Primordial Globular Clusters, X-Ray Binaries & Cosmological Reionisation
aa r X i v : . [ a s t r o - ph . C O ] F e b Mon. Not. R. Astron. Soc. , 1–8 (2009) Printed 30 October 2018 (MN L A TEX style file v2.2)
Primordial Globular Clusters, X-Ray Binaries &Cosmological Reionisation
C. Power ⋆ , G. A. Wynn, C. Combet & M. I. Wilkinson Department of Physics & Astronomy, University of Leicester, Leicester LE1 7RH, United Kingdom
ABSTRACT
Globular clusters are dense stellar systems that have typical ages of ∼
13 billion years,implying that they formed during the early epochs of galaxy formation at redshifts of z ∼ >
6. Massive stars in newly formed or primordial globular clusters could have playedan important role during the epoch of cosmological reionisation ( z ∼ >
6) as sources ofenergetic, neutral hydrogen ionising UV photons. We investigate whether or not thesestars could have been as important in death as sources of energetic X-ray photons asthey were during their main sequence lives. Most massive stars are expected to formin binaries, and an appreciable fraction of these (as much as ∼ L X ∼ erg/s) high-mass X-ray binaries (HMXBs). These sourceswould have made a contribution to the X-ray background at z ∼ > ∼ erg/sduring the first few million years, but declines to ∼ erg/s after ∼ ∼ erg/s after ∼
50 million years. Assuming a power-law spectral energy distribution forthe HMXBs, we calculate the effective number of neutral hydrogen ionisations perHMXB and show that HMXBs can be as important as sources of ionising radiation asmassive stars. Finally we discuss the implications of our results for modelling galaxyformation at high redshift and the prospects of using globular clusters as probes ofreionisation.
Key words: globular clusters: general – galaxies: formation – X-rays: binaries –cosmology:theory
Hydrogen is the most abundant element in the Universe andit is fundamental to galaxy formation, representing the prin-cipal raw material from which stars form. Approximately16% of the matter content of the Universe at present is bary-onic (cf. Spergel et al. 2007), of which about 0.34% is coldgas (most of which is atomic and molecular hydrogen; cf.Table 1 of Fukugita & Peebles 2004). From these numberswe conclude that the bulk of cosmic hydrogen is ionised atpresent, yet there must have been a period early in the his-tory of the Universe when the bulk of hydrogen was neu-tral. This is supported by a range of observational data thatprovides strong and compelling evidence that the Universeunderwent an “Epoch of Reionisation” that was completeby z ∼
6, approximately 1 billion years after the Big Bang ⋆ [email protected] (e.g. Becker et al. 2001; Spergel et al. 2007). During thisperiod the cosmic abundance of neutral hydrogen declineddramatically, “re-ionised” by a background of ionising UVand X-ray radiation whose build-up was very likely linked tothe formation of the first generations of stars and galaxies(e.g. Barkana & Loeb 2007).Understanding the precise nature of the sources of thisionising radiation background remains an important yetlargely unsolved problem facing modellers of galaxy forma-tion. It is important because reionisation is expected to havehad a dramatic impact on galaxy formation. The presenceof a photo-ionising background can inhibit the collapse ofbaryons onto low-mass dark matter haloes (e.g. Efstathiou1992; Thoul & Weinberg 1996) and suppress radiative cool-ing and subsequent star formation within dark matter haloes(e.g. Benson et al. 2002a). Reionisation has been invokedto reconcile the apparent disparity between the observedabundance of satellite galaxies in the Local Group with the c (cid:13) C. Power, G. A. Wynn, C. Combet, M. I. Wilkinson abundance inferred from simulations of galaxy halo forma-tion within the favoured Cold Dark Matter framework (e.g.Benson et al. 2002b). In addition, there is good reason tobelieve that reionisation was also important in shaping thefaint end of the luminosity function (e.g. Benson & Madau2003), the clustering of galaxies (e.g. Wyithe & Loeb 2007),the low-mass end of the HI mass function, and perhaps thespatial distribution of globular clusters (e.g. Moore et al.2006).However, despite its importance for galaxy formation,reionisation remains a largely unsolved problem becausevery little is known about the sources of re-ionising radia-tion. This is because it is technically challenging to observedirectly the Universe at z ∼ >
