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The lower limit on Ej, is 1.2 x I0 eres when the observed fluence from kkeV ts used. | The lower limit on $_{iso}$ is 1.2 $\times$ $^{50}$ ergs when the observed fluence from keV is used. |
The spectral properties of the prompt emission can. be used to estimate a lower limit on the bulk Lorentz factor Γ of the y-ray source (?A. | The spectral properties of the prompt emission can be used to estimate a lower limit on the bulk Lorentz factor $\Gamma$ of the $\gamma$ -ray source \citep{nakar2007}. |
The prompt emission of short GRBs is predominantly non-thermal. including the spectrum of 0070707. | The prompt emission of short GRBs is predominantly non-thermal, including the spectrum of 070707. |
This implies that the y-ray source is optically thin to Thomson scattering of photons on eο pairs (2)... | This implies that the $\gamma$ -ray source is optically thin to Thomson scattering of photons on $e^{+}/e^{-}$ pairs \citep{ls2001}. |
If the optical depth is ry<|. regardless of whether internal or external shocks are involved in generating the emission. a lower limit on E can be estimated using the fit to the y-ray spectrum in the equation: where « is the photon index and E,4,; is the peak energy of the cutoff power-law fit. | If the optical depth is $\tau_T < 1$ , regardless of whether internal or external shocks are involved in generating the emission, a lower limit on $\Gamma$ can be estimated using the fit to the $\gamma$ -ray spectrum in the equation: where $\alpha$ is the photon index and $E_{peak}$ is the peak energy of the cutoff power-law fit. |
We obtain Γ>25 using the cutoff. power-law model parameters from Table | and assuming a redshift of z=0.35. | We obtain $\Gamma \gtrsim 25$ using the cutoff power-law model parameters from Table \ref{spec} and assuming a redshift of $z=0.35$ . |
We note that there are large errors associated with the value of Εως. which is not well constrained by the fit to the joint data. leading to a range of Γz15-40. | We note that there are large errors associated with the value of $E_{peak}$, which is not well constrained by the fit to the joint data, leading to a range of $\Gamma \gtrsim 15-40$. |
A similar value for the limit of [>20 was obtained using the KONUS parameters. which are better constrained. | A similar value for the limit of $\Gamma \gtrsim 20$ was obtained using the KONUS parameters, which are better constrained. |
This is comparable to the lower limits calculated by ? for two other short GRBs. [z4 for 0050709 (?) and Γ>25 for 0051221a (?).. | This is comparable to the lower limits calculated by \citet{nakar2007} for two other short GRBs, $\Gamma \gtrsim 4$ for 050709 \citep{villas2005} and $\Gamma \gtrsim 25$ for 051221a \citep{051221a}. |
These model independent lower limits imply that short GRBs are ultra-relativistic. similar to long GRBs. | These model independent lower limits imply that short GRBs are ultra-relativistic, similar to long GRBs. |
The relatively low Lorentz factor implies a late deceleration time and a smaller initial radius. resulting in the possible late onset of the afterglow. | The relatively low Lorentz factor implies a late deceleration time and a smaller initial radius, resulting in the possible late onset of the afterglow. |
Thelower limits on E. for short GRBs are smaller than the average obtained for long GRBs of Γ>100 (?).. | Thelower limits on $\Gamma$ for short GRBs are smaller than the average obtained for long GRBs of $\Gamma \gtrsim 100$ \citep{ls2001}. |
The bulk Lorentz factor has been estimated to be T-400 from the early afterglows of two long bursts. 0060218 and 0060607a (?).. | The bulk Lorentz factor has been estimated to be $\Gamma \sim 400$ from the early afterglows of two long bursts, 060218 and 060607a \citep{molinari07}. |
The Lorentz factor has also been calculated from the thermal components of the prompt emission from 9970828 and 9990510 at z=0.96 and z=1.62 respectively (?).. | The Lorentz factor has also been calculated from the thermal components of the prompt emission from 970828 and 990510 at $z=0.96$ and $z=1.62$ respectively \citep{asaf07}. |
The calculated values (T=305x28.1=384+4 71. dependent on the ratio between the total fireball energy and the y-ray energy) are consistent. with the measurements of ?.. | The calculated values $\Gamma = 305 \pm 28, \Gamma = 384 \pm 71$ , dependent on the ratio between the total fireball energy and the $\gamma$ -ray energy) are consistent with the measurements of \citet{molinari07}. |
