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This lemma does not depend on (he value of N as long as N>4. and it is independent of the number of degrees of freedom for each contributing For some groups of interest. only maximum values of / are reported. below.
This lemma does not depend on the value of $N$ as long as $N \geq 4$, and it is independent of the number of degrees of freedom for each contributing For some groups of interest, only maximum values of $t$ are reported below.
In these cases. readers should regard Table 14 of TJJ as an example while remembering that /«2 in that case.
In these cases, readers should regard Table 14 of TJJ as an example while remembering that $t < 2$ in that case.
Comments are added when a maximum value of / exceeds 2.5 or if at least one nonzero value of A is detected.
Comments are added when a maximum value of $t$ exceeds 2.5 or if at least one nonzero value of $M$ is detected.
IP No<4 or if values of M. are scattered. informative values of AL are quoted instead of a limit on /.
If $N < 4$ or if values of $M$ are scattered, informative values of $M$ are quoted instead of a limit on $t$.
For readers who desire further information. relerences to (he project papers are given below.
For readers who desire further information, references to the project papers are given below.
Iu particular. those relerences should be consulted for results of scale factor tests or to inspect all values of AZ in particular groups.
In particular, those references should be consulted for results of scale factor tests or to inspect all values of $M$ in particular groups.
Because the. projects are based on two different svstems of stancarcl stars. there is an obvious need to understand the relationship between those svstems.
Because the projects are based on two different systems of standard stars, there is an obvious need to understand the relationship between those systems.
This problem has been investigated by a number of authors.
This problem has been investigated by a number of authors.
However. the meaning of their results has been obseured. by use of two different conventions for reporting them.
However, the meaning of their results has been obscured by use of two different conventions for reporting them.
Authors in the southern hemisphere prefer (o work with values of V—R and V—{νι
Authors in the southern hemisphere prefer to work with values of $V-R$ and $V-I$.
Thex find that lor both indices. there are scale [actor dillerences between (he Landolt anc southern hemisphere staucard star
They find that for both indices, there are scale factor differences between the Landolt and southern hemisphere standard star
In the same way. we have also evaluated (he upper limits on the base of Helene's Bavesian method (IIelene 1933).
In the same way, we have also evaluated the upper limits on the base of Helene's Bayesian method (Helene 1983).
The main difference respect the profile method is that in this case the upper limits are found integrating the likelihood profile (Fanetion of the source [ας F) starüng from F=0. without any assumption on its distribution.
The main difference respect the profile method is that in this case the upper limits are found integrating the likelihood profile (function of the source flux $F$ ) starting from $F=0$, without any assumption on its distribution.
Whereas (he results for the upper limits obtained with the two methods were similar. (he Davesian one gave (hose more conservative.
Whereas the results for the upper limits obtained with the two methods were similar, the Bayesian one gave those more conservative.
The results of this analvsis are reported in Table 1.
The results of this analysis are reported in Table 1.
We additionally tested that by changing the enerev threshold (from 100 to 200 MeV). the Sscience tools (from to v9r18p6). slightly different selection cuts ingtmktime. and different number of sources in the background model (including those in à ROI with size[rom 10" to 20"). all results are stable.
We additionally tested that by changing the energy threshold (from 100 to 200 MeV), the Science tools (from to ), slightly different selection cuts in, and different number of sources in the background model (including those in a ROI with sizefrom $^o$ to $^o$ ), all results are stable.
Additionally. we have repeated the analvses using an updated version of the Fermi-LAT Catalog sources. built using two vears of data and thus more compatible with the data of the HESS J1353--020 region we focus upon.
Additionally, we have repeated the analyses using an updated version of the -LAT Catalog sources, built using two years of data and thus more compatible with the data of the HESS J1858+020 region we focus upon.
With this catalog (which is vet internal to the Zermi—LAT collaboration). the number of sources closer than 20° from the HESS J1858-—020 source areLOT. while those closer (han 3° are 10.
With this catalog (which is yet internal to the -LAT collaboration), the number of sources closer than $^o$ from the HESS J1858+020 source are107, while those closer than $^o$ are 10.
No significant change in (he previous results where found.
No significant change in the previous results where found.
We have also considered that some of the closest sources could be extended. aud also found (he results to be stable.
We have also considered that some of the closest sources could be extended, and also found the results to be stable.
