A new perspective on globular clusters, their initial mass function, and their contribution to the stellar halo and to cosmic reionisation
We examine various implications from a dynamical and chemical model of globular clusters (GCs), which successfully reproduces the observed abundance patterns and the multiple populations of stars in these systems assuming chemical enrichment from fast rotating massive stars. Using the model of Decressin et al. (2007) we determine the ratio between the observed, present-day mass of globular clusters and their initial stellar mass as a function of the stellar initial mass function (IMF). We also compute the mass of low-mass stars ejected, and the amount of hydrogen ionising photons emitted by the proto globular clusters. Typically, we find that the initial masses of GCs must be 8–10 times (or up to 25 times, if second generation stars also escape from GCs) larger than the present-day stellar mass. The present-day Galactic GC population must then have contributed to approximately 5–8% (10–20%) of the low-mass stars in the Galactic halo. We also show that the detection of second generation stars in the Galactic halo, recently announced by different groups, provides a new constraint on the GC initial mass function (GCIMF). These observations appear to rule out a power-law GCIMF, whereas they are compatible with a log-normal one. Finally, the high initial masses also imply that GCs must have emitted a large amount of ionising photons in the early Universe. Our results reopen the question on the initial mass function of GCs, and reinforce earlier conclusions that old GCs could have represented a significant contribution to reionise the inter-galactic medium at high redshift.
keywords:globular clusters: general – Stars: Population II – Galaxies: star clusters general – dark ages, reionization, first stars
Although for a long time thought to be among the most simple stellar systems, globular clusters (hereafter GCs) have been subject to intense studies both observationally and through theory and simulations. These include for example detailed work on the stellar content of GCs and on chemical abundances of GC stars,searches for viable proto-GCs, studies of dynamical effects on massive star cluster evolution, cosmological simulations of their formation, estimates of their contribution to cosmic reionisation, and other related Galactic and extragalactic astrophysical topics (see e.g. reviews by Gratton, Sneden & Carretta, 2004; Brodie & Strader, 2006; Piotto, 2009; Boily, 2010; Elmegreen, 2010b).
Despite these studies many open questions remain, concerning both GCs as individual objects and as a collective population. For example, the origin of Galactic halo stars and the contribution of GCs to this population, are still unclear (see e.g. Hut & Djorgovski, 1992; Parmentier & Gilmore, 2007; Bell et al., 2008; Boley et al., 2009). Similarly, the shape of the globular cluster initial mass function (GCIMF), the nature of the present-day globular cluster mass function, and the processes and the timescales responsible for transforming the former into the latter, are debated (see Fall & Zhang, 2001; Vesperini & Zepf, 2003; Parmentier & Gilmore, 2005, 2007; Elmegreen, 2010a). Also, first steps are being made in order to understand GC formation in cosmological simulations (Bromm & Clarke, 2002; Kravtsov & Gnedin, 2005; Boley et al., 2009; Griffen et al., 2010). Finally Ricotti (2002) has shown that GCs emit enough ionising photons to reionise the Universe, provided their escape fraction is of order unity. Examining this question is also of interest in the present context, where it appears that galaxies found so far in deep surveys are insufficient to reionise the inter-galactic medium (see e.g. Bunker et al., 2010; Ouchi et al., 2009; McLure et al., 2010; Labbé et al., 2010), and where the main sources responsible of cosmic reionisation, presumably faint, low-mass galaxies, below the current detection limits (cf. Choudhury & Ferrara, 2007; Choudhury, Ferrara & Gallerani, 2008), remain thus to be identified.
A major paradigm-shift has occurred recently in the GC community, that sheds new light on these key questions. Indeed, detailed abundance studies of their long-lived low-mass stars made possible with 8-10m class telescopes, together with high-precision photometry of Galactic GCs performed with HST, have revolutionised our picture of these stellar systems. It is now clear that individual GCs host multiple stellar populations, as shown by their different chemical properties and by multimodal sequences in the colour-magnitude diagrams (Bedin et al., 2004; Piotto et al., 2007; Milone et al., 2008, 2010; Villanova et al., 2010). Indeed, although nearly all GCs111With the notable exception of Cen, M22, and M54 (see e.g. Da Costa et al., 2009; Johnson & Pilachowski, 2010; Siegel et al., 2007; Carretta et al., 2010a, and references therein). appear to be fairly homogeneous in heavy elements (i.e., Fe-peak, neutron-capture, and alpha-elements, see e.g. James et al., 2004; Sneden, 2005; Carretta et al., 2009a), they all exhibit large star-to-star abundance variations for light elements from C to Al that are the signatures of hydrogen-burning at high temperature implanted at birth in their long-lived low-mass stars (see e.g. Gratton et al., 2001; Gratton, Sneden & Carretta, 2004; Sneden, 2005; Prantzos, Charbonnel & Iliadis, 2007; Carretta et al., 2009b; Charbonnel, 2010, and reference therein). In fact, the so-called O–Na anticorrelation is ubiquitous in Galactic GCs, and is now accepted as the decisive observational criterion distinguishing bona fide GCs from other clusters (Carretta et al., 2010b).