In general. there are fewer assumptions for the prompt emission than for the afterglow emission (e.g. microphysics parameters dependent on the environment). | In general, there are fewer assumptions for the prompt emission than for the afterglow emission (e.g. microphysics parameters dependent on the environment). |
However. ? suggested that the short spectral lags observed in short GRBs may be due to a very high Lorentz factor of Γ~500-1000. since a large E is necessary to avoid a significantcontribution to the lag from the pulse duration due to relativistic beaming. | However, \citet{norris2006} suggested that the short spectral lags observed in short GRBs may be due to a very high Lorentz factor of $\Gamma \sim 500-1000$, since a large $\Gamma$ is necessary to avoid a significantcontribution to the lag from the pulse duration due to relativistic beaming. |
? recently reported host galaxy observations for 9 short GRBs. | \citet{berger2007} recently reported host galaxy observations for 9 short GRBs. |
Eight of the nine are faint (R~ 23). indicating the possible existence of a population of short GRBs at z~ 1. | Eight of the nine are faint $R \sim 23$ ), indicating the possible existence of a population of short GRBs at $z \sim 1$ . |
This was confirmed by ?.. who identified two short bursts with host galaxies at z 0.9. 0070429B and 00707I4B. This implies that the energy release of short GRBs may be higher than previously thought and in the same range as long GRBs. | This was confirmed by \citet{cenko08}, who identified two short bursts with host galaxies at $z \sim 0.9$ , 070429B and 070714B. This implies that the energy release of short GRBs may be higher than previously thought and in the same range as long GRBs. |
The isotropic energycalculated for 0070707 1s L8 x 10°! ergs at z= 0.35. and 1.5 x 107 ergs at z= I. extrapolated to the kkeV energy range. closer to the values expected from long duration bursts (?).. | The isotropic energycalculated for 070707 is 1.8 $\times$ $^{51}$ ergs at $z=0.35$ , and 1.5 $\times$ $^{52}$ ergs at $z =1$ , extrapolated to the keV energy range, closer to the values expected from long duration bursts \citep{butler07}. . |
? estimated that theexpected median redshift of host galaxieswith 25.<R27 from the Hubble Deep Field | \citet{berger2007} estimated that theexpected median redshift of host galaxieswith $25 < R <27$ from the Hubble Deep Field |
(i.e. how elusters are distributed in mass). | (i.e., how clusters are distributed in mass). |
Results of these simulations are clisplaved in Figs. | Results of these simulations are displayed in Figs. |
2. and 3. | \ref{fig:nD3.5_evol} and \ref{fig:nD4.5_evol}. |
We have shown that. irrespective of the initial elobular cluster mass spectrum. the damage performed to the initial mass content in clusters is limited to one elfective radius. that is. Ds 3kkpc(see also MeLaughlin 1999). | We have shown that, irrespective of the initial globular cluster mass spectrum, the damage performed to the initial mass content in clusters is limited to one effective radius, that is, $\lesssim 3$ kpc (see also McLaughlin 1999). |
While in this range. the spatial distribution of the cluster system mass Lattons owing to the greater cllicieney of cluster destruction processes. the overall slope remains close to its initial value. | While in this range, the spatial distribution of the cluster system mass flattens owing to the greater efficiency of cluster destruction processes, the overall slope remains close to its initial value. |
In sharp contrast. the temporal evolution of the number density profile. depends: sensitively on the initial mass spectrum. | In sharp contrast, the temporal evolution of the number density profile depends sensitively on the initial mass spectrum. |
The steepness of the space-density is stationary in case of a gaussian mass function or of a power-law truncated. at OQ MAL... | The steepness of the space-density is stationary in case of a gaussian mass function or of a power-law truncated at $^5$ $_{\odot}$. |
On the other hand. it gets significantly shallower in the case of a mass spectrum favouring low-mass clusters. e.g. a power-law extending down to 10* MM... | On the other hand, it gets significantly shallower in the case of a mass spectrum favouring low-mass clusters, e.g., a power-law extending down to $^3$ $_{\odot}$. |
For each simulation. we have compared in a least-squares sense the presently. observed: spatial distributions with the modelled ones. obtaining the X72 and the incomplete eamma function measure of probability (see Table. 4)). | For each simulation, we have compared in a least-squares sense the presently observed spatial distributions with the modelled ones, obtaining the $\chi ^2$ and the incomplete gamma function measure of probability (see Table \ref{tab:fit_evol_GCS}) ). |
