ReadingTimeMachine/rtm-sgt-ocr-v1 · Datasets at Hugging Face

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The MP and the IP seen bv an observer originate at different phases of pulsar rotation. ancl therefore they. should arise al different phases of subpulse drift and the intensities should be correlated with a certain temporal delay.	The MP and the IP seen by an observer originate at different phases of pulsar rotation, and therefore they should arise at different phases of subpulse drift and the intensities should be correlated with a certain temporal delay.
It is worth noting that this delay should not exactly correspond to the longitudinal separation between the. MP. ancl IP in the profile. since (he components travel somewhat different distances to the observer.	It is worth noting that this delay should not exactly correspond to the longitudinal separation between the MP and IP in the profile, since the components travel somewhat different distances to the observer.
The microstructure characteristic of the MP emission is also expected to be present in (he scattered component.	The microstructure characteristic of the MP emission is also expected to be present in the scattered component.
The observations of PSR 0020-05 have indeed revealed the microstructure in the IP at the timescale τιν=90 i. whereas in the MP mip=130 ys (Hankins&Corcles1931:HankinsBoriakoll1981).	The observations of PSR B0950+08 have indeed revealed the microstructure in the IP at the timescale $\tau_{\rm IP}=90\,\mu$ s, whereas in the MP $\tau_{\rm MP}=130\,\mu$ s \citep{hc81,hb81}.
. In our model. the relationship between the microstructure timescales in the two components can be estimated as follows.	In our model, the relationship between the microstructure timescales in the two components can be estimated as follows.
The intensiv is translerred between thephoton states related as p(1—9cos0)=im(1-—»cos64).	The intensity is transferred between thephoton states related as $\nu (1-\beta\cos\theta)=\nu_1 (1-\beta\cos\theta_1)$.
Differentiating (his at fixed [requencies vields p/6.N9=r4. N22. where it is taken (hal [or θιεπ.	Differentiating this at fixed frequencies yields $\nu\theta\Delta\theta =\nu_1\Delta\theta^2$ , where it is taken that $\sin\theta_1\approx\Delta\theta_1$ for $\theta_1\approx\pi$.
As "p/Typ=AMALAND and vt?f2oviPV. one can find that TipVy 2/ν0.λ0,	As $\tau_{\rm IP}/\tau_{\rm MP}=\Delta\theta_1/\Delta\theta$ and $\nu\theta^2/2\approx 2\nu_1$, one can find that $\tau_{\rm IP}(\nu_1)/\tau_{\rm MP}(\nu)=2/\sqrt{\theta\Delta\theta}$ .
Taking into account that the microstructure timescaleevolves with [recquency.	Taking into account that the microstructure timescaleevolves with frequency,
The inferred miass-loss rates AL~10£M. vrἩ, is much higher than any reasonable mass-loss rate from au O-star primary and suggests that it is connected with the unusual short-lived pliase £133 is expericucing (see LL).	The inferred mass-loss rate, $\dot{M}\sim 10^{-4}\,M_{\odot}\,$ $^{-1}$, is much higher than any reasonable mass-loss rate from an O-star primary and suggests that it is connected with the unusual short-lived phase 433 is experiencing (see 4.1).
Tt could be mass loss from a common cuvelope that has already. started to form around the binary. or a hot coronal wind from the outer parts of the accretion disk driven. e.g. by the N-ray radiation from the central compact source.	It could be mass loss from a common envelope that has already started to form around the binary, or a hot coronal wind from the outer parts of the accretion disk driven, e.g., by the X-ray irradiation from the central compact source.
With unique sampling iu the UV-plane. we have imaged the L135 system at Gecu aud 2Ocem and securely detected at both wavelengths s1000thi eiission extending over a few hundred AU perpendicular to the jet axis.	With unique sampling in the UV-plane, we have imaged the 433 system at cm and cm and securely detected at both wavelengths smooth emission extending over a few hundred AU perpendicular to the jet axis.
The most likely interpretation of this radiation is enission frou matter which has been ejected from the disk as a thermal wind with an outward speed of ~3001s.1.	The most likely interpretation of this radiation is emission from matter which has been ejected from the disk as a thermal wind with an outward speed of $\sim 300\,{\rm km\,s^{-1}}$.
tthauks the Roval Society for a Uuiversity Research Fellowship.	thanks the Royal Society for a University Research Fellowship.
MERLIN is a unational facility operated by the University of Manchester ou behalf of PPARC.	MERLIN is a national facility operated by the University of Manchester on behalf of PPARC.
The VLBA aud VLA are facilities of NRAO operated by AUT. under cooperative agreement with the NSF.	The VLBA and VLA are facilities of NRAO operated by AUI, under cooperative agreement with the NSF.
systems domiuated by metal-rich globular clusters.	systems dominated by metal–rich globular clusters.
However. noue of these cases were as extreme as NGC 3311 was previously thowelt to be.	However, none of these cases were as extreme as NGC 3311 was previously thought to be.
The existetce of a blue (metal-poor) population iu these galaxies is not excluded by hese data (because of sinall sample statistics) but Gebhardt ]xissler-Patig suggest that it is not likely to be siguilicaut. as in IC. [051.	The existence of a blue (metal–poor) population in these galaxies is not excluded by these data (because of small sample statistics) but Gebhardt Kissler-Patig suggest that it is not likely to be significant, as in IC 4051.
Iu suminary. no system has yet been observed to have a globular cluster color distribution as extremely rec as the previous claiti lor NGC 3311.	In summary, no system has yet been observed to have a globular cluster color distribution as extremely red as the previous claim for NGC 3311.
In particular.dex.	In particular,.
NGC 3311 representecl the best case of an almost. excusively metal-rich globular cluster population.	NGC 3311 represented the best case of an almost exclusively metal–rich globular cluster population.
As such it raised serious questions about our un(lerstaucding of elobular cluster and ealaxy formation. since the existence of a metal-poor poptatiou is implicit in all the current sSCellarlos.	As such it raised serious questions about our understanding of globular cluster and galaxy formation, since the existence of a metal–poor population is implicit in all the current scenarios.
In the merger picture a1 elliptical galaxy. is formed. [ro idie merger of two gas-rich spiral sealaxies.	In the merger picture an elliptical galaxy is formed from the merger of two gas–rich spiral galaxies.
The resultaut galaxy contaius a blue. metal-poor )opulation of globular clusters from the progenitor spirals aud a uetal-rich population formed di‘ine tle mereer.	The resultant galaxy contains a blue, metal–poor population of globular clusters from the progenitor spirals and a metal–rich population formed during the merger.
In this scenario the metal-poor population shoud peak at the meclian metalliciM7 of “ilthe globular cluster systems of spiral galaxies. i.e. [Fe/H] —1.5 dex.	In this scenario the metal–poor population should peak at the median metallicity of the globular cluster systems of spiral galaxies, i.e. [Fe/H] $\sim -1.5$ dex.
It is generally recogiizecl. 1howh. that mergers are unlikely. by themselves. to result i iligh specilic (requeney. galaxie. slcl as NGC 3311 (Ashina1 Zepl L998: Forbes. Brodie Crithairy 1997).	It is generally recognized, though, that mergers are unlikely, by themselves, to result in high specific frequency galaxies, such as NGC 3311 (Ashman Zepf 1998; Forbes, Brodie Grillmair 1997).
In the multi-plase ρα.re. ie blue population is fo‘inecl in a pre-ealaxy pliase. or during galaxy assembly. [roii relatively iuenriched gas and so. by definition. is metal-poor.	In the multi–phase picture, the blue population is formed in a pre–galaxy phase, or during galaxy assembly, from relatively unenriched gas and so, by definition, is metal–poor.
The red globular clister population a1 the ilk of tje galaxy stars are formed later rou enriched material.	The red globular cluster population and the bulk of the galaxy stars are formed later from enriched material.
