Mon. Not. R. Astron. Soc. 336, L33–L37 (2002)

Did globular clusters reionize the Universe?

Massimo Ricotti�†Centre for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80309, USA

Accepted 2002 August 16. Received 2002 August 2; in original form 2002 April 24

ABSTRACTA problem still unsolved in cosmology is the identification of the sources of radiation able toreionize H I in the intergalactic medium (IGM) by z ∼ 6. Theoretical work and observationsseem to indicate that the fraction, 〈 fesc〉, of H I ionizing radiation emitted from galaxies thatescapes into the IGM is small in the local Universe (〈 fesc〉 � 10 per cent). At high redshift,galaxies are more compact and probably gas-rich, implying smaller values of 〈 fesc〉 from theirdiscs or spheroids. However, if the sites of star formation are displaced from the disc or spheroidand the star formation efficiency of the proto-clusters is high, then 〈 fesc〉 should be about 1.This star formation scenario is consistent with several models for globular cluster formation.Using simple arguments based on the observed number of globular cluster systems in the localUniverse, and assuming that the oldest globular clusters formed before reionization and had〈 fesc〉 ∼ 1, I show that they produced enough ionizing photons to reionize the IGM at z ≈ 6.

Key words: globular clusters: general – galaxies: formation – cosmology: theory.

1 I N T RO D U C T I O N A N D R AT I O NA L E

Observation of Lyα absorption systems toward newly found high-redshift quasars (Becker et al. 2001; Djorgovski et al. 2001) indicatesthat the redshift of reionization of the intergalactic medium (IGM)should be close to z = 6 (Gnedin 2002; Songaila & Cowie 2002).Perhaps the recent identification of a lensed galaxy at z = 6.56 pointsto a somewhat earlier redshift of reionization (Hu et al. 2002). Al-though quasars play a dominant role in photoionizing the IGM atz ≈ 3 (Meiksin & Madau 1993), their dwindling numbers at z > 4suggest the need for another ionization source. Unless a hiddenpopulation of quasars is found, radiation emitted by high-redshiftmassive stars seems necessary to reionize the Universe. A key in-gredient in determining the effectiveness with which galaxies pho-toionize the surrounding IGM is the parameter 〈 fesc〉, defined hereas the mean fraction of Lyman continuum photons escaping fromgalaxy haloes into the IGM. To be an important source of ionizingphotons and rival with quasars, a substantial fraction (∼10 per cent)of them must escape the gas layers of the galaxies (Madau & Shull1996).

Cosmological simulations and semi-analytical models of IGMreionization by stellar sources find that the ionizing backgroundrises steeply at the redshift of reionization. Unfortunately, a directcomparison between models is difficult because of different recipesused for star formation, clumping of the IGM or the definition of〈 fesc〉. However, a result common to all the models is that, in order toreionize the IGM by z = 6–7, the escape fraction must be relatively

�Present address: Institute of Astronomy, University of Cambridge, Madin-gley Road, Cambridge CB3 0HA.†E-mail: ricotti@ast.cam.ac.uk

large: 〈 fesc〉 � 10 per cent assuming a Salpeter initial mass function(IMF) and the standard �CDM cosmological model. Benson et al.(2002) find that 〈 fesc〉 should be about 15 per cent for reionization atz = 6, but a smaller value 〈 fesc〉 � 10 per cent is consistent with theobserved ionizing background at z ∼ 3. Gnedin (2002) finds that as-suming a primordial power spectrum index n = 0.93, the preferredvalue from cosmic microwave background and large-scale structuredata, reionization at z � 6 requires a large 〈 fesc〉; but this assumptionproduces an ionizing background at z � 4 that is too large. The com-mon assumption of a universal star formation efficiency (SFE) (e.g.the coefficient in front of the Schmidt law in some models or in oth-ers the fraction f∗ of baryons converted into stars) is consistent withthe observed values of the star formation rate (SFR) at 0 < z < 5and total star fraction �∗ at z = 0. However, the assumption of aconstant 〈 fesc〉 does not seem to be consistent with observations. Anescape fraction 〈 fesc〉 ∼ 1 is required for reionization at z ∼ 6, butthe ionizing background at z ∼ 3 is consistent with 〈 fesc〉 � 10 percent (Bianchi, Cristiani & Kim 2001). Small values of 〈 fesc〉 at z � 3are also supported by direct observations of the Lyman continuumemission from Lyman-break and starburst galaxies. Giallongo et al.(2002) find an upper limit 〈 fesc〉 < 16 per cent at z ∼ 3 (but seeSteidel, Pettini & Adelberger 2001), and observations of low-redshift starbursts are consistent with 〈 fesc〉 upper limits rangingfrom a few per cent up to 10 per cent (Hurwitz, Jelinsky & Dixon1997; Deharveng et al. 2001).