The most Likely initial conditions of course correspond to the cases for which the evolved. massand number density. profiles are in good. agreement with their Old Lalo counterparts. | The most likely initial conditions of course correspond to the cases for which the evolved mass number density profiles are in good agreement with their Old Halo counterparts. |
The best match is achieved when an initial spatial distribution with a slope of 3.5 is combined with an initial mass spectrum depleted in low-mass clusters. that is. either a gaussian mass function or a power-law mass spectrum truncated at 107 MM. | The best match is achieved when an initial spatial distribution with a slope of $-3.5$ is combined with an initial mass spectrum depleted in low-mass clusters, that is, either a gaussian mass function or a power-law mass spectrum truncated at $^5$ $_{\odot}$. |
La this case. the cluster destruction rate is limited. as also is the corresponding temporal evolution. of the number. density. profile. thus preserving its initial 3.5 steepness. in agreement with what is observed for the Old Lalo(see Table 2)). | In this case, the cluster destruction rate is limited, as also is the corresponding temporal evolution of the number density profile, thus preserving its initial $-3.5$ steepness, in agreement with what is observed for the Old Halo (see Table \ref{tab:fit_pure_pl}) ). |
I£ the Galactic halo eglobular cluster svstem had actually started with this initial spatial distribution. it is very. unlikely that the initial mass spectrum was a pure power-law extending down to OMAL.. | If the Galactic halo globular cluster system had actually started with this initial spatial distribution, it is very unlikely that the initial mass spectrum was a pure power-law extending down to $_{\odot}$. |
The abundance of low-mass objects in such a elobular cluster svstenm would make the number density profile shallow with time. making it unable to fit the presen 3.5 slope. | The abundance of low-mass objects in such a globular cluster system would make the number density profile shallow with time, making it unable to fit the present $-3.5$ slope. |
We confirm Daumgardt. s (1998) [inding following which a power-law probing down to MM. combine with a steep (ie. 5= 4.5) spatial distribution leads to good agreement with the observed. present-day. number density. profile. | We confirm Baumgardt 's (1998) finding following which a power-law probing down to $_{\odot}$ combined with a steep (i.e., $\gamma
= -4.5$ ) spatial distribution leads to good agreement with the observed present-day number density profile. |
However. we caution that. the observec mass density profile is then not well fitted by its evolvec counterpart. | However, we caution that the observed mass density profile is then not well fitted by its evolved counterpart. |
In fact. owing to their robustness. all the evolved. mass. density profiles. irrespective of the initia elobular cluster mass spectrum. are locked. close to their initial 4.5 slope. | In fact, owing to their robustness, all the evolved mass density profiles, irrespective of the initial globular cluster mass spectrum, are locked close to their initial $-4.5$ slope. |
As a result. they. remain significantlv steeper. even after a GGvr long evolution. than the 3.5 slope shown by the present. spatial distribution of the Old Lalo cluster system mass. | As a result, they remain significantly steeper, even after a Gyr long evolution, than the $-3.5$ slope shown by the present spatial distribution of the Old Halo cluster system mass. |
Even though sucha possibility cannot be firmly ruled. out (Qs0.001 if disc shocking is included in the simulations). it remains much less likely than 1ο initial 2 space-density which we have just discussed. | Even though sucha possibility cannot be firmly ruled out $Q \lesssim
0.001$ if disc shocking is included in the simulations), it remains much less likely than the initial $D^{-3.5}$ space-density which we have just discussed. |
As a result. although the number density. profile alone indicates that the Galactic globular. cluster system. may have started with a very steep initial spatial clistribution and a power-law mass spectrum covering three orders. of magnitude in mass. the mass density. profile tends to dismiss this possibility. | As a result, although the number density profile alone indicates that the Galactic globular cluster system may have started with a very steep initial spatial distribution and a power-law mass spectrum covering three orders of magnitude in mass, the mass density profile tends to dismiss this possibility. |
