature. not radius. although we do not understand why.," It is possible that the metallicity variations are with temperature, not radius, although we do not understand why." If there is a corntinued decrease of metallicity as temperature decreases then t1ο low O result might be understood., If there is a continued decrease of metallicity as temperature decreases then the low O result might be understood. It is unlikely that he low metallicity gas can be introduced into the centre. and we presume that the metals are removed.," It is unlikely that the low metallicity gas can be introduced into the centre, and we presume that the metals are removed." At a temperature of 0.2 keV the cooling rate is sensitive to the metallicity., At a temperature of 0.2 keV the cooling rate is sensitive to the metallicity. One simple explanation is that the high metallicity gas is inhomogeneous. conduction is suppressed between clumps. leading to the the high metallicity regions cooling out (2)..," One simple explanation is that the high metallicity gas is inhomogeneous, conduction is suppressed between clumps, leading to the the high metallicity regions cooling out \citep{MorrisFabian03}." This means that both the injection of metals is a inhomogeneous process and the metals remain poorly mixed for a considerable time (several Gyr)., This means that both the injection of metals is a inhomogeneous process and the metals remain poorly mixed for a considerable time (several Gyr). We measure values for the N abundance of between 1.6 (from the Sx model) to 4Z. (for the 5x and lower limit from the line ratios)., We measure values for the N abundance of between 1.6 (from the $5\times$ model) to $4\Zsun$ (for the $5\times$ and lower limit from the line ratios). The nitrogen emission lines in the optical spectrum of the emission-line filamentary nebula in 44696. the central galaxy in the Centaurus cluster also indicate a high nitrogen abundance.," The nitrogen emission lines in the optical spectrum of the emission-line filamentary nebula in 4696, the central galaxy in the Centaurus cluster also indicate a high nitrogen abundance." Specifically. the [NIT/H@ line ratio found by ?. of 3.2 is higher than the ratio of less than two which can be accounted for by photoionization or shock models for a solar abundance plasma (22?.," Specifically, the $\alpha$ line ratio found by \cite{Johnstone87} of 3.2 is higher than the ratio of less than two which can be accounted for by photoionization or shock models for a solar abundance plasma \citep{Heckman89,VoitDonahue90,CrawfordFabian92}." . A high nitrogen abundance in both the optical filaments and the hot gas supports the hypothesis that they have a common origin. with the filaments representing gas which has cooled from the hotter phase.," A high nitrogen abundance in both the optical filaments and the hot gas supports the hypothesis that they have a common origin, with the filaments representing gas which has cooled from the hotter phase." We clearly detect Fe emission from the core of the Centaurus cluster., We clearly detect Fe emission from the core of the Centaurus cluster. Fitting spectral models and measuring emission line ratios shows that the temperature of the gas declines to 0.3 to 0.45 keV. These results from this deep RGS observation show the widest range in ICM temperature detected in a cluster of galaxies. with a factor of 10 or more.," Fitting spectral models and measuring emission line ratios shows that the temperature of the gas declines to 0.3 to 0.45 keV. These results from this deep RGS observation show the widest range in ICM temperature detected in a cluster of galaxies, with a factor of 10 or more." The data confirm that the metallicity of the ICM declines in the very central regions., The data confirm that the metallicity of the ICM declines in the very central regions. Whether this is a real decline in metallicity. the result of an inhomogeneous metallicity distribution (2) or excess continuum is unclear.," Whether this is a real decline in metallicity, the result of an inhomogeneous metallicity distribution \citep{MorrisFabian03} or excess continuum is unclear." We do. however. find strong nitrogen enhancement in the inner 6 kpe radius.," We do, however, find strong nitrogen enhancement in the inner 6 kpc radius." The very coolest gas is concentrated in the centre of the cluster. as previously found by (?)..," The very coolest gas is concentrated in the centre of the cluster, as previously found by \citep{SandersEnrich06}." features.,features. These lines occur at energies. likely originating from and with emission at 6.97 kkeV being particularly evident in the spectra. proving strong in Fairall 9 for which the fit improves by Ay?~24 with the introduction of a narrow Gaussian (ancl therefore two additional free parameters) at 6.98ορ kkeV and to a lesser extent in Ark 120 (Ay?~12 at 6.96(dol kkeV).," These lines occur at energies likely originating from and with emission at $\sim6.97$ keV being particularly evident in the spectra, proving strong in Fairall 9 for which the fit improves by $\triangle\chi^{2}\sim24$ with the introduction of a narrow Gaussian (and therefore two additional free parameters) at $6.98^{+0.02}_{-0.02}$ keV and to a lesser extent in Ark 120 $\triangle\chi^{2}\sim12$ at $6.96^{+0.04}_{-0.04}$ keV)." Phe only objects not showing residuals at 6.7 kkeW or 6.97 kkeV are NGC 7469 and SWIET J2127-4|5654. also in agreement with Miniutti et al. (," The only objects not showing residuals at $\sim6.7$ keV or $\sim6.97$ keV are NGC 7469 and SWIFT J2127.4+5654, also in agreement with Miniutti et al. (" 2009).,2009). Resicluals at ~6.7 kkeV are only found to be significant in two objects: Fairall 9 and Mrk 335 with improvements of Ay?~7 and ~LE respectively., Residuals at $\sim6.7$ keV are only found to be significant in two objects: Fairall 9 and Mrk 335 with improvements of $\triangle\chi^{2}\sim7$ and $\sim14$ respectively. With the aim of determining the extent to which emission. from further in to the black hole is requirect. a broad component significantly improves the quality of the fit for most. objects. typically ASATo20 for three additional (ree parameters and with line widths of the order prosaZ0-3 keV. Only in MCG-02-14-009 does the addition of a broad Caussian not make a particularly significant improvement (ντ~ 3).," With the aim of determining the extent to which emission from further in to the black hole is required, a broad component significantly improves the quality of the fit for most objects, typically $\triangle\chi^{2}>20$ for three additional free parameters and with line widths of the order $\sigma_{\rm Broad}\ga0.3$ keV. Only in MCG-02-14-009 does the addition of a broad Gaussian not make a particularly significant improvement $\triangle\chi^{2}\sim3$ )." This is surprising given evidence o the contrary by Porquet (2006) in which a prominent xoad ancl statistically significant iron line was found in a short observation with an equivalent width of EWs527πλ 00V whereas only EWον92.22 ceV is found vere., This is surprising given evidence to the contrary by Porquet (2006) in which a prominent broad and statistically significant iron line was found in a short observation with an equivalent width of $\sim527^{+277}_{-248}$ eV whereas only $\sim92^{+59}_{-56}$ eV is found here. However the observation was only kks net exposure and as a result the WI line parameters are x»orlv. constrained. while the cata also allow the xoad-band: continuum to be better constrained. (however we cannot rule out some variability between these. two observations).," However the observation was only ks net exposure and as a result the K line parameters are poorly constrained, while the data also allow the broad-band continuum to be better constrained (however we cannot rule out some variability between these two observations)." In. SWIE'T J2127.4|5654. this may be due o the relatively high. best-litting. value of the rellection component with Ro=2.5LiUN which may reduce the significance of a broad component.," In SWIFT J2127.4+5654, this may be due to the relatively high best-fitting value of the reflection component with $R=2.5^{+1.1}_{-0.8}$ which may reduce the significance of a broad component." \Irk 335. features a relatively broad Gaussian with epi=0.50vH kkeV. and I4.A eeV. however this feature is not as strong as the one found by Larsson et al. (," Mrk 335 features a relatively broad Gaussian with $\sigma_{\rm Broad}=0.50^{+0.13}_{-0.11}$ keV and $=134^{+42}_{-38}$ eV, however this feature is not as strong as the one found by Larsson et al. (" 2008) with 6=0.45.(d kkeV. and —250 PAETOS Larsson et al. (,2008) with $\sigma=0.45^{+0.10}_{-0.06}$ keV and $=250^{+40}_{-39}$ eV. Larsson et al. ( 2008) also find that the emission line does not improve the fit. however,"2008) also find that the emission line does not improve the fit, however" "Figure 14 shows that the &,,;,=20 and £,,;,=30 allowable solutions on December 6 have lower energv than the minimum enerev solution on December 14 unless they are dominated by pair plasma inertia (lar to the left of the energy minimum on December 6).",Figure 14 shows that the $E_{min}=20$ and $E_{min}=30$ allowable solutions on December 6 have lower energy than the minimum energy solution on December 14 unless they are dominated by pair plasma inertia (far to the left of the energy minimum on December 6). This violates condition 1 above. so these solutions do not appear to be physical.," This violates condition 1 above, so these solutions do not appear to be physical." The allowable solutions on December 6 can be magnetically dominated. as indicated by the location of the black arrow (to the right of the minimum energy)., The $E_{min}=10$ allowable solutions on December 6 can be magnetically dominated as indicated by the location of the black arrow (to the right of the minimum energy). However. the black arrow is below the black horizontal dashed line indicating that the energy {his of these solutions is below that of the minimum energy solution on December 14. so thev would not satisfv energy conservalion (violates condition 3D above).," However, the black arrow is below the black horizontal dashed line indicating that the energy flux of these solutions is below that of the minimum energy solution on December 14, so they would not satisfy energy conservation (violates condition 3 above)." Thus. there are no plivsically. allowed. solutions with ο=10.," Thus, there are no physically allowed solutions with $E_{min}=10$." " The red vertical arrow for the £,,;,=5 allowable solutions lies above the horizontal red dashed line. so (here is an allowed solution that is magnetically dominated on December 6 and the energv is conserved until December I4."," The red vertical arrow for the $E_{min}= 5$ allowable solutions lies above the horizontal red dashed line, so there is an allowed solution that is magnetically dominated on December 6 and the energy is conserved until December 14." A careful numerical ealeulation shows that the largest value of £5; that is allowed by these arguments is ρω=6., A careful numerical calculation shows that the largest value of $E_{min}$ that is allowed by these arguments is $E_{min}=6$. " Note (hat departures from minimum energv on December 1H. will only drop the maximum allowed value of £4, below 6."," Note that departures from minimum energy on December 14, will only drop the maximum allowed value of $E_{min}$ below 6." So. this argument is more general than one associated with just an asvimiptotic minimum energy state.," So, this argument is more general than one associated with just an asymptotic minimum energy state." The maximum allowed value of μμ is 6 for any of the possible magnetically dominated (racks through the solution space in Figure 14 (i.e.. other horizontal (racks that are not indicated by the dashed Ines).," The maximum allowed value of $E_{min}$ is 6 for any of the possible magnetically dominated tracks through the solution space in Figure 14 (i.e., other horizontal tracks that are not indicated by the dashed lines)." Table 3 displavs the parameters of solutions for C2 that approach minimum energy on December 14 and for Cl on December 6., Table 3 displays the parameters of solutions for C2 that approach minimum energy on December 14 and for C1 on December 6. The table is a useful device for understanding the time evolution of the plasmoil C2 and its relationship to Cl at late times., The table is a useful device for understanding the time evolution of the plasmoid C2 and its relationship to C1 at late times. Columns 1 and 2 in Table 3 identilv the flare., Columns 1 and 2 in Table 3 identify the flare. " The next (wo columns are Z5, and the designation of the solution as minimum enerey or not. respectively,"," The next two columns are $E_{min}$ and the designation of the solution as minimum energy or not, respectively." Columns 5 and 6 are the radius of the plasmoid model and (he magnetic field strength. respectively.," Columns 5 and 6 are the radius of the plasmoid model and the magnetic field strength, respectively." Column 7 is the ratio of magnetic energv density (irivially computable [rom column 6) (o leptonic energy (ie.. the degree of magnetic dominance).," Column 7 is the ratio of magnetic energy density (trivially computable from column 6) to leptonic energy (i.e., the degree of magnetic dominance)." Column 9 is the total number of particles in (he plasmoid., Column 9 is the total number of particles in the plasmoid. The last column is the power required to energize and eject the plasmoid at relativistic speed from the central engine as defined in equation (14)., The last column is the power required to energize and eject the plasmoid at relativistic speed from the central engine as defined in equation (14). The component sizes in Table 3 are much smaller than normally assumed in the literature and compactness might be an issue., The component sizes in Table 3 are much smaller than normally assumed in the literature and compactness might be an issue. There might be significant inverse Compton emission that could affect the basic assumptions of the model or further constrain the models., There might be significant inverse Compton emission that could affect the basic assumptions of the model or further constrain the models. A simple measure of (he significance of strong inverse Compton cooling is the brightness temperature. Ti.," A simple measure of the significance of strong inverse Compton cooling is the brightness temperature, $T_{b}$." These are evaluated [or the various models in column (8) of Table 3 by the following, These are evaluated for the various models in column (8) of Table 3 by the following masses.,masses. " In this case. the probability distribution cau be described as a Cassia with a mean My; aud a standard deviation o4,;."," In this case, the probability distribution can be described as a Gaussian with a mean $M_{0,i}$ and a standard deviation $\sigma_{M,i}$." In this and the following expressions. C; is a proper normalization constant such that This category includes 003. 1U 17. NTE J1550. 561. GRO 10. VLGLL Sex. and GS 2023|338.," In this and the following expressions, $C_i$ is a proper normalization constant such that This category includes $-$ 003, 4U $-$ 47, XTE $-$ 564, GRO $-$ 40, V4641 Sgr, and GS 2023+338." For the sources in the second category. there is only a measurement of the mass function aud constraints ou the lass ratio q.," For the sources in the second category, there is only a measurement of the mass function and constraints on the mass ratio $q$." Here. we assunie a Gaussian probability distribution over the mass function with a mean fj; aud a standard deviation συ.," Here, we assume a Gaussian probability distribution over the mass function with a mean $f_{0,i}$ and a standard deviation $\sigma_{0,i}$." For the mass ratio. we adopt a wuiform distribution between the minima aud maxinuun allowed mass ratios. qian aU (fas respectively.," For the mass ratio, we adopt a uniform distribution between the minimum and maximum allowed mass ratios, $q_{\rm min}$ and $q_{\rm max}$, respectively." For each value of the mass ratio. the lack of eclipses nuplies a asin value of the inclination. 1.6. a minima value of cosἐν such that Assuming a uniform distribution over cos/ subject to this coustraiut. ic. vields The folowing nime sources belong to this cateeory: GROJ 0122|32. GRS 1009-15. NTE JI11IS|180. Nova Mus 91. MS 135661. NTE J1650-500. CN 339- Nova Oph 77. and GS 2000|251.," For each value of the mass ratio, the lack of eclipses implies a maximum value of the inclination, i.e., a minimum value of $\cos i$, such that Assuming a uniform distribution over $\cos i$ subject to this constraint, i.e., yields The following nine sources belong to this category: GROJ 0422+32, GRS 1009-45, XTE J1118+480, Nova Mus 91, MS 1354-64, XTE J1650-500, GX 339-4, Nova Oph 77, and GS 2000+251." L. measured. aud the mass ratio has been constrained (see the discussion iu Section 2 about the inclination measurement).," This last category includes only GRS 1915+105, for which the mass function and the inclination have been measured, and the mass ratio has been constrained (see the discussion in Section 2 about the inclination measurement)." Iu this case. we calculate the probability distribution over mass using equation (7)). supplemented by a Cassia distribution over iuclinatiou Figure P shows the likelihoods P;(data| for the 16 sources iu the above three categories.," In this case, we calculate the probability distribution over mass using equation \ref{eq:prob2}) ), supplemented by a Gaussian distribution over inclination Figure \ref{fig:bh_prob} shows the likelihoods $P_i({\rm data}\vert M)$ for the 16 sources in the above three categories." The top paucl includes A) ," The top panel includes sources in categories and, while the bottom panel shows those in category." A clustering of the observed black hole masses between ~610A. is already evident from Fieure 1..," A clustering of the observed black hole masses between $\sim 6-10~M_{\odot}$ is already evident from Figure \ref{fig:bh_prob}." In the next section. we will carry out a formal Bavesian analysis to determine the parameters of the uuderlviug mass distribution that ix consistent with the observed PdatalAL) shown here.," In the next section, we will carry out a formal Bayesian analysis to determine the parameters of the underlying mass distribution that is consistent with the observed $P_i({\rm data}\vert M)$ shown here." Tf the likelihood for cach source was nurow cuough such that there was little or no overlap between them. then adding the likelihoods for the eutire sample aud. coarsely binning the resulting distribution would provide a good estimate of the uuderlving mass distribution.," If the likelihood for each source was narrow enough such that there was little or no overlap between them, then adding the likelihoods for the entire sample and coarsely binning the resulting distribution would provide a good estimate of the underlying mass distribution." Even though this condition is uot cutirely satisfied here. especially at the high mass eud. we nevertheless show in Figure 2. this approxinate mass distribution to ect a seuse of its eross properties.," Even though this condition is not entirely satisfied here, especially at the high mass end, we nevertheless show in Figure \ref{fig:prob_added} this approximate mass distribution to get a sense of its gross properties." Iu this section. we use a parametric form of the black-hole mass distribution aud the data discussed iu Sectious 2 and 3 in order to determine its parameters.," In this section, we use a parametric form of the black-hole mass distribution and the data discussed in Sections 2 and 3 in order to determine its parameters." We will first consider au exponentially decaxiug mass distribution with a cut-off given by This choice of the mass distribution is motivated by theoretical expectations based on the euergeties of superuova explosions. as well as the density profiles aud mass distributions of pre-supernova stars.," We will first consider an exponentially decaying mass distribution with a cut-off given by This choice of the mass distribution is motivated by theoretical expectations based on the energetics of supernova explosions, as well as the density profiles and mass distributions of pre-supernova stars." The typical value of the mass scale is expected to lie in the range Mic.