In the accretio1 model. the origial elliptical galaxy. (formed in a single 5) aceretes smaller (lower meallicitv) galaxies with tleir retiuues of low-metallicity globular clusters.	In the accretion model, the original elliptical galaxy (formed in a single burst) accretes smaller (lower metallicity) galaxies with their retinues of low–metallicity globular clusters.
αἱ galaxies at tlie ceuters o ‘rich galaxy «‘luste "Quay aso be expected to strip Globular clusters from the ouskirs of neighboring [n]galaxies.	Giant galaxies at the centers of rich galaxy clusters may also be expected to strip metal--poor globular clusters from the outskirts of neighboring galaxies.
Because of the globular cluster uean metallicity — pareut galaxy Undaity relation (BrocieandHuclra1991: accreted/stripped globulars must be. o1 average. of lower metallicity han those belonging to the "seed" elliptical.	Because of the globular cluster mean metallicity – parent galaxy luminosity relation \citep{bro91,for96} accreted/stripped globulars must be, on average, of lower metallicity than those belonging to the “seed” elliptical.
Coté.MarzkeandWest(1998) show bow accretion processes and the luminosity [uuction of galaxies will lead to bi-iuodal globular cluster systems iu bieht galaxies with blue ancl red peaks at [Fe/H] ~—1.5 aud ~—0.5 dex. as geerally observed.	\citet{cot98} show how accretion processes and the luminosity function of galaxies will lead to bi–modal globular cluster systems in bright galaxies with blue and red peaks at [Fe/H] $\sim -1.5$ and $\sim -0.5$ dex, as generally observed.
Sketchy arguments cau be imagined to accommodate au absence o ‘wetal-poor clusters wiltli any of the above formation scenarios.	Sketchy arguments can be imagined to accommodate an absence of metal–poor clusters within any of the above formation scenarios.
To produce oly. or predominanty. netal-rich clusters uu the "in situ scenario would require rapid star foru€ion prior to cluste ‘formation in the saine st: formation event.	To produce only, or predominantly, metal–rich clusters under the “in situ” scenario would require rapid star formation prior to cluster formation in the same star formation event.
Iun a deep gravitational potential te metals produced N the stars are retained aud the average metallicity of the system is driven to a igh value (see also Woodworth Harris 2000). conceivably before any clusters are formed.	In a deep gravitational potential, the metals produced by the stars are retained and the average metallicity of the system is driven to a high value (see also Woodworth Harris 2000), conceivably before any clusters are formed.
In acereion scenarios. the metal-poor population in the	In accretion scenarios, the metal–poor population in the
or temporal variations in the grain size distributions.	or temporal variations in the grain size distributions.
As with the Reference case. these disces are simulated. purely to analyse the energeties since we do not expect these disces to fragment.	As with the Reference case, these discs are simulated purely to analyse the energetics since we do not expect these discs to fragment.
We then choose to explore the initial and boundary temperature conditions by decreasing the magnitude of the disc temperature whilst maintaining the same surface mass clensity as the Reference case.	We then choose to explore the initial and boundary temperature conditions by decreasing the magnitude of the disc temperature whilst maintaining the same surface mass density as the Reference case.
We do this by changing the initial Foomre stability parameter profiles such that Quin=1.0.75 and 0.5 (simulations Qminl. OQmin0.75 and Qmin0.5. respectively).	We do this by changing the initial Toomre stability parameter profiles such that $Q_{\rm min} = 1, 0.75$ and $0.5$ (simulations Qmin1, Qmin0.75 and Qmin0.5, respectively).
This is equivalent to reducing the disc aspect ratios to ΗΝ~22.107. L7«10> and l.l10 respectively.	This is equivalent to reducing the disc aspect ratios to $H/R \sim 2.2 \times 10^{-2}$, $1.7 \times 10^{-2}$ and $1.1 \times 10^{-2}$, respectively.
We reiterate that the boundary emperature is the same as the temperature of the initial disc and hence this setup not only changes the disc temperature olile. but it also changes the boundary temperature profile.	We reiterate that the boundary temperature is the same as the temperature of the initial disc and hence this setup not only changes the disc temperature profile, but it also changes the boundary temperature profile.
Furthermore. we consider a combination of the above actors by simulating clises with €i=0.75 and opacitics hat are 0.1. and 0.01. the interstellar opacity values.	Furthermore, we consider a combination of the above factors by simulating discs with $Q_{\rm min} = 0.75$ and opacities that are $0.1\times$ and $0.01\times$ the interstellar opacity values.
The unfavourable conditions for fragmentation at small radii have been discussed at great. length in the past (c.g.????7)..	The unfavourable conditions for fragmentation at small radii have been discussed at great length in the past \citep[e.g.][]{Rafikov_unrealistic_conditions, Stamatellos_no_frag_inside_40AU, Boley_CA_and_GI,Rafikov_SI,Clarke2009_analytical}.
We therefore expand: our parameter. space o include disces that are a factor of 12 larger with a radii range of 3xHox300A.	We therefore expand our parameter space to include discs that are a factor of 12 larger with a radii range of $3 \le R \le 300 \rm AU$.
These dises have the same mass as the 25AU dises ancl are set up so that Quin=1.	These discs have the same mass as the 25AU discs and are set up so that $Q_{\rm min}=1$.
We simulate three different opacity values (1:10. ancl 0.1 the interstellar Rosscland mean opacities).	We simulate three different opacity values $1\times, 10\times$ and $0.1\times$ the interstellar Rosseland mean opacities).
In addition. we also simulate a Large disc with Quin=0.75 with interstellar opacity values.	In addition, we also simulate a large disc with $Q_{\rm min} = 0.75$ with interstellar opacity values.
In order to keep these disc masses ancl initial Toomre stability profiles the same as the smaller 25AU. disces. we require both the surface. mass density anc absolute temperature to be reduced.	In order to keep these disc masses and initial Toomre stability profiles the same as the smaller 25AU discs, we require both the surface mass density and absolute temperature to be reduced.
Fhese clises are therefore not only larger. but also colder than their equivalent. (in terms of initial Toomre stability profiles) small clises.	These discs are therefore not only larger, but also colder than their equivalent (in terms of initial Toomre stability profiles) small discs.
‘The simulations have been analysed in three main wavs: (i) we compare the azimuthally averaged “Toone stability profiles of the initial and final (or in the case of [ragmenting cises. shortly before. fragmentation). discs which indicates whether the bulk of the dises were able to reach a state of thermal equilibrium: with their boundary.	The simulations have been analysed in three main ways: (i) we compare the azimuthally averaged Toomre stability profiles of the initial and final (or in the case of fragmenting discs, shortly before fragmentation) discs which indicates whether the bulk of the discs were able to reach a state of thermal equilibrium with their boundary.
The surface mass density does not change significantlv throughout the simulations anc hence. changes in the ‘Toone stability parameter are due to changes in the disc temperature.	The surface mass density does not change significantly throughout the simulations and hence changes in the Toomre stability parameter are due to changes in the disc temperature.
This enables us to determine which disces are more likely to fragment.	This enables us to determine which discs are more likely to fragment.
Note that we assume s,=O in equation (	Note that we assume $\kappa_{\rm ep} = \Omega$ in equation \ref{eq:Toomre}. (
i) we examine the timescale on which the disces coo (bx considering the energy passed. from. the gas to. the radiation within the cise as well as that which is assume to be instantly raciated away from the cise surface by the boundary particles).	ii) we examine the timescale on which the discs cool (by considering the energy passed from the gas to the radiation within the disc as well as that which is assumed to be instantly radiated away from the disc surface by the boundary particles).