6, and will remain so untilthe advent of next generation instruments such as LOFAR(e.g. R¨ottgering 2003; Zaroubi & Silk 2005) and JWST (e.g.Windhorst et al. 2006; Haiman 2008). Therefore much ofour understanding of the properties of potential sources ofreionising radiation comes from a combination of cosmolog-ical simulations (e.g. Ricotti & Ostriker 2004; Sokasian etal. 2004) and (semi-)analytical galaxy formation modelling(e.g. Benson et al. 2006; Zaroubi et al. 2007), whose predic-tions can be tested against limits inferred from the spectralenergy density of the radiation background at high redshifts(e.g. Dijkstra et al. 2004) and the electron-scattering opti-cal depth of the cosmic microwave background τ e (e.g. Shull& Venkatesan 2008). Not unexpectedly, UV luminous mas-sive stars (e.g. Wyithe & Loeb 2003; Sokasian et al. 2004;Wise & Abel 2008) and systems in which there is accretiononto X-ray luminous intermediate mass and supermassiveblack holes (e.g. Ricotti & Ostriker 2004; Ricotti et al. 2005;Zaroubi et al. 2007) have been suggested as likely sourcesof the ionising radiation background. However, there aremany unanswered questions about the nature and origin ofthese ionising sources, and without direct observations ofthe galaxy population at z ∼ > ∼
13 billion yearsold). They appear to be relatively simple systems – theirstellar populations appear to be generally coeval, formingin one or more bursts, and many aspects of their dynami-cal evolution have been studied in detail by direct N -bodymethods (see, for example, Hurley et al. 2007, Praagman,Hurley & Power 2008).This apparent simplicity has led globular clusters to beused increasingly as probes of high redshift galaxy formation(see, for example, the review of Brodie & Strader 2006) be-cause they may, in principle, tell us about the conditions inwhich galaxy formation proceeded at early times. For ex-ample, the inferred ages of old metal poor globular clustersimplies that these systems formed at a time when the Uni-verse was undergoing reionisation. Reionisation is expectedto quench star formation and therefore globular cluster for-mation, and so it has been suggested that present-day spatialdistribution of metal poor globular clusters around galaxiescan be used to measure the redshift of cosmological reioni-sation (e.g. Moore et al. 2006; Bekki & Yahagi 2006).However, globular clusters themselves may be sources of ionising radiation and they could be potentially impor-tant for cosmological reionisation. Ricotti (2002) (hereafterR02) has pointed out that massive stars in primordial glob-ular clusters at high redshifts are extremely luminous atUV wavelengths, which means that they could have beeneffective ionising sources of neutral hydrogen provided theradiation could escape freely from its source (e.g. Ricotti& Shull 2000; Benson et al. 2006). Globular clusters tendto reside on the outskirts of galaxies at the present epochand if this was the case at early times then the fraction ofemitted ionising UV photons that can escape without be-ing scattered or absorbed would have been significant. R02estimated that massive stars in a primordial globular clus-ter could emit UV photons sufficiently energetic to ioniseatomic hydrogen ( E γ > . N γ ∼ × s − over the first 4 million years; this is equivalent to a massof hydrogen of between ∼ M ⊙ and ∼ M ⊙ , dependingon the local recombination rate (cf. Dijkstra et al. 2004).Massive stars in the local Universe tend to form withone or more companions (e.g. Raboud 1996; Mason et al.1998; Delgado-Donate et al. 2004), and this was likely tobe the case in primordial globular clusters. Massive bina-ries may evolve into high mass X-ray binaries (hereafterHMXBs) once the more massive star collapses to form acompact object, either a neutron star or a black hole. Thiscompact object accretes material from its companion, eithervia a stellar wind or Roche lobe overflow (RLOF), which re-sults in X-ray emission. The HMXB phase is believed tooccur soon after the first compact object is formed and itsduration is limited by the main sequence lifetime of the sec-ondary, typically ∼ years. HMXBs in our Galaxy areobserved to emit strongly in X-rays, with typical luminosi-ties of L X ∼ − erg s − (cf. Liu et al. 2006), andthere is good reason to believe that HMXBs in primordialglobular clusters at high redshifts would have been as lumi-nous, if not more so (e.g. Dray et al. 2006).This is very interesting because it suggests that mas-sive stars in globular clusters could have been important assources of both ionising UV radiation and X-rays during theepoch of cosmological radiation. Certainly, primordial glob-ular clusters would have formed an abundance of UV lumi-nous massive stars that would have had a profound impacton cold star-forming gas in their immediate surroundings.However, could primordial globular clusters have formed suf-ficient numbers of HMXBs