Abstract

The most massive Galactic globular cluster ω Cen appears to have two, or perhaps more, distinct main sequences. Its bluest main sequence is at the centre of debate because it has been suggested to have an extremely high helium abundance of Y ∼ 0.4. The same helium abundance is claimed to explain the presence of extreme horizontal branch stars of ω Cen as well. This demands a relative helium-to-metal enrichment of ΔYZ ∼ 70; that is, more than one order of magnitude larger than the generally accepted value. Candidate solutions, namely asymptotic giant branch stars, massive stars and supernovae, have been suggested; but in this study, we show that none of them is a viable channel, in terms of reproducing the high value of ΔYZ for the constrained age difference between the red and blue populations. Essentially no populations with an ordinary initial mass function, including those candidates, can produce such a high ΔYZbecause they all produce metals as well as helium. As an alternative, we investigate the possibility of the stochastic ‘first star’ contamination to the gas from which the younger generation of ω Cen formed. This requires the assumption that the Population III star formation episode overlaps with that of Population II. While the required condition appears extreme, very massive objects in the first star generation provide a solution that is at least as plausible as any other suggestions made before.

Introduction

The most massive Galactic globular cluster, ω Cen, shows a double (or more) main sequence in the colour–magnitude diagrams (CMDs), with a minority population of the bluer main sequence (bMS) and a majority population of redder MS (rMS) stars (Anderson 1997; Bedin et al. 2004). The interpretation of the bMS by a huge excess in the helium abundance (Y∼ 0.4) has been suggested via CMD fittings (Norris 2004) and supported by the spectroscopic study on the bMS stars (Piotto et al. 2005). The extreme helium abundance is claimed to explain the extremely hot horizontal-branch (HB) stars of ω Cen as well (Lee et al. 2005).

The helium-enrichment parameter ΔYZ required to explain the subpopulation of ω Cen are ∼70, more than an order of magnitude larger than the currently accepted value, 1–5 (Fernandes, Lebreton & Baglin 1996; Pagel & Portinari 1998; Jimenez et al. 2003). To explain this, several possible polluters, i.e. asymptotic giant branch (AGB) stars, stellar winds associated with massive stars during their early evolutionary phases and Type II supernovae (SNe II) have been suggested (e.g. Norris 2004; D'Antona et al. 2005). However, Bekki & Norris (2006) show that these candidates cannot reproduce such a high helium abundance for reasonable initial mass functions (IMFs) within the scheme of a closed-box self-enrichment.

The acute point is not the high helium abundance itself but the high value of ΔYZ, because populations containing those candidates produce a large amount of metals as well as helium according to canonical stellar evolution models. Maeder & Meynet (2006) have recently suggested that ‘moderately’ fast-rotating massive (∼60M) stars expel helium-dominant gas into space and thus could provide a solution to this problem. We show that this scenario provides a viable solution only if additional conditions on the mixing and escaping of metals are invoked.

As an alternative solution, we investigate the possibility that the late generation of ‘the first stars’ (Population III) might affect the chemical mixture of the minority of Population II stars. We are particularly inspired by the work of Bromm & Loeb (2006) that suggested an overlap between the Population III and II star formation episodes. The chemical yields of such supposedly heavy, zero-metal stars have been computed by Marigo, Chiosi & Kudritzki (2003). We present in this Letter the result of our investigation.

Chemical Evolution Models

In order to investigate the pattern of the helium enhancement in a population, we employ a simple chemical evolution code and a realistic initial mass function (IMF). We describe a simple chemical enrichment model essentially following the formalism of Tinsley (1980) and reduce a set of a few parameters following the formalism of Ferreras & Silk (2000, 2001). A two-component system is considered, consisting of cold gas and stellar mass. The net metallicity Z and helium content Y of two systems are traced. We assume instantaneous mixing of the gas ejecta from stars and instantaneous cooling of the hot gas component. The mass in stars, Ms(t) and in cold gas, Mg(t), are normalized to the initial gas mass,  

1
formula
where the initial state of the galaxy is assumed to be completely gaseous and without stars: μs(0) = 0.