Alb together. our results. support the hypothesis following which the Galactic halo globular cluster system started with an initial space-density scaling as 3h aud an initial mass spectrum. somehow depleted. in. low-mass clusters. that is. a bell-shaped mass function similar to the current one. or à power-law mass spectrum truncated. near Q MM... | All together, our results support the hypothesis following which the Galactic halo globular cluster system started with an initial space-density scaling as $^{-3.5}$ and an initial mass spectrum somehow depleted in low-mass clusters, that is, a bell-shaped mass function similar to the current one, or a power-law mass spectrum truncated near $^5$ $_{\odot}$ . |
This research was supported. by à. Marie. Curie Fellowships. withinNEN the 6°aq | This research was supported by a Marie Curie Intra-European Fellowships within the $6^{th}$ |
Photometric surveys for transiting extra-solar planets have become very popular since the detection of the transits exhibited by the planet-host sar HD 209458 (Charbonneauetal. 2000:: al. 20019. | Photometric surveys for transiting extra-solar planets have become very popular since the detection of the transits exhibited by the planet-host star HD 209458 \citealt{cha00}; ; \citealt{bro01}) ). |
Feor the first time the radius of an extra-solar planet was determined. and the measurement of the orbital inclination. lead to an estimae of the planetary mass. not just a lower limit. | For the first time the radius of an extra-solar planet was determined, and the measurement of the orbital inclination lead to an estimate of the planetary mass, not just a lower limit. |
The planet HD 209458b was found to have an average density of ~0.38 g/cm''. signiticantly less than the average density of Saturn (0.7 z/cm). leading to the term "hot Jupiter" for the class of Jupiter mass planes with short periods (1-10 dx. | The planet HD 209458b was found to have an average density of $\sim$ 0.38 $^3$, significantly less than the average density of Saturn (0.7 $^3$ ), leading to the term “hot Jupiter” for the class of Jupiter mass planets with short periods (1-10 d). |
Transiting planets are also very important in that their atmospheric composition may be determined from transmission spectroscopy for the brighter host stars (Charbonneauetal.2002: Brown.Libbrecht&Charbon-που 2003: Vidal-Madjaretal. 20035). | Transiting planets are also very important in that their atmospheric composition may be determined from transmission spectroscopy for the brighter host stars \citealt{cha02}; \citealt{bro02}; \citealt{vid03}) ). |
Careful modelling of the transit morphology and/or timings may be used to constrain the presence of moons or rings and to probe the limb darkening of the star (Brownetal. 2001). | Careful modelling of the transit morphology and/or timings may be used to constrain the presence of moons or rings and to probe the limb darkening of the star \citealt{bro01}) ). |
Since the discovery of the transiting nature of HD 209458b. many transit candidates have been put forwards by various groups (e.g: Streetetal.20032: Drake&Cook 2004:: Bramichetal. 2005). | Since the discovery of the transiting nature of HD 209458b, many transit candidates have been put forwards by various groups (e.g: \citealt{str03}; \citealt{dra04}; \citealt{bra05}) ). |
OGLE have been by far the most prolifie transit survey with 177 transit candidates from three observational seasons 2002az Udalskietal. 2002b:: Udalskietal. 2003:: Udalskietal. 2004). | OGLE have been by far the most prolific transit survey with 177 transit candidates from three observational seasons \citealt{uda02a}; \citealt{uda02b}; \citealt{uda03}; \citealt{uda04}) ). |
However. even with the discovery of numerous candidates. follow-up observations have confirmed the planetary status of only six. bringing the total number of transiting planets to nine (see Bramichetal.2005. and references therein: Satoetal.2005:: Bouchyetal. 2005). | However, even with the discovery of numerous candidates, follow-up observations have confirmed the planetary status of only six, bringing the total number of transiting planets to nine (see \citealt{bra05} and references therein; \citealt{sat05}; \citealt{bou05}) ). |