In past simulations that have neglecte the heating elfects of stellar. irradiation. (e.g.22). the cooling. C'. in a steady-state disc balances the heating due to eravitational stresses. Z/04. and the heating due to artificia viscosity. Jf. such that If the artificial viscosity is low. Czc£o.	In past simulations that have neglected the heating effects of stellar irradiation \citep[e.g.][]{Gammie_betacool,Rice_beta_condition}, the cooling, $C$, in a steady-state disc balances the heating due to gravitational stresses, $H_{\rm GI}$, and the heating due to artificial viscosity, $H_{\rm \nu}$, such that If the artificial viscosity is low, $C \approx H_{\rm GI}$.
In this case.thecooling timescale in units of the orbital timescale. .7 (section 1)). can be related to the gravitational stress in the disc. oc C?) ? and ? have shown that the maximum gravitational stress that a disc can support is acy=0.06. bevond which fragmentation will occur.	In this case,thecooling timescale in units of the orbital timescale, $\beta$ (section \ref{sec:intro}) ), can be related to the gravitational stress in the disc, $\alpha_{GI}$ \citep{Gammie_betacool}: \cite{Gammie_betacool} and \cite{Rice_beta_condition} have shown that the maximum gravitational stress that a disc can support is $\alpha_{GI} = 0.06$, beyond which fragmentation will occur.
In clises that do not take into account heating duc to external irradiation. this condition is equivalent to requiring the cooling timescale in terms of the orbital timescale. 3. to be smaller than the critical values. described in section 1.. for fragmentation.	In discs that do not take into account heating due to external irradiation, this condition is equivalent to requiring the cooling timescale in terms of the orbital timescale, $\beta$, to be smaller than the critical values, described in section \ref{sec:intro}, for fragmentation.
In our steacky-state dises. not only does the cooling have to balance the heating due to the gravitational instabilities and the numerical viscosity. but it also has to balance the heating due to stellar irraciation. σι. such that: In what follows. we calculate the parameter. c. which	In our steady-state discs, not only does the cooling have to balance the heating due to the gravitational instabilities and the numerical viscosity, but it also has to balance the heating due to stellar irradiation, $H_{SI}$ such that: In what follows, we calculate the parameter, $\psi$ , which
to predict the LE LL bubble size. distribution. curing the reionization epoch.	to predict the H II bubble size distribution during the reionization epoch.
In Barkana(2007) we found an accurate analytical solution for the corresponding two-point problem of two correlated random walks with linear barriers. using the two-step approximation which Scannapieco&Barkana(2002) had applied to the two-point constant barrier problem.	In \citet{b07} we found an accurate analytical solution for the corresponding two-point problem of two correlated random walks with linear barriers, using the two-step approximation which \citet{sb} had applied to the two-point constant barrier problem.
Finding the joint. probability distribution of the density. and ionization state of two points allows the calculation of the 2lem correlation function. or power spectrum (Barkana2007).	Finding the joint probability distribution of the density and ionization state of two points allows the calculation of the 21-cm correlation function or power spectrum \citep{b07}.
. Following Purlanettoetal.(2004).. the appropriate oxwrier for reionization is found bv setting the ionized raction in a region C£! equal to unity. where Zug is he collapse fraction (i.e. the gas fraction in galactic halos) and & is the overall efficiency. factor. which is the number of ionizing photons that escape Lrom galactic halos per ivdrogen atom (or ion) contained in these halos.	Following \citet{fzh04}, the appropriate barrier for reionization is found by setting the ionized fraction in a region $\zeta F_{\rm coll}$ equal to unity, where $F_{\rm coll}$ is the collapse fraction (i.e., the gas fraction in galactic halos) and $\zeta$ is the overall efficiency factor, which is the number of ionizing photons that escape from galactic halos per hydrogen atom (or ion) contained in these halos.
This simple version of the model remains approximately valid even with recombinations if the ellective ¢ is divided. by one. plus he number of recombinations per hvdrogen atom in the IGAL assuming this factor is roughly uniform.	This simple version of the model remains approximately valid even with recombinations if the effective $\zeta$ is divided by one plus the number of recombinations per hydrogen atom in the IGM, assuming this factor is roughly uniform.
In order to ind fap a good starting point is the formula of ShethTormen (1999).. which accurately fits the cosmic mean 1alo abundance in simulations.	In order to find $F_{\rm coll}$, a good starting point is the formula of \citet{Sheth}, which accurately fits the cosmic mean halo abundance in simulations.
However. an exact analytical &eneralization is not known for the biased. δω in regions of various mean density [uctuation à.	However, an exact analytical generalization is not known for the biased $F_{\rm coll}$ in regions of various mean density fluctuation $\del$.
Barkana&Loch(2004) suggested a hybrid prescription hat adjusts the abundance in various regions based on he extended: Press-Schechter formula (Bondetal.1991).. and showed that it fits a broad. range of simulation results.	\citet{BLflucts} suggested a hybrid prescription that adjusts the abundance in various regions based on the extended Press-Schechter formula \citep{bc91}, and showed that it fits a broad range of simulation results.
In. general. we denote by f(9.(2).9)dS the mass raction contained at z within halos with mass in the range corresponding to variance S to S\|dS. where ὃς) is the critical density for halo collapse at z.	In general, we denote by $f(\del_c(z),S)\, dS$ the mass fraction contained at $z$ within halos with mass in the range corresponding to variance $S$ to $S+d S$, where $\del_c(z)$ is the critical density for halo collapse at $z$.
Phen the biased mass "unction in a region of size f? (corresponding todensity variance Sy) and mean density [luctuation 0 is (Barkana&Loeb2004) where firs and. for are. respectively. the Press-Schechter anc Sheth-VTormen halo mass functions.	Then the biased mass function in a region of size $R$ (corresponding todensity variance $S_R$ ) and mean density fluctuation $\del$ is \citep{BLflucts} where $f_{\rm PS}$ and $f_{\rm ST}$ are, respectively, the Press-Schechter and Sheth-Tormen halo mass functions.
The valuc of {μου(C).ὃςI.9) is the integral of fii over S. from 0 up o the value Syin that corresponds to the minimum halo mass My, or circular velocity Vi.=VOMwinHa (where Rey is the virial radius of a halo of mass Mj, at 2).	The value of $F_{\rm coll}(\del_c(z),\delta,R,S)$ is the integral of $f_{\rm bias}$ over $S$, from 0 up to the value $S_{\rm min}$ that corresponds to the minimum halo mass $M_{\rm min}$ or circular velocity $V_{\rm c}=\sqrt{G M_{\rm min}/R_{\rm vir}}$ (where $R_{\rm vir}$ is the virial radius of a halo of mass $M_{\rm min}$ at $z$ ).
We hen numerically find the value of o that gives Choy=1 at S=0 and its derivative with respect to S. vielding the incar approximation to the barrier: 605)z7\|ps.	We then numerically find the value of $\delta$ that gives $\zeta F_{\rm coll}=1$ at $S=0$ and its derivative with respect to $S$, yielding the linear approximation to the barrier: $\delta(S) \approx \nu + \mu S$.
Note hat Barkana(2007) and Darkana&Loeb(2008). used an approximation in which effectively each factor on the right-1and side of equation (1)) was integrated separately over 5. vielding a simple analytical formula for the ellective linear xurier.	Note that \citet{b07} and \citet{diffPDF} used an approximation in which effectively each factor on the right-hand side of equation \ref{eq:bias}) ) was integrated separately over $S$, yielding a simple analytical formula for the effective linear barrier.