~5.59M. (as we inter from the various figures in Frver Ialogcra 2001). whereas the cutoff mass is simply expected to be the maxima neutron star mass.," The typical value of the mass scale is expected to lie in the range $M_{\rm scale} \sim 5.5 - 9~M_\odot$ (as we infer from the various figures in Fryer Kalogera 2001), whereas the cutoff mass is simply expected to be the maximum neutron star mass." Our eval is to find the values of the mass scale M. adii the exponcutial aud the cut-off mass Af. that maximize a properly defined likelihood and to estimate their πουταλα, Our goal is to find the values of the mass scale $M_{\rm scale}$ in the exponential and the cut-off mass $M_{\rm c}$ that maximize a properly defined likelihood and to estimate their uncertainties. " We will show below that the particular choice of the functional form of the mass distribution docs not affect the mainλος, conclusious of the paper.", We will show below that the particular choice of the functional form of the mass distribution does not affect the main conclusions of the paper. "groups of these protoclusters as well. which we will simple refer to here as ""star formation centres” orSFCs.","groups of these protoclusters as well, which we will simple refer to here as `star formation centres' or." . The formation of the actually occurs very rapidly., The formation of the actually occurs very rapidly. The mass of the 16 most massive of these centres is shown as a function of time in figure2., The mass of the 16 most massive of these centres is shown as a function of time in figure. Within SMyr tor 2.5 Myr after the onset of star formation) the 15 most massive all have masses greater than about 100.. and are beginning to get to a size where there is good possibility of them forming massive stars (this will be discussed in section 4).," Within 5Myr (or 2.5 Myr after the onset of star formation) the 15 most massive all have masses greater than about 100, and are beginning to get to a size where there is good possibility of them forming massive stars (this will be discussed in section )." A desirable feature of an initially unbound GMC is that cloud dispersal and star formation are occurring. simultaneously., A desirable feature of an initially unbound GMC is that cloud dispersal and star formation are occurring simultaneously. This removes the necessity for feedback mechanisms to disperse the cloud. or at the very least makes their task much easier.," This removes the necessity for feedback mechanisms to disperse the cloud, or at the very least makes their task much easier." The timescale for star formation is thus comparable to the timescale for the eloud's dispersal., The timescale for star formation is thus comparable to the timescale for the cloud's dispersal. The dynamics of an unbound cloud is therefore naturally in keeping with the recent observations that star formation and cloud dispersal occur in a few crossing times., The dynamics of an unbound cloud is therefore naturally in keeping with the recent observations that star formation and cloud dispersal occur in a few crossing times. There is also the added bonus that star formation efficiencies will be kept low. since most of the gas around a protocluster clump will be unbound to it and moving away.," There is also the added bonus that star formation efficiencies will be kept low, since most of the gas around a protocluster clump will be unbound to it and moving away." This prevents the material getting involved in the accretion once a starts to form., This prevents the material getting involved in the accretion once a starts to form. Figure shows the density distribution of the gas at three yoints in the simulation., Figure shows the density distribution of the gas at three points in the simulation. The vertical dot-dashed line marks the original density of the cloud., The vertical dot-dashed line marks the original density of the cloud. Just before the first protocluster orms at 2.4 Myr we see that the most common density is roughly το1077 vem* (the solid line curve). an order of magnitude igher than at the start of the simulation.," Just before the first protocluster forms at 2.4 Myr we see that the most common density is roughly $7 \times 10^{-22}$ $^{-3}$ (the solid line curve), an order of magnitude higher than at the start of the simulation." " Note however that very ittle material at this point is as dense as το10.74 "".showing hat the turbulence does not allow much material to get up to typical star forming densities (222)."," Note however that very little material at this point is as dense as $7 \times 10^{-21}$ $^{-3}$, showing that the turbulence does not allow much material to get up to typical star forming densities \citep*{Falgaroneetal1991, Padoan1995, Zinnecker2002}." After 7 Myr the peak in the distribution falls back to roughly he starting density. however there is mueh more spread in the distribution.," After 7 Myr the peak in the distribution falls back to roughly the starting density, however there is much more spread in the distribution." This spread is controlled by two mechanisms., This spread is controlled by two mechanisms. The vigh density tail increases as the grow by accretion and he subsequent rise in the potential energy., The high density tail increases as the grow by accretion and the subsequent rise in the potential energy. This causes yet more, This causes yet more he relationship between vsini and the presence of planets. we calculated vsini dillerences using the A) index.,"the relationship between vsini and the presence of planets, we calculated vsini differences using the $\Delta_1$ index." We show he results for the same SWI's plotted in Figure 5 in Figure 6., We show the results for the same SWPs plotted in Figure 5 in Figure 6. Figure 6b shows that the vsini values are smaller than hose of the comparison stars among the cooler stars: they are nearly the same for SWPs near 6000 Ix and much larger or the hottest ones., Figure 6b shows that the vsini values are smaller than those of the comparison stars among the cooler stars; they are nearly the same for SWPs near 6000 K and much larger for the hottest ones. We can improve our comparison of vsini values by employing the SWP and comparison star samples [rom Valenti&Fischer(2005)., We can improve our comparison of vsini values by employing the SWP and comparison star samples from \citet{vf05}. . Xpplving the same Tar and log & limits we used to prepare our samples above. we produced a samples of 82 οΑς and 596 comparison We show the resulting vsini dillerences. calculated in the same wav as in Figure 6 in Figure 7.," Applying the same $_{\rm eff}$ and $\log$ g limits we used to prepare our samples above, we produced a samples of 82 SWPs and 596 comparison We show the resulting vsini differences calculated in the same way as in Figure 6 in Figure 7." These larger samples confirm our results from Figure 6., These larger samples confirm our results from Figure 6. From the data in Figure Th. we find that ολος with Tr between 5800 and 5950 Ix have an average vsini value of 0.77250.19 (s.e.m.)," From the data in Figure 7b, we find that SWPs with $_{\rm eff}$ between 5800 and 5950 K have an average vsini value of $-0.77 \pm 0.19$ (s.e.m.)" knis + relative to the comparison stars: the corresponding average dilIerence for stars hotter than 5950 Ix is. |0.4520.39 (μ.ομα.), km $^{\rm -1}$ relative to the comparison stars; the corresponding average difference for stars hotter than 5950 K is $+0.45 \pm 0.39$ (s.e.m.) kms, km $^{\rm -1}$. The pattern of Li abundance dillerences between SWI'sS and comparison stars shows a remarkable correspondence with the pattern of dillerences in vsini., The pattern of Li abundance differences between SWPs and comparison stars shows a remarkable correspondence with the pattern of differences in vsini. Both Li and. vsini are smaller for cool SWDPs and larger for hot ολλος., Both Li and vsini are smaller for cool SWPs and larger for hot SWPs. These results confirm the preliminary finding of Takedaetal.(2007a) that solar analogs with slower rotation have lower Li abundances., These results confirm the preliminary finding of \citet{tak07} that solar analogs with slower rotation have lower Li abundances. They. reached this conclusion after having conducted: detailed: spectroscopic analyses of 118 solar analogs., They reached this conclusion after having conducted detailed spectroscopic analyses of 118 solar analogs. μον measured line widths. which allowed them to determine. vsini|macroturbulence. for cach star.," They measured line widths, which allowed them to determine vsini+macroturbulence for each star." Unlike Valenti&Fischer.(2005).. however. they did not determine separate vsini and macroturbulence velocities.," Unlike \citet{vf05}, however, they did not determine separate vsini and macroturbulence velocities." What's more. they only included 5 SWPs in their sample. limiting their conclusions about the possible relationship between SWDPs. rotation ancl Li abundance.," What's more, they only included 5 SWPs in their sample, limiting their conclusions about the possible relationship between SWPs, rotation and Li abundance." stellar chromospheric activity is known to correlate with rotation., Stellar chromospheric activity is known to correlate with rotation. If the pattern in vsini values we found among the SWPs is a real elfect. then there should. be similar patterns in measures of chromospheric activity.," If the pattern in vsini values we found among the SWPs is a real effect, then there should be similar patterns in measures of chromospheric activity." We can test this prediction using the yy chromospheric activity index.," We can test this prediction using the $R^{'}_{\rm HK}$ chromospheric activity index," (he interaction signatures in high z galaxies because of poor spatial resolutions and the cosmic climming.,the interaction signatures in high z galaxies because of poor spatial resolutions and the cosmic dimming. " In contrast. il is easy (ο define binary galaxies quantitatively. aud objectively,"," In contrast, it is easy to define binary galaxies quantitatively and objectively." This makes an objectively defined. comparison between local merger events and high z merger events possible., This makes an objectively defined comparison between local merger events and high z merger events possible. However. earlier studies of pair [fraction and ils cosmic evolution have suffered seriously from (he contamination of unphlivsical pairs because of the lack of redshifts or hiehlv incomplete redshift data (Zepl Άου 1939: Burkey οἱ al 1994: Carlberg et al.," However, earlier studies of pair fraction and its cosmic evolution have suffered seriously from the contamination of unphysical pairs because of the lack of redshifts or highly incomplete redshift data (Zepf Koo 1989; Burkey et al 1994; Carlberg et al." 1994: Yee Ellington 1995: Woocds et al., 1994; Yee Ellington 1995; Woods et al. 1995: Patton et al., 1995; Patton et al. LOOT: Wu Ixeel 1993)., 1997; Wu Keel 1998). In two recent studies using samples of galaxies with measured redshifts. Le Févvre et al (2000) and Patton et al. (," In two recent studies using samples of galaxies with measured redshifts, Le Févvre et al (2000) and Patton et al. (" "2002) found i=2.70.6 and in=2.3dz0.7. respectively, where m is (he evolution index in the evolution function of the merger rate: Z2,x(1+z)"".","2002) found $m=2.7\pm 0.6$ and $m=2.3\pm 0.7$, respectively, where m is the evolution index in the evolution function of the merger rate: $R_{mg} \propto (1+z)^m$." In a series of papers. Patton οἱ al. (," In a series of papers, Patton et al. (" 1997: 2000: 2002) pointed out that in studies of merger rate aud evolution. il is verv important (o correct various svstemaltic biases. and results from comparisons between mismatched samples of low-z and high-z galaxies are not verv meaningful.,"1997; 2000; 2002) pointed out that in studies of merger rate and evolution, it is very important to correct various systematic biases, and results from comparisons between mismatched samples of low-z and high-z galaxies are not very meaningful." The best wav to constrain the merger rate and its cosmic evolution is (o compare dilferential pair [raction functions at different redshifts., The best way to constrain the merger rate and its cosmic evolution is to compare differential pair fraction functions at different redshifts. A differential pair fraction function (DPFF) is delined by ratios between number of paired galaxies ancl (he (total number of ealaxies in luminosity (or stellar mass) bins., A differential pair fraction function (DPFF) is defined by ratios between number of paired galaxies and the total number of galaxies in luminosity (or stellar mass) bins. Such functions are not sensitive to sample selection (flux limited or volume limited) aud therelore can be compared without. bias between different studies., Such functions are not sensitive to sample selection (flux limited or volume limited) and therefore can be compared without bias between different studies. DPFF can be determined by comparing the Iuminosity. (mass) function of paired galaxies with that of total galaxies., DPFF can be determined by comparing the luminosity (mass) function of paired galaxies with that of total galaxies. In this paper. we estimate the local Ix. (2.165011) band luminosity function of close major-merger pairs. and derive [rom it (he DPFF in the z=0 universe.," In this paper, we estimate the local ${\rm K_s}$ $\mu m$ ) band luminosity function of close major-merger pairs, and derive from it the DPFF in the z=0 universe." " The very close relation between the IX, band buninosity. and (he stellar mass means (hat for the first time we can have the mass function of the paired ealaxies and the mass dependence of (he merger rate.", The very close relation between the ${\rm K_s}$ band luminosity and the stellar mass means that for the first time we can have the mass function of the paired galaxies and the mass dependence of the merger rate. Since (his can be compared directly, Since this can be compared directly Since the wave travels racially outward at the sound speed. the total euergy [flux past auy poiut is [t is iustructive to compare this result with j. the angular momentum flux in equation (37a).,"Since the wave travels radially outward at the sound speed, the total energy flux past any point is It is instructive to compare this result with $j$, the angular momentum flux in equation (37a)." From equations (35a) aud (056). we have Thus. the auetular ποια flux may be written as where we have again replaced the density by its equilibrium value.," From equations (35a) and (35c), we have Thus, the angular momentum flux may be written as where we have again replaced the density by its equilibrium value." Integrating € aud j over the entire shell. we obtain a relationship between the global energy loss rate E aud J: Siuce both the energy aud angular momentum are being extracted from the binary. tlie same relationship between their loss rates should apply to that system.," Integrating ${\dot{\cal E}}$ and $j$ over the entire shell, we obtain a relationship between the global energy loss rate $\dot E$ and $\dot J$: Since both the energy and angular momentum are being extracted from the binary, the same relationship between their loss rates should apply to that system." We now slow that this is the case., We now show that this is the case. Referring back to Figure 1. the angular momentum of the binary is The binarys total euergy is But we also have From. this equation. applying staudard mauipulatious. we find that the potential euergy is so that Comparison with equation (13) reveals that," Referring back to Figure 1, the angular momentum of the binary is The binary's total energy is But we also have From this equation, applying standard manipulations, we find that the potential energy is so that Comparison with equation (43) reveals that" Huportant to note that theFUSE SiC channels suffer from scattered solar light problems iu the 2001 data. aud in this paper we oulv use the data from the LiF channels (detailsregardingthedesignaudperformanceofFUSE can be found2002).,"important to note that the SiC channels suffer from scattered solar light problems in the 2004 data, and in this paper we only use the data from the LiF channels \citep[details regarding the design and performance of {\it FUSE} can be found." Iu Figure l.. we compare theFUSE observations of LAIC X-3 obtained in 2001 (black histograms) aud in 2001 (red histogram) in the wavelength range near the ddoublet Gu this figure. all of the data obtained in 2001 are accumulated into a sinele spectrum aud likewise all of the 2001 data are coadded).," In Figure \ref{OVIcmp}, we compare the observations of LMC X-3 obtained in 2001 (black histogram) and in 2004 (red histogram) in the wavelength range near the doublet (in this figure, all of the data obtained in 2001 are accumulated into a single spectrum, and likewise all of the 2004 data are coadded)." Bright airelow cussion lines from the Earth's atinosphiere are marked (1). aud well-detected absorption lines frou the ddoublet aud A1036.3 near c(heliocentzic) z: 0 lau are also labeled (analvsisoftheabsorptiontheFUSE spectiuii of LMC X-3 is reported2005).," Bright airglow emission lines from the Earth's atmosphere are marked $\oplus$ ), and well-detected absorption lines from the doublet and $\lambda$ 1036.3 near $v$ (heliocentric) $\approx$ 0 km $^{-1}$ are also labeled \citep[analysis of the absorption lines in the {\it FUSE} spectrum of LMC X-3 is reported." The substantial variation in the UV flux is iuuediately obvious. but we note that the fiux variation cannot be described with a simple scale factor applied to the entire spectrum.," The substantial variation in the UV flux is immediately obvious, but we note that the flux variation cannot be described with a simple scale factor applied to the entire spectrum." For example. the coutimm£na is roughly two times brighter at A~ 1015 bbut is roughly 1« brighter near the putative comission at A5 1031A.," For example, the continuum is roughly two times brighter at $\lambda \approx$ 1045 but is roughly $4\times$ brighter near the putative emission at $\lambda \approx$ 1034." It is difficult to draw conchisions about the long-term UV flux variability with observations at only two epochs. but it appears that while the eenission intensity decreased along with the continua in the 2001 observation. there is not a strict correlation.," It is difficult to draw conclusions about the long-term UV flux variability with observations at only two epochs, but it appears that while the emission intensity decreased along with the continuum in the 2004 observation, there is not a strict correlation." We will show below that narrow eenission lines are detected in the 2004 data. but it is possible that thebread eenission was not present in the later observation for sole reason.," We will show below that narrow emission lines are detected in the 2004 data, but it is possible that the emission was not present in the later observation for some reason." The shape of the ταν spectrum of LAIC N-3 also changed between 2001 aud 2001 (sce 3.1). so it is possible that the changes of the broad ffeature are related to changes iu the N-ray fiux.," The shape of the X-ray spectrum of LMC X-3 also changed between 2001 and 2004 (see \ref{sec:xrayobs}) ), so it is possible that the changes of the broad feature are related to changes in the X-ray flux." There are some limitations of the spectroscopic UV dataset fromFUSE prescuted in the previous section., There are some limitations of the spectroscopic UV dataset from presented in the previous section. Fist. LMC N-3 is a challenging target for because the UV flux is relatively low. so the data cau be noisy.," First, LMC X-3 is a challenging target for because the UV flux is relatively low, so the data can be noisy." Also. in theFUSE waveleneth range. enüssiou lines from the Earth's atiuosplhere are a potential source of confusion (see below).," Also, in the wavelength range, emission lines from the Earth's atmosphere are a potential source of confusion (see below)." Moreover.FUSE is no longer operating. so we cannot conteimiplate follow-upFUSE spectroscopy.," Moreover, is no longer operating, so we cannot contemplate follow-up spectroscopy." Fortunately. all of these problems can be overcome with COS (Creenetal.2003).. the new spectrograph onLST. with some caveats.," Fortunately, all of these problems can be overcome with COS \citep{green03}, the new spectrograph on, with some caveats." COS has lamited scusitivity iu the 912 1130$ , but at the expense of missing the OVI doublet." However. other highly ionized species are accessible iu the A>1130 iranee (e.g. ÀA1238.8. 