This is due to the ubiquity of eclipsing binaries and the many observational scenarios involving these systems that mimic a transit event (Brown 2003)). | This is due to the ubiquity of eclipsing binaries and the many observational scenarios involving these systems that mimic a transit event \citealt{bro03}) ). |
Spectroscopic and multi-band photometric observations are required to rule out the eclipsing binary scenarios and determine the mass of the companion (e.g: Alonsoetal. 2004). | Spectroscopic and multi-band photometric observations are required to rule out the eclipsing binary scenarios and determine the mass of the companion (e.g: \citealt{alo04}) ). |
When hunting for new planets. the main advantage of the transit method over the radial-velocity technique is that many stars may be monitored in parallel and to fainter magnitudes. thus probing out beyond the Solar neighbourhood. | When hunting for new planets, the main advantage of the transit method over the radial-velocity technique is that many stars may be monitored in parallel and to fainter magnitudes, thus probing out beyond the Solar neighbourhood. |
Even though only a small fraction (0.156) of stars are expected to exhibit a hot Jupiter transit signal. by using a large field of view instrument on a crowded star field one can monitor enough stars to the precision required to detect a number of transiting planets. | Even though only a small fraction $\sim$ ) of stars are expected to exhibit a hot Jupiter transit signal, by using a large field of view instrument on a crowded star field one can monitor enough stars to the precision required to detect a number of transiting planets. |
Consequently large charge-coupled device (CCD) mosaic cameras are essential to the planet catch potential of a transit survey. | Consequently large charge-coupled device (CCD) mosaic cameras are essential to the planet catch potential of a transit survey. |
A transit survey produces transit candidates that need follow- observations to determine the nature of the transit signals. | A transit survey produces transit candidates that need follow-up observations to determine the nature of the transit signals. |
Candidates confirmed as transiting planets add to our database of extra-solar planets and constrain their poorly known mass-radius relationship (Burrowsetal. 20043). | Candidates confirmed as transiting planets add to our database of extra-solar planets and constrain their poorly known mass-radius relationship \citealt{bur04}) ). |
To estimate the fraction of stars that harbour a planet (the planet fraction) as a function of spectral type and planet type we compare the number of transiting planets detected with acalculation of the expected number of transiting | To estimate the fraction of stars that harbour a planet (the planet fraction) as a function of spectral type and planet type we compare the number of transiting planets detected with acalculation of the expected number of transiting |
For a given superbubble. [rom the observed values of 22. e and np. we derive the corresponding age ἐς and (he equivalent mechanical lunünositv Lax. | For a given superbubble, from the observed values of $R$ , $v$ and $n_0$, we derive the corresponding age $t_7$ and the equivalent mechanical luminosity $L_{\rm SN}$. |
The number Noy of stars that become supernovae (SN) over the time scale / is given by Ney=Laxl/Ex. | The number $N_{\rm SN}$ of stars that become supernovae (SN) over the time scale $t$ is given by $N_{\rm SN}=L_{\rm SN}t/E_{\rm SN}$. |
Although stellar winds from the OD association will produce a hot bubble before the first SN goes olf. these winds are not important compared to SNe for the later diinamies of the supershell (AleCray Ixafatos 1987: Mae Low AleCray 1988). | Although stellar winds from the OB association will produce a hot bubble before the first SN goes off, these winds are not important compared to SNe for the later dynamics of the supershell (McCray Kafatos 1987; Mac Low McCray 1988). |
Also. while the early times ol the bubble evolution are sensitive to the details of the rate of energv injection (which is assumed constant in the Weaver οἱ al. | Also, while the early times of the bubble evolution are sensitive to the details of the rate of energy injection (which is assumed constant in the Weaver et al. |
model). the late phase of the bubble is (Shull Saken 1995). | model), the late phase of the bubble is (Shull Saken 1995). |
We should point out that the factor Nay estimated using the equations above is (vpically a factor of (han the equivalent number estimated using (he energy Ey—5.3οpbPPHPVE. eres which would be required to produce the shell by a sudden explosion (Chevalier 1974). | We should point out that the factor $N_{\rm SN}$ estimated using the equations above is typically a factor of than the equivalent number estimated using the energy $E_{\rm E}=5.3\times 10^{43}