to make an interesting contribu-tion to the ionising X-ray background during the epoch ofreionisation? Whereas UV photons are readily absorbed byneutral hydrogen, X-rays are much more penetrating (thephoto-ionising absorption cross section of neutral hydrogendecreases with photon energy roughly as E − γ ) and can es-cape into the inter-galactic medium.In this paper we consider what fraction of massive starsin primordial globular clusters must evolve into HMXBs forthese sources to make a significant contribution to the X-ray ionising background. We address this question using aMonte Carlo model of a primordial globular cluster of mass10 M ⊙ . We assume that all massive stars form in binaries(see, for example, Dray 2006) and explore what fraction ofthese binaries must eventually form HMXBs to be an im-portant source of reionising photons.The layout of the paper is as follows; in § c (cid:13) , 1–8 rimordial Globular Clusters, XRBs & Reionisation ries that survive to evolve into HMXBs ( f sur ) and, providedthey survive, their X-ray luminosities. In § § In the following subsections, we consider the factors thatregulate the formation of high mass X-ray binaries ( § § § f sur Not all massive binaries will evolve to become HMXBs. If amassive binary is to survive and become a HMXB, then thestars in the binary must not merge during the more mas-sive stars’ main sequence (MS) and post-MS evolution, andthe binary must survive the supernova of the more massivestar. Whether or not a massive binary merges during the MSlifetime of the more massive star is determined principallyby the details of stellar evolution at low metallicities andthe initial binary separation. If the binary survives withoutmerging, then the issue of whether or not the binary survivesthe first supernova depends on a number of factors, includ-ing the precise mass of the more massive star, the fractionof mass lost during the supernova and the kick velocity im-parted during the supernova. However, binary evolution inglobular clusters at very low metallicities is not particularlywell understood. Examples of complicating factors includethe fact that lower metallicity stars are expected to retainmore of their mass because stellar winds are inefficient atlow metallicities; therefore these stars will be more massiveat the end of their main sequence lives and will form blackholes rather than neutron stars (cf. Heger et al. 2003b). Thisis consistent with the expectation that the ratio of black holeto neutron star remnants is much higher at low metallicities(e.g. Heger & Woosley 2008). Also, less mass is lost duringthe supernova when the remnant is a black hole rather thana neutron star, and black holes may suffer less violent natalkicks. These arguments suggest that binaries that surviveto become HMXBs in primordial globular clusters are morelikely to contain black holes, which suggests in turn thatthey could be more X-ray luminous than typical HMXBsin the local Universe, which are dominated by neutron starsystems.To avoid some of the uncertainty surrounding the stel-lar physics in primordial globular clusters we introduce asurvival fraction f sur which indicates the likelihood of anindividual binary becoming an HMXB. For each primordialbinary, we determine whether or not the binary will remainbound when the more massive star goes supernova by esti-mating the fraction of mass lost in the supernova explosion; if the binary remains bound, then it has a probability of f sur that it will evolve into a HMXB. We find that typically 70%of high-mass binaries become unbound following the super-nova of the more massive star, and so at most ∼
30% of theinitial binary population will evolve to become HMXBs. Wenote that those that survive tend to host black holes ratherthan neutron stars. It is the fraction f sur of this remaining ∼
30% of bound binaries which go on to become HMXBs.This approach allows us to investigate the potential effec-tiveness of HXMBs as sources of reionising radiation in arobust manner, even if the factors that determine the valueof f sur are not well understood, we can speculate on whatthe most important determinants of f sur are likely to be. We wish to assess the potential importance of the HMXBpopulation in globular clusters for the X-ray backgroundat high redshifts, and so we require a model of the stellarpopulation in a typical globular cluster. We use a MonteCarlo model of a globular cluster of 10 stars and follow theevolution of its population of massive stars over its first 100million years, through their main sequence lives and intothe HMXB phase. The main features of our model can besummarised as follows; • The Initial Mass Function.