(20066).
6).
elongation along PA=445°).
elongation along ${\rm PA}=+45^\circ$ ).
It is possible that a weak jet emanates [rom the YSO. perpendicular to the disk. resulting in the extended appearance at the center.
It is possible that a weak jet emanates from the YSO, perpendicular to the disk, resulting in the extended appearance at the center.
Clearly. higher sensitivity observations are needed to understand this structure.
Clearly, higher sensitivity observations are needed to understand this structure.
What are the physical conditions in the ssource?
What are the physical conditions in the source?
To answer (his question. one must know the emission mechanism (opacity source) for the em-wave photons.
To answer this question, one must know the emission mechanism (opacity source) for the cm-wave photons.
The em-to-mm wavelength spectrum of the entire source can be characterized as a power law with flux density. 5,. rising wilh observing frequency. p. as 5,xvb? (Menten&Reid1995:Deutheretal.2006).. approaching that of a black body.
The cm-to-mm wavelength spectrum of the entire source can be characterized as a power law with flux density, $S_\nu$, rising with observing frequency, $\nu$, as $S_\nu \propto \nu^{1.6}$ \citep{MR95,B06}, approaching that of a black body.
Since the source is not well resolved spatially at lower frequencies with the VLA. the spectral index does not allow us to discriminate between an inhomogeneous. single-component model (where (he spectral index is shallower (than 2.0. because unity oplical-depth occurs at a smaller radius at. higher frequencies) aud a two-component model (wilh an optically thick central component and a partially optically Chin disk-like structure).
Since the source is not well resolved spatially at lower frequencies with the VLA, the spectral index does not allow us to discriminate between an inhomogeneous, single-component model (where the spectral index is shallower than 2.0, because unity optical-depth occurs at a smaller radius at higher frequencies) and a two-component model (with an optically thick central component and a partially optically thin disk-like structure).
We think it unlikely that dust emission could be a dominant contributor to the em- to mnm-wavelenegth emission ofL.
We think it unlikely that dust emission could be a dominant contributor to the cm- to mm-wavelength emission of.
A dense. warm. dusty disk would be expected to show a plethora of molecular lines at mam/sub-mm wavelengths.
A dense, warm, dusty disk would be expected to show a plethora of molecular lines at mm/sub-mm wavelengths.
While Deutheretal.(2006). find numerous. strong. molecular lines toward the nearby “hot core.” thev find no strong lines toward (he position of (Conly weak SO lines and. of course. the strong SiO masers slightly offset from I])).
While \citet{B06} find numerous, strong, molecular lines toward the nearby “hot core,” they find no strong lines toward the position of (only weak SO lines and, of course, the strong SiO masers slightly offset from ).
Thus. we look to other emission mechanisms to explain both the YSO peak and the elongated disk components.
Thus, we look to other emission mechanisms to explain both the YSO peak and the elongated disk components.
The observations could be modeled with gas al 228000 IX. where hydrogen is fully ionized (proton-electron bremsstrahlung).
The observations could be modeled with gas at $\approx8000$ K, where hydrogen is fully ionized (proton-electron bremsstrahlung).
In (his case. the data require an optically. thick central component and a partially optically thin disk component.
In this case, the data require an optically thick central component and a partially optically thin disk component.
Alternatively. the emission could be partially opticallv-Chick [rom eas al <5000 Ix. where hydrogen is predominantly neutral and [ree electrons come from low ionization-potential metals (H-100nus free-DIree).
Alternatively, the emission could be partially optically-thick from gas at $<5000$ K, where hydrogen is predominantly neutral and free electrons come from low ionization-potential metals (H-minus free-free).
The latter case applies in (he. "radio photospheres” of Mira. variables al roughly 2 stellar radii (Reid&Menten1997).
The latter case applies in the “radio photospheres” of Mira variables at roughly 2 stellar radii \citep{RM97}.
.. In the following subsections. we present two classes of models for the ceniwave emission.
In the following subsections, we present two classes of models for the cm-wave emission.
These models are exploratory and designed only to elucidate characteristic physical conditions.
These models are exploratory and designed only to elucidate characteristic physical conditions.
In several wavs
In several ways
There are also radio sources with properties intermediate between the FRIs and FRIIs, e.g., the “Fat Doubles" (Owen and Laing 1989).