Here we solve numerically for the barrier using the exact formulas (though the cillerence in the final results is small).	Here we solve numerically for the barrier using the exact formulas (though the difference in the final results is small).
ὃν the relonization epoch. there are expected. to. be sullicient. radiation. backgrounds of X-ravs and of Lya photons so that the cosmic gas has been heated to well above the cosmic microwave background. temperature and the 21-cm level occupations have come into equilibrium with the ea	By the reionization epoch, there are expected to be sufficient radiation backgrounds of X-rays and of $\alpha$ photons so that the cosmic gas has been heated to well above the cosmic microwave background temperature and the 21-cm level occupations have come into equilibrium with the gas temperature \citep{Madau}.
s temperature (Macauctal.1997)..	In this case, the observed 21-cm brightness temperature relative to the CMB is independent of the spin temperature and, for our assumed cosmological parameters, is given by \citep{Madau} T_b = _b(z) _b(z) = 25, with, where $x^n$ is the neutral hydrogen fraction and the linear overdensity at $z$ is the growth factor $D(z)$ times $\del$ (which is the density linearly extrapolated to redshift 0).
In this case. the obser	Under these conditions, the 21-cm power spectrum is thus $P_{21} = \tilde{T}_b^2 P_\Psi$, and thus a model of the relation between the density and the ionization is all that is needed for calculating the 21-cm power spectrum.
ved 21-em brightness	The analytical model thus consists of the following: For a given efficiency $\zeta$ and minimum halo circular velocity $V_{\rm c}$ at redshift $z$, find the corresponding linear barrier coefficients $\nu$ and $\mu$, calculate the 21-cm correlation function as a function of separation $d$ (where at each $d$ we numerically integrate equation (49) of \citet{b07})), and then Fourier transform to find the power spectrum at the desired values of $k$.
temperature relative t	Even with the analytical model, this procedure is too slow to apply directly in the $\chi^2$ fitting, but the power spectrum can be interpolated from a large precomputed table as a function of the three variables $\zeta$, $V_{\rm c}$, and $z$.
o the CALB is in	Note that our assumption of a fixed $\zeta$ (at a given $z$ ) for all halos above the minimum $V_{\rm c}$ is not as strong a restriction as it may appear.
dependent of the s	Since the halo mass function declines rapidly with mass at the high redshifts of the reionization era, once $V_{\rm c}$ is fixed, most of the ionizing sources are close in mass (i.e., within a factor of a few) to the minimum mass.
pin temperature and.	Thus, even if in the real universe $\zeta$ varies with mass at a given redshift, it is unlikely that the total ionized volume will receive large contributions from a wide range of halo masses.
for our as	With the basic setup just described, we are free to apply any values of $\zeta$ and $V_{\rm c}$ at various redshifts where the power spectrum can be observed.
sumed cosmo	The simplest model we use is thus a two-parameter model where $\zeta$ and $V_{\rm c}$ are both assumed to be constant with redshift.
logical parameters. is given	However, complex, time-variable feedbacks are likely to be operating during reionization, such as X-ray and UV photo-heating, supernovaeand stellar winds, metal enrichment (and the consequent changes in gas cooling and stellar populations), feedback from mini-quasars, and radiative feedbacks that affect $H_2$ formation and destruction.
by (Macauetal.	Many of these feedbacks involve scales that are far too small for direct numerical simulation, certainly within a cosmological context, so instead of trying to use particular models we prefer to parametrize our ignorance using additional free parameters.
1997) posee	The third parameter that we add is a coefficient that gives $V_{\rm c}$ a linear dependence on $z$, and the fourth allows a linear redshift-dependence in $\zeta$.
btepma ΠΠ”.	Similarly, a fifth and sixth parameter allow a quadratic redshift-dependence in $\zeta$ and $V_{\rm c}$, thus permitting these parameters to vary more flexibly with redshift (including a slope that may even change in sign during reionization).
11D]. where xà" is the ne	Our main goal is to see whether the 21-cm power spectrum can help determine both the reionization history and key properties of the ionizing sources, even if we allow for such flexible models of the ionizing sources with six free parameters that are not restricted based on specific models of feedback.
Numerical simulations of reionization are a rapidly developing field.	Numerical simulations of reionization are a rapidly developing field.
Current simulations are based. on purely eravitational N-bocky codes that are used to locate and weigh forming halos as a function of time.	Current simulations are based on purely gravitational N-body codes that are used to locate and weigh forming halos as a function of time.
Radiative transfer codes are then used to find the reionization topology clue o ionizing photons coming from the source halos.	Radiative transfer codes are then used to find the reionization topology due to ionizing photons coming from the source halos.
“Phus. simulations oller the potential advantages of fully realistic source halo distributions ancl accurate racliative transfer.	Thus, simulations offer the potential advantages of fully realistic source halo distributions and accurate radiative transfer.
tesources. though. are still stretched when attempts are made to resolve the smallest. source. halos while having sulliciently large. boxes for tracking ionizing photons with he longest mean free paths.	Resources, though, are still stretched when attempts are made to resolve the smallest source halos while having sufficiently large boxes for tracking ionizing photons with the longest mean free paths.
Also. while prospects are good or also including hydrodynamics. it seems that astrophysics or the foreseeable future must be included: schematically. as in an analvtical model.	Also, while prospects are good for also including hydrodynamics, it seems that astrophysics for the foreseeable future must be included schematically, as in an analytical model.
The important aspects of astrophysics that are inserted by. hand include at least. the star formation rate within each halo. properties of the stellar populations. supernova feedback. (including suppression of star formation. metal enrichment. ancl dust. formation). photo-heating feedback. and the escape of ionizing photons from each galaxy.	The important aspects of astrophysics that are inserted by hand include at least the star formation rate within each halo, properties of the stellar populations, supernova feedback (including suppression of star formation, metal enrichment, and dust formation), photo-heating feedback, and the escape of ionizing photons from each galaxy.
Since the analytical model we use is. limited. in using spherical statistics as à simple approximation for radiative transfer. it is useful to compare ijt to results of numerical simulations.	Since the analytical model we use is limited in using spherical statistics as a simple approximation for radiative transfer, it is useful to compare it to results of numerical simulations.
We compare our 21-cm power spectrum. predictions based on Barkana(2007) to those measured in numerical simulations of Zahnetal.(2007)simulation... Lievetal.(2008). ancl Santosetal.(2008). in Figures 1.. 2 and 3.. respectively.	We compare our 21-cm power spectrum predictions based on \citet{b07} to those measured in numerical simulations of \citet{zahn}, \citet{iliev} and \citet{santos} in Figures \ref{f:test1}, \ref{f:test2} and \ref{f:test3}, respectively.
For comparison. the figures also show the shape of the 21-cm power spectrum if it arose purely from density Huctuations: the normalization of these curves Corresponds to a uniformly ionizing universe (see also the next subsection).	For comparison, the figures also show the shape of the 21-cm power spectrum if it arose purely from density fluctuations; the normalization of these curves corresponds to a uniformly ionizing universe (see also the next subsection).
Phe figures show the brightness temperature [uctuation	The figures show the brightness temperature fluctuation .