We adopt three differ-ent IMFs – those of Salpeter (1955), Kroupa (2001) andChabrier (2001) – with lower and upper mass cut-offs of0 . ⊙ and 100M ⊙ respectively. The most important pre-requisite for a HMXB to form is that the primary is eithera neutron star or a black hole, which sets a lower mass limitof M ∼ > ⊙ for the primary (cf. Figure 1 of Heger et al.2003a); this is the threshold for neutron star formation. Themean number of stars with masses in excess of 8 M ⊙ and 20M ⊙ (the threshold for black hole formation) are for Salpeter2621 (753), for Kroupa 11126 (3174) and for the top-heavyChabrier 131935 (27024). • Binary Formation.
We assume that all massive starsform in binaries. Initial binary orbital parameters are as-signed following the approach of Dray (2006) – companionmasses are drawn from a uniform distribution between 0.1and 100 M ⊙ and orbital periods are distributed uniformlyin logarithm between 1 and 10 days. • Massive Star Lifetimes.
Massive stars have shortmain sequence lifetimes, the duration of which are deter-mined principally by their metallicity. We obtain estimatesfor these lifetimes using the results of Ekstr¨om et al. (2008),Schaerer et al. (1993) and Meynet & Maeder (2000) for Z=0,0.008 and 0.02 (i.e. solar metalicity) respectively. • HMXB Formation.
When the more massive star inthe binary reaches the end of its main sequence lifetime, weassume that it goes supernova and forms either a neutronstar or black hole. The remnant’s mass – which is determinedby the mass of the star at the end of its main sequence life– is estimated following Figure 3 of (Heger et al. 2003a). Wecalculate revised binary parameters (i.e. semi-major axis andperiod) although there are additional factors which compli-cate matters (e.g. velocity kick imparted by the supernova).If the system loses more than half its mass in the supernova,it becomes unbound and we remove it from the list of po- c (cid:13) , 1–8 C. Power, G. A. Wynn, C. Combet, M. I. Wilkinson
Figure 1. Variation of Total Bolometric Luminosity withTime . The light dotted curve corresponds to the contribution ofmassive stars during their main sequence lives, while the dashedcurve corresponds to the contribution of the HMXBs. The solidcurve indicates the net luminosity. tential HMXB candidates; this removes ∼
70% of binariesfrom consideration if we assume a Kroupa IMF. We thendraw a fraction f sur of the remaining ∼
30% at random andconsider them as HMXBs. • HMXB Luminosities.
If a binary survives and formsan HMXB, we estimate its X-ray luminosity. Although bi-nary parameters are likely to play a role in determining theX-ray luminosity (see, for example, Dray 2006), we take asimpler approach, drawing luminosities from a Weibull dis-tribution with a peak fixed at L X ∼ erg/s but pre-venting a HMXB from accreting at greater than its Ed-dington limit. This sets an upper limit of approximately L X ≃ . × ( M/ M ⊙ ) erg/s. We note that this is con-sistent with the luminosities of compact X-ray sources innearby galaxies whose X-ray binary populations are domi-nated by HMXBs (cf. Figure 1 of Gilfanov et al. 2004); see § • HMXB Lifetimes.
We assume that HMXBs are activeuntil the companion star evolves off the main sequence andgoes supernova.Note that although we investigate the sensitivity of ourmodel’s results to the choice of IMF (i.e. Salpeter, Kroupa orChabrier), for clarity we concentrate on models that assumethe Kroupa IMF only.In Figure 1 we show how the total bolometric luminos-ity of our model cluster varies with time, where we haveassumed that f sur =1, i.e. all of the ∼
30% of the initialmassive binary population that remain bound after the pri-mary goes supernova. During the first few million years theluminosity is dominated by the contribution from massivestars, but this declines rapidly as these massive stars evolveoff the main sequence and in some cases become HMXBs.The HMXB contribution grows rapidly once the most mas-sive main sequence stars go supernova (after ∼ . ∼ ∼ erg/s during the first few million years, but itdeclines rapidly and has dropped to ∼ erg/s after ∼ ∼ ∼
30 over the next ∼
80 mil-lion years, during which time the luminosity is dominatedby the contribution of HMXBs. From this we may concludethat massive stars are indeed energetic sources of radiationduring their MS lives and in terms of their total bolometricluminosity they produce as much energy as HMXBs, whosecontribution extends over a much longer period.