There are also radio sources with properties intermediate between the FRIs and FRIIs, e.g., the “Fat Doubles” (Owen and Laing 1989).
The two main unsolved issues concern the origin of the FR I / FR II dichotomy (how it is related to different acceleration and emission and the nature of the different emission line regionsprocesses), between LEGs and HEGs (see Chiaberge et al.
The two main unsolved issues concern the origin of the FR I / FR II dichotomy (how it is related to different acceleration and emission processes), and the nature of the different emission line regions between LEGs and HEGs (see Chiaberge et al.
2002 and Hardcastle et al.
2002 and Hardcastle et al.
2007).
2007).
The morphological features of extragalactic radio sources can be described naturally with a small number of components: core, jets, hotspots and lobes.
The morphological features of extragalactic radio sources can be described naturally with a small number of components: core, jets, hotspots and lobes.
While their radio to optical emission is typically described in terms of synchrotron radiation by relativistic particles, the origin of X-ray emission in extended structures (jets and hotspots) is still unclear, but certainly non-thermal (Harris Krawczynski 2002).
While their radio to optical emission is typically described in terms of synchrotron radiation by relativistic particles, the origin of X-ray emission in extended structures (jets and hotspots) is still unclear, but certainly non-thermal (Harris Krawczynski 2002).
The main open question lies in which mechanism, synchrotron or inverse Compton (IC) scattering, dominates the X-ray emission.
The main open question lies in which mechanism, synchrotron or inverse Compton (IC) scattering, dominates the X-ray emission.
The former describes emission from low power jets (Harris Krawczynski 2006), while the latter provides a good explanation for high power radio galaxy and quasar jets, in which the seed photons for the IC scattering could be the Cosmic Microwave Background (CMB) (Tavecchio et al.
The former describes emission from low power jets (Harris Krawczynski 2006), while the latter provides a good explanation for high power radio galaxy and quasar jets, in which the seed photons for the IC scattering could be the Cosmic Microwave Background (CMB) (Tavecchio et al.
2000).
2000).
Only by combining X-ray observations with historical and/or simultaneuos data in other wavebands, is possible to build up the Spectral Energy Distribution (SED) of cores, jets and hotspots and compare them with synchrotron or inverse Compton models to the of their emission.
Only by combining X-ray observations with historical and/or simultaneuos data in other wavebands, is possible to build up the Spectral Energy Distribution (SED) of cores, jets and hotspots and compare them with synchrotron or inverse Compton models to investigate the origin of their emission.
During the last few years investigateseveral originsnapshot surveys of 3C radio galaxies have been carried out using the Hubble Space Telescope in red, blue, ultraviolet and near-IR continuum and optical spectroscopy which approaches the statistical completeness of the radio catalog: ~90%.
During the last few years several snapshot surveys of 3C radio galaxies have been carried out using the Hubble Space Telescope in red, blue, ultraviolet and near-IR continuum and optical spectroscopy which approaches the statistical completeness of the radio catalog: $\sim 90$.
. A ground based spectroscopic program for the whole sample with the Galileo Telescope has been completed (Buttiglione et al 2009).
A ground based spectroscopic program for the whole sample with the Galileo Telescope has been completed (Buttiglione et al 2009).
We also obtained deep ground based IR K-band imaging.
We also obtained deep ground based IR $K$ -band imaging.
Radio images with arcsec resolution are available for most 3C sources from colleagues, the NRAO VLA Archive Survey (NVAS), and the archives of the VLA and MERLIN.
Radio images with arcsec resolution are available for most 3C sources from colleagues, the NRAO VLA Archive Survey (NVAS), and the archives of the VLA and MERLIN.
VLBA data for some 3C objects with z«0.2 have already been obtained (see e.g. Giovannini et al.
VLBA data for some 3C objects with $z<0.2$ have already been obtained (see e.g. Giovannini et al.
2001, Liuzzo et al.
2001, Liuzzo et al.
2009 and references therein).
2009 and references therein).
mareinally allected by the presence of tori. as suggested from Vig. &..
marginally affected by the presence of tori, as suggested from Fig. \ref{fig:kauff_agnFrac}.
Paper 1 focused on the study of 278 SDSS/SWIRLE quasars and the properties of dust. surrounding them.