The current explanation for these chemical patterns is the so-called “self-enrichment” scenario that calls for the formation of at least two stellar generations in all GCs during their infancy: The first generation stars were born with the proto-cluster original composition, which is that of contemporary field halo stars, while the second generation stars formed from original gas polluted to various degrees by hydrogen-burning processed material ejected by more massive, short-lived, first generation GC stars. Details and references can be found e.g. in Prantzos & Charbonnel (2006), who discuss the pros and cons of two versions of this “self-enrichment scenario”, invoking either massive AGB stars (e.g. Cottrell & Da Costa, 1981; Ventura et al., 2001; Ventura & D’Antona, 2009), or fast rotating massive stars (e.g. Decressin, Charbonnel & Meynet, 2007) as polluters.
Whatever the actual polluting stars, an immediate consequence of this scenario is that, in order to reproduce the present proportion of first to second generation stars with acceptable values of the polluters IMF, the initial stellar masses of GCs must have been considerably larger than their present-day value (Prantzos & Charbonnel, 2006; Decressin, Charbonnel & Meynet, 2007; D’Ercole et al., 2008; Decressin et al., 2010; Carretta et al., 2010b). However, most of the extra-galactic studies have not yet incorporated this revised picture, or have not yet explored the resulting implications. Furthermore, the recent discovery of stars with signatures characteristic of 2 generation GC stars among the metal-poor halo population (Carretta et al., 2010b; Martell & Grebel, 2010) sheds new light on the amount of low-mass stars ejected from GCs and on the initial mass function of these clusters, as we shall show below.
In the present paper, we explore several consequences of this new paradigm, based on the model that was developed by Decressin, Charbonnel & Meynet (2007, hereafter DCM07) to describe the early chemical and dynamical evolution of GCs. In this model fast-rotating massive ( 25 M) stars are responsible for the GC pollution. The model successfully explains the observed abundance patterns of present-day GC stars, and has also been tested with N-body and hydrodynamical simulations (see Decressin, Baumgardt & Kroupa, 2008; Decressin et al., 2010). Its main assumptions are briefly described and summarised in §2. Within this framework, we constrain the relation between the initial and the present stellar mass of GCs (§3), as well as the contribution to the stellar halo (§4), taking the recent observational identification of second generation stars in the Galactic halo (Martell & Grebel, 2010; Carretta et al., 2010b) into account. Implications on the GCIMF are derived in §5. Finally, we derive in §6 a well-defined ionising photon production rate for proto-GCs, taking all the detailed observational constraints from nearby GCs into account, and estimate their contribution to cosmic reionisation. Our main conclusions are summarised in §7.
2 The adopted chemical and dynamical evolution model
DCM07 and Decressin et al. (2007) have shown that the O-Na anticorrelation observed in GC stars can be explained if a second generation of low-mass stars form from the ejecta of first stellar generation fast rotating massive stars mixed with some original interstellar material. In their model, the first generation forms the full mass spectrum of stars described by a power-law IMF at the high end and a log-normal below 0.8 M. The second generation of “polluted” stars is assumed to form only low-mass stars, following the same log-normal IMF (see below). The model allows for dynamical cluster evolution, and more specifically for the evaporation of stars due to primordial gas expulsion driven by supernovae as well as for long-term dynamical processes as described by Decressin, Baumgardt & Kroupa (2008); Decressin et al. (2010).
The main free parameter of the model is the IMF slope above 0.8 Mof the first stellar generation, the low-mass IMF being set for both the first and second stellar populations to the present-day mass function observed in GCs (Paresce & De Marchi, 2000). Second generation low-mass stars are then formed from the mass of slow wind ejecta predicted by the stellar evolution models of Decressin et al. (2007) and after dilution of this material with interstellar gas. The parameter describing this dilution is inferred from the observed Li–Na anticorrelation (see Decressin, Charbonnel & Meynet, 2007; Charbonnel & Decressin, 2011). We adopt from DCM07 as our standard value and comment on the (relatively weak) dependence of our results on this parameter.
Allowing for the escape of a fraction of first generation stars, the model then predicts the relative number of 1 and 2 generation stars, as well as detailed abundances ratios of these stars, which successfully reproduce observed abundance patterns and anticorrelations (see DCM07).
The fraction of “unpolluted”, pristine 1 generation long-lived stars still present today in GCs can be determined observationally from the distribution of stars along the O-Na anticorrelation (see e.g. Prantzos & Charbonnel, 2006). In the nomenclature of DCM07 one has , where and are the number of 1 and 2 generation low-mass, long-lived stars, respectively. Observations of the O-Na anticorrelation in a large GC sample by Carretta et al. (2010b) provide a median value ( 68 % CL) of both for the total sample and for the lowest metallicity ([Fe/H] ) hence oldest subsample. The semianalytical model of DCM07 predicts as a function of the IMF slope, the dilution parameter , and the fraction of low-mass, 1 generation stars being lost from the cluster due to dynamical processes (see Eqs. 20, 23 of DCM07). We can therefore invert this problem to determine, for each value of the IMF slope, the lost stellar mass fraction from the observed value of . With this at hand, all the properties of the two stellar generations mixed within the GC can be determined (see DCM07). Here we are in particular interested in the relation between the present-day, observed stellar mass and its total, initial value, as well as in the mass of stars ejected from the cluster. These are derived below.