n_0^{1.12}R^{3.12}V^{1.4}$ ergs which would be required to produce the shell by a sudden explosion (Chevalier 1974). |
The latter. larger. number has been the one often used in the literature to estimate superbubble energies (Lleiles 1979: Rhode et al. | The latter, larger, number has been the one often used in the literature to estimate superbubble energies (Heiles 1979; Rhode et al. |
1999: MeClIure-Grifith et al. | 1999; McClure-Griffith et al. |
2002). | 2002). |
The initial mass function for massive stars can be written as(Garmany. Conti Chiosi 1982)πμ”... where ;2]~2.6. | The initial mass function for massive stars can be written as(Garmany, Conti Chiosi 1982), where $\beta\sim 2.6$. |
We assume Adi,=3AL. and μας=140M. for the minimum and maximum mass ol the distribution. respectively. | We assume $M_{\rm min}=3 M_\odot$ and $M_{\rm max}=140 M_\odot$ for the minimum and maximum mass of the distribution, respectively. |
The main-sequence lifetimes of massive starsare given approximately by (Stothers 1972: Chiosi. NasiSreenivasan LOTS) .. | The main-sequence lifetimes of massive starsare given approximately by (Stothers 1972; Chiosi, NasiSreenivasan 1978) . |
Studies of the interstellar iiediuni in the Magellanic Clouds (MC) explore different cuviroumental conditions frou: those typically probed im our own Galactic ISM. | Studies of the interstellar medium in the Magellanic Clouds (MC) explore different environmental conditions from those typically probed in our own Galactic ISM. |
On average. MC stars aud II IE regions have metallicities below solar values by 0.3 dex (LAIC) aud 0.6{VT dex (SMC). though therelative elemental abuudauces (e.g. [N/Zu]. for elements X that we consider) are eoncrally similar to those found for analogous Galactic objects ες [22]: [20|: [15))). | On average, MC stars and H II regions have metallicities below solar values by 0.3 dex (LMC) and 0.6–0.7 dex (SMC), though the elemental abundances (e.g., [X/Zn], for elements X that we consider) are generally similar to those found for analogous Galactic objects \cite{rd92}; ; \cite{wlb97}; ; \cite{wfs99}; \cite{ven99}) ). |
The ISM in both MC generally las lower dust-to-gas ratios. strouecr anmbieut racliation fields. aud siguificant differences in UV extinction (especially in the SAIC}. | The ISM in both MC generally has lower dust-to-gas ratios, stronger ambient radiation fields, and significant differences in UV extinction (especially in the SMC). |
Deteiauimation of clemeutal abuudances. depletions. and physical conditions oei the MC ISM therefore provides interestiug tests for theoretical models of interstellar clouds aud dust erains. and should also vield insights iuto the nature of the even lower metallicity QSO absorption-line svstenis. | Determination of elemental abundances, depletions, and physical conditions in the MC ISM therefore provides interesting tests for theoretical models of interstellar clouds and dust grains, and should also yield insights into the nature of the even lower metallicity QSO absorption-line systems. |
Most studies ofthe optical absorption lines of Ca IT iud Na I have focused ou the kinematics aud structure of the MC (AeBS. Ls}: but see [17])). | Most studies of the optical absorption lines of Ca II and Na I have focused on the kinematics and structure of the MC (e.g., \cite{way90}; but see \cite{vmm93}) ). |
While UV spectra of many MC stars were obtained with JUL. the relatively low resolution (FWIIM ~ 2025 kins 7) and ecuerally ow S/N nude it very difficult to determine accurate abundances aud plivsical conditions for individual imterstellar clouds iu the generally complex MC sightlines (e.g.. [3]: [2})). | While UV spectra of many MC stars were obtained with , the relatively low resolution (FWHM $\sim$ 20–25 km $^{-1}$ ) and generally low S/N made it very difficult to determine accurate abundances and physical conditions for individual interstellar clouds in the generally complex MC sightlines (e.g., \cite{fs83}; \cite{dfs85}) ). |
New observing capabilities (both ou tlie ground and ii space) are enabling much more detailed stu of iesthe MC ISM. rowever (e.e.. | New observing capabilities (both on the ground and in space) are enabling much more detailed studies of the MC ISM, however (e.g., \cite{iau190}) ). |