Paper 1 focused on the study of 278 SDSS/SWIRE quasars and the properties of dust surrounding them.
Comparing the results between the "restricted" run. where only high To; models were allowed and the “full” run. where optical depths as low as O.1 were allowed. the hypothesis of the existence of low optical depth tori could not be ruled out.
Comparing the results between the “restricted” run, where only high $\tau_{9.7}$ models were allowed and the “full” run, where optical depths as low as 0.1 were allowed, the hypothesis of the existence of low optical depth tori could not be ruled out.
In fact. the majority of objects found a better match of their SEDs with low 70.7 models (76.7«1).
In fact, the majority of objects found a better match of their SEDs with low $\tau_{9.7}$ models $\tau_{9.7} < 1)$.
Phe computed average inner radius was of ~2.6 pc with a tendency for higher Rowf Iud (5100) for the full ran (590)) with respect to the restricted run )). as reported in Paper 1.
The computed average inner radius was of $\sim$ 2.6 pc with a tendency for higher $R_{out}/R_{in}$ i (=100) for the full run ) with respect to the restricted run ), as reported in Paper 1.
The covering [actor depended of course on the choice of the optical depth but had a relatively flat clistribution in both cases. taking values from as low as <0.1 to as high as 0.95.
The covering factor depended of course on the choice of the optical depth but had a relatively flat distribution in both cases, taking values from as low as $< 0.1$ to as high as 0.95.
As for the dust density. there was no clear preference between >=0.0 and =6.0 models. in any of the runs. while 2<0.0 moclels were always favoured.
As for the dust density, there was no clear preference between $\gamma=0.0$ and $\gamma=6.0$ models, in any of the runs, while $\beta<0.0$ models were always favoured.
The aceretion and Ht luminosities were the two better constrained quantities ancl were almost
The accretion and IR luminosities were the two better constrained quantities and were almost
and eravilational radiation (GR:Landau&Lifshitz1975).. these authors found that the biftweation period is in the range Jy0.4—0.7 day lor LAINBs. and stronelv depends on magnetic braking efficiency.
and gravitational radiation \citep[GR;][]{landau}, these authors found that the bifurcation period is in the range $P_{\rm bif}\sim 0.4-0.7$ day for LMXBs, and strongly depends on magnetic braking efficiency.
Ergmaetal.(1998). included mass loss [rom the binary svstem and re-caleulated the biftweation period for two mass configurations (Wy/AL.. anel (1.4.1.5) and two chemical compositions (Z=0.003. 0.03).
\citet{ergma98} included mass loss from the binary system and re-calculated the bifurcation period for two mass configurations $M_1/M_\sun$, $M_2/M_\sun)= (1.4,1)$ and $(1.4,1.5)$ and two chemical compositions $Z=0.003$, $0.03$ ).
Thev pointed out that (he mass loss from the binary system also plavs an impotent role besides magnetic braking in determining the value of Pir. while the chemical composition could only cause small change in JJ. Their bifurcation periods are f,0.85—1.05 day under conservative mass transfer. and 1.6—1.7 times larger if moderate non-conservative mass transler is assumecl.
They pointed out that the mass loss from the binary system also plays an impotent role besides magnetic braking in determining the value of $P_{\rm bif}$, while the chemical composition could only cause small change in $P_{\rm bif}$ Their bifurcation periods are $P_{\rm bif}\sim 0.85-1.05$ day under conservative mass transfer, and $1.6-1.7$ times larger if moderate non-conservative mass transfer is assumed.
Podsiadlowskietal.(2002) found. a bifurcation period around 18 hr for a 1.44. NS and a 1M. companion star. where (μον defined the bifurcation period as (he orbital period when the Roche lobe overflow just began. instead of the initial orbital period.
\citet{pod02} found a bifurcation period around $18$ hr for a $1.4M_\sun$ NS and a $1M_\sun$ companion star, where they defined the bifurcation period as the orbital period when the Roche lobe overflow just began, instead of the initial orbital period.
vanderSluysetal.(2005a.b) also investigated the bifurcation period in LAINBs focusing the formation of ultra-compact X-ray. binaries (UCNDs). and specified (he bifurcation period as "the longest initial period that leads to UCXDBs within a IIubble time (13.7 Gyr).