To do so, we generalise the dynamical evolution scenario discussed in depth by DCM07 that allows for mass loss from the cluster (as described by in their “Scenario II”) due to mass segregation and evaporation of stars. We consider the IMF slope above 0.8 M as a free parameter, and we determine the allowed values of from the observed value of given above. However, it is understood that most observations for proto-GCs indicate an IMF slope close to Salpeter () in this mass range (see e.g. Chabrier, 2003; De Marchi, Paresce & Portegies Zwart, 2010; Bastian, Covey & Meyer, 2010). While DCM07 assume that all second generation stars are retained within the cluster ( in their notation), we will subsequently relax this assumption, motivated by recent findings of some chemically polluted, second generation stars in the Galactic halo (Carretta et al., 2010b; Martell & Grebel, 2010).
We now follow the semianalytical model of DCM07 and their notation. The current mass of 1 generation long-lived (i.e. low-mass) stars, , in a GC is , where is the fraction of 1 generation stars determined from observations (cf. above), and is the “observed”, current stellar mass of the globular cluster, excluding stellar remnants222Following standard stellar evolution, stellar remnants constitute approximately 30% of the total cluster mass after 12 Gyr. This fraction may, however, depend also on the dynamical evolution of the cluster (Kruijssen & Lamers, 2008, cf.).. Allowing for dynamical mass loss of stars from the cluster, the total (initial) stellar mass of the cluster can be written as
where stands for the fraction of stellar mass forming low-mass stars (in the 1 generation), i.e. the mass fraction of the IMF found at M, and where is the fraction of low-mass stars from the 1 generation having escaped from the cluster during its history. The total mass of ejected low-mass stars is then
where we also allow for a fraction of low-mass stars of the second generation to escape (see §4).
In the dynamical GC scenario discussed by DCM07, can be determined from the observed fraction of 1 generation stars for a given slope of the massive stars IMF, assuming a value for the global dilution factor (see their Fig. 4)333One obtains from their Eqs. 3 and 23, for the assumptions of scenario II, but relaxing the hypothesis of , i.e. allowing also for loss of 2 generation stars.. Since depends only on the IMF, it is straightforward to compute the relation between the observed and the total initial mass of GCs (Eq. 1) and the amount of stellar mass ejected (Eq. 2).
3 The initial mass of globular clusters
The ratio between the initial and present-day stellar mass computed in this manner is shown in the left panel of Fig. 1. Blue lines show the case of as in DCM07, the green and magenta curves when accounting for and respectively (see below). As can be seen, the steeper the IMF, the higher the ratio between the initial and current mass. This is the case since in the present framework massive stars are responsible for the chemical pollution of the GC that leads to the formation of second generation low-mass stars. Hence for a steeper IMF, a larger total mass of stars is required to compensate the relative decrease of massive stellar polluters in order to reproduce . In this way, the same total mass of massive star ejecta incorporated into the second generation stars can be produced. As mentioned above, all results shown here are computed adopting for the dilution parameter. A stronger dilution of the ejecta from the rapidly rotating massive stars (i.e. increasing ) would imply lower values of and , since more material is then available to form the 2 generation stars. In practice, changing by a factor 2 (3) around our “standard” value implies changes of 40–50 (100) % in the initial and ejected masses, comparable to the differences between the different cases illustrated in Fig. 1.
For a Salpeter IMF as assumed in DCM07, the initial cluster mass is found to be 8–10 times larger than the current (observed) mass when no second generation stars are lost, as seen in Fig. 1. Considering massive AGBs as potential GC polluters (instead of massive stars), and assuming that none of the second generation stars is lost, Prantzos & Charbonnel (2006) and Carretta et al. (2010b) also found that the original cluster population should have been larger than the current one by one order of magnitude for a Salpeter IMF. This agreement is dictated by the amount of initial mass of polluters needed to provide enough material for the second stellar generation. If we attribute the recently observed 2 generation stars in the halo to the present population of GCs (cf. §4.) we must allow for a loss of 2 generation stars (i.e. ), which implies even higher initial masses, as shown by the green and magenta curves in Fig. 1. In this case we typically find initial cluster masses (in stars) 15–25 times the present-day mass, for a Salpeter slope. Of course, the masses of proto-GC clouds must be even higher, depending on their star-formation efficiency.
4 Contribution to the Galactic stellar halo
The ratio between the ejected stellar mass and the present-day mass and its dependence on the IMF slope is illustrated in the right panel of Fig. 1. The total amount of low-mass ( M), long-lived stars (both the first and second generation) ejected from the cluster shown by the blue lines corresponds to times the observed, present-day mass of globular clusters, for a Salpeter IMF in the case where no second generation stars are lost as assumed by DCM07. This amount increases for a steeper IMF. These stars must contribute to the population of the Galactic halo.