Calculations of 〈 fesc〉 from first principles are difficult. The maincomplications arise in simulating a realistic interstellar medium(ISM) that includes small-scale physics and feedback processes.Moreover, the mean 〈 fesc〉 results from the contribution of a varietyof galaxies with ISM properties that are largely unknown at highredshift. Theoretical models (Dove, Shull & Ferrara 2000; Ciardi,

C© 2002 RAS

L34 M. Ricotti

Bianchi & Ferrara 2002) for the radiative transfer of ionizing radi-ation through the disc layer of spiral galaxies similar to the MilkyWay find 〈 fesc〉 ∼ 6–10 per cent. At high redshift the mean valueof 〈 fesc〉 is expected to decrease almost exponentially with increas-ing redshift (Ricotti & Shull 2000; Wood & Loeb 2000); at z > 6,〈 fesc〉 � 0.1–1 per cent even assuming star formation rates typicalof starburst galaxies (e.g. SFR ∼10 times that of the Milky Way).Using Monte Carlo simulations, Ricotti & Shull (2000) have studiedhow 〈 fesc〉 depends on galactic parameters. Assuming a gas densityprofile in hydrostatic equilibrium in the dark matter (DM) potential,a stellar density proportional to the gas density and a power lawfor the luminosity function of the OB associations, they found that〈 fesc〉 ∝ (ε fg MDM)−1/3 exp[−(zvir +1)ε−1/3]. Here ε is proportionalto the SFE, fg is the fraction of collapsed gas, zvir is the virializationredshift and MDM is the DM halo mass. The majority of photonsthat escape the halo come from the most luminous OB associationslocated in the outermost parts of the galaxy. Indeed, Ricotti & Shull(2000) have shown that changing the luminosity function of the OBassociation and the density distribution of the stars has major effectson 〈 fesc〉 (see their figs 8 and 9). In the aforementioned models, 〈 fesc〉should be regarded as an upper limit, since dust extinction and ab-sorption of ionizing radiation from the molecular cloud in whichOB associations are born are neglected.

The theoretical suggestion of a decreasing 〈 fesc〉 with increas-ing redshift is in contrast with models for reionization that require〈 fesc〉 ∼ 1 at z = 6. A different star formation mode, with very lumi-nous OB associations forming in the outer parts of galaxy haloes,could explain the large 〈 fesc〉 required for reionization. Globularclusters (GCs) are possible observable relics of such a star forma-tion mode. Their redshift of formation is compatible with redshiftof reionization (Gnedin, Lahav & Rees 2002). Because of theirlarge stellar density they survived tidal destruction and representthe most luminous tail of the luminosity distribution of primordialOB associations. In Section 2.2 I explain that several models forthe formation of proto-GCs imply an 〈 fesc〉 ∼ 1. I will also showthat the total amount of stars in GCs observed today is sufficientto reionize the Universe at z ∼ 6 if their 〈 fesc〉 ∼ 1. This conclusionis reinforced if the GCs that we observe today are only a fraction,1/ fdi, of primordial GCs as a consequence of mass segregation andtidal stripping.

The paper is organized as follows. In Section 2 I briefly reviewrecent progress in our understanding of GC properties and formationtheories; in Section 3 I discuss the model assumptions in light ofGC observations and present the results. In Section 4 I present myconclusions.

2 S H O RT R E V I E W O N G C S Y S T E M S

In this section I review some observational and theoretical results onGCs that are useful to the aim of this paper. I also try to justify myassumption 〈 fesc〉 ∼ 1 for GCs on the basis of theoretical models ofproto-GC formation.

2.1 Observations

Most galaxies have a bimodal GC distribution indicating that lu-minous galaxies experience at least two major episodes of GC for-mation. The bulk of the globulars in the main body of the Galactichalo appear to have formed during a short-lived burst (∼0.5–2 Gyr)that took place about 13 Gyr ago. This was followed by a secondburst associated with the formation of the galactic bulges. Clustersmay have been formed in dwarf spheroidal galaxies and accreted by

the Galactic halo (van den Bergh 1999). Massive cluster formationoccurred in galaxies as small as the Fornax dwarf spheroidal, butnot in massive ones such as the Small Magellanic Cloud (Zepf et al.1999).