1212.8 or AALS We have I8.2.1550.8).," However, other highly ionized species are accessible in the $\lambda > 1130$ range (e.g., $\lambda \lambda$ 1238.8, 1242.8 or $\lambda \lambda$ 1548.2,1550.8)." recently observed LMC N-3 with COS using the high-resolution (ΤΟΝΤ aud GLGOAL modes (Programs 11612)., We have recently observed LMC X-3 with COS using the high-resolution G130M and G160M modes (Program 11642). The target was observed ou 15 December 2009 with total exposure times of 16.9 ks (CI30MD) and 2.7 ss (CGI60ND., The target was observed on 15 December 2009 with total exposure times of 16.9 ks (G130M) and 2.7 ks (G160M). The data were calibrated with the pipeline CALCOS (version 2.11b). and major fixed-patter noise ccatures due to eid wires in the cross delay line detector were removed with a flat field developed by IX. France.," The data were calibrated with the pipeline CALCOS (version 2.11b), and major fixed-pattern noise features due to grid wires in the cross delay line detector were removed with a flat field developed by K. France." This flat field does not correct for all types of fixed-ρα{οχι noise in COS spectra (c.e..Salinowetal.2010).. mt for the measurement of broad. aud. bright emission ines presented in this paper. the lower-level fixed pattern roise does not have a significant inipact ou the results.," This flat field does not correct for all types of fixed-pattern noise in COS spectra \citep[e.g.,][]{sahnow10}, but for the measurement of broad and bright emission lines presented in this paper, the lower-level fixed pattern noise does not have a significant impact on the results." The regions of the COS GI30M. aud GI60M. spectra of LMC X-3 covering the πας eenüsson les are shown iu Figure 2.., The regions of the COS G130M and G160M spectra of LMC X-3 covering the and emission lines are shown in Figure \ref{fig:COSNVALL}. Enüssion iu hese species was previously detected from LAIC X-3 w Cowleyctal.(1991) using low-resolution spectra obtained with the Faint Object Spectrograph onLST ax well as theExplorer., Emission in these species was previously detected from LMC X-3 by \citet{cowley94} using low-resolution spectra obtained with the Faint Object Spectrograph on as well as the. " Our ιο COS data offer two advantages over the previous observations: (1) the spectral resolution is z10 times üsgher. so variations in the velocity ceutroids cau be neasured more accurately, aud (2) the S/N is higher. aud consequcutly the data cau be divided into phase bius for investigation of euission variability vs. binary phase."," Our new COS data offer two advantages over the previous observations: (1) the spectral resolution is $\approx$ 10 times higher, so variations in the velocity centroids can be measured more accurately, and (2) the S/N is higher, and consequently the data can be divided into phase bins for investigation of emission variability vs. binary phase." As we will show below. the yvelocities are consistent with the optical orbital velocities of LAIC| N-3 and are also consistent with the velocity trends exhibited by the ddoublet.," As we will show below, the velocities are consistent with the optical orbital velocities of LMC X-3 and are also consistent with the velocity trends exhibited by the doublet." The CAlGOAD spectrum is considerably uoisicr and the ccluission features are weaker. so in this paper we will focus on the velocity and amplitude variations of tle lines and their comparison to the CCLUSSION.," The G160M spectrum is considerably noisier and the emission features are weaker, so in this paper we will focus on the velocity and amplitude variations of the lines and their comparison to the emission." We have analyzed the optical observations of LAIC X-3 ia a neuner analogous to the recent study of LAIC N-1 (Oroszetal.2009)., We have analyzed the optical observations of LMC X-3 in a manner analogous to the recent study of LMC X-1 \citep{orosz09}. . Amone the 53 optical spectra that we obtained with the Magellau-Clav. telescope. we exclude seven observations from our analysis due to their relatively huge residuals in the radial Tle remaining 16 radial velocities are then fitted to a circular orbit model. which returus the systemic velocity Vy. the time of inferior conjunction of the optical star Ty (phase 0). aud the velocity semiuuuplitude of the secondary Ap. when eiven the value of the orbital period P.," Among the 53 optical spectra that we obtained with the Magellan-Clay telescope, we exclude seven observations from our analysis due to their relatively large residuals in the radial The remaining 46 radial velocities are then fitted to a circular orbit model, which returns the systemic velocity $V_{\rm 0}$, the time of inferior conjunction of the optical star $T_0$ (phase 0), and the velocity semiamplitude of the secondary $K_B$, when given the value of the orbital period $P$." We construct a periodoerai as shown in the top panel of Figure 3. using a wide range of trial periods., We construct a periodogram as shown in the top panel of Figure \ref{period} using a wide range of trial periods. The best fit indicates P=1.701820+0.000012 davs aud Ty=ILJD2.151.(51.9962 40.0011. where the uncertaiutics ou the individual measurements are scaled to eive \2z1.," The best fit indicates $P=1.704820\pm 0.000012$ days and $T_0={\rm HJD}\, 2,454,454.9962\pm 0.0011$ , where the uncertainties on the individual measurements are scaled to give $\chi_{\nu}^{2}\approx 1$." We also tried including the radial velocities published in C83 im order to refine our 1icasuremoent., We also tried including the radial velocities published in C83 in order to refine our measurement. However. the systemic velocities obtained from the two data sets are quite different: £06 kan s+ for MOISE and 310 kins+ forCowley ct al.," However, the systemic velocities obtained from the two data sets are quite different: 406 km $s^{-1}$ for MIKE and 310 km $s^{-1}$ forCowley et al." The cause for this difference is notclear. although it is nof unconuuou to find that the systemic velocity chanecs depending ou what line is used (one even sees shifts when one uses different Daliner lues).," The cause for this difference is notclear, although it is not uncommon to find that the systemic velocity changes depending on what line is used (one even sees shifts when one uses different Balmer lines)." models: besides this. it is reasonable to allow for moderate light bending involving the blurred component.,"models; besides this, it is reasonable to allow for moderate light bending involving the blurred component." In conclusion. a model consisting of both a warn reflection Component arising from the photoionizec disc surface. blurred. by relativistic cllects. and a colel one ascribable to a much. more clistant reprocessor proves. το be successful in reproducing the broadband X-ray spectrum of Ark 120.," In conclusion, a model consisting of both a warm reflection component arising from the photoionized disc surface, blurred by relativistic effects, and a cold one ascribable to a much more distant reprocessor proves to be successful in reproducing the broadband X-ray spectrum of Ark 120." Limited to this peculiar source. this scenario stands as the most convincing among those presented: so far. also due to the minimal set of ecometrical and physical assumptions involved.," Limited to this peculiar source, this scenario stands as the most convincing among those presented so far, also due to the minimal set of geometrical and physical assumptions involved." As we have already mentioned in the introduction. several other models have been adopted in the last decade to fully reproduce the high-quality 20.5.10. keV. spectra of AGN provided. by and/or.INAMAI-Newtlon.. specifically concerning the soft excess component.," As we have already mentioned in the introduction, several other models have been adopted in the last decade to fully reproduce the high-quality $\sim$ 0.5–10 keV spectra of AGN provided by and/or, specifically concerning the soft excess component." Over the vears. most of these interpretations have been either. discarded as loo phenomenological or disputed. because of some yhvsical limitations.," Over the years, most of these interpretations have been either discarded as too phenomenological or disputed because of some physical limitations." Nevertheless. for the sake of a fitting comparison extending up to 40 keV against the blurred rellection model. we have also explored. some of the most common alternatives. on which we give a brief report. in his section.," Nevertheless, for the sake of a fitting comparison extending up to $\sim$ 40 keV against the blurred reflection model, we have also explored some of the most common alternatives, on which we give a brief report in this section." ALL the mocdels listed below diller from that xwed on blurred. rellection only in the ingredients apt to describe the soft. excess., All the models listed below differ from that based on blurred reflection only in the ingredients apt to describe the soft excess. In. particular. they all require a cold. rellection component with iron abundance —1.11.5 +0.4). accounting for ~46 and ~2030 per cent of he AIS and HEND/PIN observed. Dux. respectively. and also for the narrow emission feature at 6.4 keV. Other two unresolved. gaussian lines are always needed in the GAT6.70 and 6.937.01 keV range: even if loosely consistent. with lle-like iron emission. the former is apparently trving to compensate somehow for the lack of the broaclened disc line.," In particular, they all require a cold reflection component with iron abundance $\sim$ 1.1–1.5 $\pm 0.4$ ), accounting for $\sim$ 4–6 and $\sim$ 20–30 per cent of the XIS and HXD/PIN observed flux, respectively, and also for the narrow emission feature at 6.4 keV. Other two unresolved gaussian lines are always needed in the 6.47–6.70 and 6.93–7.01 keV range: even if loosely consistent with He-like iron emission, the former is apparently trying to compensate somehow for the lack of the broadened disc line." In the following. we just provide the Κον parameters of the soft excess component in some illustrative cases.," In the following, we just provide the key parameters of the soft excess component in some illustrative cases." 1) (Nz/d.o4.= 0.995/471): the best-itting disc temperature is «0.124. keV. and therefore lies in. the range characteristic to the thermal scenario.," 1) $\chi^2_\nu/\rmn{d.o.f.}=0.995/471$ ): the best-fitting disc temperature is $\sim$ 0.14 keV, and therefore lies in the range characteristic to the thermal scenario." No significant improvement can be obtained by adopting a more realistic (e.g. multicolour) blackbody profile., No significant improvement can be obtained by adopting a more realistic (e.g. multicolour) blackbody profile. 2) (ALcof.= 0.963/471): as one can immediately see from Fig. 1..," 2) $\chi^2_\nu/\rmn{d.o.f.}=0.963/471$ ): as one can immediately see from Fig. \ref{rp}," a couble-sloped power law is sullicient to achieve a good Lit to the low-energv spectrum., a double-sloped power law is sufficient to achieve a good fit to the low-energy spectrum. The soft photon index is 72.33. the hard one is 72.00: the break-point energy is established at 1.73 keV. 3) (ALcho.=1.02 /470): we have used the model to mimic absorption in a partially ionized relativistic gas. even if the latest simulations of the velocity. ancl density structure of any possible accretion disc wind or outllow rule out this scenario as the origin of a smooth soft excess (Schurch οἱ al.," The soft photon index is $\sim$ 2.33, the hard one is $\sim$ 2.00; the break-point energy is established at 1.73 keV. 3) $\chi^2_\nu/\rmn{d.o.f.}=1.02/470$ ): we have used the model to mimic absorption in a partially ionized relativistic gas, even if the latest simulations of the velocity and density structure of any possible accretion disc wind or outflow rule out this scenario as the origin of a smooth soft excess (Schurch et al." 2009)., 2009). The column denisty of the putative absorber is Nyz17107? and the ionization parameter is log£23.3.," The column denisty of the putative absorber is $N_\rmn{H} \simeq 17 \times 10^{22}$ $^{-2}$, and the ionization parameter is $\log \xi \simeq 3.3$." The gaussian velocity dispersion. in this warm eas is the maximum allowed. Le. e/e=0.5.," The gaussian velocity dispersion in this warm gas is the maximum allowed, i.e. $v/c=0.5$." Since the power-law index is slightly steeper than usual. being ~2.12. this model presents larger deviations from the data at the higher energies.," Since the power-law index is slightly steeper than usual, being $\sim$ 2.12, this model presents larger deviations from the data at the higher energies." 4) (AZd.o.[.=0.918/470): many codes with a dillerent. degree of complexity are available o describe. Comptonization (e.g. Poutanen and. Svensson 1996)., 4) $\chi^2_\nu/\rmn{d.o.f.}=0.918/470$ ): many codes with a different degree of complexity are available to describe Comptonization (e.g. Poutanen and Svensson 1996). Llowever. it is not. possible to put firm. constraints on the plasma properties and geometrical structure with he present cata quality ancl energy coverage: we have herefore adopted the essential code of Titarchuk (1994).," However, it is not possible to put firm constraints on the plasma properties and geometrical structure with the present data quality and energy coverage; we have therefore adopted the essential code of Titarchuk (1994)." The exact. temperature of seed. photons is not. very important. provided that its value is reasonably low. so it jas been frozen to 50 eV as broadly. presumable for à source ike Ark 120.," The exact temperature of seed photons is not very important, provided that its value is reasonably low, so it has been frozen to 50 eV as broadly presumable for a source like Ark 120." The cold corona turns out to have an electron emperature of ~0.28 keV. with an optical depth of —13. even if the two parameters are expected to be degenerate o some extent.," The cold corona turns out to have an electron temperature of $\sim$ 0.28 keV with an optical depth of $\sim$ 13, even if the two parameters are expected to be degenerate to some extent." " ""This optically thick soft component xw a Luminosity of —1075 erg and can be roughly approximated by a blackbody."," This optically thick soft component has a luminosity of $\sim$ $^{43}$ erg $^{-1}$, and can be roughly approximated by a blackbody." This gives a size of the emitting region of ~4.107 em. whereas SD1012 em (the mass of the black hole in Ark 120 is estimated [rom reverberation mapping to be Mg21.510Αντ Peterson et al.," This gives a size of the emitting region of $\sim 4 \times 10^{11}$ cm, whereas $r_\rmn{g} \sim 2 \times 10^{13}$ cm (the mass of the black hole in Ark 120 is estimated from reverberation mapping to be $M_\rmn{BH} \simeq 1.5 \times 10^8 M_{\sun}$; Peterson et al." 2004)., 2004). Summarizing. the Comptonization scenario can be regarded at present as the only physical alternative to the blurred. reflection. model in order to account. for the soft excess of Ark 120. but its details are dillieult to probe: the argued. compactness of the soft. N-rav. emitting region represents a further problem for the nature and the geometry of the C'omptonizing plasma.," Summarizing, the Comptonization scenario can be regarded at present as the only physical alternative to the blurred reflection model in order to account for the soft excess of Ark 120, but its details are difficult to probe; the argued compactness of the soft X-ray emitting region represents a further problem for the nature and the geometry of the Comptonizing plasma." In addition. to spectral fitting. the other fundamental approach to understand the properties of the central engine in AGN is the studs of variability.," In addition to spectral fitting, the other fundamental approach to understand the properties of the central engine in AGN is the study of variability." In. principle. the latter can also provide independent information to discriminate between the cold Comptonization and the blurred reflection scenario for the soft excess. since the two models make quite divergent predictions. about the. behaviour of the source in the time domain.," In principle, the latter can also provide independent information to discriminate between the cold Comptonization and the blurred reflection scenario for the soft excess, since the two models make quite divergent predictions about the behaviour of the source in the time domain." In a very. simplistic way. the ime lags allecting the cdillerent energy bands that have en. observed in many ACN can be regarded. as a natural consequence of a Comptonization process: the time delay »etween the hard and the soft X-ray variations is due to he larger number of scattering events that the high-energv Whotons have to experience. before. escaping to infinity.," In a very simplistic way, the time lags affecting the different energy bands that have been observed in many AGN can be regarded as a natural consequence of a Comptonization process: the time delay between the hard and the soft X-ray variations is due to the larger number of scattering events that the high-energy photons have to experience before escaping to infinity." However. matters appear to be much more complicated han this naive picture (e.g. Arévyvalo Uttles 2006: Mellardy et al.," However, matters appear to be much more complicated than this naive picture (e.g. Arévvalo Uttley 2006; McHardy et al." 2007)., 2007). On the other hand. if the soft excess isa reflection signature. the soft band should lag behind the ard power-law component as expected in a reverberation context. after sineline out the timescale corresponding to he light crossing time from the primary source to the reflector and back.," On the other hand, if the soft excess is a reflection signature, the soft band should lag behind the hard power-law component as expected in a reverberation context, after singling out the timescale corresponding to the light crossing time from the primary source to the reflector and back." Evidence in this sense has been recently ound in 1110707.495 (Fabian et al., Evidence in this sense has been recently found in 1H0707–495 (Fabian et al. 2009: Zoehbi et al., 2009; Zoghbi et al. 2010)., 2010). Although is not an ideal observatory to carry out detailed. timing studies of AGN. mainly because of the frequent gaps induced. by the short orbital period. it is worth checking the variability pattern of Ark 120. for," Although is not an ideal observatory to carry out detailed timing studies of AGN, mainly because of the frequent gaps induced by the short orbital period, it is worth checking the variability pattern of Ark 120 for" (Boufilsetal.2005:Udrv2007).. and (2) the application of the massradius relationship (Ribas2006) together with the spectroscopicallv determined stellar effective temperature of T;=3180 K (Beanetal.2006)..,"\citep{bonfils05,udry07}, and (2) the application of the mass–radius relationship \citep{ribas06} together with the spectroscopically determined stellar effective temperature of $T_e = 3480$ K \citep{bean06}. ." Both methods vield £L=0.013+0.002L.., Both methods yield $L=0.013 \pm 0.002~L_\odot$. Selsisetal.