Recent observations have found indications for chemically polluted, 2 generation stars in the Galactic halo, with a frequency of 1.4–2.5% (Carretta et al., 2010b; Martell & Grebel, 2010). While Vesperini et al. (2010) have examined the ejection of these stars with hydrodynamic cluster models, we follow here a different approach. If these stars originate from the population of present day GCs, we can easily infer the escape fraction of 2 generation stars , where 2% is the fraction of present-day GC of the total stellar halo mass (Freeman & Bland-Hawthorn, 2002). For 1 (2.5)% we obtain 0.43 (0.65), i.e. a loss of approximately half of the second generation low-mass stars. With such a loss, the initial cluster masses and the total amount of ejected stars must be even higher than discussed above. The corresponding values are shown in Fig. 1 with green and magenta lines. Typically both initial and ejected mass are increased by a factor 1.7–3.5 compared to the case of =0. For a Salpeter slope the mass of ejected low-mass stars is then 5–10 times the present day GC mass.
From the current total mass of halo Galactic globular clusters of M and the total halo mass M (Freeman & Bland-Hawthorn, 2002), i.e. the above 2%, we therefore find that low-mass stars ejected from the present-day population of GCs make up 5–8% of the mass of halo stars if =0, or 10–20% (for the above values ) if all halo 2 generation stars also come from these clusters. These numbers could be a factor 0.75 lower if a lower mass-to-light ratio of (Dubath & Grillmair, 1997; Larsen et al., 2002, cf.) instead of 2 adopted by (Freeman & Bland-Hawthorn, 2002, and others) was more appropriate.
For comparison, Carretta et al. (2010b) estimate a minimum contribution of GC stars to the stellar halo of 2.8%, but up to a factor 10 more, while from Martell & Grebel (2010) one obtains a contribution of 17.5% 444Their estimated 50% of the halo mass corresponds to the total stellar mass including the full mass spectrum. For a Salpeter slope one has a fraction 0.35 of low-mass stars; i.e. 17.5%.. These estimates, based on the observed fraction of 2 generation stars in the halo and on models accounting for multiple stellar generations, agree with ours. Other authors, using calculations of the GC survival fraction or their destruction rate (cf. Gnedin & Ostriker, 1997), estimate contributions of % (Parmentier & Gilmore, 2007) or less (Boley et al., 2009, 3-8 %) to the Galactic halo from the present-day GC population. Other estimates, based on a variety of different initial mass functions of stellar clusters range e.g. from 4–40 % (Fall & Zhang, 2001), 40–50% (Baumgardt, Kroupa & Parmentier, 2008), or up to 30–80 % (Boley et al., 2009). However, these studies neglect the observed multiple stellar generations in GC and their implications.
5 Implications for the initial globular cluster mass function
The fact that GCs show – now basically by definition (cf. Carretta et al., 2010b) – stellar generations, distinct by their chemical abundances, allows us to take a new step in constraining their initial cluster mass function. Indeed since stars showing the abundances characteristic of 2 generation stars have recently been found in the Galactic halo (Carretta et al., 2010b; Martell & Grebel, 2010), their frequency among normal halo stars provides interesting, new constraints within the framework of the model examined here.
Consider two limiting cases. First let us assume that all 2 generation stars found in the halo originate from the present-day population of GCs. As discussed above, one then finds for the initial mass of GCs typically . The globular cluster initial mass function (GCIMF) must then be equal to the observed one – commonly described by a log-normal with a characteristic mass M (cf. Harris, 1991) – but with increased by a factor 15–20, i.e. M. Besides this, there is no room left for other proto-GCs, since these would otherwise contribute – by definition – additional 2 generation stars to the halo.
Now assume the other extreme, namely none of the observed 2 generation halo stars are from the observed GCs. This corresponds to =0, and we know then that the present-day GC population had an initial mass function with a characteristic mass (8–10) times the present value ( M) and a total mass of M. In addition, however, other, dissolved GCs must be invoked to explain the presence of these peculiar stars in the halo. Let us assume that the total GCIMF is given by a power law with a slope , as often studied (e.g. Fall & Zhang, 2001; Boley et al., 2009). The lowest normalisation we can chose is the one tangential to, i.e. osculating the log-normal initial mass function of the present-day GCs, as discussed e.g. in Boley et al. (2009). From this we compute the total initial mass of GCs to be dissolved, , by subtracting from given by the integral of the GCIMF over the same range considered by Boley et al. (2009)555Approximately over , corresponding to a range of magnitudes V from -12 to -2 for the present-day GC mass function.. Since our osculating mass is (8–10) times higher than the one of Boley et al. (2009) we obtain M, from which 90% (or more) is in globular clusters which must be dissolved. Since the fraction of low-mass ( M) stars is for a Salpeter slope, all the globulars then contribute approximately 50–70% of the present-day stellar halo mass666Assuming instead of 2 (cf. above), this percentage would be lower by a factor 0.75.
From Eq. 1 and counting the fraction low-mass stars, we finally obtain the total amount of 2 generation stars produced in these clusters , which corresponds to a fraction 12–15% of the halo mass. If we adopt a lower mass-to-light ratio () and assume that 30% of the present GC mass consists of stellar remnants, the expected fraction of 2 generation stars in the halo may be somewhat lower, 6–8 %. To compute this value we have implicitly assumed – in the absence of other information – that all GCs can be described by the same values of and as those derived from the present-day GCs.