The MP and the IP seen bv an observer originate at different phases of pulsar rotation. ancl therefore they. should arise al different phases of subpulse drift and the intensities should be correlated with a certain temporal delay.

The MP and the IP seen by an observer originate at different phases of pulsar rotation, and therefore they should arise at different phases of subpulse drift and the intensities should be correlated with a certain temporal delay.

It is worth noting that this delay should not exactly correspond to the longitudinal separation between the. MP. ancl IP in the profile. since (he components travel somewhat different distances to the observer.

It is worth noting that this delay should not exactly correspond to the longitudinal separation between the MP and IP in the profile, since the components travel somewhat different distances to the observer.

The microstructure characteristic of the MP emission is also expected to be present in (he scattered component.

The microstructure characteristic of the MP emission is also expected to be present in the scattered component.

The observations of PSR 0020-05 have indeed revealed the microstructure in the IP at the timescale τιν=90 i. whereas in the MP mip=130 ys (Hankins&Corcles1931:HankinsBoriakoll1981).

The observations of PSR B0950+08 have indeed revealed the microstructure in the IP at the timescale $\tau_{\rm IP}=90\,\mu$ s, whereas in the MP $\tau_{\rm MP}=130\,\mu$ s \citep{hc81,hb81}.

. In our model. the relationship between the microstructure timescales in the two components can be estimated as follows.

In our model, the relationship between the microstructure timescales in the two components can be estimated as follows.

The intensiv is translerred between thephoton states related as p(1—9cos0)=im(1-—»cos64).

The intensity is transferred between thephoton states related as $\nu (1-\beta\cos\theta)=\nu_1 (1-\beta\cos\theta_1)$.

Differentiating (his at fixed [requencies vields p/6.N9=r4. N22. where it is taken (hal [or θιεπ.

Differentiating this at fixed frequencies yields $\nu\theta\Delta\theta =\nu_1\Delta\theta^2$ , where it is taken that $\sin\theta_1\approx\Delta\theta_1$ for $\theta_1\approx\pi$.

As "p/Typ=AMALAND and vt?f2oviPV. one can find that TipVy 2/ν0.λ0,

As $\tau_{\rm IP}/\tau_{\rm MP}=\Delta\theta_1/\Delta\theta$ and $\nu\theta^2/2\approx 2\nu_1$, one can find that $\tau_{\rm IP}(\nu_1)/\tau_{\rm MP}(\nu)=2/\sqrt{\theta\Delta\theta}$ .

Taking into account that the microstructure timescaleevolves with [recquency.

Taking into account that the microstructure timescaleevolves with frequency,

The inferred miass-loss rates AL~10£M. vrἩ, is much higher than any reasonable mass-loss rate from au O-star primary and suggests that it is connected with the unusual short-lived pliase £133 is expericucing (see LL).

The inferred mass-loss rate, $\dot{M}\sim 10^{-4}\,M_{\odot}\,$ $^{-1}$, is much higher than any reasonable mass-loss rate from an O-star primary and suggests that it is connected with the unusual short-lived phase 433 is experiencing (see 4.1).

Tt could be mass loss from a common cuvelope that has already. started to form around the binary. or a hot coronal wind from the outer parts of the accretion disk driven. e.g. by the N-ray radiation from the central compact source.

It could be mass loss from a common envelope that has already started to form around the binary, or a hot coronal wind from the outer parts of the accretion disk driven, e.g., by the X-ray irradiation from the central compact source.

With unique sampling iu the UV-plane. we have imaged the L135 system at Gecu aud 2Ocem and securely detected at both wavelengths s1000thi eiission extending over a few hundred AU perpendicular to the jet axis.

With unique sampling in the UV-plane, we have imaged the 433 system at cm and cm and securely detected at both wavelengths smooth emission extending over a few hundred AU perpendicular to the jet axis.

The most likely interpretation of this radiation is enission frou matter which has been ejected from the disk as a thermal wind with an outward speed of ~3001s.1.

The most likely interpretation of this radiation is emission from matter which has been ejected from the disk as a thermal wind with an outward speed of $\sim 300\,{\rm km\,s^{-1}}$.

tthauks the Roval Society for a Uuiversity Research Fellowship.

thanks the Royal Society for a University Research Fellowship.

MERLIN is a unational facility operated by the University of Manchester ou behalf of PPARC.

MERLIN is a national facility operated by the University of Manchester on behalf of PPARC.

The VLBA aud VLA are facilities of NRAO operated by AUT. under cooperative agreement with the NSF.

The VLBA and VLA are facilities of NRAO operated by AUI, under cooperative agreement with the NSF.

systems domiuated by metal-rich globular clusters.

systems dominated by metal–rich globular clusters.

However. noue of these cases were as extreme as NGC 3311 was previously thowelt to be.

However, none of these cases were as extreme as NGC 3311 was previously thought to be.

The existetce of a blue (metal-poor) population iu these galaxies is not excluded by hese data (because of sinall sample statistics) but Gebhardt ]xissler-Patig suggest that it is not likely to be siguilicaut. as in IC. [051.

The existence of a blue (metal–poor) population in these galaxies is not excluded by these data (because of small sample statistics) but Gebhardt Kissler-Patig suggest that it is not likely to be significant, as in IC 4051.

Iu suminary. no system has yet been observed to have a globular cluster color distribution as extremely rec as the previous claiti lor NGC 3311.

In summary, no system has yet been observed to have a globular cluster color distribution as extremely red as the previous claim for NGC 3311.

In particular.dex.

In particular,.

NGC 3311 representecl the best case of an almost. excusively metal-rich globular cluster population.

NGC 3311 represented the best case of an almost exclusively metal–rich globular cluster population.

As such it raised serious questions about our un(lerstaucding of elobular cluster and ealaxy formation. since the existence of a metal-poor poptatiou is implicit in all the current sSCellarlos.

As such it raised serious questions about our understanding of globular cluster and galaxy formation, since the existence of a metal–poor population is implicit in all the current scenarios.

In the merger picture a1 elliptical galaxy. is formed. [ro idie merger of two gas-rich spiral sealaxies.

In the merger picture an elliptical galaxy is formed from the merger of two gas–rich spiral galaxies.

The resultaut galaxy contaius a blue. metal-poor )opulation of globular clusters from the progenitor spirals aud a uetal-rich population formed di‘ine tle mereer.

The resultant galaxy contains a blue, metal–poor population of globular clusters from the progenitor spirals and a metal–rich population formed during the merger.

In this scenario the metal-poor population shoud peak at the meclian metalliciM7 of “ilthe globular cluster systems of spiral galaxies. i.e. [Fe/H] —1.5 dex.

In this scenario the metal–poor population should peak at the median metallicity of the globular cluster systems of spiral galaxies, i.e. [Fe/H] $\sim -1.5$ dex.

It is generally recogiizecl. 1howh. that mergers are unlikely. by themselves. to result i iligh specilic (requeney. galaxie. slcl as NGC 3311 (Ashina1 Zepl L998: Forbes. Brodie Crithairy 1997).

It is generally recognized, though, that mergers are unlikely, by themselves, to result in high specific frequency galaxies, such as NGC 3311 (Ashman Zepf 1998; Forbes, Brodie Grillmair 1997).

In the multi-plase ρα.re. ie blue population is fo‘inecl in a pre-ealaxy pliase. or during galaxy assembly. [roii relatively iuenriched gas and so. by definition. is metal-poor.