ΣΕthis contribution. we focus on recent studies of the predomiuautlv neutral ogas iu the MC. based on high-resolution optical spectra aud ou UV spectra fromfC.ITST (CRS and STIS). audFUSE. | In this contribution, we focus on recent studies of the predominantly neutral gas in the MC, based on high-resolution optical spectra and on UV spectra from, (GHRS and STIS), and. |
We compare relative gas-phase abundauces [X/Zu| (which esseutiallv eivethe depletion ofX) inthe MC ISM with representative | We compare relative gas-phase abundances [X/Zn] (which essentially givethe depletion ofX) inthe MC ISM with representative |
Naturally. at. some point when the level of noise is similar to the level of polarised foreground. leakage in the Faraday dispersion function a confusion limit will be found. | Naturally, at some point when the level of noise is similar to the level of polarised foreground leakage in the Faraday dispersion function a confusion limit will be found. |
‘This has been tackled in the following way. | This has been tackled in the following way. |
First. by fitting for RAL ancl polarisation angle using f° (rather than £1) where the level of confusion will be less since the peaks corresponding to Faradav-rotating structures will be larger than their Stokes £ counterparts. | First, by fitting for RM and polarisation angle using $F$ (rather than $F_I$ ) where the level of confusion will be less since the peaks corresponding to Faraday-rotating structures will be larger than their Stokes $I$ counterparts. |
Secondly. since the data cubes comprise of integrated data. the level of noise can. to a certain degree. be controlled by the integration timo. | Secondly, since the data cubes comprise of integrated data, the level of noise can, to a certain degree, be controlled by the integration time. |
In this paper. we emplov the dimensionless power spectrum. ASQ212) as the key statistical measure. which is the contribution to the variance of the τοςαπο 21-cmi brightness temperature. contrast. οΕν). per logarithmic interval in wavenumber. &=27/A. | In this paper, we employ the dimensionless power spectrum, $\Delta_{21}^2(k,z)$, as the key statistical measure, which is the contribution to the variance of the redshifted 21-cm brightness temperature contrast, $\delta T_{\rm b}(z)$, per logarithmic interval in wavenumber, $k = 2\pi/\lambda$. |
This measure is related to the dimensional form of the power spectrum. £2)(4.2). by Poi(hoz) is estimated by averaging over all n modes of the Fourier transform. (2°) of (2) in à thin spherical shell in A-space. Note that we must use caution when emploving this statistical measure since the spherical svmmetry of the signal is broken by redshift evolution over certain ranges of redshift (Asz2 [or a 32 Mllz band centred on 2=8.5). | This measure is related to the dimensional form of the power spectrum, $P_{21}(k,z)$, by $P_{21}(k,z)$ is estimated by averaging over all $m$ modes of the Fourier transform $\hat{T}$ ) of $T(z)$ in a thin spherical shell in $k$ -space, Note that we must use caution when employing this statistical measure since the spherical symmetry of the signal is broken by redshift evolution over certain ranges of redshift $\Delta z \approx 2$ for a 32 MHz band centred on $z = 8.5$ ). |
This issue has been discussed bv a number of authors (see.e.g.?2?7) and its effect. on the sensitivity of the 21-cm power spectrum has been investigated by 2.. | This issue has been discussed by a number of authors \citep[see, e.g.,][]{morales2004,bl2005,mcquinn2006} and its effect on the sensitivity of the 21-cm power spectrum has been investigated by \cite{mcquinn2006}. |
Following the removal of both the continuum ane polarised foregrounds. the full 32 MlIE cata cube is divided into four S MllIz sub-bands (Az<0.5 for ay<z«8.5). each of which is independently reduced into a power spectrum. | Following the removal of both the continuum and polarised foregrounds, the full 32 MHz data cube is divided into four 8 MHz sub-bands $\Delta z \lsim\,\,0.5$ for $z_{\rm ov} < z < 8.5$ ), each of which is independently reduced into a power spectrum. |
This sub-banding. together with continuum foreground removal. eliminates measurements of the largest spatial scales along the line-of-ight direction (these corresponding to the lowest | nmicdes) and imposes a minimum accessible wavenumber of μα&OLOJ(0L|23/7.5]+ +). | This sub-banding, together with continuum foreground removal, eliminates measurements of the largest spatial scales along the line-of-sight direction (these corresponding to the lowest $k_{\parallel}$ modes) and imposes a minimum accessible wavenumber of $k_{\rm min} \approx 0.04[(1+z)/7.5]^{-1}$ $^{-1}$ ]. |