As can be seen, our theoretical prediction for the fraction of 2 generation stars in the halo is considerably larger than the current observational values of 1.4–2.5 % from Carretta et al. (2010b) and Martell & Grebel (2010). The simplest conclusion from this contradiction is that the GCIMF cannot be a simple power law with , as suggested by numerous authors (cf. Fall & Zhang, 2001; Boley et al., 2009; Elmegreen, 2010a), at least not over the mass range considered here. However, to reconcile our prediction with the observed value of , one would need to strongly reduce range of the initial cluster masses, since each decade in mass contains the same amount of total mass for this power law distribution. In other words, reducing the predicted by a factor 4 or more would imply an initial cluster mass function over less than 1 dex, compared to our assumption of . Similarly, postulating e.g. that clusters below a certain mass (say the present day value of suggested by Carretta et al. (2010b)) will not become globulars, does not solve our problem. Alternatively, in most clusters the fraction of unpolluted stars could be higher than the value observed in present-day GCs, in which case one could avoid “overproducing” the number of 2 generation stars in the halo. In this case, however, we cannot properly speak of an initial mass function for GCs, since these objects with much higher values of cannot be the progenitors of the present-day GC population.
We are therefore naturally drawn to abandon the picture of a “universal” initial power law mass function for all clusters, including super star clusters, young massive clusters etc. and for progenitors of present-day GCs. Then, as already discussed above, the observations of the 2 generation halo stars can be understood if the GCIMF is log-normal, as e.g. proposed by Vesperini & Zepf (2003) and Parmentier & Gilmore (2005, 2007). However, other initial mass functions, e.g. a power-law with a turn-over or Schechter-type functions, cannot yet be excluded.
In any case we have shown here that the observed fraction 2 generation stars in the halo can in principle provide very useful information on the distribution of the initial masses of globular clusters, the GCIMF. Of course, our analysis does not constrain the initial mass function of other (non-globular) clusters. In fact, since the percentage of halo stars originating from GCs is typically 20% in our scenarii, there is room for other clusters, accreted satellites, or others to provide the rest of the present-day stellar halo. After many recent studies proposing a “unified” picture for the formation and evolution of clusters of all kinds including GCs (cf. Brodie & Strader, 2006; Meurer, 1995; Fall & Zhang, 2001; Vesperini & Zepf, 2003; Elmegreen, 2010a, and references therein), it may well be that recent progress on GC stars and the finding of 2 generation stars among the halo population forces us again to revise this picture. One of the main questions arising now is actually what distinguishes “normal” clusters from globulars and “globulars-to-become”, i.e. what causes a cluster to form one or two separate stellar populations. Is this e.g. related to their initial central density, to external conditions, or maybe to completely different formation scenarios, as e.g. suggested by Searle & Zinn (1978); Freeman (1993); Böker (2008) or can this be understood within the framework of current hydrodynamic and cosmological formation models (e.g Boley et al., 2009; Elmegreen, 2010a)?
New detailed (hydro-)dynamic models of cluster formation and evolution taking into account recent insights gained from scenarii explaining the detailed behaviour of observed abundance pattern in GC stars (e.g. Decressin, Baumgardt & Kroupa, 2008; D’Ercole et al., 2008; Decressin et al., 2010) are clearly likely needed to progress further on this issue. In parallel it will be useful to firm up the first studies of second generation stars found in the Galactic halo, as they currently suffer e.g. from poor statistics (Carretta et al., 2010b) or from uncertainties in observational criteria identifying these stars (Martell & Grebel, 2010).
6 The contribution of globular clusters to reionisation
Since the initial masses of GCs may be substantially larger than their present day values, their output of ionising radiation and their contribution to cosmic reionisation also needs to be revised.
In Fig. 2 we plot the predicted H ionising photon output (i.e. the total number of photons emitted above 13.6 eV) during the life of a GC normalised to its current number of baryons777To convert photon/baryon into photon/mass one has e.g. baryon., , as a function of the IMF slope for the dynamical scenario described previously. The Lyman continuum flux was computed using the evolutionary synthesis code of Schaerer (2003); Raiter, Schaerer & Fosbury (2010) for a low metallicity typical of GCs888Adopting a different metallicity leads to small changes (typically 0.1–0.2 dex). Similarly, using the stellar evolutionary tracks of fast rotating stars used in the study of DCM07 would lead to relatively small changes compared to the effects discussed here..
Interestingly, the predicted ionising photon output is quite independent of the IMF slope (see Fig. 2), since both the metals explaining the observed abundance pattern and the ionising photons are made primarily in massive stars. Should the “pollution” of 2 generation stars be related to massive AGB stars, we expect a similarly large emission of ionising photons per baryon, since the ratio between the initial and present-day mass is similar in both scenarios (cf. above). In the AGB scenario the dependence of on the IMF should, however, but somewhat stronger, since the masses responsible for the stellar ejecta and the ionising photons are more distinct than in the fast rotating, massive star scenario. Of course, one also finds an increased output of ionising photons per unit present-day mass (or baryon number) if loss of second generation stars is allowed (green and magenta lines) compared to the case where (blue lines). This increase is simply due to higher initial mass of GCs, discussed previously.