In the multi–phase picture, the blue population is formed in a pre–galaxy phase, or during galaxy assembly, from relatively unenriched gas and so, by definition, is metal–poor.

The red globular clister population a1 the ilk of tje galaxy stars are formed later rou enriched material.

The red globular cluster population and the bulk of the galaxy stars are formed later from enriched material.

In the accretio1 model. the origial elliptical galaxy. (formed in a single 5) aceretes smaller (lower meallicitv) galaxies with tleir retiuues of low-metallicity globular clusters.

In the accretion model, the original elliptical galaxy (formed in a single burst) accretes smaller (lower metallicity) galaxies with their retinues of low–metallicity globular clusters.

αἱ galaxies at tlie ceuters o ‘rich galaxy «‘luste "Quay aso be expected to strip Globular clusters from the ouskirs of neighboring [n]galaxies.

Giant galaxies at the centers of rich galaxy clusters may also be expected to strip metal--poor globular clusters from the outskirts of neighboring galaxies.

Because of the globular cluster uean metallicity — pareut galaxy Undaity relation (BrocieandHuclra1991: accreted/stripped globulars must be. o1 average. of lower metallicity han those belonging to the "seed" elliptical.

Because of the globular cluster mean metallicity – parent galaxy luminosity relation \citep{bro91,for96} accreted/stripped globulars must be, on average, of lower metallicity than those belonging to the “seed” elliptical.

Coté.MarzkeandWest(1998) show bow accretion processes and the luminosity [uuction of galaxies will lead to bi-iuodal globular cluster systems iu bieht galaxies with blue ancl red peaks at [Fe/H] ~—1.5 aud ~—0.5 dex. as geerally observed.

\citet{cot98} show how accretion processes and the luminosity function of galaxies will lead to bi–modal globular cluster systems in bright galaxies with blue and red peaks at [Fe/H] $\sim -1.5$ and $\sim -0.5$ dex, as generally observed.

Sketchy arguments cau be imagined to accommodate au absence o ‘wetal-poor clusters wiltli any of the above formation scenarios.

Sketchy arguments can be imagined to accommodate an absence of metal–poor clusters within any of the above formation scenarios.

To produce oly. or predominanty. netal-rich clusters uu the "in situ scenario would require rapid star foru€ion prior to cluste ‘formation in the saine st: formation event.

To produce only, or predominantly, metal–rich clusters under the “in situ” scenario would require rapid star formation prior to cluster formation in the same star formation event.

Iun a deep gravitational potential te metals produced N the stars are retained aud the average metallicity of the system is driven to a igh value (see also Woodworth Harris 2000). conceivably before any clusters are formed.

In a deep gravitational potential, the metals produced by the stars are retained and the average metallicity of the system is driven to a high value (see also Woodworth Harris 2000), conceivably before any clusters are formed.

In acereion scenarios. the metal-poor population in the

In accretion scenarios, the metal–poor population in the

or temporal variations in the grain size distributions.

As with the Reference case. these disces are simulated. purely to analyse the energeties since we do not expect these disces to fragment.

As with the Reference case, these discs are simulated purely to analyse the energetics since we do not expect these discs to fragment.

We then choose to explore the initial and boundary temperature conditions by decreasing the magnitude of the disc temperature whilst maintaining the same surface mass clensity as the Reference case.

We then choose to explore the initial and boundary temperature conditions by decreasing the magnitude of the disc temperature whilst maintaining the same surface mass density as the Reference case.

We do this by changing the initial Foomre stability parameter profiles such that Quin=1.0.75 and 0.5 (simulations Qminl. OQmin0.75 and Qmin0.5. respectively).

We do this by changing the initial Toomre stability parameter profiles such that $Q_{\rm min} = 1, 0.75$ and $0.5$ (simulations Qmin1, Qmin0.75 and Qmin0.5, respectively).

This is equivalent to reducing the disc aspect ratios to ΗΝ~22.107. L7«10> and l.l10 respectively.

This is equivalent to reducing the disc aspect ratios to $H/R \sim 2.2 \times 10^{-2}$, $1.7 \times 10^{-2}$ and $1.1 \times 10^{-2}$, respectively.

We reiterate that the boundary emperature is the same as the temperature of the initial disc and hence this setup not only changes the disc temperature olile. but it also changes the boundary temperature profile.

We reiterate that the boundary temperature is the same as the temperature of the initial disc and hence this setup not only changes the disc temperature profile, but it also changes the boundary temperature profile.

Furthermore. we consider a combination of the above actors by simulating clises with €i=0.75 and opacitics hat are 0.1. and 0.01. the interstellar opacity values.

Furthermore, we consider a combination of the above factors by simulating discs with $Q_{\rm min} = 0.75$ and opacities that are $0.1\times$ and $0.01\times$ the interstellar opacity values.

The unfavourable conditions for fragmentation at small radii have been discussed at great. length in the past (c.g.????7)..

The unfavourable conditions for fragmentation at small radii have been discussed at great length in the past \citep[e.g.][]{Rafikov_unrealistic_conditions, Stamatellos_no_frag_inside_40AU, Boley_CA_and_GI,Rafikov_SI,Clarke2009_analytical}.

We therefore expand: our parameter. space o include disces that are a factor of 12 larger with a radii range of 3xHox300A.

We therefore expand our parameter space to include discs that are a factor of 12 larger with a radii range of $3 \le R \le 300 \rm AU$.

These dises have the same mass as the 25AU dises ancl are set up so that Quin=1.

These discs have the same mass as the 25AU discs and are set up so that $Q_{\rm min}=1$.

We simulate three different opacity values (1:10. ancl 0.1 the interstellar Rosscland mean opacities).

We simulate three different opacity values $1\times, 10\times$ and $0.1\times$ the interstellar Rosseland mean opacities).

In addition. we also simulate a Large disc with Quin=0.75 with interstellar opacity values.

In addition, we also simulate a large disc with $Q_{\rm min} = 0.75$ with interstellar opacity values.

In order to keep these disc masses ancl initial Toomre stability profiles the same as the smaller 25AU. disces. we require both the surface. mass density anc absolute temperature to be reduced.

In order to keep these disc masses and initial Toomre stability profiles the same as the smaller 25AU discs, we require both the surface mass density and absolute temperature to be reduced.

Fhese clises are therefore not only larger. but also colder than their equivalent. (in terms of initial Toomre stability profiles) small clises.

These discs are therefore not only larger, but also colder than their equivalent (in terms of initial Toomre stability profiles) small discs.

‘The simulations have been analysed in three main wavs: (i) we compare the azimuthally averaged “Toone stability profiles of the initial and final (or in the case of [ragmenting cises. shortly before. fragmentation). discs which indicates whether the bulk of the dises were able to reach a state of thermal equilibrium: with their boundary.

The simulations have been analysed in three main ways: (i) we compare the azimuthally averaged Toomre stability profiles of the initial and final (or in the case of fragmenting discs, shortly before fragmentation) discs which indicates whether the bulk of the discs were able to reach a state of thermal equilibrium with their boundary.

The surface mass density does not change significantlv throughout the simulations anc hence. changes in the ‘Toone stability parameter are due to changes in the disc temperature.

The surface mass density does not change significantly throughout the simulations and hence changes in the Toomre stability parameter are due to changes in the disc temperature.

This enables us to determine which disces are more likely to fragment.

This enables us to determine which discs are more likely to fragment.