A Schmidt-type star formation law (Schmidt 1963) is assumed:  

2
formula
where the parameter Ceff implies the star formation efficiency. We assume n= 1, that is, a linear law ψ(t) =CeffMg(t).

Exponential infall of primordial gas is assumed:  

3
formula
where Θ(t) is a step function. The parameters Ainfinf and τlag are the infall rate, time-scale and delay, respectively. In order to explain the G-dwarf problem (Tinsley 1980), gas infall has been considered as a solution (Larson 1972).

Some cold gas is heated to high temperature by supernovae and/or active galactic nuclei and can be driven out: outflows. It is also an important factor to the final chemical properties of galaxies (Larson 1974; Arimoto & Yoshii 1987). We use a free parameter Bout that represents the fraction of gas ejected following the formalism of Ferreras & Silk (2000). This parameter should be a function of the mass of the galaxy, the potential well of which determines whether the winds are strong enough to escape its gravitational potential.

There are five input parameters, Ceff, Bout, Ainf, τinf and τlag, with the following initial conditions: the initial metallicity Z0= 10−4, the initial helium Y0= 0.235, the IMF slopes and cut-offs.

Mass evolution

The evolution of gas mass is given by  

4
formula
where the stellar mass ejecta E(t) is defined as  
5
formula
where φ(m) is the Scalo IMF (Scalo 1986) with cut-offs at 0.1 and 100M. We adopt the broken power-law of Ferreras & Silk (2000, equation 6) for the stellar lifetime. The remnant mass for a star with main-sequence mass m, wm, is adopted from Ferreras & Silk (2000).

Chemical evolution

The chemical evolution of gas is given by  

6
formula
 
7
formula
where pm denotes the mass fraction of a star of mass m that is newly converted to metals or helium and ejected. We approximate it by a polynomial fit to the pm prediction of Maeder (1992). In Fig. 1, we show Maeder's chemical yields for metal-poor (Z= 0.001) stars and our fitting functions. For our reference model, we use these chemical yields.

Figure 1

Top: the chemical yields of metal-poor (Z= 0.001) stars from Maeder (1992) and our fits to them. The red dash–dotted line is for our ad hoc case employing the Z= 0.00001 rotating massive models by Maeder & Meynet (2006) for M≥ 50M. Bottom: the resulting helium-to-metal ratios (bottom). The red line is for the ad hoc case.

Figure 1

Top: the chemical yields of metal-poor (Z= 0.001) stars from Maeder (1992) and our fits to them. The red dash–dotted line is for our ad hoc case employing the Z= 0.00001 rotating massive models by Maeder & Meynet (2006) for M≥ 50M. Bottom: the resulting helium-to-metal ratios (bottom). The red line is for the ad hoc case.

We also show the metal yields of extremely metal-poor (Z= 0.00001) rotating stars (Maeder & Meynet 2006) using a dotted line. Maeder & Meynet computed the yields for 60-M stars, and in order to demonstrate their effects to the ΔYZ of an integrated population we set up an extreme assumption that the newly proposed metal yields may be applicable to all heavy stars of M≥ 50.

The crucial point shown here is that canonical stellar models produce and spread into space metals as well as helium. No combination of these stars can produce a ΔYZ that exceeds the values of the constituent stars. The rotating metal-poor massive star models by Maeder & Meynet (2006) are the exception and indeed can produce high values of ΔYZ. Thus we explore below whether a population including such stars can indeed present a solution to our problem.

SNe Ia are generally considered important in chemical evolution studies because they eject a considerable amount of iron-peak elements: ∼0.7M (Tsujimoto et al. 1995). For our exercise, we have tried the most up-to-date SN Ia rate of Scannapieco & Bildsten (2005), consisting of two components: star formation rate and the total stellar mass of the system. The contribution by SNe Ia is negative in our study because they are copious producers of metals. We remove its effects for simplicity.

We have found that gas infall or outflows of the processed material have negligible impacts on ΔYZ unless specific chemical elements alone (e.g. helium or metals) are affected. Hence, only the closed-box model is considered.