The total bolometric luminosity is an interesting number,but what fraction of this energy is available to ionise neutralhydrogen? We compute the total number of ionising photonsemitted per second by both massive stars during their mainsequence lives and by HMXBs and show its variation withtime over the first 100 million years of the globular cluster’slife in Figure 2. We model the ionising luminosity of massivestars using the
Starburst99 code (cf. Leitherer et al. 1999) forthe specific case of a cluster of 10 stars, assuming that all ofthe stars were formed in an instantaneous burst and Genevatracks with high mass loss for metallicities of Z =0.001, 0.008and 0.02 (i.e. solar). The ionising luminosity of HMXBs iscalculated by assuming a spectral energy distribution thatfollows a simple power-law F ( E ) ∝ E − α between lower andupper energy cut-offs of E min =0.1 eV and E max =10 eVrespectively. The total energy liberated during accretion isthen E tot = ( A/ (2 − α ))( E − α max − E − α min )and so given the luminosity it is straightforward to computethe normalisation constant A for a given HMXB. We esti-mate the effective number of hydrogen ionising photons tobe N γ, eff = (13 . − Z E lim . F(E)dE (1)where E lim is the energy above which the mean free pathof photons becomes of order the Hubble length (i.e. atomichydrogen becomes transparent to hard X-rays). We obtain E lim by requiring that σ ( E lim ) = ( H ( z ) /c ) /n ( z ) where σ ( E )is the ionisation cross section of neutral hydrogen, H ( z ) isthe Hubble parameter at redshift z , n ( z ) is the mean baryondensity and c is the speed of light. For the redshifts in ques-tion ( z ∼ >
6) we find that E lim ∼ > E lim has relatively little impact on N γ . Equation 1makes the simple assumption that an energetic photon canionise multiple hydrogen atoms, and so we treat secondaryelectrons that ionise hydrogen atoms as effective photons.In Figure 2 we show how the rate of emission of ionis-ing photons from massive stars (dotted curve), from HMXBs(dashed curve) and from ionising sources regardless of theirnature (solid curve) varies with time, assuming F ( E ) ∝ E − , which allows us to gauge the effectiveness of HMXBs c (cid:13) , 1–8 rimordial Globular Clusters, XRBs & Reionisation Figure 2. Variation of Rate of Emission of Hydrogen Ion-ising Photons with Time . Figure 3. Ionsing Power and Dependence on AssumedHardness of Energy Spectrum . as ionising sources as a function of f sur . At their peak, mas-sive stars produce hydrogen ionising photons at a rate of ∼ × s − during the first few million years of the glob-ular clusters life, but this declines rapidly. We note that thepeak value is a factor of ∼
10 lower than is quoted by Ricotti(2002) but this reflects different assumptions he made about,for example, metallicity ( Z ∼ Z ⊙ ) and the IMF (Salpter).As one expects, the effective number of ionising photons pro-duced by HMXBs depends strongly on what one assumes for f sur and as f sur decreases, so too does the strength and du-ration of the HMXB population as a source of (effective)ionising photons. For survival fractions f sur between 50% and 100% the peak rate at which (effective) ionising pho-tons are emitted is between ∼ × s − and 10 s − , butthis declines gradually and after 30 million years the rate is ∼ s − .It is important to note that we have assumed a partic-ular hardness for our energy spectrum ( α = 1); in Figure 3we show how our results depend on α , with lower values of α corresponding to harder energy spectra. As energy spec-tra become harder (i.e. as α decreases) HMXBs become lesseffective as ionising sources; this is unsurprising because theproportion of energetic photons increases as the hardness ofthe source increases, with a corresponding decrease in thenumber that can be absorbed by neutral hydrogen. Thisprovides an interesting additional constraint on the precisenature of HMXBs in primordial globular clusters, if they areto be considered as important contributors to cosmologicalreionsiation.Figure 2 suggests that the hydrogen ionising power ofa single young globular cluster is at its most effective whenits massive star population is still on the main sequence.However, the ionisation cross section of neutral hydrogen isa strong function of photon energy, decreasing roughly as E − , so that the mean free path of a UV photon is muchshorter than that of an X-ray photon. Therefore we expectUV photons to be most effective ionising the relatively highdensity surroundings of galaxies while X-ray photons can es-cape unscathed from the galaxy to potentially ionise a muchlarger volume (e.g. Ripamonti et al. 2008). Because UV pho-tons are absorbed in higher density surroundings, we expectrecombination to be important and so several UV photonsmay be required to ionise a single atom of hydrogen. Thishas been noted by Dijkstra et al. (2004), who estimate that ∼
10 UV photons are required to ionise a single hydrogenatom, compared to ∼ < ∼
10 estimatedby Dijkstra et al. (2004)) are required to ionise a single hy-drogen atom, the relative importance of HMXBs is boosteddramatically and these systems now dominate as sources ofionising radiation. Provided the survival fraction f sur ∼ > . α ≃
1, we would expect a single globular cluster of 10 stars to ionise of order ∼ × M ⊙ of neutral hydrogenduring its first ∼
100 million years. How precisely one inter-prets this number is not straightforward because UV pho-tons are absorbed locally whereas X-ray photons contributeto a global X-ray background. Nevertheless, it suggests thatthe HMXB population that we expect to be present in newlyformed globular clusters at high redshifts could have beenas important as massive stars for cosmological reionisation(cf. Ricotti 2002).