Note that we assume s,=O in equation (

Note that we assume $\kappa_{\rm ep} = \Omega$ in equation \ref{eq:Toomre}. (

i) we examine the timescale on which the disces coo (bx considering the energy passed. from. the gas to. the radiation within the cise as well as that which is assume to be instantly raciated away from the cise surface by the boundary particles).

ii) we examine the timescale on which the discs cool (by considering the energy passed from the gas to the radiation within the disc as well as that which is assumed to be instantly radiated away from the disc surface by the boundary particles).

In past simulations that have neglecte the heating elfects of stellar. irradiation. (e.g.22). the cooling. C'. in a steady-state disc balances the heating due to eravitational stresses. Z/04. and the heating due to artificia viscosity. Jf. such that If the artificial viscosity is low. Czc£o.

In past simulations that have neglected the heating effects of stellar irradiation \citep[e.g.][]{Gammie_betacool,Rice_beta_condition}, the cooling, $C$, in a steady-state disc balances the heating due to gravitational stresses, $H_{\rm GI}$, and the heating due to artificial viscosity, $H_{\rm \nu}$, such that If the artificial viscosity is low, $C \approx H_{\rm GI}$.

In this case.thecooling timescale in units of the orbital timescale. .7 (section 1)). can be related to the gravitational stress in the disc. oc C?) ? and ? have shown that the maximum gravitational stress that a disc can support is acy=0.06. bevond which fragmentation will occur.

In this case,thecooling timescale in units of the orbital timescale, $\beta$ (section \ref{sec:intro}) ), can be related to the gravitational stress in the disc, $\alpha_{GI}$ \citep{Gammie_betacool}: \cite{Gammie_betacool} and \cite{Rice_beta_condition} have shown that the maximum gravitational stress that a disc can support is $\alpha_{GI} = 0.06$, beyond which fragmentation will occur.

In clises that do not take into account heating duc to external irradiation. this condition is equivalent to requiring the cooling timescale in terms of the orbital timescale. 3. to be smaller than the critical values. described in section 1.. for fragmentation.

In discs that do not take into account heating due to external irradiation, this condition is equivalent to requiring the cooling timescale in terms of the orbital timescale, $\beta$, to be smaller than the critical values, described in section \ref{sec:intro}, for fragmentation.

In our steacky-state dises. not only does the cooling have to balance the heating due to the gravitational instabilities and the numerical viscosity. but it also has to balance the heating due to stellar irraciation. σι. such that: In what follows. we calculate the parameter. c. which

In our steady-state discs, not only does the cooling have to balance the heating due to the gravitational instabilities and the numerical viscosity, but it also has to balance the heating due to stellar irradiation, $H_{SI}$ such that: In what follows, we calculate the parameter, $\psi$ , which

to predict the LE LL bubble size. distribution. curing the reionization epoch.

to predict the H II bubble size distribution during the reionization epoch.

In Barkana(2007) we found an accurate analytical solution for the corresponding two-point problem of two correlated random walks with linear barriers. using the two-step approximation which Scannapieco&Barkana(2002) had applied to the two-point constant barrier problem.

In \citet{b07} we found an accurate analytical solution for the corresponding two-point problem of two correlated random walks with linear barriers, using the two-step approximation which \citet{sb} had applied to the two-point constant barrier problem.

Finding the joint. probability distribution of the density. and ionization state of two points allows the calculation of the 2lem correlation function. or power spectrum (Barkana2007).

Finding the joint probability distribution of the density and ionization state of two points allows the calculation of the 21-cm correlation function or power spectrum \citep{b07}.

. Following Purlanettoetal.(2004).. the appropriate oxwrier for reionization is found bv setting the ionized raction in a region C£! equal to unity. where Zug is he collapse fraction (i.e. the gas fraction in galactic halos) and & is the overall efficiency. factor. which is the number of ionizing photons that escape Lrom galactic halos per ivdrogen atom (or ion) contained in these halos.

Following \citet{fzh04}, the appropriate barrier for reionization is found by setting the ionized fraction in a region $\zeta F_{\rm coll}$ equal to unity, where $F_{\rm coll}$ is the collapse fraction (i.e., the gas fraction in galactic halos) and $\zeta$ is the overall efficiency factor, which is the number of ionizing photons that escape from galactic halos per hydrogen atom (or ion) contained in these halos.

This simple version of the model remains approximately valid even with recombinations if the ellective ¢ is divided. by one. plus he number of recombinations per hvdrogen atom in the IGAL assuming this factor is roughly uniform.

This simple version of the model remains approximately valid even with recombinations if the effective $\zeta$ is divided by one plus the number of recombinations per hydrogen atom in the IGM, assuming this factor is roughly uniform.

In order to ind fap a good starting point is the formula of ShethTormen (1999).. which accurately fits the cosmic mean 1alo abundance in simulations.

In order to find $F_{\rm coll}$, a good starting point is the formula of \citet{Sheth}, which accurately fits the cosmic mean halo abundance in simulations.

However. an exact analytical &eneralization is not known for the biased. δω in regions of various mean density [uctuation à.

However, an exact analytical generalization is not known for the biased $F_{\rm coll}$ in regions of various mean density fluctuation $\del$.

Barkana&Loch(2004) suggested a hybrid prescription hat adjusts the abundance in various regions based on he extended: Press-Schechter formula (Bondetal.1991).. and showed that it fits a broad. range of simulation results.

\citet{BLflucts} suggested a hybrid prescription that adjusts the abundance in various regions based on the extended Press-Schechter formula \citep{bc91}, and showed that it fits a broad range of simulation results.

In. general. we denote by f(9.(2).9)dS the mass raction contained at z within halos with mass in the range corresponding to variance S to S|dS. where ὃς) is the critical density for halo collapse at z.

In general, we denote by $f(\del_c(z),S)\, dS$ the mass fraction contained at $z$ within halos with mass in the range corresponding to variance $S$ to $S+d S$, where $\del_c(z)$ is the critical density for halo collapse at $z$.

Phen the biased mass "unction in a region of size f? (corresponding todensity variance Sy) and mean density [luctuation 0 is (Barkana&Loeb2004) where firs and. for are. respectively. the Press-Schechter anc Sheth-VTormen halo mass functions.

Then the biased mass function in a region of size $R$ (corresponding todensity variance $S_R$ ) and mean density fluctuation $\del$ is \citep{BLflucts} where $f_{\rm PS}$ and $f_{\rm ST}$ are, respectively, the Press-Schechter and Sheth-Tormen halo mass functions.

The valuc of {μου(C).ὃςI.9) is the integral of fii over S. from 0 up o the value Syin that corresponds to the minimum halo mass My, or circular velocity Vi.=VOMwinHa (where Rey is the virial radius of a halo of mass Mj, at 2).

The value of $F_{\rm coll}(\del_c(z),\delta,R,S)$ is the integral of $f_{\rm bias}$ over $S$, from 0 up to the value $S_{\rm min}$ that corresponds to the minimum halo mass $M_{\rm min}$ or circular velocity $V_{\rm c}=\sqrt{G M_{\rm min}/R_{\rm vir}}$ (where $R_{\rm vir}$ is the virial radius of a halo of mass $M_{\rm min}$ at $z$ ).

We hen numerically find the value of o that gives Choy=1 at S=0 and its derivative with respect to S. vielding the incar approximation to the barrier: 605)z7|ps.

We then numerically find the value of $\delta$ that gives $\zeta F_{\rm coll}=1$ at $S=0$ and its derivative with respect to $S$, yielding the linear approximation to the barrier: $\delta(S) \approx \nu + \mu S$.