The star formation efficiency parameter Ceff has a small effect. When a range Ceff= 0.1–5.0Gyr−1 is considered, a population can reach ΔYZ≈ 1–2 after a 1-Gyr evolution. We show a typical case of Ceff= 1 in Fig. 2 as a solid line. The value of our reference model is consistent with the most recent observational mean value of the helium enrichment parameter of the galactic gas.

Figure 2

The helium enrichment parameters resulting from the stochastic effect. Our reference model is shown in solid line. Other lines are for the cases that pm,Y is doubled for (i) all stars, (ii) 6–10 M stars (AGB progenitors) stars and (iii) 40–50 M (SNii progenitors). Finally, triple-dot–dashed line shows the model that assumes that all heavy stars (M≥ 50) are fast-rotating, showing yields of Maeder & Meynet (2006). All models are for the case of Ceff= 1 and the chemical mixing time-scale of 50 Myr.

Figure 2

The helium enrichment parameters resulting from the stochastic effect. Our reference model is shown in solid line. Other lines are for the cases that pm,Y is doubled for (i) all stars, (ii) 6–10 M stars (AGB progenitors) stars and (iii) 40–50 M (SNii progenitors). Finally, triple-dot–dashed line shows the model that assumes that all heavy stars (M≥ 50) are fast-rotating, showing yields of Maeder & Meynet (2006). All models are for the case of Ceff= 1 and the chemical mixing time-scale of 50 Myr.

Having failed to recover the high ΔYZ in the standard chemical enrichment model, we consider the stochastic effect in the helium yields pm,Y. We assume that the stars in a specific mass range can have larger values of pm,Y than the current stellar physics suggest.

Fig. 2 presents part of the result of the stochastic-effect test, where Ceff= 1 is assumed; (i) when pm,Y is doubled for all the stars, (ii) when pm,Y is doubled for 6–10M stars, maximising the AGB effect, and (iii) when pm,Y is doubled for 40–50M stars, allowing the SN II effect to dominate. Lastly, the triple-dot–dashed line is for the model where all heavy stars (M≥ 50) are fast-rotating showing yields of Maeder & Meynet (2006). Because instant recycling of chemical elements is unrealistic, we use the chemical mixing time-scale of 50 Myr.

The ΔYZ value after a 13-Gyr evolution of the AGB-dominant system is merely ∼2 times greater than that of the reference system. The effect is even smaller for the SNe II dominant system. Even if we double the values of pm,Y for all stars, the system could attain only ΔYZ≈ 4. But of course, for our purpose, we need a much higher helium enrichment within a much shorter time-scale (≈1 Gyr).

Doubling the helium yields is ad hoc and hard to justify in terms of nucleosynthesis. Even in this unphysical test, however, the stochastic effect does not help us achieve the high ΔYZ. This is because (i) ordinary stars produce and spread into space not only helium but also metals, and (ii) most notably in the ‘Maeder & Meynet case’, there are many more low-mass stars in the ordinary IMF than massive stars.

Other possible contributing factors, e.g. IMF slope and the remnant mass wm, also have some influence. One may wonder about the effect of radically different IMFs (e.g. with a reversed slope). This indeed would produce more helium but even more metals in ordinary stellar populations, hence in fact lowering the resulting value of ΔYZ. On the other hand, a reversed IMF slope would dramatically increase ΔYZ in the ‘Maeder & Meynet case’. However, this is not expected to be common because otherwise all populations with massive stars would have enhanced helium.

When assuming that the helium enrichment of bMS of ω Cen is due to the ejecta from the rMS formed earlier, the candidate solution is even more severely constrained. For example, low-mass stars which produce mainly helium can generate high values of ΔYZ up to ∼8 but they take much too long to spread the processed materials into space, when compared to the age difference between the two sub-systems in ω Cen, i.e. 1–2 Gyr (Lee et al. 2005). Any star with a life-time that is longer than this would have no impact at all.