Globular clusters are old, dense and relatively simple stel-lar systems whose dynamical properties and evolution arewell understood. These properties have led to increasing in-terest in globular clusters as probes of the conditions underwhich galaxies formed at high redshifts (cf. Brodie & Strader2006). The study of Ricotti (2002) has suggested that mas- c (cid:13) , 1–8 C. Power, G. A. Wynn, C. Combet, M. I. Wilkinson sive stars in primordial globular clusters could have made animportant contribution to cosmological reionisation as ex-tremely luminous sources of UV photons. We have exploredthe contribution that these massive stars could have madeto cosmological reionisation once they evolved off the mainsequence, by assuming that a fraction formed in binariesthat evolved into HMXBs.Using a Monte Carlo model of a primordial globularcluster, we have investigated the conditions under which asufficient number of HMXBs form to have a meaningful im-pact on the ionising power of the cluster. We assume thatall massive stars formed in binaries and we consider onlythose binaries that remain bound once the more massivestar goes supernova, typically ∼
30% of massive binaries.Of this ∼ f sur survives toform HMXBs. Note that this is a conservative estimate be-cause we have neglected the effect of mass loss over the MSlifetime of the more massive star.Our results show that we require f sur ∼ > . f sur ∼ L X ∼ erg / s, we find that HMXBs produceionising photons at an effective rate of ∼ > s − over thefirst 40 million years of the cluster’s life. This is comparableto the rate at which massive stars produce ionising UV pho-tons during the first few million years. Note however thatresult is sensitive to the assumed hardness of the energyspectrum of the HMXBs – the harder the energy spectrum(i.e. the smaller the power-law exponent α ), the less effectiveHMXBs are as ionising sources.By its nature, our modelling is speculative – we knowrelatively little about the conditions in primordial globularclusters, and little about binary evolution at low metallic-ities. Yet, we know that many globular clusters formed athigh redshifts – at least as many as we can observe in thepresent day Universe – and we have a good understandingof the initial mass function and metallicities of the stars.This allows us to estimate how many massive stars theremight have been and what their typical lifetimes were. Ouranalysis indicates that under the right conditions, HMXBsin primordial globular clusters can be effective sources ofionising radiation. If these conditions are satisfied (high sur-vival rate f sur , softer energy spectra) then it reveals thataccretion power onto neutron stars and stellar mass blackholes can make a contribution to reionisation.We have assumed that the typical X-ray luminosityof an HMXB in a primordial globular cluster is L X ∼ erg / s. This is more luminous than is typical of localHMXBs in our Galaxy and the neighbouring Large andSmall Magellanic Clouds (e.g. there is a single source with L X ∼ erg / s in the SMC; cf. Shtykovskiy & Gilfanov2005), but these environments are atypical of the kind wemight expect to find primordial globular clusters forming in.Instead, if we consider HMXB populations in galaxies thathave undergone recent merging activity and/or show highstar formation rates, we find that L X ∼ erg / s is typi-cal (cf. Figure 1 of Gilfanov et al. 2004). For example, theHMXB populations in recent galaxy mergers such as “TheAntennae” (cf. Fabbiano et al. 2001) and “The Cartwheel”(cf. Wolter & Trinchieri 2004) have X-ray luminosities in ex-cess of L X ∼ erg / s. This is interesting because, as wediscuss below, young star clusters in such galaxy mergers are likely to be local analogues of primordial globular clus-ters, and suggests that our assumed X-ray luminosities arereasonable.It is less straightforward to assess whether or notHMXBs form in the numbers we might expect based on ourmodel in young star clusters in “The Antennae” or “TheCartwheel”. The luminosity functions presented in Gilfanovet al. (2004) and Wolter & Trinchieri (2004) can provide uswith some insight, however.We find that approximately 70% of massive binariesare disrupted before they can become HMXBs in our model.Therefore we expect at most 786 HMXBs for a Salpeter IMFand 952 HMXBs for a Kroupa IMF to survive in a 1e6 solarmass cluster, and we introduce a factor f sur f sur = 1. In this case, for our adopted probability distri-bution, approximately 10% will have luminosities in excessof L X ∼ erg/s – corresponding