(2007) estimated the stellar age as at least 7 Cyr based ou the nou-detection of C1 581 X-ray flux considering the sensitivity limit of ROSAT (Schinittetal.1995:Vogesal. 2000).," \cite{selsis07} estimated the stellar age as at least 7 Gyr based on the non-detection of Gl 581's X-ray flux considering the sensitivity limit of ROSAT \citep{schmitt95,voges00}." . In the following. we adopt a definition of the WZ previously used bv Francketal.(2000a.b).," In the following, we adopt a definition of the HZ previously used by \cite{franck00a,franck00b}." . Tere vabitability at all times does not just depend on the xuuneters of the central star. but also ou the properties of the planet.," Here habitability at all times does not just depend on the parameters of the central star, but also on the properties of the planet." In particular. habitabilitv is linked to he photosvuthetic activity of the planet. which iu turu depends on the plauctary atmospheric CO» concentration ogether with the presence of liquid water. and is thus strouely influenced by the planetary dvuaimics.," In particular, habitability is linked to the photosynthetic activity of the planet, which in turn depends on the planetary atmospheric $_2$ concentration together with the presence of liquid water, and is thus strongly influenced by the planetary dynamics." We call lis defuition the plotosvuthesissustainime habitable zone. pIIZ.," We call this definition the photosynthesis-sustaining habitable zone, pHZ." Iu principle. this leads to additional spatialtemporal linitations of habitability because the plIZ (defined for à specific type of plane} beconies narrower with tine owing to the persistent decrease of the planetary atmospheric CÓ» concentration.," In principle, this leads to additional spatial limitations of habitability because the pHZ (defined for a specific type of planet) becomes narrower with time owing to the persistent decrease of the planetary atmospheric $_2$ concentration." " The cliuatie habitable zone at a eiven time for a star with huninosity £ aud effective temperature 7). different from the Sun can be calculated following al.(2003) based ou previous work by Ixastiugetal.(1993) as with 5;4,07,) and Soit(2)) described as secoud order polynomials.", The climatic habitable zone at a given time for a star with luminosity $L$ and effective temperature $T_e$ different from the Sun can be calculated following \cite{underwood03} based on previous work by \cite{kasting93} as with $S_{\mathrm{in}}(T_e)$ and $S_{\mathrm{out}}(T_e)$ described as second order polynomials. To assess the habitabilitv of a terrestrial planet. an Earth-svstem model is applied to calculate the evolution of the temperature aud atmospheric COs coucentration.," To assess the habitability of a terrestrial planet, an Earth-system model is applied to calculate the evolution of the temperature and atmospheric $_2$ concentration." Ou Earth. the carbonatesilicate cvele is the crucial element for a long-term homeostasis under increasing solar iminositv.," On Earth, the carbonate–silicate cycle is the crucial element for a long-term homeostasis under increasing solar luminosity." On ecological time-scales. the deeper parts of —ιο Earth are cousiderable sinks and sources of carbon.," On geological time-scales, the deeper parts of the Earth are considerable sinks and sources of carbon." " Our nunuerical model previously applied to Gl Sale and Cl 581d (vonBlohetal.2007) couples the stellar ininositv L. the silicaterock weathering rate Fy, aud he global euergv balance to obtain estunates of the λαΤα pressure of atinospherie carbon dioxide Pow,. the nean elobal surface temperature με and the biological xoductivitv ID as a function of time £ (Fie. 1))."," Our numerical model previously applied to Gl 581c and Gl 581d \citep{vonbloh07} couples the stellar luminosity $L$, the silicate–rock weathering rate $F_{\mathrm{wr}}$ and the global energy balance to obtain estimates of the partial pressure of atmospheric carbon dioxide $P_{\mathrm{CO}_2}$, the mean global surface temperature $T_{\mathrm{surf}}$, and the biological productivity $\Pi$ as a function of time $t$ (Fig.\ref{block}) )." The nain point is the persistent balance between the CO» sink in the atimosphereocean system and the metamorphic (plate tectonic) sources., The main point is the persistent balance between the $_2$ sink in the atmosphere–ocean system and the metamorphic (plate tectonic) sources. This is expressed through the dimensionless quantities where A)=FRAG) is the weathering rate. Εν=Alt)fay is the continental area; aud f(f£)=ο)Sy i the areal spreading rate. which are all normalized by their present values of Earth.," This is expressed through the dimensionless quantities where $f_{\mathrm{wr}}(t) \equiv F_{\mathrm{wr}}(t)/F_{\mathrm{wr},0}$ is the weathering rate, $f_A(t) \equiv A_c(t)/A_{c,0}$ is the continental area, and $f_{\mathrm{sr}}(t) \equiv S(t)/S_0$ is the areal spreading rate, which are all normalized by their present values of Earth." Eq. (2)), Eq. \ref{gfr}) ) can be rearranged by introducing the eeoplivsical forcing ratio GER (Volk1987) as Tere we asstune that the weathering rate ouly depends ou the elobal surface temperature aud the atmospheric CO» concentration., can be rearranged by introducing the geophysical forcing ratio GFR \citep{volk87} as Here we assume that the weathering rate only depends on the global surface temperature and the atmospheric $_2$ concentration. For the investigation of a super-Earth under external forcing. we adopt a model planet with a prescribed continental area.," For the investigation of a super-Earth under external forcing, we adopt a model planet with a prescribed continental area." The fraction of coutinental area with respect to the total planetary surface f4 is varied between 0.1 aud 0.9., The fraction of continental area with respect to the total planetary surface $f_A$ is varied between $0.1$ and $0.9$. The connection between the stellar parameters aud the planctary climate can be obtained VW using a radiation balance equation (Willams1998) nzwhere e denotes the planetary albedo. Ly the outeoine infrared fux. and R the distauce from the central star.," The connection between the stellar parameters and the planetary climate can be obtained by using a radiation balance equation \citep{williams98} where $a$ denotes the planetary albedo, $I_R$ the outgoing infrared flux, and $R$ the distance from the central star." The climate model does not iuclude clouds. which are particularly iniportant for deteriiniug the ier boundary of the TZ (Selsisetal.2007).," The climate model does not include clouds, which are particularly important for determining the inner boundary of the HZ \citep{selsis07}." . The Eqs. (3)), The Eqs. \ref{gfr2}) ) aud (1)) constitute a set of two coupled equations with two uuknowuns. Tiare aud Doo. if the parameterization of the weathering rate. he huuinositv. the distance to the ceutral star and the geoplivsical forcing ratio are specified.," and \ref{L}) ) constitute a set of two coupled equations with two unknowns, $T_{\mathrm{surf}}$ and $P_{\mathrm{CO}_2}$ , if the parameterization of the weathering rate, the luminosity, the distance to the central star and the geophysical forcing ratio are specified." Therefore. a numerical solutioncan be attained in a straightforward mauncer.," Therefore, a numerical solutioncan be attained in a straightforward manner." obstacles that can decelerate the flow: (1) centrifugal barrier due to the fluids angular momentum. (2) gas pressure-gradient. (3) radiation pressure-gradient. and (4) magnetic forces (i.e.. pressure-gradient and/or tension force).,"obstacles that can decelerate the flow: (1) centrifugal barrier due to the fluid's angular momentum, (2) gas pressure-gradient, (3) radiation pressure-gradient, and (4) magnetic forces (i.e., pressure-gradient and/or tension force)." Although our model is purely adiabatie and hydrodynamic [thus (3) and. (4) are absent]. flows are still under the influence of the deceleration mechanisms (1) aud (2).," Although our model is purely adiabatic and hydrodynamic [thus (3) and (4) are absent], flows are still under the influence of the deceleration mechanisms (1) and (2)." Following the previous works(seeYang&Ixafatos1995:LuYuan1998).. let us assume jmp conditions (hat allow energy. angular momentum and mass loss al a standing shock front.," Following the previous works\citep[see][]{Yang95,Lu98}, let us assume jump conditions that allow energy, angular momentum and mass loss at a standing shock front." Figure 1 illustrates a schematic description of our model.," Figure \ref{fig:schematic} illustrates a schematic description of our model." " From equation (11)) we have where (he subscripts ""1 and 72 denote the quantities for upstream and clownstream flows evaluated al a shock location (r= ry). respectively,"," From equation \ref{eq:energy2}) ) we have where the subscripts “1” and “2” denote the quantities for upstream and downstream flows evaluated at a shock location $r=r_{\rm sh}$ ), respectively." We require £4>E» and define the energy dissipation and its fraction as where 0 E_2$ and define the energy dissipation and its fraction as where $0 < f_E < 1$. " The associated angular momentum carried by the outflows is then eiven by AL=L4—Ls ANE,"," The associated angular momentum carried by the outflows is then given by $\Delta L \equiv L_1 - L_2 = \lambda \Delta E$ ." has never been observed in any other XBL (Ciliegi et al. 1995.,"has never been observed in any other XBL (Ciliegi et al. \cite{Ciliegi}," Lamer at al. 1996))., Lamer at al. \cite{Lamer96}) ). The spectrum measured on 16 April 1997 by SAX in about the same energy band (2.14-10 keV) is even slightly harder (&.=0.59. Pian et al. 1997)).," The spectrum measured on 16 April 1997 by SAX in about the same energy band (2.14-10 keV) is even slightly harder $\alpha=0.59$, Pian et al. \cite{Pian}) )." As the PCA has no sensitivity below 2 keV. we are not able to verify the break at ~2keV in the SAX spectrum.," As the PCA has no sensitivity below 2 keV, we are not able to verify the break at $\sim 2\; {\rm keV}$ in the SAX spectrum." Above the break point the PCA spectrum steepens by up to 0.3 in energy index., Above the break point the PCA spectrum steepens by up to 0.3 in energy index. In some of the spectra à» exceeds unity. indicating that the maximum of the synchrotron power output is reached in the hard X-ray range.," In some of the spectra $\alpha_2$ exceeds unity, indicating that the maximum of the synchrotron power output is reached in the hard X-ray range." However. there 1s no evidence for further steepening of the spectrum up to 100 keV. During the RXTE observations the PCA count-rate varied by ~30%. but in contrast to the results from the April 1997 SAX observations an anti-correlation of flux and spectral hardness was observed both below and above the spectral break.," However, there is no evidence for further steepening of the spectrum up to 100 keV. During the RXTE observations the PCA count-rate varied by $\sim 30\%$, but in contrast to the results from the April 1997 SAX observations an anti-correlation of flux and spectral hardness was observed both below and above the spectral break." Such an anti-correlation has never been reported in Mrk 501 and is quite unusual for X-ray BL Lac objects altogether., Such an anti-correlation has never been reported in Mrk 501 and is quite unusual for X-ray BL Lac objects altogether. Pian et al., Pian et al. found a spectral hardening by Aa=0.32 in the SAX MECS 2-10 keV band during an increase of the flux in this energy band by a factor of 2.4., found a spectral hardening by $\Delta \alpha = 0.32$ in the SAX MECS 2-10 keV band during an increase of the flux in this energy band by a factor of 2.4. The large degree of spectral variability and its latiion. with total flux implies great differences between the light curves in the individual X-ray energy bands., The large degree of spectral variability and its ion with total flux implies great differences between the light curves in the individual X-ray energy bands. We hence derived light curves for seven and four different channel ranges of the PCA and HEXTE detectors. respectively (Figs.," We hence derived light curves for seven and four different channel ranges of the PCA and HEXTE detectors, respectively (Figs." 3 and [ Lj)., \ref{pca_lc} and \ref{hexte_lc}) ). The light curves in the softer bands show a decline by over 3 days with a well defined minimum at MJD 50643.3 and a subsequent increase by during the following 3 days., The light curves in the softer bands show a decline by over 3 days with a well defined minimum at MJD 50643.2 and a subsequent increase by during the following 2 days. On the other hand the hardest bands are dominated by a feature with a broad maximum around MJD 50642., On the other hand the hardest bands are dominated by a feature with a broad maximum around MJD 50642. A smooth transition with superpositions of both morphologies is observed | the intermediate energy bands., A smooth transition with superpositions of both morphologies is observed in the intermediate energy bands. The independent variability of soft and hard X-rays requires the existence of at least two emisslIol components which is not evident from the X-ray spectrum alone., The independent variability of soft and hard X-rays requires the existence of at least two emission components which is not evident from the X-ray spectrum alone. The sharpest feature in the 2-20 keV lightcurves is a decrease in flux by within 4.5 hours., The sharpest feature in the 2-20 keV lightcurves is a decrease in flux by within 4.5 hours. In an EXOSAT ME lightcurve (0.7-8 keV. Giommi et al. 1990))," In an EXOSAT ME lightcurve (0.7-8 keV, Giommi et al. \cite{Giommi}) )" similar timescales and amplitudes have been found., similar timescales and amplitudes have been found. In an investgation of the spectral variability of 6 BL Lac objects Giommi et al., In an investgation of the spectral variability of 6 BL Lac objects Giommi et al. found tight correlations of flux and spectral hardness for any of the objects. including Mrk 501.," found tight correlations of flux and spectral hardness for any of the objects, including Mrk 501." This highlights the peculiarity of the spectral variability reported here., This highlights the peculiarity of the spectral variability reported here. Our RXTE observations from July 1997 show that the period of increased X-ray brightness continued throughout 1997 and was not limited to a short flare in April., Our RXTE observations from July 1997 show that the period of increased X-ray brightness continued throughout 1997 and was not limited to a short flare in April. The object clearly was in a long-lasting high-state in 1997 rather than exhibiting à short. spectacular X-ray flare during the epoch of the SAX observations.," The object clearly was in a long-lasting high-state in 1997 rather than exhibiting a short, spectacular X-ray flare during the epoch of the SAX observations." We confirm the extraordinary hard. X-ray spectrum which extends up to 100 keV. The peak of the synchrotron emission is observed in the hard X-rays. more than 2 orders of magnitude higher than in earlier observations (e.g. by ROSAT in 1991. Lamer et al. 1996)).," We confirm the extraordinary hard X-ray spectrum which extends up to 100 keV. The peak of the synchrotron emission is observed in the hard X-rays, more than 2 orders of magnitude higher than in earlier observations (e.g. by ROSAT in 1991, Lamer et al. \cite{Lamer96}) )." During the RXTE observations in July the total flux and the spectral hardness show an anti-correlation., During the RXTE observations in July the total flux and the spectral hardness show an anti-correlation. This is a very unusual spectral behaviour for any BL Lac object. it has not been observed previously in Mrk 501 and ts in marked contrast to the fact that the SAX observations of Pian et al.," This is a very unusual spectral behaviour for any BL Lac object, it has not been observed previously in Mrk 501 and is in marked contrast to the fact that the SAX observations of Pian et al." showed a flatter spectrum during the brighter stage (there are only two different brightness and spectral levels in the SAX data set rather than a well-established correlation)., showed a flatter spectrum during the brighter stage (there are only two different brightness and spectral levels in the SAX data set rather than a well-established correlation). The flux-spectral index relations should hence not be regarded as universal and viable models should explain both kinds of behaviour., The flux-spectral index relations should hence not be regarded as universal and viable models should explain both kinds of behaviour. The broken power law (or gradual steepening of the spectrum) is consistent with synchrotron cooling of a single component and does not require the superposition of different particle. distributions., The broken power law (or gradual steepening of the spectrum) is consistent with synchrotron cooling of a single component and does not require the superposition of different particle distributions. A homogeneous jet and a magnetic field of 0.LC are capable of producing the integrated spectral signature., A homogeneous jet and a magnetic field of $0.4 {\rm G}$ are capable of producing the integrated spectral signature. We have found rather dramatic spectral differences in the light curves which cannot be