The ‘Maeder & Meynet case’ is noteworthy as it is the only scenario where high values of ΔYZ can be achieved during a short period of time. Assuming all stars form simultaneously in a population, ΔYZ can be as high as we need during the first few Myr until intermediate-mass stars begin to spread a large amount of gas into space. In this sense, this scenario provides a solution if the bMS population of ω Cen is only slightly younger than its rMS population. However, the time window (∼107−8 yr) for this to happen is very small compared to the constraint from CMD studies (Lee et al. 2005). The possibility of difference in the effect of stellar wind for helium and metals demands further studies, and the role of the local black hole accretion on metals may also be noteworthy (Maeder & Meynet 2006).

Very Massive Objects

We finally explore the plausibility of the ‘first’ Pop III star pollution. The first stars in the Universe are thought to have formed out of the metal-free gas at redshifts z≳ 10 (Bromm & Larson 2004; Ciardi & Ferrara 2005). These Pop III stars are often predicted to be very massive, M≳ 100M (Bromm, Coppi & Larson 2002; Abel, Bryan & Norman 2002), although a different suggestion has also been made (Silk & Langer 2006). They are considered to be significant contributors to various phenomena (Carr, Bond & Arnett 1984).

We have calculated the chemical enrichment evolution of the closed-box system made only of very massive objects (VMOs). Marigo et al. (2003) give the evolutionary properties of VMOs including lifetime, helium and metal yields, carbon and helium cores at central C-ignition and mass loss for 120–1000M. Two different mass loss rates are considered by them: the radiation-driven mass-loss model and the rotation-driven model. The yields and mass-loss rates of the two models are slightly different from each other, and we use the rotation-driven model because it produces a larger amount of helium. We find linear fits to these yields in the logarithmic scale (Fig. 3) and show the resulting ΔYZ for each mass of VMO. The helium enrichment parameter of VMOs ranges between 63–6 × 107!

Figure 3

Top: symbols represent pm,Y, pm,Z and the newly synthesized and ejected helium or metal mass fraction, calculated from yields of Marigo et al. (2003) for 120, 250, 500, 750 and 1000M VMOs. The lines between the symbols show our interpolation based on the five points given. Bottom: the ΔYZ of each mass of VMO.

Figure 3

Top: symbols represent pm,Y, pm,Z and the newly synthesized and ejected helium or metal mass fraction, calculated from yields of Marigo et al. (2003) for 120, 250, 500, 750 and 1000M VMOs. The lines between the symbols show our interpolation based on the five points given. Bottom: the ΔYZ of each mass of VMO.

We have calculated ΔYZ for a population of VMOs with various mass cuts and IMF slopes. The ΔYZ value after the 1-Gyr evolution in a closed-box system varies with IMF slope and mass cut-off. The values of ΔYZ as a function of the lower mass cut-off are shown in Fig 4. We fix the high mass cut-off as 1000M assuming the Salpeter IMF. The resulting range of ΔYZ after 1Gyr of evolution is two orders of magnitude higher than that of an ordinary system. Our model matches the values of both Y (∼0.4) and ΔYZ (∼70) at the age ∼1 Gyr suggested for the bMS subpopulation, as marked in Fig. 5. Interestingly, the solution suggests M(VMO) ∼995–1000M; but considering the uncertainty in the VMO yields, it may not be significant.

Figure 4

The mass cut-off dependence of ΔYZ of the ejecta from VMOs. We constrain the high mass cut-off of IMF as 1000M and the IMF slope as a canonical value, x= 1.35. The system consisting of 120 ∼1000M VMOs with the Salpeter IMF slope results in ΔYZ∼ 520, and a 995 ∼ 1000M system produces ΔYZ∼72.

Figure 4

The mass cut-off dependence of ΔYZ of the ejecta from VMOs. We constrain the high mass cut-off of IMF as 1000M and the IMF slope as a canonical value, x= 1.35. The system consisting of 120 ∼1000M VMOs with the Salpeter IMF slope results in ΔYZ∼ 520, and a 995 ∼ 1000M system produces ΔYZ∼72.

Figure 5

Chemical evolution in the gas of the VMO system for different values of star formation efficiency. The values of helium and ΔYZ of the bMS population of ω Cen are marked (squares) in each panel.

Figure 5

Chemical evolution in the gas of the VMO system for different values of star formation efficiency. The values of helium and ΔYZ of the bMS population of ω Cen are marked (squares) in each panel.