Note hat Barkana(2007) and Darkana&Loeb(2008). used an approximation in which effectively each factor on the right-1and side of equation (1)) was integrated separately over 5. vielding a simple analytical formula for the ellective linear xurier.

Note that \citet{b07} and \citet{diffPDF} used an approximation in which effectively each factor on the right-hand side of equation \ref{eq:bias}) ) was integrated separately over $S$, yielding a simple analytical formula for the effective linear barrier.

Here we solve numerically for the barrier using the exact formulas (though the cillerence in the final results is small).

Here we solve numerically for the barrier using the exact formulas (though the difference in the final results is small).

ὃν the relonization epoch. there are expected. to. be sullicient. radiation. backgrounds of X-ravs and of Lya photons so that the cosmic gas has been heated to well above the cosmic microwave background. temperature and the 21-cm level occupations have come into equilibrium with the ea

By the reionization epoch, there are expected to be sufficient radiation backgrounds of X-rays and of $\alpha$ photons so that the cosmic gas has been heated to well above the cosmic microwave background temperature and the 21-cm level occupations have come into equilibrium with the gas temperature \citep{Madau}.

s temperature (Macauctal.1997)..

In this case, the observed 21-cm brightness temperature relative to the CMB is independent of the spin temperature and, for our assumed cosmological parameters, is given by \citep{Madau} T_b = _b(z) _b(z) = 25, with, where $x^n$ is the neutral hydrogen fraction and the linear overdensity at $z$ is the growth factor $D(z)$ times $\del$ (which is the density linearly extrapolated to redshift 0).

In this case. the obser

Under these conditions, the 21-cm power spectrum is thus $P_{21} = \tilde{T}_b^2 P_\Psi$, and thus a model of the relation between the density and the ionization is all that is needed for calculating the 21-cm power spectrum.

ved 21-em brightness

The analytical model thus consists of the following: For a given efficiency $\zeta$ and minimum halo circular velocity $V_{\rm c}$ at redshift $z$, find the corresponding linear barrier coefficients $\nu$ and $\mu$, calculate the 21-cm correlation function as a function of separation $d$ (where at each $d$ we numerically integrate equation (49) of \citet{b07})), and then Fourier transform to find the power spectrum at the desired values of $k$.

temperature relative t

Even with the analytical model, this procedure is too slow to apply directly in the $\chi^2$ fitting, but the power spectrum can be interpolated from a large precomputed table as a function of the three variables $\zeta$, $V_{\rm c}$, and $z$.

o the CALB is in

Note that our assumption of a fixed $\zeta$ (at a given $z$ ) for all halos above the minimum $V_{\rm c}$ is not as strong a restriction as it may appear.

dependent of the s

Since the halo mass function declines rapidly with mass at the high redshifts of the reionization era, once $V_{\rm c}$ is fixed, most of the ionizing sources are close in mass (i.e., within a factor of a few) to the minimum mass.

pin temperature and.

Thus, even if in the real universe $\zeta$ varies with mass at a given redshift, it is unlikely that the total ionized volume will receive large contributions from a wide range of halo masses.

for our as

With the basic setup just described, we are free to apply any values of $\zeta$ and $V_{\rm c}$ at various redshifts where the power spectrum can be observed.

sumed cosmo

The simplest model we use is thus a two-parameter model where $\zeta$ and $V_{\rm c}$ are both assumed to be constant with redshift.

logical parameters. is given

However, complex, time-variable feedbacks are likely to be operating during reionization, such as X-ray and UV photo-heating, supernovaeand stellar winds, metal enrichment (and the consequent changes in gas cooling and stellar populations), feedback from mini-quasars, and radiative feedbacks that affect $H_2$ formation and destruction.

by (Macauetal.

Many of these feedbacks involve scales that are far too small for direct numerical simulation, certainly within a cosmological context, so instead of trying to use particular models we prefer to parametrize our ignorance using additional free parameters.

1997) posee

The third parameter that we add is a coefficient that gives $V_{\rm c}$ a linear dependence on $z$, and the fourth allows a linear redshift-dependence in $\zeta$.

btepma ΠΠ”.

Similarly, a fifth and sixth parameter allow a quadratic redshift-dependence in $\zeta$ and $V_{\rm c}$, thus permitting these parameters to vary more flexibly with redshift (including a slope that may even change in sign during reionization).

11D]. where xà" is the ne

Our main goal is to see whether the 21-cm power spectrum can help determine both the reionization history and key properties of the ionizing sources, even if we allow for such flexible models of the ionizing sources with six free parameters that are not restricted based on specific models of feedback.

Numerical simulations of reionization are a rapidly developing field.

Current simulations are based. on purely eravitational N-bocky codes that are used to locate and weigh forming halos as a function of time.

Current simulations are based on purely gravitational N-body codes that are used to locate and weigh forming halos as a function of time.

Radiative transfer codes are then used to find the reionization topology clue o ionizing photons coming from the source halos.

Radiative transfer codes are then used to find the reionization topology due to ionizing photons coming from the source halos.

“Phus. simulations oller the potential advantages of fully realistic source halo distributions ancl accurate racliative transfer.

Thus, simulations offer the potential advantages of fully realistic source halo distributions and accurate radiative transfer.

tesources. though. are still stretched when attempts are made to resolve the smallest. source. halos while having sulliciently large. boxes for tracking ionizing photons with he longest mean free paths.

Resources, though, are still stretched when attempts are made to resolve the smallest source halos while having sufficiently large boxes for tracking ionizing photons with the longest mean free paths.

Also. while prospects are good or also including hydrodynamics. it seems that astrophysics or the foreseeable future must be included: schematically. as in an analvtical model.

Also, while prospects are good for also including hydrodynamics, it seems that astrophysics for the foreseeable future must be included schematically, as in an analytical model.

The important aspects of astrophysics that are inserted by. hand include at least. the star formation rate within each halo. properties of the stellar populations. supernova feedback. (including suppression of star formation. metal enrichment. ancl dust. formation). photo-heating feedback. and the escape of ionizing photons from each galaxy.

The important aspects of astrophysics that are inserted by hand include at least the star formation rate within each halo, properties of the stellar populations, supernova feedback (including suppression of star formation, metal enrichment, and dust formation), photo-heating feedback, and the escape of ionizing photons from each galaxy.

Since the analytical model we use is. limited. in using spherical statistics as à simple approximation for radiative transfer. it is useful to compare ijt to results of numerical simulations.

Since the analytical model we use is limited in using spherical statistics as a simple approximation for radiative transfer, it is useful to compare it to results of numerical simulations.

We compare our 21-cm power spectrum. predictions based on Barkana(2007) to those measured in numerical simulations of Zahnetal.(2007)simulation... Lievetal.(2008). ancl Santosetal.(2008). in Figures 1.. 2 and 3.. respectively.

We compare our 21-cm power spectrum predictions based on \citet{b07} to those measured in numerical simulations of \citet{zahn}, \citet{iliev} and \citet{santos} in Figures \ref{f:test1}, \ref{f:test2} and \ref{f:test3}, respectively.

For comparison. the figures also show the shape of the 21-cm power spectrum if it arose purely from density Huctuations: the normalization of these curves Corresponds to a uniformly ionizing universe (see also the next subsection).

For comparison, the figures also show the shape of the 21-cm power spectrum if it arose purely from density fluctuations; the normalization of these curves corresponds to a uniformly ionizing universe (see also the next subsection).

Phe figures show the brightness temperature [uctuation

The figures show the brightness temperature fluctuation .