explained by a single population but requires the contributions of at least two. if not more spectral components.," We have found rather dramatic spectral differences in the light curves which cannot be explained by a single population but requires the contributions of at least two, if not more spectral components." This illustrates the great importance of well-sampled monitoring with instruments covering a wide spectral range., This illustrates the great importance of well-sampled monitoring with instruments covering a wide spectral range. and K (Mukherjeeet a1]2006)]].,and $K$ \citep{eu}] ]. The paper is presented as follows: in the next section we describe the relevant field equations., The paper is presented as follows: in the next section we describe the relevant field equations. In section three we discuss the methods applied to constrain the parameters from (i) Observed Hubble Data (OHD)(Sternet and (ii) SDSS data measuring a model independent al]B010)BAO peak parameter , In section three we discuss the methods applied to constrain the parameters from (i) Observed Hubble Data \citep{stern} and (ii) SDSS data measuring a model independent BAO peak parameter \citep{bao}. section four we study the Density Parameters (DP) of the Inmodel (at the present epoch) and finally we discuss the results in section 5., In section four we study the Density Parameters (DP) of the model (at the present epoch) and finally we discuss the results in section 5. Friedmann equation in a flat universe reads as: where H is the Hubble parameter and a is the scale factor of the Universe., Friedmann equation in a flat universe reads as: where $H$ is the Hubble parameter and $a$ is the scale factor of the Universe. The usual conservation equation holds: Using the EOS given by eq. (1)),The usual conservation equation holds: Using the EOS given by eq. \ref{eos1}) ) in (8) and eq. ()), in \ref{fr1}) ) and eq. \ref{csv}) ) one obtains: where ’z’ represents the cosmological redshift., one obtains: where $z$ ' represents the cosmological redshift. The first term in the right hand side of is a constant which can be interpreted as cosmological 5)constant and describing dark energy., The first term in the right hand side of \ref{rho1}) ) is a constant which can be interpreted as cosmological constant and describing dark energy. Eq. (6) , Eq. \ref{rho1}) ) can be written as: where p1= p2= and p3=(45) represents densities at (qa).the present Gaepoch.," can be written as: where $\rho_{1}=\left(\frac{B}{A+1}\right)^{2}$, $\rho_{2}=\frac{2 B K}{\left(A+1\right)^2}$ and $\rho_{3}=\left(\frac{K}{A+1}\right)^{2}$ represents densities at the present epoch." The Friedmann equation (eq. , The Friedmann equation (eq. \ref{fr1}) ) "can now be written in terms of redshift and density parameterBJ) as follows: where we define density parameter: Q=8zGp3H2Q(A,B, K)."," can now be written in terms of redshift and density parameter as follows: where we define density parameter: $\Omega=\frac{8 \pi G \rho}{3H_{0}^{2}}=\Omega\left(A, B, K\right)$ ." For a given A=Ao (say) we note that the nature of evolution for the variable parts of the matter energy density may now be established., For a given $A=A_{0}$ (say) we note that the nature of evolution for the variable parts of the matter energy density may now be established. " Hence, choice of a suitable value for A leads to a known composition of fluids."," Hence, choice of a suitable value for $A$ leads to a known composition of fluids." " For example, considered the case A=0 with dark energy, dark matter and dust in the Universe."," For example, \citet{eu2} considered the case $A=0$ with dark energy, dark matter and dust in the Universe." Fixing A one can re-write eq. (7) , Fixing $A$ one can re-write eq. \ref{fr2}) ) "as: where, Here we have replaced the constant part of the DP (1) by a new notation Qa."," as: where, Here we have replaced the constant part of the DP $\Omega_{1}$ ) by a new notation $\Omega_{\Lambda}$ ." i=2. i» ο §=T/|W| 1 VW (4. o0.27 O.LL (Chandrasckhar1969)., $m=2$ $m$ $e^{\pm im\varphi}$ $\beta=T/|W|$ $T$ $W$ $\beta_{\rm c}$ $\beta_c\sim 0.27$ $0.14$ \citep{chandra69}. . and more involved models for the core collapse scenario., and more involved models for the core collapse scenario. Newtoman livdrodvuanucal simulations have shown that the value of ος is quite independent of the stiffuess of the equation of state. provided the star is not strougly differentially rotating (see Touseretal.(1991):Newetal.(2000):Liu(2002). and references therein).," Newtonian hydrodynamical simulations have shown that the value of $\beta_{\rm c}$ is quite independent of the stiffness of the equation of state, provided the star is not strongly differentially rotating (see \citet{houser94,new00,liu02} and references therein)." Ou the other haud. relativistic simulations (Shibataetal.2000) have vielded a sheltly simaller value of the dynamical iustability parameter (6~0.210.25).," On the other hand, relativistic simulations \citep{shibata00} have yielded a slightly smaller value of the dynamical instability parameter $\beta_{\rm c}\sim 0.24-0.25$ )." They have also shown that the αναλος of the process closely resembles that found in Newtonian theory. that is. unstable models with large οποιο. . develop spiral arms following the formation of bars. ejecting mass and redistributing the aneulay momentum.," They have also shown that the dynamics of the process closely resembles that found in Newtonian theory, that is, unstable models with large enough $\beta$ develop spiral arms following the formation of bars, ejecting mass and redistributing the angular momentum." Further relativistic simulations (Baiottictal.2007) have shown he appearance of nonlinear mode-couplius which can iuit. and even suppress. the persistence of the αι”uode deformation.," Further relativistic simulations \citep{baiotti07} have shown the appearance of nonlinear mode-coupling which can limit, and even suppress, the persistence of the bar-mode deformation." It is also worth mentioning that. as he degree of differcutial rotation becomes higher aud nore extreme. Newtonian simulations (Shibatactal.2002.2003) have also shown that rotating stars are dynamically uustable agaist barauodoe deformation even or values of ο) of order 0.01.," It is also worth mentioning that, as the degree of differential rotation becomes higher and more extreme, Newtonian simulations \citep{shibata02,shibata03} have also shown that rotating stars are dynamically unstable against bar-mode deformation even for values of $\beta$ of order 0.01." Whether the requirements for the development of he instability inferred from nuinerical simulations are imet bv the collapse progenitors remains unclear., Whether the requirements for the development of the instability inferred from numerical simulations are met by the collapse progenitors remains unclear. Observations of surface velocities imply that a laree raction of progenitor cores are rapidly rotating., Observations of surface velocities imply that a large fraction of progenitor cores are rapidly rotating. However. it has been shown that magnetic torques can spin down the core of the progenitor. leacing to slowly rotating neutron stars at birth (Spruit&Phinney1998).," However, it has been shown that magnetic torques can spin down the core of the progenitor, leading to slowly rotating neutron stars at birth \citep{spruit98}." . The most recent computations of the evolution of massive stars. which include angular momentum redistribution by magnetic torques aud spin estimates of neutron stars at birth. lead to core collapse progenitors which do not seen to rotate fast enough toguaranteethe unambiguouserowth of the canonical bar-mocde instability (οσα 2006)..," The most recent computations of the evolution of massive stars, which include angular momentum redistribution by magnetic torques and spin estimates of neutron stars at birth, lead to core collapse progenitors which do not seem to rotate fast enough toguaranteethe unambiguousgrowth of the canonical bar-mode instability \citep{heger05,ott06}. ." These estimates are iu aereenment with observed periods of voune neutron stars., These estimates are in agreement with observed periods of young neutron stars. 1t has been shown that mergers can lead to both morpholoev. ancl luminosity segregation (Fusco-Femiano Aencei 1998: Yopes. Domínnguez-Tenreiro Del Pozo-Sanz 1991). and observations suggest that ealaxies are segregated in both groups (Alaheavi 1999: Girardi 2003) and clusters (Adami. Biviano Mazure. 1998: Diviano 2002: Lares. Lambas Sánnchez 2004).,"It has been shown that mergers can lead to both morphology and luminosity segregation (Fusco-Femiano Menci 1998; Yepes, Domínnguez-Tenreiro Del Pozo-Sanz 1991), and observations suggest that galaxies are segregated in both groups (Mahdavi 1999; Girardi 2003) and clusters (Adami, Biviano Mazure 1998; Biviano 2002; Lares, Lambas Sánnchez 2004)." Since mergers will also allect the relative number of galaxies at a given luminositv. one might expect the prevalence. of mergers in groups to influence the shape of the group luminosity. function.," Since mergers will also affect the relative number of galaxies at a given luminosity, one might expect the prevalence of mergers in groups to influence the shape of the group luminosity function." This is. in fact. a possible explanation. of the commonly observed: 7dip. indicative of intermediate mass ealaxies merging to form more luminous ones (c.g. Trenthanm Tull 2002: Miles 2004).," This is, in fact, a possible explanation of the commonly observed “dip”, indicative of intermediate mass galaxies merging to form more luminous ones (e.g. Trentham Tully 2002; Miles 2004)." Lt is also worth noting that recent observations of ram-pressure stripping in groups (e.g. Bureau Carignan 2002: Ixantharia 2005: Rasmussen. Ponman Alulchacy 2006) support the results of numerical simulations which suggest that group-level rani-pressure stripping could also play some role in group galaxy evolution (Llester 2006).," It is also worth noting that recent observations of ram-pressure stripping in groups (e.g. Bureau Carignan 2002; Kantharia 2005; Rasmussen, Ponman Mulchaey 2006) support the results of numerical simulations which suggest that group-level ram-pressure stripping could also play some role in group galaxy evolution (Hester 2006)." Typical studies. of poor groups may classify 10-20 galaxies as eroup members. the majority of which— nave had their membership assigned. using photometric or morphological criteria.," Typical studies of poor groups may classify 10-20 galaxies as group members, the majority of which have had their membership assigned using photometric or morphological criteria." More robust studies have included only galaxies for which recession velocity measurements are available (e.g. Zablucoll Alulehacy 199s: Carlhere 2001: Brough 2006a). however this often leads to the need to stack groups in order to measure their properties due to the low numbers of redshifts typically available.," More robust studies have included only galaxies for which recession velocity measurements are available (e.g. Zabludoff Mulchaey 1998; Carlberg 2001; Brough 2006a), however this often leads to the need to stack groups in order to measure their properties due to the low numbers of redshifts typically available." The problem with stacking groups. however. is that while it is then possible to constrain the ecneralisecl elobal properties of groups (e.g. mass distribution. velocity dispersion profile ete.)," The problem with stacking groups, however, is that while it is then possible to constrain the generalised global properties of groups (e.g. mass distribution, velocity dispersion profile etc.)" the individual properties of any single group are washed out., the individual properties of any single group are washed out. llere we aim to address this issue by establishing 16 properties of the group and. its galaxies independently., Here we aim to address this issue by establishing the properties of the 5044 group and its galaxies independently. By studying a 55044.single rich group we are able o examine evidence for dvnamical segregation. substructure and peculiarities in its dynamical properties that are washed out when stacking multiple groups.," By studying a single rich group we are able to examine evidence for dynamical segregation, substructure and peculiarities in its dynamical properties that are washed out when stacking multiple groups." In this paper. we oresent new deep spectroscopic data that allow us. to spectroscopically confirm ~40 new group members.," In this paper, we present new deep spectroscopic data that allow us to spectroscopically confirm $\sim40$ new group members." With he addition of these velocities. we create a new list of 111 confirmed group members that then allows a comprehensive analvsis of the dynamical attributes of the 55044 eroup and its constituent. galaxies out to nearly two virial racii.," With the addition of these velocities, we create a new list of 111 confirmed group members that then allows a comprehensive analysis of the dynamical attributes of the 5044 group and its constituent galaxies out to nearly two virial radii." In future work we will use these data to examine the stellar populations of the group galaxies in relation to their position in the group. IHE gas properties. star formation rates and dynamical. properties.," In future work we will use these data to examine the stellar populations of the group galaxies in relation to their position in the group, HI gas properties, star formation rates and dynamical properties." This paper is organised as follows: in ον and §3 we describe some general properties of the group and the data set we have assembled., This paper is organised as follows: in $\S$ \ref{n5044} and $\S$ \ref{data} we describe some general properties of the 5044 group and the data set we have assembled. 54 describes.55044. the method we have used to select. group. members/— from. our list of potential candidates., $\S$ \ref{fof} describes the method we have used to select group members from our list of potential candidates. Ehe global group properties are acelressed in §5.. and the properties related. to individual ealaxies are summuarised in 5$6..," The global group properties are addressed in $\S$ \ref{global}, , and the properties related to individual galaxies are summarised in $\S$ \ref{galaxy}." Throughout this paper we assume £45 = pe where applicable ancl recession velocities. are quoted. in terms of ος., Throughout this paper we assume $H_0$ = $^{-1}$ where applicable and recession velocities are quoted in terms of $z$. We adopt. the distance. modulus of Tonrv (2001). (mAM)y=32.31 MMpec). measured using surface brightness Uuetuations with corrections applied. to adjust. for the improved Cephoeid distance measurements of Jensen (2003).," We adopt the distance modulus of Tonry (2001), $(m-M)_0=32.31$ Mpc), measured using surface brightness fluctuations with corrections applied to adjust for the improved Cepheid distance measurements of Jensen (2003)." Magnitudes have beencorrected. for galactic extinction using the dust maps of Schlegel. Finkbeiner Davis (1998).," Magnitudes have beencorrected for galactic extinction using the dust maps of Schlegel, Finkbeiner Davis (1998)." Following convention we use £2 to denote 2D. projected radii ancl + to indicate 3D. deprojected racii," Following convention we use $R$ to denote 2D, projected radii and $r$ to indicate 3D, deprojected radii." We have selected. the 55044. group. as the Locus of this work as it is our goal to describe the properties of a eroup. and its large galaxy population is sullicient to perform a statistical analysis.," We have selected the 5044 group as the focus of this work as it is our goal to describe the properties of a group, and its large galaxy population is sufficient to perform a statistical analysis." Ferguson Sandage (1990. hereafter. E890: 1991. hereafter. E8591). photometrically studied. T nearby groups ancl clusters. including 55044. constructing group luminosity functions and examining the relative fractions of chvarl and giant. galaxies.," Ferguson Sandage (1990, hereafter FS90; 1991, hereafter FS91) photometrically studied 7 nearby groups and clusters, including 5044, constructing group luminosity functions and examining the relative fractions of dwarf and giant galaxies." In their work. FSO show that the earlv-tvpe dwarf to giant. ratio (EDGR) correlates nearly monotonically with richness.," In their work, FS91 show that the early-type dwarf to giant ratio (EDGR) correlates nearly monotonically with richness." Phe intermediate richness of the 55044. eroup. means that its EDCR. occupies the transition between groups and clusters.," The intermediate richness of the 5044 group, means that its EDGR occupies the transition between groups and clusters." They. also. found evidence for a steep. faint-end luminosity function in the 55044. group. however their photometric selection. is likely to contain significant background contamination.," They also found evidence for a steep faint-end luminosity function in the 5044 group, however their photometric selection is likely to contain significant background contamination." The 55044. group has also been studied: as part of the Group Evolution Alulti-wavelength Survey (GEAIS: Osmond Ponman 2004: Forbes 2006) ancl so ws been observed at both X-ray and LL wavelengths (Osmoncd Ponman 2004: Melxay 2004: Wilborn in preparation. hereafter. INOS).," The 5044 group has also been studied as part of the Group Evolution Multi-wavelength Survey (GEMS; Osmond Ponman 2004; Forbes 2006) and so has been observed at both X-ray and HI wavelengths (Osmond Ponman 2004; McKay 2004; Kilborn in preparation, hereafter K08)." “Phe GEMS. group sample was selected from the availability of ROSAT PSPC »ntings., The GEMS group sample was selected from the availability of ROSAT PSPC pointings. Further N-rav observations of the 55044 eroup have been carried out using both Chandra: ancl NMAMNewton (Buote 2003: ανα 2003: Duote. Brighenti Mathews 2004).," Further X-ray observations of the 5044 group have been carried out using both Chandra and XMM–Newton (Buote 2003; Tamura 2003; Buote, Brighenti Mathews 2004)." Phese authors found the eroup to have a cool-core component of ~0.7 kkeV. within Ükkpc (consistent with the kinetic temperature of stars in 55044 itself). anc a warmer L4tkkeV outside of kkpe (characteristic of the group halo).," These authors found the group to have a cool-core component of $\sim$ keV within kpc (consistent with the kinetic temperature of stars in 5044 itself), and a warmer keV outside of kpc (characteristic of the group halo)." The large racial extent of X-ray emission (00 κκρο and high Ly/Le ratio (logphx/Lg=31.52+0.01 eergs s th+: Osmond Ponman 2004) are key indications that the hot σας is associated with a group sized. potential rather than just 55044 itself., The large radial extent of X-ray emission $r>$ kpc) and high $L_X/L_B$ ratio $\mathrm{log}_{10}L_X/L_B=31.82\pm0.01$ ergs $^{-1}$ $_{\odot}^{-1}$; Osmond Ponman 2004) are key indications that the hot gas is associated with a group sized potential rather than just 5044 itself. We used the photometrically determined 55044 group catalogue of 00 as the target. list. lor new spectral observations., We used the photometrically determined 5044 group catalogue of FS90 as the target list for new spectral observations. The E890 catalogue was constructed: using photographic plates covering —2.3ddeg? taken at the 2.5m duPont Telescope at the Las Campanas Observatory., The FS90 catalogue was constructed using photographic plates covering $\sim$ $^2$ taken at the 2.5m duPont Telescope at the Las Campanas Observatory. AXOmega's 3ddeg? Bield-of-view. allowed. us to observe all 162 objects in the FS9O 55044. eroup catalogue simultaneously., AAOmega's $^2$ field-of-view allowed us to observe all 162 objects in the FS90 5044 group catalogue simultaneously. " FS90 used a B-banel radial cut. of 16"". estimated to be 27 mag 7oat the distance of 55044). to. limit background. contamination."," FS90 used a B-band radial cut of $^{\prime\prime}$ , estimated to be 27 mag $^{-2}$ at the distance of 5044), to limit background contamination." Group membershipwas then, Group membershipwas then the cise to the active corona dedecreasing £) not only increases the X.ray illuminating Lux. but it also decreases the disc thickness. thus decreasing the eravity.,"the disc to the active corona decreasing $\xi$ ) not only increases the X–ray illuminating flux, but it also decreases the disc thickness, thus decreasing the gravity." Based on results of previous Section we expect the variability of the Fe line flux to be reduced. compared. to. the amplitude of variability. of the driving continuum. even though it does not seen possible to obtain absolutely constant [lux of the line.," Based on results of previous Section we expect the variability of the Fe line flux to be reduced compared to the amplitude of variability of the driving continuum, even though it does not seem possible to obtain absolutely constant flux of the line." Here we estimate the reduction of the vvariabilitv of the Fe line. compared. with an assumed vvariabilitv of its driving continuum.," Here we estimate the reduction of the variability of the Fe line, compared with an assumed variability of its driving continuum." To this end we will use results of our calculations of τι.