2.1.1 Absolute and relative ages

The method for determining the absolute age of GCs is based onfitting the observed colour–magnitude diagram with theoretical evo-lutionary tracks. The systematics in the evolutionary model and thedetermination of the cluster distance are the major sources of er-rors. Recent determinations of the absolute age of old GCs findtgc = 12.5 ± 1.2 Gyr (Chaboyer et al. 1998), consistent with ra-dioactive dating of a very metal-poor star in the halo of our Galaxy(Cayrel et al. 2001). Relative ages of Galactic GCs can be determinedwith greater accuracy, since many systematic errors can be elimi-nated. In our Galaxy �tgc = 0.5 Gyr, but differences in age betweenGC systems in different galaxies could be �tgc ∼ 2 Gyr (Stetson,Vandenberg & Bolte 1996).

2.1.2 Specific frequency

The specific frequency is defined as the number, N, of GCsper MV = −15 of parent galaxy light, SN = N × 100.4(MV +15)

(Harris & van den Bergh 1981). The most striking characteristicis that SN (ellipticals) > SN (spirals). SN = 0.5 in Sc/Ir galaxies(Harris 1991), SN = 1 in spirals of types Sa/Sb, and SN = 2.5 in fieldellipticals (Kundu & Whitmore 2001a,b). Converting to luminosity(LV /L� = 10−0.4 (MV − 4.83)) we have N = (L/L�)SN /8.55 × 107. Ican therefore calculate the efficiency of GC formation defined as

εgc = Mgc

M= fdi Nmgc

M= SN fdi

(M/L)V× 0.00585, (1)

where Mgc is the total mass of the GC system, mgc = 5 × 105 M� isthe mean mass of GCs today, M is the stellar mass and (M/L)V is themass-to-light ratio of the galaxy. In the next paragraph I show that,because of dynamical evolution, mgc and N are expected to be largerat the time of GC formation than today. Therefore the parameterfdi � 1 is introduced to account for dynamical disruption of GCsduring their lifetime.

2.1.3 IMF, metallicity and dynamical evolution

The IMF of GCs is not known. The present mass function is knownonly between 0.2 and 0.8 M�, since high-mass stars are lost becauseof two-body relaxation and stellar evolution processes. Theoreticalmodels show that the shape is consistent with a Salpeter-like IMF.The mean metallicity of old GCs is Z ∼ 0.03 Z�. One of the mostremarkable properties of GCs is the uniformity of their internalmetallicity: �[Fe/H] � 0.1. This implies that the bulk of the starsthat constitute a GC formed in a single monolithic burst of starformation. A typical GC emits S ≈ 3 × 1053 s−1 ionizing photons ina burst lasting 4 Myr: about 300 times the ionizing luminosity oflargest OB associations in our Galaxy.

During their lifetime GCs lose a large part of their initial mass orare completely destroyed by internal and external processes. Promi-nent internal processes are mass loss by stellar evolution (about halfof the initial mass is lost) and two-body relaxation, the effects ofwhich are mass segregation (change in the mass function) and corecollapse (expansion and evaporation). External processes can be

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Did globular clusters reionize the Universe? L35

divided roughly into two classes: gravitational shocks from GC mo-tion through the disc or bulge of the galaxy, and tidal forces, whichcause mass loss as a result of tidal truncation. Numerical simulationsshow that about 50–90 per cent of the mass of GCs is lost because ofexternal processes, depending on the host galaxy environment, ini-tial concentration and IMF of the proto-GCs (Chernoff & Weinberg1990; Gnedin & Ostriker 1997). Many of the low-metallicity halofield stars in the Milky Way could be debris of disrupted GCs. Themass in stars in the halo is about 100 times the mass in GCs. There-fore the parameter fdi, defined in Section 2.1.2, could be as largeas fdi = 100. Overall fdi is not well constrained since it dependson unknown properties of the proto-GCs. According to results ofN-body simulations fdi should be in the fdi ∼ 2–10 range.

2.2 Why is 〈 f esc〉 ∼ 1 plausible for GCs?

I discuss separately two issues: (i) the 〈 fesc〉 from the gas cloud inwhich the GC forms; and (ii) the 〈 fesc〉 through any surrounding gasin the galaxy.