Ricotti (2002) has estimated the output of GCs per baryon as , with 999Making the same assumptions as Ricotti we confirm this value. and 2–10 (with a maximum of ), where – the equivalent of our ratio – is a factor accounting for dynamical disruption of GCs during their lifetime. In our case, the total photon output is 4.8–4.9 photon/baryon if all second generation stars remain within the cluster, which is approximately a factor 5 higher than the typical value adopted by Ricotti (2002) for . The amount of emitted ionising photons must be even higher if 2 generation stars were lost from these clusters (), as illustrated by the green and magenta lines.
Using simple but elegant arguments to estimate the number of ionising photons emitted per baryon during the formation of GCs, and using a Press-Schechter model to compute the GC formation rate, Ricotti (2002) has estimated the contribution of GCs to cosmic reionisation. He has shown that the old GCs produced enough ionising photons to reionise the inter-galactic medium at , if the escape fraction of ionising photons, , from these objects was close to unity. Our finding of a high ionising photon production in GCs reinforces the conclusions of Ricotti (2002) and leaves room for lower values of or for other less favourable assumptions (e.g. uncertainties in the age of GCs). It appears that old GCs, formed as massive super star clusters shortly after the Big Bang, could provide a significant if not dominant source of UV radiation to reionise the Universe at high redshift, In any case, it seems unavoidable to seriously consider their contribution.
With a typical mass of a young proto-GC is expected to have a peak UV (say 1500 Å) magnitude of at an age Myr, before fading by 4 mags within Myr just due to stellar evolution (see e.g. models of Leitherer et al., 1999; Schaerer, 2003) or faster when evaporation (mass loss) sets in. At redshifts of 7–10 this would correspond to a typical UV restframe magnitude of at the peak, just slightly fainter than the current detection limits of the deepest near-IR images taken with the WFC3 camera onboard HST (cf. Bouwens et al., 2010). In any case, single, massive proto-GCs during their youth might be detectable in situ with current instrumentation, and are certainly well within the reach of even deeper near-IR observations, which will be achieved with the JWST. However, whether the two proposed scenarii (massive AGB or fast rotating, massive stars as the origin of the bulk of material out which 2 generation stars form in GCs) can be distinguished observationally at high redshift, appears a priori quite difficult, if not impossible.
7 Summary and conclusions
In light of the recently recognised, general existence of multiple stellar generations in globular clusters (GCs) implying significant losses of 1 generation stars from these clusters, we have re-examined the initial masses of GCs, the contribution of low-mass stars ejected from GCs to the stellar halo of our Galaxy, and the contribution of GCs to the ionising photon production necessary to reionise the inter-galactic medium at high redshift.
These quantities have been estimated from the chemical and dynamical model of Decressin, Charbonnel & Meynet (2007), which successfully reproduces the main observational constraints from 1 and 2 generation stars, by invoking pollution from fast rotating massive stars. The main free parameters of this model are the slope of IMF for high masses ( 0.8 M, the IMF being fixed to the observed log-normal distribution for lower masses), the relative number of 1/2 generations stars, given by the fraction of 1 generation stars determined from the detailed spectroscopic observations of Carretta et al. (2010b), and a dilution parameter inferred from the Li-Na anticorrelation observed in GCs (Decressin, Charbonnel & Meynet, 2007; Charbonnel & Decressin, 2011).
The dynamical scenario we have explored allows for the evaporation of stars from the 1 generation (corresponding to an escape fraction of 2 generation stars of zero, ), or from both generations, as suggested by recent observations finding stars characteristic of the 2 generation in GCs in the Milky Way halo (Carretta et al., 2010b; Martell & Grebel, 2010). The latter case translates to 0.43–0.65.
We have obtained the following main results for an IMF with a Salpeter slope above 0.8 M:
The initial stellar masses of GCs must have been 8–10 times larger than the current (observed) mass, when no second generation stars are lost, in agreement with the earlier results of Prantzos & Charbonnel (2006) and Carretta et al. (2010b). If all 2 generation halo stars originate from the present population of GCs, the initial cluster masses must have been times larger than the current mass.
The mass in low-mass stars ejected from GCs must be times their observed, stellar mass if all 2 generation stars were retained, or 5–10 times the present day mass if 0.43–0.65. These numbers translate to a contribution of 5–8% or 10–20% respectively of the ejected low-mass stars to the Galactic stellar halo mass. We have compared our estimate with earlier values obtained from various methods (cf. §4).
The observations of 2 generation stars in the Galactic halo can constrain the initial mass function of the GC population (GCIMF). In particular we have shown that a power-law with a slope , as often assumed, is in contradiction with recent determinations of the fraction of 2 generation stars in the halo, whereas a log-normal GCIMF is compatible with these observations. This finding revives the question about a common mass function and about the physical processes leading to a distinction between globular clusters with multiple stellar populations and other clusters.