η) ator=10r.," To this end we will use results of our calculations of $\tauh(\xi, \eta)$ at $r=10\,\Rg$." In this way we will obtain the upper limit to the considered effect. since nar) reaches maximum at reI0 7. for a given pair (ένη) (see Γιο. 3)).," In this way we will obtain the upper limit to the considered effect, since $\tauh(r)$ reaches maximum at $r\approx 10\,\Rg$ , for a given pair $(\xi, \eta)$ (see Fig. \ref{fig:taurad}) )." First. we construct a simulated. light curve of. hard Xrav continuum by summing Fourier components. with random phases F'Esonis 1992 for an adopted. form. of power spectral density. (PSD). PC).," First, we construct a simulated light curve of hard X–ray continuum by summing Fourier components with random phases Tsonis 1992), for an adopted form of power spectral density (PSD), $P(f)$." For the PSD we adopt ↾↓∖↓↥⊀↓⊳∖↓≻↓⋅∪∖⋰⊓⇂∢⊾⊳∖⋜↧⋏∙≟∪⋯⇂∠⇂∢⊾≻≼∼↓⋅↕↓≻⇂↕⋖⋟↓↥∪⇂⋅↓⋯↓⋅∠⇂⇀∖↓⋅⋜↧∙∖⇁↓↴↔⊥≻ ∪⇂∎⋖⋅⋡⋏∙≟↪∖∟∖∐⊲≺∶≼≨−∶∫≻∪−↓⋅∏⋡∖∖⋰↓↿↓↕∣↓↕⋖⊾≼∼⋯∪∐⋅∐⋅⋖⋅⊏↥⋯⊾⊔≼∼∙∖⇁⇠∕⊲≼∶↓∪ ∐∠⊳⇂↓↕∢⊾⊳∖↓∪↓≻⋖⋅∣↗∶↓⋅≟⋜⋯∠⇂⇂↓↕∢⊾↓↕∢≱↓⋅↓↥↓⋜↧⇂↕∠⋜↧⇂↕⋖≱↓↥≼↛∪↓⋅↓⋅⋖⋅⊳∖↓≻∪↓∐⇂⊲↓⊔⋏∙≟∣∪ vvariability ofis2 ↓≻⋖↓⊓⊔↿↿∖≺∶↓⋅∢⊾⋖⋅⊔⊳↳∖↓≼⇍∐⋜⋯⇂∙∖⇁⊾∖↽∟⋖⋅↓∐∪ 1993: ChianeCzerny Le 1907 ⋯↥∪∪∣⊓⋅↿⋜↧↓⊳⊔≤⋗≤⋗⊤∶↓∖⊽∪∖∖⊽⋜↧↳⊾∖↽ 2000: Revnolels 2006).," For the PSD we adopt This provides a good description of hard X–ray PSD of MCG–6-30-15, with the cutoff frequency $\fc=10^{-5}$ Hz, the slope $p=1.4$ and the normalization corresponding to variability of 20 per cent (Green, McHardy Lehto 1993; Czerny Lehto 1997; Yaqoob et 1997; Nowak Chiang 2000; Reynolds 2000)." We take these parameters to be representative for Sevfert 1 galaxies., We take these parameters to be representative for Seyfert 1 galaxies. The light curve is scaled to have a given mean value C., The light curve is scaled to have a given mean value ${\overline C}$. Next. the light curve in enerev banc containing the line photons is constructed according to where ο is the fraction of line photons contributing to total counts in the considered. energy band. while A?€'(4] is the relative amplitude of the reprocessed component. as a function of the illuminating hard Xray flux.," Next, the light curve in energy band containing the line photons is constructed according to where $\Al$ is the fraction of line photons contributing to total counts in the considered energy band, while $R[C(t)]$ is the relative amplitude of the reprocessed component as a function of the illuminating hard X–ray flux." Writing equation (13)) we have assumed no time lag in the response of the Fe line emission after the continuum variations. consistent with observations Hltevnolkdis 2000).," Writing equation \ref{equ:lineflux}) ) we have assumed no time lag in the response of the Fe line emission after the continuum variations, consistent with observations Reynolds 2000)." The amplitude £2(ΟΕ is computed as follows: we choose a value for the elfective amplitude of the reprocessed component at the mean flux level. RCC).," The amplitude $R[C(t)]$ is computed as follows: we choose a value for the effective amplitude of the reprocessed component at the mean flux level, $R({\overline C})$." We then assume that R(C') corresponds to a pair (£5.go). which is located. on atrajectory in the € a plane that the system travels while changing its luminosity.," We then assume that $R({\overline C})$ corresponds to a pair $(\xi_0, \eta_0)$, which is located on atrajectory in the $\xi$ $\eta$ plane that the system travels while changing its luminosity." Phe trajectory describes how changes of£ and ij contribute to the variability., The trajectory describes how changes of $\xi$ and $\eta$ contribute to the variability. Since our understanding of variability mechanisms is rather limited. we will simply test a number of arbitrary. trajectories. to ect an idea of available range of results.," Since our understanding of variability mechanisms is rather limited, we will simply test a number of arbitrary trajectories, to get an idea of available range of results." As discussed. in oevious Section. variations along the £-axis give largest xossible. change of / for a given change of Fx. therefore our chosen trajectories have a significant component along he £ axis.," As discussed in previous Section, variations along the $\xi$ -axis give largest possible change of $R$ for a given change of $\FX$, therefore our chosen trajectories have a significant component along the $\xi$ axis." Next. we construct the lightcurve of the observed iud Xrav continuum. which has a contribution [from hotons backscattered in. the hot. [aver. Fa)=C(t)[11palΤιrotCCA} }}.," Next, we construct the lightcurve of the observed hard X–ray continuum, which has a contribution from photons backscattered in the hot layer, $F(t) = C(t) \{1+\Prefl\{\tauh[C(t)]\}\}$ ." Pinall. the vvariability is computed for F(1)| and La) according to First we set cl)=1 wwe consider the light curve of the Fe line alone. without any continuum photons.," Finally, the variability is computed for $F(t)$ and $L(t)$ according to First we set $\Al=1$ we consider the light curve of the Fe line alone, without any continuum photons." An example of the simulated light. curves is. plotted in Fig. 5.., An example of the simulated light curves is plotted in Fig. \ref{fig:simlcurve}. . Phey were obtained assuming that the mean Lux of the intrinsic cont C. corresponds to £;=0.5 and yo=1 (which yields inim.(67)&0.75. see Fig. 4)).," They were obtained assuming that the mean flux of the intrinsic continuum, $\overline C$, corresponds to $\xi_0 = 0.5$ and $\eta_0 = 1$ (which yields $R({\overline C})\approx 0.75$, see Fig. \ref{fig:reflfhard}) )," and that the variability is only due to changing £., and that the variability is only due to changing $\xi$. The line Lux is reduced. at all times. since (C) is significantly lower than 1. and its vvariabilitv is reduced by=5 per cent compared with the vvariabilitv of dts driving continuum. C'(/).," The line flux is reduced at all times, since $R({\overline C})$ is significantly lower than 1, and its variability is reduced by$\approx 5$ per cent compared with the variability of its driving continuum, $C(t)$ ." Phe observed hard X.ray continuum. £'(/). contains a contribution from photons backscatteredin the hot laver. which increase its vvariabilitv by z1 per," The observed hard X–ray continuum, $F(t)$ , contains a contribution from photons backscatteredin the hot layer, which increase its variability by $\approx 1$ per" of near-infrared emission from ILerbig AeBe stars (Eisner et 22007:—-—Ίντα» et 22007: Tannirkulam et 22008a.b: Isella et 22008).,"of near-infrared emission from Herbig AeBe stars (Eisner et 2007; Kraus et 2007; Tannirkulam et 2008a,b; Isella et 2008)." The compact cont emission is attributed by these authors to emission [rom a gaseous disk interior to the dust sublimation radius., The compact continuum emission is attributed by these authors to emission from a gaseous disk interior to the dust sublimation radius. Such a gaseous disk is expected to show significant spectral structure due (to emission lines of CO and water aud other opacily sources (e.e.. Muzerolle et 22004: Eisner 2007).," Such a gaseous disk is expected to show significant spectral structure due to emission lines of CO and water and other opacity sources (e.g., Muzerolle et 2004; Eisner 2007)." llere we report high resolution. A-band spectroscopy of two voung stars. MWC. 480 and V1331 Cvg.," Here we report high resolution $K$ -band spectroscopy of two young stars, MWC 480 and V1331 Cyg." MAC 480 CID 31648: A3pshe+) is a Herbig Ae star with a stellar mass ol 2.344. that is surrounded. by a rotating disk of gas ancl dust. (Mannings οἱ 11997)., MWC 480 (HD 31648; A3pshe+) is a Herbig Ae star with a stellar mass of $2.3\Msun$ that is surrounded by a rotating disk of gas and dust (Mannings et 1997). CO fundamental emission is detected rom the source (Blake Boogert 2004)., CO fundamental emission is detected from the source (Blake Boogert 2004). Spatially resolved millimeter aud infrared interferometric studies of the emission from AIWC 480 derive an inclination of 7 —2638 degrees for the disk (Simon et 22000: Eisner et 22004)., Spatially resolved millimeter and infrared interferometric studies of the emission from MWC 480 derive an inclination of $i=$ 26–38 degrees for the disk (Simon et 2000; Eisner et 2004). spectrally dispersed interferometric observations find evidence for an emission excess located interior to the dust sublimation radius with a spectral shape that suggests emission [from hot water vapor (Eisner 2007)., Spectrally dispersed interferometric observations find evidence for an emission excess located interior to the dust sublimation radius with a spectral shape that suggests emission from hot water vapor (Eisner 2007). Evidence lor active accretion in this source includes the presence of associated HII objects and emission lines of Si IV.(1394À.. 1403A)) that arise from hol accreting σας (Silko οἱ 22008: also Valenti et 22000 and Muzerolle et 22004).," Evidence for active accretion in this source includes the presence of associated HH objects and emission lines of Si IV, ) that arise from hot accreting gas (Sitko et 2008; also Valenti et 2000 and Muzerolle et 2004)." The other source in our study. V1331. Cvg (Lklla 120). is a pre-amain-sequence star in the LOSS dark cloud complex.," The other source in our study, V1331 Cyg (LkHa 120), is a pre-main-sequence star in the L988 dark cloud complex." The distance to. L988 (see Herbie Dahm 2006 [or a summarv) has been estimated as ppc. based on photometry ancl spectroscopy of nebulous sources in the L983 region (Chavarria 1981: Chavarria-Ix de Lara 1981)., The distance to L988 (see Herbig Dahm 2006 for a summary) has been estimated as pc based on photometry and spectroscopy of nebulous sources in the L988 region (Chavarria 1981; Chavarria-K de Lara 1981). Studies | » extinction in the region toward the clouds determine a closer distance for the elouds X ppe (Shevehenko οἱ 11991) and 500+LOO ppe Alves οἱ ((1993)., Studies of the extinction in the region toward the clouds determine a closer distance for the clouds of pc (Shevchenko et 1991) and $500\pm100$ pc Alves et (1998). Various studies suggest a spectral tvpe for V1331 Cve CA8-G5) that [alls between those ol Herbig Ae stars and tvpical T Tauri stars (Ixuhi 1964; Chavarria 1981: ILanann Personn 1992)., Various studies suggest a spectral type for V1331 Cyg (A8-G5) that falls between those of Herbig Ae stars and typical T Tauri stars (Kuhi 1964; Chavarria 1981; Hamann Personn 1992). V1331 (νο has an associated molecular outflow (Levreault 1938) and a massive jrcunmstellar disk (0.537. assuming ppe distance: MeMüuldroch et 11993: see also Weintraub et 11991) that is surrounded by a flattened gaseous envelope and a ring of reflection nebulositv viewed al an inclination of /~30 degrees., V1331 Cyg has an associated molecular outflow (Levreault 1988) and a massive circumstellar disk $0.5\Msun$ assuming pc distance; McMuldroch et 1993; see also Weintraub et 1991) that is surrounded by a flattened gaseous envelope and a ring of reflection nebulosity viewed at an inclination of $i \sim 30$ degrees. V1331 Cvg is known to show enission in CO overtone bands (Carr 1989)., V1331 Cyg is known to show emission in CO overtone bands (Carr 1989). Hieh resolution L-band spectroscopy that shows water and OIL emission from V1331 (νο has also been presented. previously (Najita οἱ 22005)., High resolution $L$ -band spectroscopy that shows water and OH emission from V1331 Cyg has also been presented previously (Najita et 2005). A high resolution A-band spectrum of V1331. Cvg was obtained by one of us (JRG), A high resolution $K$ -band spectrum of V1331 Cyg was obtained by one of us (JRG) ddata were reduced using the software and the calibration data available us of July: 2009. and according to the method described. in Nevalainenctal.(2005).,"data were reduced using the software and the calibration data available as of July 2009, and according to the method described in \citet{nevalainen2005}." .. In particular. periods of high background. that affected the second half of the observation were eccluded.," In particular, periods of high background that affected the second half of the observation were excluded." " We used a local background as nicasiered. im α peripheral region of cach detector, sindlar to the method used for the ουσία"," We used a local background as measured in a peripheral region of each detector, similar to the method used for the data." ", For the purpose of mass calculation aud comparison to known scaling relations. we elected to ouly use clusters for which archival data are available. aud with at least 300 source photons."," For the purpose of mass calculation and comparison to known scaling relations, we elected to only use clusters for which archival data are available, and with at least 300 source photons." This selection leaves us with seven clusters:5211323...3612...J0910]15122.. 1152.. J1252-2927.. aand J2215.," This selection leaves us with seven clusters:, and ." 9-17238.. Eveut files for cach cluster were merged if more than one observation was available. and images extracted using photous in the 0.7-7 keV baud for ACIS-I observations. and in the 0.5-7 keV band for ACIS-S. EPIC-AIOS and EPIC-PN observations (see Table 2)).," Event files for each cluster were merged if more than one observation was available, and images extracted using photons in the 0.7-7 keV band for ACIS-I observations, and in the 0.5-7 keV band for ACIS-S, EPIC-MOS and EPIC-PN observations (see Table \ref{tab:chandra-data}) )." The same table also presents the muuber of source photons. after subtracting the expected muuber of background photous frou the peripheral region.," The same table also presents the number of source photons, after subtracting the expected number of background photons from the peripheral region." " The eas density is described using au isothermal .j model which. given the Igaited unuuuber of source photons. provides a good fit to all clusters with X-ray data: Model parameters iy and r, are constrained usns a Markov chain Moute Carlo method described in Bonameuteetal. (2001).. aud are presented in Table 3.."," The gas density is described using an isothermal $\beta$ model which, given the limited number of source photons, provides a good fit to all clusters with X-ray data: Model parameters $n_{e,0}$ and $r_{c}$ are constrained using a Markov chain Monte Carlo method described in \citet{bonamente2004}, , and are presented in Table \ref{tab:xray}." We fix J=0.7 throughout., We fix $\beta=0.7$ throughout. Use of the beta model permits a direct comparison with the scaling relations prescuted in BOs. obtained using the same isothermal model.," Use of the beta model permits a direct comparison with the scaling relations presented in B08, obtained using the same isothermal model." " The spectra for cach cluster were extracted from a circular region about the ceutroid of the N-rav ciissiou eiven in Table τν,", The spectra for each cluster were extracted from a circular region about the centroid of the X-ray emission given in Table \ref{tab:ubertable}. A radius of <30” wwas used. foro allo clusters excepto aud13612... for which we use «ού. the background. spectrum was extracted. from the surrounding rregion.," A radius of $<$ was used for all clusters except and, for which we use $<$; the background spectrum was extracted from the surrounding region." Given the limited S/N of the spectra. the metal abuudances were fixed at a fiducial value of A=03Z.. for all clusters.," Given the limited S/N of the spectra, the metal abundances were fixed at a fiducial value of $A=0.3$ for all clusters." This approximation has a neeheible impact ou the results of our analysis., This approximation has a negligible impact on the results of our analysis. We performed spectral fits to au optically thin model using the APEC ciissivity code (Smithetal.2001): the redshift. Galactic ITE column density and solar abiuudauce are fixed for each cluster (Table 2)). leaving just the electron temperature and a normalisation constant.," We performed spectral fits to an optically thin model using the APEC emissivity code \citep{smith2001}; the redshift, Galactic HI column density and solar abundance are fixed for each cluster (Table \ref{tab:chandra-data}) ), leaving just the electron temperature and a normalisation constant." The resulting clectrou temperatures are prescuted in Table 3.., The resulting electron temperatures are presented in Table \ref{tab:xray}. The gas model parameters determined frou the X-ray nuages and spectral coustraints on the eas teniperature are used to measure the N-rav gas massX, The gas model parameters determined from the X-ray images and spectral constraints on the gas temperature are used to measure the X-ray gas mass. "-ray) This is calculated via a spherical iutegration of à», out to rosoo for cach sample in the Markov chain: this choice of radius allows a comparison of 3 aud tto the scaling relations of BOs.", This is calculated via a spherical integration of $n_{e}$ out to $r_{2500}$ for each sample in the Markov chain; this choice of radius allows a comparison of $Y$ and to the scaling relations of B08. The values of συ aud oof each cluster are shown in Table 23. with the conrparison to Y and previously measured scaling relations in Figure 2..," The values of $r_{2500}$ and of each cluster are shown in Table \ref{tab:xray}, with the comparison to $Y$ and previously measured scaling relations in Figure \ref{fig:scaling}." The oobservations presented here demoustrate the efficacy of using the SZ effect as a cluster mass. discrininator. independent of redshift.," The observations presented here demonstrate the efficacy of using the SZ effect as a cluster mass discriminator, independent of redshift." The SZ effect of the high mass clusters in the ad hoc sample of 271 clusters was detected with SZA iuteeration times comparable to those required for similar mass clusters at low redshifts., The SZ effect of the high mass clusters in the ad hoc sample of $z >1$ clusters was detected with SZA integration times comparable to those required for similar mass clusters at low redshifts. " Specifically, the SZ effect. wasdetected in the three clusters for which xac1077 "," Specifically, the SZ effect wasdetected in the three clusters for which $\gtrsim10^{13}$ " ANCERIE) and IN(CIEDBID. resulting in quite large error bars in the estimates of 2.,"$N(-{\rm FRII})$ and $N(+{\rm FRII})$, resulting in quite large error bars in the estimates of $\varepsilon$." The analysis was based upon an analysis of the sample of 132 EFIE 3CTU radio sources selected from the catalogue of Laing. Rilev and Longair (1993) which lay in the area of sky &>10° and |b|>10.," The analysis was based upon an analysis of the sample of 132 FRII 3CR radio sources selected from the catalogue of Laing, Riley and Longair (1993) which lay in the area of sky $\delta \ge 10^{\circ}$ and $|b| \ge 10^{\circ}$." The jet-side could be determined for 103 of the 3CTU sources using the following criteria in order of preference: The remaining 29 sources could not be classified for a number of reasons., The jet-side could be determined for 103 of the 3CRR sources using the following criteria in order of preference: The remaining 29 sources could not be classified for a number of reasons. In a number of cases. excellent. racio maps were obtained by Fernini (1993. 