(i) The evidence for 〈 fesc〉 ∼ 1 comes from the observed prop-erties of present-day GCs. The fact that they are compact self-gravitating systems with low and uniform metallicity points to ahigh efficiency of conversion of gas into stars. A longer time-scaleof star formation would have enriched the gas of metals and the me-chanical feedback from supernova explosions would have stoppedfurther star formation. If f∗ ≈ 10 per cent of the gas is convertedinto stars in a single burst (with duration < 4 Myr) at the centreof a spheroidal galaxy, following the simple calculations shown inRicotti & Shull (2000) [see their equation (18)] at z = 6 we have

fesc = 1 − 0.06(1 − f∗)2

f∗

(1 + z

7

)3

∼50 per cent. (2)

(ii) The justification for 〈 fesc〉 ∼ 1 is model-dependent, but ingeneral there are two main arguments: (a) the high efficiency of starformation f∗; and (b) the sites of proto-GC formation in the outer-most parts of the galaxy halo.

In the ‘cosmological objects model’ (30 < zf < 7) of Pee-bles & Dicke (1968), GCs form with efficiency f∗ ≈ 100per cent, implying 〈 fesc〉 = 1 [note that such a high f∗ isnot found in numerical simulations of first object formation(Ricotti, Gnedin & Shull 2002a,b)]. In ‘hierarchical formation mod-els’ (10 < zf < 3) (Larson 1993; Harris & Pudritz 1994; McLaughlin& Pudritz 1996; Gnedin et al. 2002), GCs form in the disc or spheroidof galaxies with gas mass Mg ∼ 107–109 M�. Compact GCs survivethe accretion by larger galaxies while the rest of the galaxy is tidallystripped. Assuming that 1–10 GCs form in a galaxy with Mg ∼ 107–108 M� implies f∗ ∼ 10 per cent and therefore 〈 fesc〉 � 50 per cent.〈 fesc〉 is larger than in equation (2) if proto-GCs are located off-centre (e.g. if they form from cloud–cloud collisions during thegalaxy assembly) or if part of the gas in the halo is collisionallyionized as a consequence of the virialization process.

In models such as the ‘supershell fragmentation’ model (zf < 10)of Taniguchi, Trentham & Ikeuchi (1999) or the ‘thermal instabil-ity’ model (zf < 7) of Fall & Rees (1985), 〈 fesc〉 ≈ 1 since proto-GCsform in the outermost part of an already collisionally ionized halo.

In summary, since 〈 fesc〉 depends strongly on the luminosity ofthe OB associations and on their location, proto-GCs, being severalhundred times more luminous than Galactic OB associations, shouldhave a comparably larger 〈 fesc〉.

Table 1. Star census at z = 0.

Type ω∗ (per cent) SN (M/L)V εgc (per cent)

Sph 6.5+4−3 2.4 ± 0.4 5.4 ± 0.3 0.26 ± 0.06

Disc 2+1.5−0.5 1 ± 0.1 1.82 ± 0.4 0.32 ± 0.1

Irr 0.15+0.15−0.05 0.5 1.33 ± 0.25 0.22 ± 0.04

Total 9+5.5−3.5 – – 0.3 ± 0.07

3 M E T H O D A N D R E S U LT S

In this Section I estimate the number of ionizing photons emittedper baryon per Hubble time, Nph, by GC formation. In Section 3.1I derive Nph assuming that all GCs observed at z = 0 formed ina time period �tgc with constant formation rate. In Section 3.2 Iuse the Press–Schechter formalism to model more realistically theformation rate of old GCs.

3.1 The simplest estimate

I start by estimating the fraction, ωgc, of cosmic baryons convertedinto GC stars. By definition ωgc = ω∗εgc, where ω∗ is the fraction ofbaryons in stars at z = 0 and εgc is the efficiency of GC formationdefined in Section 2.1.2. In all the calculations I assume �b = 0.04.In Table 1, I summarize the star census at z = 0 according toPersic & Salucci (1992) and I derive εgc using equation (1), as-suming fdi = 1. Using similar arguments McLaughlin (1999) findsa universal efficiency of GC formation εgc = 0.26 ± 0.05 per cent,in agreement with the simpler estimate presented here. It followsthat ωgc = fdi(2.7+2.3