Due to their high initial masses, the amount of Lyman continuum photons emitted by GCs during their youth must have been substantial. Indeed, we find that their output corresponds to a total number of ionising photons emitted per baryon, for , or 1.7–3.5 times more if 0.4-0.6. Our results reinforce the conclusion of Ricotti (2002) that GCs should contribute significantly to reionise the IGM at very high redshift (). Individual, young proto-GCs with typical masses few times could just be detectable at high redshift in ultra-deep images with the HST, and are certainly within the reach of the JWST.
The dependence of the initial and ejected masses on the IMF slope has been illustrated in Fig. 1. The ionising photon production is found to be quite insensitive to the high mass IMF, since both the ejecta “polluting” the 2 generation stars and the Lyman continuum flux originates from massive stars. Our main results should also be valid for the massive AGB scenario, at least qualitatively.
We thank Thibault Decressin, Andrea Ferrara, and Massimo Ricotti for comments on an earlier version of this paper. This work was supported by the Swiss National Science Foundation.
- Bastian, Covey & Meyer (2010) Bastian N., Covey K. R., Meyer M. R., 2010, ARA&A, 48, 339
- Baumgardt, Kroupa & Parmentier (2008) Baumgardt H., Kroupa P., Parmentier G., 2008, MNRAS, 384, 1231
- Bedin et al. (2004) Bedin L. R., Piotto G., Anderson J., Cassisi S., King I. R., Momany Y., Carraro G., 2004, ApJL, 605, L125
- Bell et al. (2008) Bell E. F. et al., 2008, ApJ, 680, 295
- Boily (2010) Boily C. M., 2010, in IAU Symposium, Vol. 266, IAU Symposium, R. de Grijs & J. R. D. Lépine, ed., pp. 238–249
- Böker (2008) Böker T., 2008, ApJL, 672, L111
- Boley et al. (2009) Boley A. C., Lake G., Read J., Teyssier R., 2009, ApJL, 706, L192
- Bouwens et al. (2010) Bouwens R. J. et al., 2010, ArXiv e-prints
- Brodie & Strader (2006) Brodie J. P., Strader J., 2006, ARA&A, 44, 193
- Bromm & Clarke (2002) Bromm V., Clarke C. J., 2002, ApJL, 566, L1
- Bunker et al. (2010) Bunker A. J. et al., 2010, MNRAS, 1378
- Carretta et al. (2009a) Carretta E., Bragaglia A., Gratton R., D’Orazi V., Lucatello S., 2009a, A&A, 508, 695
- Carretta et al. (2009b) Carretta E., Bragaglia A., Gratton R., Lucatello S., 2009b, A&A, 505, 139
- Carretta et al. (2010a) Carretta E. et al., 2010a, ApJL, 714, L7
- Carretta et al. (2010b) Carretta E., Bragaglia A., Gratton R. G., Recio-Blanco A., Lucatello S., D’Orazi V., Cassisi S., 2010b, A&A, 516, A55+
- Chabrier (2003) Chabrier G., 2003, PASP, 115, 763
- Charbonnel (2010) Charbonnel C., 2010, in IAU Symposium, Vol. 266, IAU Symposium, R. de Grijs & J. R. D. Lépine, ed., pp. 131–142
- Charbonnel & Decressin (2011) Charbonnel C., Decressin T., 2011, A&A, 718, in preparation
- Choudhury & Ferrara (2007) Choudhury T. R., Ferrara A., 2007, MNRAS, 380, L6
- Choudhury, Ferrara & Gallerani (2008) Choudhury T. R., Ferrara A., Gallerani S., 2008, MNRAS, 385, L58
- Cottrell & Da Costa (1981) Cottrell P. L., Da Costa G. S., 1981, ApJL, 245, L79
- Da Costa et al. (2009) Da Costa G. S., Held E. V., Saviane I., Gullieuszik M., 2009, ApJ, 705, 1481
- De Marchi, Paresce & Portegies Zwart (2010) De Marchi G., Paresce F., Portegies Zwart S., 2010, ApJ, 718, 105
- Decressin et al. (2010) Decressin T., Baumgardt H., Charbonnel C., Kroupa P., 2010, A&A, 516, A73+
- Decressin, Baumgardt & Kroupa (2008) Decressin T., Baumgardt H., Kroupa P., 2008, A&A, 492, 101
- Decressin, Charbonnel & Meynet (2007) Decressin T., Charbonnel C., Meynet G., 2007, A&A, 475, 859
- Decressin et al. (2007) Decressin T., Meynet G., Charbonnel C., Prantzos N., Ekström S., 2007, A&A, 464, 1029
- D’Ercole et al. (2008) D’Ercole A., Vesperini E., D’Antona F., McMillan S. L. W., Recchi S., 2008, MNRAS, 391, 825