\citet{sluys05a,sluys05b} also investigated the bifurcation period in LMXBs focusing the formation of ultra-compact X-ray binaries (UCXBs), and specified the bifurcation period as “the longest initial period that leads to UCXBs within a Hubble time $13.7$ Gyr)".
UCABs are bright X-ray sources with very short orbital periods (2<1 h).
UCXBs are bright X-ray sources with very short orbital periods $P \la 1$ h).
The donor has to be a compact source like a white dwarf or a compact core of an evolved giant star to fit inthe small Roche lobe size.
The donor has to be a compact source like a white dwarf or a compact core of an evolved giant star to fit inthe small Roche lobe size.
Such sources may be formed (rough dvnanmical processes including stellar collisions and common envelop evolution (Clarketal.1975:Rasioal. 2006).
Such sources may be formed through dynamical processes including stellar collisions and common envelop evolution \citep{clark75,rasio00,lombard06}.
. An alternative scenario for the formation of such sources is through stable mass transfer in X-ray binaries with a low- or imtermecdiate-mass donor star. which may explain the negative derivative of the Ll-imin source in NGC! 6624 (vanderIxlis&Grindlay 2001).
An alternative scenario for the formation of such sources is through stable mass transfer in X-ray binaries with a low- or intermediate-mass donor star, which may explain the negative derivative of the 11-min source in NGC 6624 \citep{klis93,chou01}.
. It has been found that svstems with initial orbital period just below the bihucation period may form UCXDs (Nelsonetal.1986:Tutukoveavonije1983:Podsiadlowskietal.
It has been found that systems with initial orbital period just below the bifurcation period may form UCXBs \citep{nelson86,tutukov87,pylyser88,pod02,sluys05a}.
2002:vanderSluvs 2005a).. (2002) showed that the closer the initial orbital period to the biburcation period Irom below. (he siialler (he minimum orbital period will be achieved.
\citet{pod02} showed that the closer the initial orbital period to the bifurcation period from below, the smaller the minimum orbital period will be achieved.
So the value of bifurcation period is crucial to understanding the formation of UCXDs (vanderSluvsetal.2005b).
So the value of bifurcation period is crucial to understanding the formation of UCXBs \citep{sluys05b}.
. In this paper we make a svstematic investieation on the bilurcation period for binary svslelus containng an NS will a main-sequence (MS) companion of mass from 0.5.M. (o 21...
In this paper we make a systematic investigation on the bifurcation period for binary systems containing an NS with a main-sequence (MS) companion of mass from $0.5M_\sun$ to $2M_\sun$.
This work was motivated by recent progress in studies on mass and angular momentum loss mechanisms in LMXD evolution.
This work was motivated by recent progress in studies on mass and angular momentum loss mechanisms in LMXB evolution.
ln previous works the MD law originally postulated by Verbunt&Zwaan(1981). and Rappaportetal.(1983). was usually adopted.
In previous works the MB law originally postulated by \citet{verbunt81} and \citet{rappaport83} was usually adopted.
However. this law predicts too fast spin-down of low-mass AIS stus. contradicted with the observation of rapid rotators in voung open clusters (Sillsοἱal.2000:Andronovet 2003).
However, this law predicts too fast spin-down of low-mass MS stars, contradicted with the observation of rapid rotators in young open clusters \citep{sills00,andronov03}.
.Obviously a modification of the MD law will have significant influence on the period evolution (van 2005b)..
.Obviously a modification of the MB law will have significant influence on the period evolution \citep{sluys05b}. .
Additionally. there is strong evidence that during LAINB evolution
Additionally, there is strong evidence that during LMXB evolution
For comparison with the previous figures. figure 3. shows the locus of main sequence. giants. white dwarf and brown dwarf stars.
For comparison with the previous figures, figure \ref{fig:coltheory} shows the locus of main sequence, giants, white dwarf and brown dwarf stars.
The stellar locus for main sequence. subgiant- and red-giant branch stars typical of the old low-metallicity halo and the young solar-type metallicity disk was taken from the models of Bertelli (1994) extendingdown to 0.6 M..
The stellar locus for main sequence, subgiant- and red-giant branch stars typical of the old low-metallicity halo and the young solar-type metallicity disk was taken from the models of Bertelli (1994) extendingdown to 0.6 $M_{\odot}$.