1997). but no evidence for jets could. be discerned.," In a number of cases, excellent radio maps were obtained by Fernini (1993, 1997), but no evidence for jets could be discerned." In. other cases. radio maps of sullicientlv high quality have not been published.," In other cases, radio maps of sufficiently high quality have not been published." Scheuer (1995) used the statistics of the structural asvmmetries of thelobes. rather thanhol-spols. to define the fractional separation cdillerences. arguing that the hot-spots are ephemeral structures which can change their location within the volume of the lobe: the largest. lobe length is therefore likely to be a more stable measure of the mean growth rate of the lobe.," Scheuer (1995) used the statistics of the structural asymmetries of the, rather than, to define the fractional separation differences, arguing that the hot-spots are ephemeral structures which can change their location within the volume of the lobe; the largest lobe length is therefore likely to be a more stable measure of the mean growth rate of the lobe." Means. ancl standard deviations of the fractional separation clillerences for the lobes and hot-spots in the present sample are irj=O.07—E0.18 and Fy=0.064 0.22. respectively.," Means and standard deviations of the fractional separation differences for the lobes and hot-spots in the present sample are $\overline{x}_{\rm l}=0.07 \pm 0.18$ and $\overline{x}_{\rm h}= 0.06 \pm 0.22$ , respectively." The greater standard eviation of wy as compared with that of wy shows that the —ocations of hot-spots are on the average more asynimetric ian the lobe lengths. consistent with Scheuer's argument.," The greater standard deviation of ${x}_{\rm h}$ as compared with that of ${x}_{\rm l}$ shows that the locations of hot-spots are on the average more asymmetric than the lobe lengths, consistent with Scheuer's argument." For this reason. the fractional separation cilference of Lobes has been used in the rest of the analysis.," For this reason, the fractional separation difference of lobes has been used in the rest of the analysis." It should be noted that the Iarger dispersion inary às compared with wry) means that the high mean velocities of expansion found by Longair Riley (1979). Banhatti (1980) ancl Best (1995) are overestimates.," It should be noted that the larger dispersion in $x_{\rm h}$ as compared with $x_{\rm l}$ means that the high mean velocities of expansion found by Longair Riley (1979), Banhatti (1980) and Best (1995) are overestimates." Details of the sources included in this analysis and the criteria used. as well as the adopted: values of the fractional separation dillerences wr for the lobes ancl spots are eiven in the Appendix.," Details of the sources included in this analysis and the criteria used, as well as the adopted values of the fractional separation differences $x$ for the lobes and hot-spots are given in the Appendix." Of the 103. FRIL sources. 7 were radio galaxies ancl 32 were quasars.," Of the 103 FRII sources, 71 were radio galaxies and 32 were quasars." Among the Tlgaleries. the jet-side was determined. () by the presence. of jets (34 cases) and probable jets (21 cases). (ii) [rom clepolarization asvmumetries (12 cases) and (iii) from spectral index asvnimetries (4 cases).," Among the 71, the jet-side was determined (i) by the presence of jets (34 cases) and probable jets (21 cases), (ii) from depolarization asymmetries (12 cases) and (iii) from spectral index asymmetries (4 cases)." Among the 32/quasars. 28 cases of jets and two probable jets were found: the jet-side was founcl from depolarization asvmmoetries ancl from. spectral index asymimetries in one case each.," Among the 32, 28 cases of jets and two probable jets were found; the jet-side was found from depolarization asymmetries and from spectral index asymmetries in one case each." Pwo jets among the 36 radio galaxies were detected on the parsec-scale from. VLBI images., Two jets among the 36 radio galaxies were detected on the parsec-scale from VLBI images. Among the 103 sources. there are 67. |FRIL sources (6543) and 36 ERIL sources (85%)).," Among the 103 sources, there are 67 +FRII sources ) and 36 $-$ FRII sources )." Of the 71 radio ealaxies. 43 are |PRIL and 28 are. EIL sources: among the 32 quasars. 24 are |EIE and S PRIDE sources.," Of the 71 radio galaxies, 43 are +FRII and 28 are $-$ FRII sources; among the 32 quasars, 24 are +FRII and 8 $-$ FRII sources." Fig., Fig. 5 shows the clistributions of the fractional separation cilferences for the svmmoetric (ϐκμι< 1) andasymmetric pictures Loxor< 1)., \ref{fig-5} shows the distributions of the fractional separation differences for the symmetric $0<|x_{\rm l}|<1$ ) andasymmetric pictures $-1 1. ¢=1 corresponds to the Bolin luit). i». the electron lass. and the electron charge."," 2000) where $u_s\approx c$ is the shock speed, $B$ is the magnetic field strength, and $\lambda(\gamma) = \xi\gamma m_ec^2/(eB)$ is the mean free path of electrons assumed to be proportional to the electron Larmor radius, with $\xi$ being a parameter $\xi\geq1$ , $\xi=1$ corresponds to the Böhhm limit), $m_e$ the electron mass,and $e$ the electron charge." " The radiative cooling time fau)e of relativistic clectrous through svuchrotron aud iuverse-Conpton eniüssion Is where στ is the Thomsou cross-section. and Up=I?(Απ) aud U,. aye the energy deusities of maeuctic field and raciation (produced in or outside the jet). respectively,"," The radiative cooling time $t_{cool}(\gamma)$ of relativistic electrons through synchrotron and inverse-Compton emission is where $\sigma_T$ is the Thomson cross-section, and $U_B = B^2/(8\pi)$ and $U_r$ are the energy densities of magnetic field and radiation (produced in or outside the jet), respectively." " Since £,,:5) is proportional to 5 while ως) is inversely proportional to 5. at tyes)=test). electrons: are accelerated to the maxima euerev. sya. (dwik ot al."," Since $t_{acc}(\gamma)$ is proportional to $\gamma$ while $t_{cool}(\gamma)$ is inversely proportional to $\gamma$, at $t_{acc}(\gamma) = t_{cool}(\gamma)$, electrons are accelerated to the maximum energy, $\gamma_{max}$ (Kirk et al." 1998: I&usunose et al., 1998; Kusunose et al. 2000)., 2000). Combining equations (1) aud (2) vields where D=U./Upn is the “Compton dominance” the(e.g... typicalClisellinà ct al.," Combining equations (1) and (2) yields where $D\equiv U_r/U_B$ is the “Compton dominance"" (e.g., Ghisellini et al." 1998)., 1998). In the jet comoving frame. svuchrotron cussion frequency of relativistic electrons of +. averaged over pitch angles. is where vp=6Bf(2zinc) is Larmor frequency.," In the jet comoving frame, the typical synchrotron emission frequency of relativistic electrons of $\gamma$, averaged over pitch angles, is where $\nu_B = eB/(2\pi m_{e}c)$ is Larmor frequency." " Tn ters of vy. equation (3) can be expressed as Setting tacltows)=L du equation (5). the asin svuchrotron frequency Via, of 5,,4,5""* Ia the observers friune 1s where + is the redshift of the source. à is the Doppler factor 6=Pi?cos0] Pop ds the bulk Loreutz factor. and 0 is the viewing augle of the jet."," In terms of $\nu_s$, equation (3) can be expressed as Setting $t_{acc}(\gamma)/t_{cool}(\gamma)=1$ in equation (5), the maximum synchrotron frequency $\nu_{max}$ of $\gamma_{max}$ in the observer's frame is where $z$ is the redshift of the source, $\delta$ is the Doppler factor $\delta = [\Gamma(1-\beta\cos\theta)]^{-1}$, $\Gamma$ is the bulk Lorentz factor, and $\theta$ is the viewing angle of the jet." The kpc scale jet is au extension of the imner jet. and is still relativistic. as indicated by the observed counterjet intensity asviunietry.," The kpc scale jet is an extension of the inner jet, and is still relativistic, as indicated by the observed $-$ counterjet intensity asymmetry." Therefore. & aud à do uot chauge much aloug the jet from small scales to kpe scales. unlike B which decreases quickly along thedonnant jet.," Therefore, $\xi$ and $\delta$ do not change much along the jet from small scales to kpc scales, unlike $B$ which decreases quickly along the jet." Ou large scales. from subkpe to tens of kpc. the cooling process in theD. jets is svuchrotron cuussion (Celotti et al.," On large scales, from subkpc to tens of kpc, the dominant cooling process in the jets is synchrotron emission (Celotti et al." --- 2001). i.6.. 1|1.," 2001), i.e., $1+D_{kpc} \sim 1$." " Thus. according to equation (0). (l1D,Jr,aíé-0Qc)."," Thus, according to equation (6), $\nu_{max}({\rm kpc}) \sim (1+D_{pc})\nu_{max}({\rm pc})$." " Iu the iuner jets of some sources. such as Myk 501. N-ravs are due to svuchrotron cluission. aud the dominant cooling process is svuchrotron cooling. Le. 1|Dy.71. πο 145,4, is roughly constant along the jet (though +), is wach higher on kpe scales). and clectrous can be re-accelerated to energies Liel enough to enut svuchrotron X-rays on kpe or even larecr scales if shocks exist on these scales."," In the inner jets of some sources, such as Mrk 501, X-rays are due to synchrotron emission, and the dominant cooling process is synchrotron cooling, i.e., $1+D_{pc} \sim 1$, so $\nu_{max}$ is roughly constant along the jet (though $\gamma_{max}$ is much higher on kpc scales), and electrons can be re-accelerated to energies high enough to emit synchrotron X-rays on kpc or even larger scales if shocks exist on these scales." Iu the inner jets of OVV. quasars aud probably FR II radio galaxies. the svuchrotron peak frequencies are in the IR/optical bands. aud the dominant cooling process is inverse-Colpton cuaission.," In the inner jets of OVV quasars and probably FR II radio galaxies, the synchrotron peak frequencies are in the IR/optical bands, and the dominant cooling process is inverse-Compton emission." " Τα these sources. D,, ls typically in the rauee of 19 100 and as auch as 1000 in some huninous quasars (Urrv 1999)."," In these sources, $D_{pc}$ is typically in the range of 10 – 100, and as much as 1000 in some luminous quasars (Urry 1999)." " It is obvious that iu some sources, the maxinuun svuchrotron frequencies aud hence the peak frequencies in the kpc scale jets are more than 100 times larger than those in the iuner jets. aud that N-ravs are donunated by svuchrotron emission."," It is obvious that in some sources, the maximum synchrotron frequencies and hence the peak frequencies in the kpc scale jets are more than 100 times larger than those in the inner jets, and that X-rays are dominated by synchrotron emission." That is to sax. electrons in kpe scale onshjets of these sources can be accelcrated to energies high to produce svuchrotron X-ray.shocks jets if shocks exist on these scales.," That is to say, electrons in kpc scale jets of these sources can be accelerated to energies high enough to produce synchrotron X-ray jets if shocks exist on these scales." Therefore. ii inost Lhuge scale jets can re-accelerate electrons to cnereies high euough to cuit svuchrotron A-ravs.," Therefore, shocks in most large scale jets can re-accelerate electrons to energies high enough to emit synchrotron X-rays." It is uot strange that electrons in large scale jets can be accelerated to energies higher than the aN enerev in Πιο jets., It is not strange that electrons in large scale jets can be accelerated to energies higher than the maximum energy in inner jets. Even the opticabenüttiug electrous in some large scale optical kuots have higher chereics than the imaxiumn energy. in the innerelectrons jets., Even the optical-emitting electrons in some large scale optical knots have higher energies than the maximum energy in the inner jets. For example. im 3€ 273. the energies of optical n knot D aud IL are ~>107 (Rosser Moeiseuheimier 1991). jiuchi larger thau the masiunun cucrey of >~104 in thle inner jet(Cilüselliui ct al.," For example, in 3C 273, the energies of optical electrons in knot D and H are $\gamma>10^5$ (Rösser Meisenheimer 1991), much larger than the maximum energy of $\gamma\sim 10^4$ in the inner jet (Ghisellini et al." 1998)., 1998). It cau be seen in equation (1) that high energy electrous enüt svuchrotron radiation at high frequencies aud cool. cluitting at progressively lower frequencies aud resulting in time lag between high (74) aud low (79) frequencies.," It can be seen in equation (4) that high energy electrons emit synchrotron radiation at high frequencies and cool, emitting at progressively lower frequencies and resulting in time lags between high $\nu_1$ ) and low $\nu_2$ ) frequencies." " The tine lagof emission at v2 (το) to ciission at vy (51) is the time for electrons to lose energy Ay=>, σον l6. where ⋅σττthe|TC,)s72gηο) is: the cooling. rate at 5. aud tag IS dn jet comoving frame."," The time lagof emission at $\nu_2$ $\gamma_2$ ) to emission at $\nu_1$ $\gamma_1$ ) is the time for electrons to lose energy $\Delta\gamma =\gamma_1 - \gamma_2$ , i.e., where $\dot{\gamma} = -4\sigma_T(U_B+U_r)\gamma^2/(3m_{e}c)$ is the cooling rate at$\gamma$ and $t_{lag}$ is in the jet comoving frame." " Integration vields That is to sax; the time lag of svuchrotrou cussion at 15 to that at vy, is equal to the difference between the cooling time of electrous of energies of ου and 54."," Integration yields That is to say, the time lag of synchrotron emission at $\nu_2$ to that at $\nu_1$ is equal to the difference between the cooling time of electrons of energies of $\gamma_2$ and $\gamma_1$ ." πι terms of η aud 125. tag Is," In terms of $\nu_1$ and$\nu_2$ , $t_{lag}$ is" The ongoing discovery of extrasolar giant planets as stimulated renewed interest in the theory of planet ormation (e.g. Alavor Queloz L995: Marcy. Cochran. Aavor L999; Vost et al.,"The ongoing discovery of extrasolar giant planets has stimulated renewed interest in the theory of planet formation (e.g. Mayor Queloz 1995; Marcy, Cochran, Mayor 1999; Vogt et al." 2002: Santos ct al., 2002; Santos et al. 2003)., 2003). In 10 most commonly. accepted theory of how planets form. 16 so.called core instability model. eas giant. planets form wough the build.up of a rocky and icy core of ~15 Earth masses. which then undergoes gas accretion resulting in a easgiant planet (e.g. Bodenheimer Pollack 1986: Pollack et al.," In the most commonly accepted theory of how planets form, the so–called core instability model, gas giant planets form through the build–up of a rocky and icy core of $\sim 15$ Earth masses, which then undergoes gas accretion resulting in a gas–giant planet (e.g. Bodenheimer Pollack 1986; Pollack et al." 1996)., 1996). An alternative model involves the formation of giant planets through the gravitational fragmentation of the protostellar disc during the earlier phases of its evolution (Boss 2001)., An alternative model involves the formation of giant planets through the gravitational fragmentation of the protostellar disc during the earlier phases of its evolution (Boss 2001). In either case disc.planet interaction will play an important role in the subsequent. evolution., In either case disc–planet interaction will play an important role in the subsequent evolution. The gravitational interaction between protostellar disces and embedded: protoplanets has been the subject of a large number of studies over the last couple of decades., The gravitational interaction between protostellar discs and embedded protoplanets has been the subject of a large number of studies over the last couple of decades. In the standard. picture. a protoplanet exerts torques on a protostellar disc through the excitation of spiral density waves at Lindblad resonances. ancl possibly through interaction at corotation resonance (eg. Coldreich ‘Tremaine 1979: Lin Papaloizou 1979: Papaloizou Lin 1984: Ward 1986. 