Our numerical power spectrum. measurements are subject to sample variance. arising from the finite number of independent modes. counted. in. cach &-shell.. which corresponds to the finite number of independent wavelengths that can fit into the simulated volume. | Our numerical power spectrum measurements are subject to sample variance, arising from the finite number of independent modes counted in each $k$ -shell, which corresponds to the finite number of independent wavelengths that can fit into the simulated volume. |
Any racio interferometer is also subject. to instrumental noise ancl has limited sensitivity arising from the finite volume of the observation. | Any radio interferometer is also subject to instrumental noise and has limited sensitivity arising from the finite volume of the observation. |
We consider observational parameters corresponding to the design specications of the AIWA. and of a hypothetical follow-up to the MIWA (which we term the AIWAS5000). | We consider observational parameters corresponding to the design specications of the MWA, and of a hypothetical follow-up to the MWA (which we term the MWA5000). |
The AIWA 5000 is assumed to follow the basic design of the MIWA. | The MWA 5000 is assumed to follow the basic design of the MWA. |
The quantitative cifferences are that we assume the JIWAS5O00 to have 5000 tiles within a diameter of 2 km. with a [lat antenna density core of racius 40 m. In cach case. we assume one field is observed for an integrate time of 1000 hr. | The quantitative differences are that we assume the MWA5000 to have 5000 tiles within a diameter of 2 km, with a flat antenna density core of radius 40 m. In each case, we assume one field is observed for an integrated time of 1000 hr. |
We compute the sensitivity with which the 21-em power spectum could be detected following the procedure outlines bv ? and ?.. | We compute the sensitivity with which the 21-cm power spectum could be detected following the procedure outlined by \cite{mcquinn2006} and\cite{bowman2006}. . |
Section A2 of the Appendix contains a ful derivation of the sensitivitv-related quantities used. | Section \ref{App:Power spectrum measurement} of the Appendix contains a full derivation of the sensitivity-related quantities used. |
Written in terms of the cosmic wavevector k=kj|ki. where k and Ay are the components of & parallel and perpendicular to the line of sight respectively. (sce Appendix A2)). the resulting error in the 21-cm power spectrum is ∖∖⋎↓↥⋖⋅↓⋅∢⋅∫⊽∖∖∖≈⇉⋅↱≻∪↕⊔↴∶∃ie lx ijs the svstem temperature of the instrument. (2) is the comoving distance to the point of emission at redshift z. AL is the comoving depth of the survey volume corresponding to the bandwidth D. fy is the total integration time. mi(C.v) is the number density of baselines that can observe the visibility U. where C—kíD/2zx and À is the observed wavelength. | Written in terms of the cosmic wavevector $\kvec = \kvec_\parallel + \kvec_\perp$, where $\kvec_\parallel$ and $k_\perp$ are the components of $\kvec$ parallel and perpendicular to the line of sight respectively (see Appendix \ref{App:Power spectrum measurement}) ), the resulting error in the 21-cm power spectrum is where $T_{\rm sys} \approx 250[(1+z)/7]^{2.6}$ K is the system temperature of the instrument, $D(z)$ is the comoving distance to the point of emission at redshift $z$ , $\Delta D$ is the comoving depth of the survey volume corresponding to the bandwidth $B$, $t_0$ is the total integration time, $n_{\rm b}(U,\nu)$ is the number density of baselines that can observe the visibility $\Uvec$, where $U = k_\perp D/2\pi$ and $\lambda$ is the observed wavelength. |
Although the observed. 21-cm power spectrum. is not spherically svimmetric. it is symmetric about the line of sight. | Although the observed 21-cm power spectrum is not spherically symmetric, it is symmetric about the line of sight. |
This makes it possible to calculate the overall power-spectral sensitivity. of the radio interferometer using the Fouricr modes. contained. within an infinitesimal annulus around the line of sight of constant (4.4). wherecos(8) k.zík(Eisthe unit vector pointing in the directionof the line of sight). | This makes it possible to calculate the overall power-spectral sensitivity of the radio interferometer using the Fourier modes contained within an infinitesimal annulus around the line of sight of constant $(k,\theta)$ , where$\cos(\theta) = \kvec \cdot \hat{\zvec}/k$ $\hat{\zvec}$ is the unit vector pointing in the directionof the line of sight). |
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