Discussion

By means of a simple chemical evolution test, we conclude that ordinary populations cannot produce ΔYZ values much greater than 4. None of the candidates succeeds in reproducing the large helium enrichment claimed for the bMS stars of ω Cen. The reason for this is simple: the evolution of ordinary stars result only in a modest value ΔYZ∼ 1–5. We confirm the result of Karakas et al. (2006), who rejected the AGB solution on a similar ground. The massive rotating star models of Maeder & Meynet (2006) reach high values of ΔYZ, but it is difficult to maintain the high value longer than a few Myr in a population with a realistic mass spread.

We present Pop III VMOs as an alternative solution. They produce both the helium abundance and the helium-to-metal ratio searched for at the age t≈ 1 Gyr demanded by the observational constraint. This scenario requires an overlap between the star formation episodes of Pop III and Pop II. Suppose that ω Cen formed in the era of overlap of Pop III and Pop II formation. Earlier generations of Pop III stars form and their mass ejecta are mixed in the short time-scale of roughly 107−8 yr. The first generation of Pop II stars start forming globally (this is not part of ω Cen) and the processed gas gets recycled and mixed in the proto-system until the gas reaches 〈Z〉∼0.001. By now, the mixed mean helium abundance is not any more extraordinary but contains severe irregularities. The rMS population of ω Cen forms with the mean chemical composition. A group of Pop III VMOs form in the tail of the Pop III episode nearby out of a pristine (irregularity) gas cloud. Soon after this, that is, before their ejecta are mixed fully, the younger stars of ω Cen (bMS) form under the heavy influence of this helium-rich ejecta. After the dynamical relaxation, the two chemically distinct populations could be in one system. As this is a geographic and chronological stochastic effect, it would not be significant in the galactic scale.

The plausibility of our scenario strongly depends on the validity of Marigo et al.'s yields. Other groups have computed the yields for zero-metallicity VMOs (e.g. Bond, Arnett & Carr 1984; Ober, El Eid & Fricke 1983; Klapp 1984), and Marigo et al.'s yields are not in a smooth continuation with the yields of low-mass zero-metal stars given by Limongi & Chieffi (2002). The discontinuity may not be a big issue if the mass loss in VMOs may happen in an extreme fashion (Smith 2006). Considering the acute dependence of our conclusion on the reliability of the chemical yields, it is urgent to perform detailed independent stellar evolution modelling for VMOs.

The second question about this scenario is on the condition of VMO formation. The Pop II star formation is allowed in the broad regions of Pop III objects (Tsujimoto, Shigeyama & Yoshii 1999; Susa & Umemura 2006). The bMS population of ω Cen has ∼30 per cent of the cluster mass (Lee et al. 2005). Assuming Mtot∼106M, the helium-rich population mass would be MbMS∼3 × 105M. Assuming the primordial helium abundance is 23 per cent, 17 per cent of the bMS population mass, MHe∼ 5 × 104M, is the newly generated helium mass. To generate 5 × 104M pure helium from 1000-M VMOs, we need at least ∼200 VMOs simultaneously. However, Abel et al. (2002) suggest that metal-free stars form in isolation due to the immense radiation from the first-forming star. Moreover, such a large number of Pop III stars forming close to each other, if that is possible at all, would make the site extremely hostile for the younger generation of ω Cen to form. This poses serious challenges to our scenario. By definition, this stochastic effect works only on small scales and not in the galactic scale. However, the number of VMOs required would be smallest in the deepest local gravitational potential, which means that this rare event of achieving a high ΔYZ would prefer larger gravitationally bound objects, such as massive globular clusters rather than small ones.

Acknowledgments

We thank the anonymous referee for useful comments. We are grateful to Ignacio Ferreras, Nobuo Arimoto, Volker Bromm, Greg Bryan, Brad Gibson, Young-Wook Lee, Jason Tumlinson and Suk-Jin Yoon for stimulating discussions. This was supported by grant No. R01-2006-000-10716-0 from the Basic Research Program of the Korea Science and Engineering Foundation and by Yonsei University Research Fund of 2005 (SKY).

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