The color-color cooling sequence for pure-Hydrogen WD was taken from Bergeron. Wesemael. Beauchamp (1995).
The color-color cooling sequence for pure-Hydrogen WD was taken from Bergeron, Wesemael, Beauchamp (1995).
Finally. the locus for very low mass stars and/or brown dwarfs down to 0.08 M. is taken from the models of Baratfe (1998).
Finally, the locus for very low mass stars and/or brown dwarfs down to 0.08 $M_{\odot}$ is taken from the models of Baraffe (1998).
This curves are presented in the Jonhson-Cousins system. close to the EIS magnitude system except for the B band (paper I).
This curves are presented in the Jonhson-Cousins system, close to the EIS magnitude system except for the $B-$ band (paper III).
However. the differences are relatively small and have no significant impact on the adopted selection criteria described below.
However, the differences are relatively small and have no significant impact on the adopted selection criteria described below.
Also shown in figure 3. is the track of quasars in the color- diagram as a function of redshift anc the typical color scatter along the sequence due to the different assumptions for their typical spectra and intervening absorption.
Also shown in figure \ref{fig:coltheory} is the track of quasars in the color-color diagram as a function of redshift and the typical color scatter along the sequence due to the different assumptions for their typical spectra and intervening absorption.
QSO colors were simulatec using synthetic QSO spectra. which cover a range of intrinsic spectral properties. and the response functions of the EIS filters (paper D.
QSO colors were simulated using synthetic QSO spectra, which cover a range of intrinsic spectral properties, and the response functions of the EIS filters (paper I).
The method is the same as that used by Warren. Hewett Osmer (1994) and Hall (1996). and is a modified version of the method of Warren (1991).
The method is the same as that used by Warren, Hewett Osmer (1994) and Hall (1996), and is a modified version of the method of Warren (1991).
QSO spectra were synthesised assuming that the QSO continuum has the form of a single power law with spectral index & (S(v)ος v) and assuming fixed emission line strengths relative to Lya+NV.
QSO spectra were synthesised assuming that the QSO continuum has the form of a single power law with spectral index $\alpha$ $\rm{S}(\nu)\propto\nu^{\alpha}$ ) and assuming fixed emission line strengths relative to $\alpha$ +NV.
Three different values of the spectral index α—(.0.25.0.75.1.25) were used. and three different values for the emission line strength. defined by the Lya@+NV rest-frame equivalent width. EW(LyoNV)2(42. 84 and 168A)).
Three different values of the spectral index $\alpha=(-0.25, -0.75, -1.25)$ were used, and three different values for the emission line strength, defined by the $\alpha$ +NV rest-frame equivalent width, $\alpha$ +NV)=(42, 84 and ).
For each set of assumptions. spectra were generated at intervals of 0.1] in z over the range (3.0<z« 5.0).
For each set of assumptions, spectra were generated at intervals of 0.1 in $z$ over the range $3.0 < z < 5.0$ ).
Absorption by intervening HI was taken into account by simulating absorption spectra. following the method of Warren. Hewett Osmer (1994) and based on the work of Moller and Jacobsen (1990).
Absorption by intervening HI was taken into account by simulating absorption spectra, following the method of Warren, Hewett Osmer (1994) and based on the work of ller and Jacobsen (1990).
For each set of intrinsic properties. ten QSO spectra were generated at each z step. each using a different realization of the absorptior spectrum appropriate for that redshift.
For each set of intrinsic properties, ten QSO spectra were generated at each $z$ step, each using a different realization of the absorption spectrum appropriate for that redshift.
Thus at each redshift a total of 90 spectra were generated.
Thus at each redshift a total of 90 spectra were generated.
Because patch B is close to the South Galactic Pole galactic extinction was neglected i1 the present calculation.
Because patch B is close to the South Galactic Pole galactic extinction was neglected in the present calculation.
Figure 3. shows the median and the scatter corresponding to the various simulations as a function of redshift.
Figure \ref{fig:coltheory} shows the median and the scatter corresponding to the various simulations as a function of redshift.
In addition. in figure 3 all the 19 known quasars present in the field are shown in their measured EIS magnitudes.
In addition, in figure \ref{fig:coltheory} all the 19 known quasars present in the field are shown in their measured EIS magnitudes.