−1.7 × 10−4) at z = 0.The total number of ionizing photons per unit time emitted by GCs

is ηω fgc/�tgc, where η is the number of ionizing photons emitted per

baryon converted into stars, and ω fgc ≈ 2.1ωgc takes into account the

mass loss due to stellar winds and supernova explosions adopting aninstantaneous-burst star formation law. GCs did not recycle this lostmass since they formed in a single burst of star formation. η dependson the IMF and on the metallicity of the star. I calculate η usinga Salpeter IMF and stellar metallicity Z = 0.03 Z� (see Section2.1.3) with the STARBURST99 code (Leitherer et al. 1999), and findη = 8967. The number of ionizing photons per baryon emitted in aHubble time at z = 6 is

N gcph = ηω f

gc

tH(z = 6)

�tgc= (

5.1+4.3−3.2

) fdi

�tgc(Gyr), (3)

where I have assumed 〈 fesc〉 = 1 and the Hubble time at z = 6 istH = 1 ± 0.1 Gyr. I expect 1 � fdi � 100 and 0.5 ��tgc � 2 Gyr. Aconservative estimate of fdi � 2 and �tgc � 2 Gyr (i.e. 10 <zf < 3)implies that fdi/�tgc � 1. The IGM is reionized when Nph = C ,where C = 〈n2

H II〉/〈nH II〉2 is the ionized IGM clumping factor. Ac-cording to the adopted definition of 〈 fesc〉, C = 1 for a homogeneousIGM, or 1 � C � 10 taking into account IGM density fluctuationsproducing the Lyα forest (Miralda-Escude, Haehnelt & Rees 2000;Gnedin 2000). The estimate from equation (3) is rather rough be-cause I have implicitly assumed that the SFR is constant during theperiod of GC formation �tgc. A more realistic SFR as a functionof redshift requires assuming a specific model for the formation ofGCs. I try to address this question in the next section.

3.2 A bit of modelling

I assume that the formation rate of stars or GCs in galaxies isproportional to the merger rate of galaxy haloes (each galaxy

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L36 M. Ricotti

undergoes a major starburst episode when it virializes). Using thePress–Schechter formalism I calculate

dω fgc(z)

dt= A

∫ M2

M1

d�(MDM, z)

dtd ln MDM, (4)

dω f∗ (z)

dt= B

∫ ∞

Mm

d�(MDM, z)

dtd ln MDM, (5)

where �(MDM, z) d ln(MDM) is the mass fraction in virialized DMhaloes of mass MDM at redshift z. I determine the constants A andB1 by integrating equations (4)–(5) with respect to time, and as-suming ω f

gc = 0.1 per cent (i.e. fdi = 2) and ω f∗ = 1.4ω∗ = 13 per

cent at z = 0 (the factor 1.4 takes into account the mass loss ow-ing to stellar winds and supernova explosions adopting a contin-uous star formation law). I assume that GCs form in haloes withmasses M1 < MDM < M2. The choice of M1 and M2 determines themean redshift, zf, and time period, �tgc, for the formation of oldGCs. In order to be consistent with observations I consider threecases: (i) haloes with virial temperature 2 × 104 < Tvir < 5 × 104 K;(ii) 5 × 104 < Tvir < 105 K; and (iii) 105 < Tvir < 5 × 105 K. In cases(i), (ii) and (iii) �tgc = 2.2, 3.7 and 5.2 Gyr, respectively, and the GCformation rate has a peak at z = 7.5, 6 and 4.6, respectively. Discand spheroid stars form in haloes with MDM > Mm . At z > 10 I as-sume that the first objects form in haloes with Mm corresponding to ahalo virial temperature Tvir = 5 × 103 K. At z < 10 only objects withTvir > 2 × 104 K can form (see Ricotti et al. 2002b). The comovingstar formation rate, given by ρ∗ = ρω f

∗ , where ρ = 5.51 × 109 M�Mpc−3 is the mean baryon density at z = 0, is shown in Fig. 1. Thepoints show the observed SFR from Lanzetta et al. (2002). In Fig. 2I showNph for GCs (thick lines) and for galaxies (thin lines) definedas

N gcph = η fdi

dω fgc

dttH(z), (6)

N ∗ph = η〈 fesc〉ωf

∗dt

tH(z). (7)

The thick solid, dashed and short-dashed lines show N gcph for cases

(i), (ii) and (iii), respectively. For comparison, I show (thin solid line)N ∗

ph assuming 〈 fesc〉 = 0.1 × exp(−z/2), chosen to fit the observedvalues (squares) of N ∗

ph at z = 2, 3 and 4 (Miralda-Escude et al.2000). The thin dashed line shows N ∗

ph assuming constant 〈 fesc〉 = 5per cent.