1997: Tanaka. Tacheuchi Ward 2002).," In the standard picture, a protoplanet exerts torques on a protostellar disc through the excitation of spiral density waves at Lindblad resonances, and possibly through interaction at corotation resonance (e.g. Goldreich Tremaine 1979; Lin Papaloizou 1979; Papaloizou Lin 1984; Ward 1986, 1997; Tanaka, Tacheuchi Ward 2002)." The spiral waves carry with them an associated angular momentum flux., The spiral waves carry with them an associated angular momentum flux. This angular momentum is deposited. in the disc material where the waves are damped. leading to an exchange of angular momentum between protoplanet and disc.," This angular momentum is deposited in the disc material where the waves are damped, leading to an exchange of angular momentum between protoplanet and disc." The disc that lies exterior to the protoplanet orbit exerts à negative torque on the planet. and the interior disc exerts a positive torque.," The disc that lies exterior to the protoplanet orbit exerts a negative torque on the planet, and the interior disc exerts a positive torque." For most dise models the negative orque dominates and the protoplanct migrates inwarels., For most disc models the negative torque dominates and the protoplanet migrates inwards. For protoplanets of ~15 Earth masses. the migration ime is estimated to be between 103 and. 107 ve CLanaka. ‘Tacheuchi. Ward 2002). which is very much shorter than he estimated gas accretion phase of giant planet formation cY Myr (Pollack et al.," For protoplanets of $\sim 15$ Earth masses, the migration time is estimated to be between $10^4$ and $10^5$ yr (Tanaka, Tacheuchi, Ward 2002), which is very much shorter than the estimated gas accretion phase of giant planet formation $\simeq 7$ Myr (Pollack et al." 1996)., 1996). Taken at face value. this resents a serious problem for the core.instability model of gas giant planet formation.," Taken at face value, this presents a serious problem for the core–instability model of gas giant planet formation." We note. however. this analysis »ertains only to smooth. laminar cise models.," We note, however, this analysis pertains only to smooth, laminar disc models." lor protoplancts in the Jovian mass range. the interaction is non linear anc gap formation occurs (Papaloizou Lin 1984: Bryden ct al.," For protoplanets in the Jovian mass range, the interaction is non linear and gap formation occurs (Papaloizou Lin 1984; Bryden et al." 1999: WKley 1999)., 1999; Kley 1999). In this case the orbital migration of the planet. becomes ocked to the viscous evolution of the cise. ancl migration is expected to occur on a time scale of 10 vr(Lin& Papaloizou 1986: Nelson ct al.," In this case the orbital migration of the planet becomes locked to the viscous evolution of the disc, and migration is expected to occur on a time scale of $10^5$ yr (Lin Papaloizou 1986; Nelson et al." 2000: D'Angelo. Ixlev llenning 2002).," 2000; D'Angelo, Kley Henning 2002)." Until quite recently. most. models of viscous accretion dises used the Shakura Sunvaev (1973) à moclel for the anomalous cise viscosity., Until quite recently most models of viscous accretion discs used the Shakura Sunyaev (1973) $\alpha$ model for the anomalous disc viscosity. This assumes that the viscous stress is proportional to the thermal pressure in the disc. without specifving the origin of the viscous stress. (but assumed to arise from some form of turbulence).," This assumes that the viscous stress is proportional to the thermal pressure in the disc, without specifying the origin of the viscous stress (but assumed to arise from some form of turbulence)." Work bv Balbus Lawley (1991) indicated. that significant angular momentum transport. in weakly magnetised. clises could. arise from the magnetorotational instability (MIU or the BalbusLawley instability)., Work by Balbus Hawley (1991) indicated that significant angular momentum transport in weakly magnetised discs could arise from the magnetorotational instability (MRI -- or the Balbus–Hawley instability). Subsequent non linear numerical simulations performed using a local shearing box formalism (e.g. Lawley Balbus 1991: Lawley. Ciammie. Balbus 1996: Brandenburg et al.," Subsequent non linear numerical simulations performed using a local shearing box formalism (e.g. Hawley Balbus 1991; Hawley, Gammie, Balbus 1996; Brandenburg et al." 1996) confirmed. this and showed that the saturated non linear outcome of the AMIRI is MILD turbulence with an associated viscous stress xvameter o of between ~55LO? and ~0.1. depending on 1e initial magnetic field configuration.," 1996) confirmed this and showed that the saturated non linear outcome of the MRI is MHD turbulence with an associated viscous stress parameter $\alpha$ of between $\sim 5 \times 10^{-3}$ and $\sim 0.1$, depending on the initial magnetic field configuration." More recent global simulations of MUD turbulent discs e.g. Armitage 1998: Lawley 2000: Llawley 2001: Steinacker Papaloizou 2002: -apaloizou Nelson 2003] confirm the picture provided by 1 local shearing box simulations., More recent global simulations of MHD turbulent discs [e.g. Armitage 1998; Hawley 2000; Hawley 2001; Steinacker Papaloizou 2002; Papaloizou Nelson 2003] confirm the picture provided by the local shearing box simulations. This is the fourth in a series of papers that. examine 16 interaction between disc models undergoing MIID urbulence with zero net [ux magnetic fields and embedded otoplanets., This is the fourth in a series of papers that examine the interaction between disc models undergoing MHD turbulence with zero net flux magnetic fields and embedded protoplanets. In. Papaloizou Nelson (2003 hereafter (er 1) we examined and characterised. the turbulence obtained in a variety of ΑΔΗ) cüsc. models., In Papaloizou Nelson (2003 – hereafter paper I) we examined and characterised the turbulence obtained in a variety of MHD disc models. " In. Nelson. '""apaloizou. (2003 hereafter paper LL) we examined. the interaction between a global cvlindrical disc model and a massive (5 Jupiter mass) protoplanet.", In Nelson Papaloizou (2003 – hereafter paper II) we examined the interaction between a global cylindrical disc model and a massive (5 Jupiter mass) protoplanet. X similar. study was undertaken by Winters. Balbus. Lawley (20035).," A similar study was undertaken by Winters, Balbus, Hawley (2003b)." In à companion paper to this one (Papaloizou. Nelson. Snellerove 2003 herealvo paper HE) we presented 1e results of global evlindrical cise simulations and local garearing box simulations of turbulent dises interacting with otoplanets of dilferent mass.," In a companion paper to this one (Papaloizou, Nelson, Snellgrove 2003 – hereafter paper III) we presented the results of global cylindrical disc simulations and local shearing box simulations of turbulent discs interacting with protoplanets of different mass." “Phe main focus of paper LLL was to characterise the changes in flow: morphology. and ise structure as a function of planet mass. and to examine 1ο transition [rom linear to non linear interaction leading o gap formation.," The main focus of paper III was to characterise the changes in flow morphology and disc structure as a function of planet mass, and to examine the transition from linear to non linear interaction leading to gap formation." In this paper we continue to examine dese simulations. but now focus on the gravitational torques exerted on the protoplanet. by the cise and the associated migration rate of the protoplanct.," In this paper we continue to examine these simulations, but now focus on the gravitational torques exerted on the protoplanet by the disc and the associated migration rate of the protoplanet." We find that in all simulations performed. the torque experienced by the protoplanet is a highly. variable quantity on account ofthe protoplanet interacting with the turbulen density wakes that shear past it.," We find that in all simulations performed, the torque experienced by the protoplanet is a highly variable quantity on account of the protoplanet interacting with the turbulent density wakes that shear past it." For low mass protoplanets. the torque i8. dominated by these. Uuetuations. such that the usua istinction between inner (positive) am outer (negative) dise torques is blurred.," For low mass protoplanets, the torque is dominated by these fluctuations, such that the usual distinction between inner (positive) and outer (negative) disc torques is blurred." The net. torque experienced. by embedded: protoplancts oscillates between negative ancl positive values. such that. the. protoplane migration is likely to occur as a random walk.," The net torque experienced by embedded protoplanets oscillates between negative and positive values, such that the protoplanet migration is likely to occur as a random walk." This is in contrast to the monotonic inward crit normally associato with tvpe L migration., This is in contrast to the monotonic inward drift normally associated with type I migration. A running time average of the orques Fails to converge for the embedded protoplanet runs. at least lor the run times that are currently feasible. so hat definitive statements about the direction and rate of migration of low mass planets in turbulent disces cannot vet x: mace.," A running time average of the torques fails to converge for the embedded protoplanet runs, at least for the run times that are currently feasible, so that definitive statements about the direction and rate of migration of low mass planets in turbulent discs cannot yet be made." Ina manner that is consistent with the results of paper LIL we find that the results show a definite trend. as a unction of planet mass.," In a manner that is consistent with the results of paper III, we find that the results show a definite trend as a function of planet mass." For very low mass planets the urbulent density wakes are of much higher amplitude than, For very low mass planets the turbulent density wakes are of much higher amplitude than The solution. of the non-LTE multilevel-atom radiative transfer problem is a classical one in astrophysics., The solution of the non-LTE multilevel-atom radiative transfer problem is a classical one in astrophysics. Indeed. the assumption of non-LTE implies. consistently with the departure of the source functions from Planck functions. that the population density of the atomic or molecular levels considered depart from what can be derived at LTE. in a straightforward manner. using Saha and Boltzmann relations (see e.g.. Mihalas 1978).," Indeed, the assumption of non-LTE implies, consistently with the departure of the source functions from Planck functions, that the population density of the atomic or molecular levels considered depart from what can be derived at LTE, in a straightforward manner, using Saha and Boltzmann relations (see e.g., Mihalas 1978)." " In the non-LTE case. one has on the contrary to solve simultaneously and self-consistently for a set of M; equations of radiative transfer together with Nj, equations of statistical equilibrium (hereafter ESE) describing the detailed balanced between excitation and de-excitation processes between every atomic or molecular levels."," In the non-LTE case, one has on the contrary to solve simultaneously and self-consistently for a set of $N_{\rm T}$ equations of radiative transfer together with $N_{\rm L}$ equations of statistical equilibrium (hereafter ESE) describing the detailed balanced between excitation and de-excitation processes between every atomic or molecular levels." Since absorption and stimulated emission radiative rates depends explicitely on the radiation field. which itself depends on the level populations. this problem is intrinsically a search for the solution of coupled equations.," Since absorption and stimulated emission radiative rates depends explicitely on the radiation field, which itself depends on the level populations, this problem is intrinsically a search for the solution of coupled equations." Since the beginning of numerical radiative transfer in the late 60's. the two most popular methods used for tackling this problem have been the complete linearization method of Auer Mihalas (1969) and the Accelerated A-Iteration based scheme called MALI (Rybicki Hummer 1991).," Since the beginning of numerical radiative transfer in the late 60's, the two most popular methods used for tackling this problem have been the complete linearization method of Auer Mihalas (1969) and the Accelerated $\Lambda$ -Iteration based scheme called MALI (Rybicki Hummer 1991)." Despite their apparent differences. they have however in common the fact that basically. one Is conducted to deal with equations.," Despite their apparent differences, they have however in common the fact that basically, one is conducted to deal with equations." An interesting comparative study of these two approaches have been made by Socas-Navarro Trujillo Bueno (1997)., An interesting comparative study of these two approaches have been made by Socas-Navarro Trujillo Bueno (1997). In this study. we investigate on the use of a quasi-Newton numerical method for the solution of the nonlinear ESE.," In this study, we investigate on the use of a quasi-Newton numerical method for the solution of the nonlinear ESE." Our choice went to Broyden's method (1965) whose elements will be presented in $22., Our choice went to Broyden's method (1965) whose elements will be presented in 2. To the best of our knowledge. Koesterke et al. (," To the best of our knowledge, Koesterke et al. (" 1992) were the first to bring this numerical scheme into the field of radiation transfer.,1992) were the first to bring this numerical scheme into the field of radiation transfer. Their study was presented in the context of the modelling of spherically expanding atmospheres of hot and massive Wolf-Rayet stars., Their study was presented in the context of the modelling of spherically expanding atmospheres of hot and massive Wolf-Rayet stars. Broyden's method was more recently invoked in the context of the coupled-escape probability method (Elitzur Asensio Ramos 2006)., Broyden's method was more recently invoked in the context of the coupled-escape probability method (Elitzur Asensio Ramos 2006). Besides from the required algebra and mention to caveats related to the implementation of the method. it remains however difficult to figure out from Koesterke et al. (," Besides from the required algebra and mention to caveats related to the implementation of the method, it remains however difficult to figure out from Koesterke et al. (" 1992) the actual performances of such an approach.,1992) the actual performances of such an approach. " A comparison with another method have also been barely evoked by the authors. who mentioned however a significant speed-up provided by Broyden algorithm for large Nj, atomic models."," A comparison with another method have also been barely evoked by the authors, who mentioned however a significant speed-up provided by Broyden algorithm for large $N_{\rm L}$ atomic models." In particular. being contemporary with the publication of Rybicki Hummer (1991). it is a pity that no comparison with the MALI method could be made yet.," In particular, being contemporary with the publication of Rybicki Hummer (1991), it is a pity that no comparison with the MALI method could be made yet." Such an evaluation is the scope of the present work., Such an evaluation is the scope of the present work. For à N;-level atomic model. the ESE will in general write as a set of elementary equations: where the A;; and B;; stand respectively for the spontaneous emission. and the absorption and stimulated emission rates. 1; represents the population density for each energy level. and J;; is the scattering integral for each radiatively allowed transition we shall consider.," For a $N_{L}$ -level atomic model, the ESE will in general write as a set of elementary equations: where the $A_{ij}$ and $B_{ij}$ stand respectively for the spontaneous emission, and the absorption and stimulated emission rates, $n_i$ represents the population density for each energy level, and $\bar{J}_{ij}$ is the scattering integral for each radiatively allowed transition we shall consider." Besides the radiative processes. the C;; are collisional excitation and de-excitation rates.," Besides the radiative processes, the $C_{ij}$ are collisional excitation and de-excitation rates." In general. these rates depend on the electronic density so that. if the latter is not known a priori. terms like 1;C;; are nonlinear in the population densities.," In general, these rates depend on the electronic density so that, if the latter is not known a priori, terms like $n_i C_{ij}$ are nonlinear in the population densities." Hereafter we shall consider only cases for which the collisional rates are known a priori., Hereafter we shall consider only cases for which the collisional rates are known a priori. The scattering integral entering the ESE ts formally written as: where. assuming complete redistribution in frequency. the source function is defined as:," The scattering integral entering the ESE is formally written as: where, assuming complete redistribution in frequency, the source function is defined as:" (Reeall that 7;=1a).,(Recall that $\beta^\prime=1-\alpha$ ). mThe speed of⋅ hydromagnetic. waves is. significantly. greater than the speed wy of the background How (see eq. 14))., The speed of hydromagnetic waves is significantly greater than the speed $w_0$ of the background flow (see eq. \ref{wc}) ). The dispersion relation that follows from eq. (30)), The dispersion relation that follows from eq. \ref{matrix}) ) is an impressively lengthy. sixth-order polynomial in c in which all coefficients. [rom sixth order to zeroth order are non-zero: it is easiest to explore various limits by working with eq. (30)), is an impressively lengthy sixth-order polynomial in $\sigma$ in which all coefficients from sixth order to zeroth order are non-zero; it is easiest to explore various limits by working with eq. \ref{matrix}) ) directly., directly. We first confirm a previous result of 2. for perfect pinning (a=3%0). no background How (wo=0). and no entrainment {ον= 0).," We first confirm a previous result of \citet{vl08} for perfect pinning $\alpha=\beta=0$ ), no background flow $w_0=0$ ), and no entrainment $\epsilon_n=0$ )." In this case. the polynomial factors into the form If we deline and form the combination we obtain eq. (35)).," In this case, the polynomial factors into the form If we define and form the combination we obtain eq. \ref{dra}) )," so two of the non-zero modes are given by the the simpler quacatic expression., so two of the non-zero modes are given by the the simpler quadratic expression. Reacing ο and D [rom eq. (300) , Reading $A$ and $B$ from eq. \ref{matrix}) ) gives the dispersion relation as found. by 292.7 l, gives the dispersion relation as found by \citet{vl08}. aFor Qo=0. the system has only clamped hycromagnetic. waves that travel at speed. eg.," For $\Omega_0=0$, the system has only damped hydromagnetic waves that travel at speed $v_B$." We will not present here an analysis of the full mode structure of the system. but focus on two low-frequency modes that appear for imperfect. pinning.," We will not present here an analysis of the full mode structure of the system, but focus on two low-frequency modes that appear for imperfect pinning." For small à. 2. and c. the two zero-Lrequeney modes of eq. (35))," For small $\alpha$, $\beta$, and $\epsilon_n$, the two zero-frequency modes of eq. \ref{dra}) )" become small. anc we can obtain these modes by working to second. order in 0.," become small, and we can obtain these modes by working to second order in $\sigma$." Since wy is much smaller than eg (eqs., Since $w_0$ is much smaller than $v_B$ (eqs. 14. and 34)). we can further simplify the problem by taking the limit eg=x: for finite wy.," \ref{wc} and \ref{vb}) ), we can further simplify the problem by taking the limit $v_B\rightarrow\infty$ for finite $w_0$." We take this limit by keeping only terms that multiply. eL. the highest order at which eg appears.," We take this limit by keeping only terms that multiply $v_B^4$, the highest order at which $v_B$ appears." With these approximations. eq. (30))," With these approximations, eq. \ref{matrix}) )" gives The electron viscosity does not appear at this level of approximation: in the eg—7ox limit. the [ux tube array is infinitely rigid. and. vortex motion proceeds without producing shear in the proton-electron Iuid.," gives The electron viscosity does not appear at this level of approximation; in the $v_B\rightarrow\infty$ limit, the flux tube array is infinitely rigid, and vortex motion proceeds without producing shear in the proton-electron fluid." The validity of this approximation is confirmed below., The validity of this approximation is confirmed below. “Phe solutions to eq. (89)), The solutions to eq. \ref{dr})) are For 6=0. the modes are Imperfect pinning has introduced. two low-frequeney modes to the svstem that are associated with slow vortex motion under the Magnus force.," are For $\theta=0$, the modes are Imperfect pinning has introduced two low-frequency modes to the system that are associated with slow vortex motion under the Magnus force." The modes are underdamped for 3