- Dubath & Grillmair (1997) Dubath P., Grillmair C. J., 1997, A&A, 321, 379
- Elmegreen (2010a) Elmegreen B. G., 2010a, ApJL, 712, L184
- Elmegreen (2010b) —, 2010b, in IAU Symposium, Vol. 266, IAU Symposium, R. de Grijs & J. R. D. Lépine, ed., pp. 3–13
- Fall & Zhang (2001) Fall S. M., Zhang Q., 2001, ApJ, 561, 751
- Freeman & Bland-Hawthorn (2002) Freeman K., Bland-Hawthorn J., 2002, ARA&A, 40, 487
- Freeman (1993) Freeman K. C., 1993, in Astronomical Society of the Pacific Conference Series, Vol. 48, The Globular Cluster-Galaxy Connection, G. H. Smith & J. P. Brodie, ed., pp. 608–+
- Gnedin & Ostriker (1997) Gnedin O. Y., Ostriker J. P., 1997, ApJ, 474, 223
- Gratton, Sneden & Carretta (2004) Gratton R., Sneden C., Carretta E., 2004, ARA&A, 42, 385
- Gratton et al. (2001) Gratton R. G. et al., 2001, A&A, 369, 87
- Griffen et al. (2010) Griffen B. F., Drinkwater M. J., Thomas P. A., Helly J. C., Pimbblet K. A., 2010, MNRAS, 405, 375
- Harris (1991) Harris W. E., 1991, ARA&A, 29, 543
- Hut & Djorgovski (1992) Hut P., Djorgovski S., 1992, Nature, 359, 806
- James et al. (2004) James G., François P., Bonifacio P., Carretta E., Gratton R. G., Spite F., 2004, A&A, 427, 825
- Johnson & Pilachowski (2010) Johnson C. I., Pilachowski C. A., 2010, ApJ, 722, 1373
- Kravtsov & Gnedin (2005) Kravtsov A. V., Gnedin O. Y., 2005, ApJ, 623, 650
- Kruijssen & Lamers (2008) Kruijssen J. M. D., Lamers H. J. G. L. M., 2008, A&A, 490, 151
- Labbé et al. (2010) Labbé I. et al., 2010, ApJL, 708, L26
- Larsen et al. (2002) Larsen S. S., Brodie J. P., Sarajedini A., Huchra J. P., 2002, AJ, 124, 2615
- Leitherer et al. (1999) Leitherer C. et al., 1999, ApJS, 123, 3
- Martell & Grebel (2010) Martell S. L., Grebel E. K., 2010, A&A, 519, A14+
- McLure et al. (2010) McLure R. J., Dunlop J. S., Cirasuolo M., Koekemoer A. M., Sabbi E., Stark D. P., Targett T. A., Ellis R. S., 2010, MNRAS, 403, 960
- Meurer (1995) Meurer G. R., 1995, Nature, 375, 742
- Milone et al. (2008) Milone A. P. et al., 2008, ApJ, 673, 241
- Milone et al. (2010) —, 2010, ApJ, 709, 1183
- Ouchi et al. (2009) Ouchi M. et al., 2009, ApJ, 706, 1136
- Paresce & De Marchi (2000) Paresce F., De Marchi G., 2000, ApJ, 534, 870
- Parmentier & Gilmore (2005) Parmentier G., Gilmore G., 2005, MNRAS, 363, 326
- Parmentier & Gilmore (2007) —, 2007, MNRAS, 377, 352
- Piotto (2009) Piotto G., 2009, in IAU Symposium, Vol. 258, IAU Symposium, E. E. Mamajek, D. R. Soderblom, & R. F. G. Wyse, ed., pp. 233–244
- Piotto et al. (2007) Piotto G. et al., 2007, ApJL, 661, L53
- Prantzos & Charbonnel (2006) Prantzos N., Charbonnel C., 2006, A&A, 458, 135
- Prantzos, Charbonnel & Iliadis (2007) Prantzos N., Charbonnel C., Iliadis C., 2007, A&A, 470, 179
- Raiter, Schaerer & Fosbury (2010) Raiter A., Schaerer D., Fosbury R., 2010, ArXiv e-prints
- Ricotti (2002) Ricotti M., 2002, MNRAS, 336, L33
- Schaerer (2003) Schaerer D., 2003, A&A, 397, 527
- Searle & Zinn (1978) Searle L., Zinn R., 1978, ApJ, 225, 357
- Siegel et al. (2007) Siegel M. H. et al., 2007, ApJL, 667, L57
- Sneden (2005) Sneden C., 2005, in IAU Symposium, Vol. 228, From Lithium to Uranium: Elemental Tracers of Early Cosmic Evolution, V. Hill, P. François, & F. Primas, ed., pp. 337–344
- Ventura & D’Antona (2009) Ventura P., D’Antona F., 2009, A&A, 499, 835
- Ventura et al. (2001) Ventura P., D’Antona F., Mazzitelli I., Gratton R., 2001, ApJL, 550, L65
- Vesperini et al. (2010) Vesperini E., McMillan S. L. W., D’Antona F., D’Ercole A., 2010, ApJL, 718, L112
- Vesperini & Zepf (2003) Vesperini E., Zepf S. E., 2003, ApJL, 587, L97
- Villanova et al. (2010) Villanova S., Piotto G., Marino A. F., Milone A. P., Bellini A., Bedin L. R., Momany Y., Renzini A., 2010, in IAU Symposium, Vol. 266, IAU Symposium, R. de Grijs & J. R. D. Lépine, ed., pp. 326–332