4 C O N C L U S I O N S

Observed Lyman break galaxies at z ∼ 3 are probably the most lu-minous starburst galaxies of a population that produced the bulkof the stars in our Universe. Their formation epoch corresponds tothe assembly of the bulges of spirals and ellipticals. Nevertheless,the observed upper limit on 〈 fesc〉 from Lyman break galaxies is〈 fesc〉 � 10 per cent, insufficient to reionize the IGM according tonumerical simulations. Recently Ferguson, Dickinson & Papovich(2002), using different arguments, have claimed that the radiationemitted from Lyman break galaxies is insufficient to reionize theIGM assuming a continuous star formation mode.

1By definition∫ ∞

0�(MDM, z) d ln(MDM) = 1. I find the following values

of the constants: A= 1.3, 1.6 and 0.6 per cent for cases (i), (ii) and (iii)respectively (see text), and B= 12 per cent.

Figure 1. The solid line in the top panel shows the comoving SFR as afunction of time in our model. The solid, dashed and short-dashed linesshow the SFR of GCs for cases (i), (ii) and (iii), respectively (assumingfdi = 2). The bottom panel shows ω

f∗ as a function of time. The segment

with arrows is a visual aid to compare ωfgc (assuming fdi = 20) with ω

f∗

around z ∼ 6. This figure is available in colour in the electronic version ofthe journal on Synergy.

Figure 2. Emissivity (photons per baryon per Hubble time) as a function ofredshift. The thick solid, dashed and short-dashed lines show the contributionof GCs for cases (i), (ii) and (iii), respectively (assuming fdi = 2). The thinlines show the contribution of galaxies assuming a realistic 〈 fesc〉 = 0.1 ×exp(−z/2) (solid) and a constant 〈 fesc〉 = 5 per cent (dashed). This figure isavailable in colour in the electronic version of the journal on Synergy.

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Did globular clusters reionize the Universe? L37

I propose that GCs could produce enough ionizing photons toreionize the IGM. Assuming fdi = 2 (i.e. during their evolution GCshave lost half of their original mass), I find ω f

gc ≈ 0.1 per cent, smallcompared with the total ω f

∗ ∼ 10 per cent at z = 0. However, GCsare around 12–13 Gyr old and, if they formed in the redshift interval7 < z < 5 (in about 0.5 Gyr), the expected total ω f

∗ formed dur-ing this time period is about ω f

∗ ∼ 1 per cent, only 10 times largerthan ω f

gc. Assuming fdi = 20, expected from the results of N-bodysimulations, I find ω f

gc ≈ 1 per cent, suggesting that GC formationis an important mode of star formation at high redshift. The spe-cial star formation mode required to explain the formation of GCssuggests an 〈 fesc〉 ∼ 1 from these objects. This is because 〈 fesc〉 isdominated by the most luminous OB associations and GCs are ex-tremely luminous, emitting S ∼ 3 × 1053 s−1 ionizing photons inbursts lasting 4 Myr. Moreover, according to many models, GCsform in the hot, collisionally ionized galaxy halo, from which allthe ionizing radiation emitted can escape into the IGM. Therefore itis not too surprising, if GCs started forming before z = 6, that theircontribution to reionization is large. I find that the number of ion-izing photons per baryon emitted in a Hubble time at z = 6 by GCsis N gc

ph = (5.1+4.3−3.2) fdi/�tgc > 1, therefore sufficient to reionize the

IGM even if we assume fdi = 1. Here, �tgc ∼ 0.5–2 is the period offormation of the bulk of old GCs in Gyr. Using simple calculationsbased on the Press–Schechter formalism (see Fig. 2) I find that, ifnormal star formation in galaxies has 〈 fesc〉 � 5 per cent, the GCcontribution to reionization should be important. If GCs formed bythermal instability in the halo of Tvir ∼ 105 K galaxies (case iii), theionizing sources are located in rare peaks of the initial density field.Therefore the mean size of intergalactic H II regions before overlapis large and reionization is inhomogeneous on large scales.