to between 80 and 100HMXBs in a single cluster. These numbers will scale in pro-portion to f sur , so f sur = 0 . L X ∼ erg/sOf order 50 HMXB candidates are known in “The An-tennae”. Without knowing the detailed spatial distributionof these candidates, it is difficult to do a straightforwardcomparison – the sources may be associated with a singlecluster, in which case f sur = 1 would seem to be favoured,or they could be associated with 10 clusters in which case f sur = 0 . f sur . For HMXBs in pri-mordial globular clusters to be an important source ofionising radiation, we require f sur to be of order unity.We expect f sur to depend on many factors, one of whichwill be metallicity; f sur may decrease as stars becomemore metal rich, and so it may very well be the casethat f sur = 0 . ∼ f sur and how these factors may depend on redshiftis something that we would like to investigate in futurework, but at present the discussion is necessarily speculative.We have focussed on the ionising power of HMXBs inprimordial globular clusters, but it is important to note thatthe longer mean free path of X-rays compared to UV meansthat HMXBs in galactic discs could have been as effective asHMXBs in globular clusters. We focus on globular clustersbecause we have a reasonable understanding of what theIMF could have been, and therefore we have a reasonableidea of how many HMXBs were likely to form. In contrast,we know very little about the initial mass function in star-forming galactic discs at high redshifts, but this is not tosay that HMXBs in discs should be discounted. Rather itsuggests that stellar mass black holes could make an inter-esting contribution to reionisation and merit further study.The contribution of globular cluster HMXBs to the reionis-ing background considered in this paper could be consideredas a lower limit.More broadly our analysis strongly indicates that glob- c (cid:13) , 1–8 rimordial Globular Clusters, XRBs & Reionisation ular clusters could have been important ionising sources inthe high redshift Universe. This has interesting implicationsfor galaxy formation at high redshifts and the use of globu-lar clusters as probes of reionisation. As yet, we do not havea satisfactory theory for the formation of globular clusterswithin a cosmological context. Nevertheless, if they were tobe effective sources of UV radiation then they must havemoved quickly from their formation site, presumably a co-coon rich in cold dense gas, to the rarified environs of the hotgaseous halo; if this did not happen on a timescale shorterthan a fraction of a few million years, a good fraction of theirUV radiation would have been absorbed by the cold densegas. This would favour globular cluster forming in gas-richmergers akin to the “super star clusters” that we observein present day mergers (e.g. Whitmore & Schweizer 1995;Meurer 1995) rather than in the gas-rich discs (e.g Kravtsov& Gnedin 2005).We have argued that ionising radiation from the glob-ular clusters could have been effective in ionising neutralhydrogen surrounding their host galaxy, but this radiationcould also damage cold dense gas within the galaxy (bothneutral and molecular), thus affecting the star formationrate and potentially suppressing further star formation. Thishas particular implications for the use of globular clustersas probes of cosmological reionisation. The argument is thatthe spatial distribution of globular clusters around galaxiesand in galaxy clusters can be used to measure the epoch ofreionisation – the more centrally concentrated the distribu-tion of globular clusters, the earlier the epoch of reionisation.Yet if the star formation efficiency in a galaxy is high, andconsequently the rate at which globular clusters form is high,then we might expect feedback from early-forming globularclusters to be extremely damaging for later-forming globu-lar clusters (e.g. Moore et al. 2006). This would suppressthe star formation and globular cluster formation efficiency.How could one separate this local effect from the effect of aglobally driven period of reionisation? This is a question weshall be pursuing in future work. ACKNOWLEDGEMENTS
We thank the anonymous referee for their very helpful com-ments. CP, CC and GW acknowledge the support of thetheoretical astrophysics rolling grant at the University ofLeicester. MIW acknowledges support from a Royal SocietyUniversity Research Fellowship.This paper has been typeset from a TEX/ L A TEX file preparedby the author.
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