In this Letter I have considered the possibility that an increasing〈 fesc〉 at z ∼ 6 because of GC formation could explain IGM reioniza-tion and still be consistent with the observed values of the ionizingbackground at z < 3. Alternatively, an increasing production of ion-izing photons per baryon converted into stars, owing to a varyingIMF, would have similar effects on the IGM. Chemical evolutionstudies should be able to distinguish between these two scenarios.

AC K N OW L E D G M E N T S

I thank Oleg and Nick Gnedin for their helpful support with themanuscript.

R E F E R E N C E S

Becker R. H. et al., 2001, AJ, 122, 2850Benson A. J., Lacey C. G., Baugh C. M., Cole S., Frenk C. S., 2002, MNRAS,

333, 156

Bianchi S., Cristiani S., Kim T.-S., 2001, A&A, 376, 1Cayrel R. et al., 2001, Nat, 409, 691Chaboyer B., Demarque P., Kernan P. J., Krauss L. M., 1998, ApJ, 494,

96Chernoff D. F., Weinberg M. D., 1990, ApJ, 351, 121Ciardi B., Bianchi S., Ferrara A., 2002, MNRAS, 331, 463Deharveng J.-M., Buat V., Le Brun V., Milliard B., Kunth D., Shull J. M.,

Gry C., 2001, A&A, 375, 805Djorgovski S. G., Castro S., Stern D., Mahabal A. A., 2001, ApJ, 560, L5Dove J. B., Shull J. M., Ferrara A., 2000, ApJ, 531, 846Fall S. M., Rees M. J., 1985, ApJ, 298, 18Ferguson H. C., Dickinson M., Papovich C., 2002, ApJ, 569, L65Giallongo E., Cristiani S., D’Odorico S., Fontana A., 2002, ApJ, 568, L9Gnedin N. Y., 2000, ApJ, 535, 530Gnedin N. Y., 2002, submitted (astro-ph/0110290)Gnedin O. Y., Ostriker J. P., 1997, ApJ, 474, 223Gnedin O. Y., Lahav O., Rees M. J., 2002, submitted (astro-ph/0108034)Harris W. E., 1991, ARA&A, 29, 543Harris W. E., Pudritz R. E., 1994, ApJ, 429, 177Harris W. E., van den Bergh S., 1981, AJ, 86, 1627Hu E. M., Cowie L. L., McMahon R. G., Capak P., Iwamuro F., Kneib J.-P.,

Maihara T., Motohara K., 2002, ApJ, 568, L75Hurwitz M., Jelinsky P., Dixon W. V. D., 1997, ApJ, 481, L31Kundu A., Whitmore B. C., 2001a, AJ, 121, 2950Kundu A., Whitmore B. C., 2001b, AJ, 122, 1251Lanzetta K. M., Yahata N., Pascarelle S., Chen H., Fernandez-Soto A., 2002,

ApJ, 570, 492Larson R. B., 1993, in Smith G. H., Brodie J. P., eds, ASP Conf. Ser. Vol.

48, The Globular Cluster–Galaxy Connection. Astron. Soc. Pac., SanFrancisco, p. 675

Leitherer C. et al., 1999, ApJS, 123, 3McLaughlin D. E., 1999, AJ, 117, 2398McLaughlin D. E., Pudritz R. E., 1996, ApJ, 457, 578Madau P., Shull J. M., 1996, ApJ, 457, 551Meiksin A., Madau P., 1993, ApJ, 412, 34Miralda-Escude J., Haehnelt M., Rees M. J., 2000, ApJ, 530, 1Peebles P. J. E., Dicke R. H., 1968, ApJ, 154, 891Persic M., Salucci P., 1992, MNRAS, 258, 14P

Ricotti M., Shull J. M., 2000, ApJ, 542, 548Ricotti M., Gnedin N. Y., Shull J. M., 2002a, ApJ, 575, 33Ricotti M., Gnedin N. Y., Shull J. M., 2002b, ApJ, 575, 49Songaila A., Cowie L. L., 2002, AJ, 123, 2183Steidel C. C., Pettini M., Adelberger K. L., 2001, ApJ, 546, 665Stetson P. B., Vandenberg D. A., Bolte M., 1996, PASP, 108, 560Taniguchi Y., Trentham N., Ikeuchi S., 1999, ApJ, 526, L13van den Bergh S., 1999, A&AR, 9, 273Wood K., Loeb A., 2000, ApJ, 545, 86Zepf S. E., Ashman K. M., English J., Freeman K. C., Sharples R. M., 1999,

AJ, 118, 752

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