hierarchical formation of the galactic halo and the origin ... - IOPscience

The Astrophysical Journal, 696:L79–L83, 2009 May 1  C 2009.

doi:10.1088/0004-637X/696/1/L79

The American Astronomical Society. All rights reserved. Printed in the U.S.A.

HIERARCHICAL FORMATION OF THE GALACTIC HALO AND THE ORIGIN OF HYPER METAL-POOR STARS Yutaka Komiya1,2 , Asao Habe3 , Takuma Suda3,4 , and Masayuki Y. Fujimoto3 2

1 Astronomical Institute, Tohoku University, Sendai, Miyagi 980-8578, Japan Astronomy Data Center, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan 3 Department of Cosmoscience, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan 4 Astrophysics Group, EPSAM, Keele University, Keele, Staffordshire ST5 5BG, UK Received 2008 October 19; accepted 2009 March 18; published 2009 April 16

ABSTRACT Extremely metal-poor (EMP) stars in the Galactic halo are unique probes into the early universe and the first stars. We construct a new program to calculate the formation history of EMP stars in the early universe with the chemical evolution, based on the merging history of the Galaxy. We show that the hierarchical structure formation model reproduces the observed metallicity distribution function and also the total number of observed EMP stars, when we take into account the high-mass initial mass function and the contribution of binaries, as proposed by Komiya et al. The low-mass survivors divide into two groups of those born before and after the mini-halos are polluted by their own first supernovae. The former has observational counterparts in the hyper metal-poor (HMP) stars below [Fe/H] < −4, while the latter represents the majority of EMP stars with [Fe/H] > −4. In this Letter, we focus on the origin of the extremely small iron abundances of HMP stars. We compute the change in the surface abundances of individual stars through the accretion of the metal-enriched interstellar gas along with the dynamical and chemical evolution of the Galaxy, to demonstrate that after-birth pollution of Population III stars is sufficiently effective to explain the observed abundances of HMP stars. Metal pre-enrichment by possible pair instability supernovae is also discussed, to derive constraints on their roles and on the formation of the first low-mass stars. Key words: Galaxy: evolution – Galaxy: formation – stars: abundances – stars: Population II

formed in early universe as “EMP population.” They show that a high-mass initial mass function (IMF) of typical mass ∼10 M , in combination with the binary formation and evolution, can provide an account of the statistics of carbon-enhanced metalpoor stars (both with and without the enrichment of s-process elements), the chemical evolution of the Galactic halo, and the total number of observed EMP survivors. In particular, they argue that the EMP survivors were mostly formed as the secondary companions of binaries. In Paper II, we proposed a new scenario for the scarcity of stars with [Fe/H] < −4, incorporating the hierarchical structure formation process. According to the contemporary theory, in the early universe, small mini-halos are formed and star-forming gas is captured into them. The first stars are formed in the mini-halos of mass ∼106 M with a baryonic content ∼2 × 105 M (Tegmark et al. 1997; Nishi & Susa 1999). When the massive first star in such mini-halos explodes as a Type II supernova, it enriches its host halo with about 0.07 M of iron, raising metallicity of the gas from primordial to log(0.07 M /2 × 105 M ) − log Z  −3.5 on average. We name this event “first pollution,” which sets a lower limit on the metallicity of the second and subsequent generations of stars. In our scenario, HMP stars of [Fe/H] < −4 must be assigned to the stars formed prior to the first pollution event. In this Letter, we first investigate the above scenario within the context of a realistic structure formation process by semianalytically constructing the merger trees for the formation of the Galaxy according to the extended Press–Schechter approach (Bond et al. 1991; Lacey & Cole 1993). We adopt a high-mass IMF with the contribution of binaries, as discussed in Paper I, and follow the star formation history and chemical evolution along these trees. The resultant metallicity distribution functions (MDFs) are compared with available observations.

1. INTRODUCTION The most metal-deficient stars are the most ancient objects in terms of chemical evolution and can provide insight into the first stars and the early universe. It is widely assumed that the first stars were born from the primordial gas, and hence, totally devoid of metals. However, direct proof of the existence of these stars, called as Population III stars, is elusive despite longstanding efforts to identify their low-mass survivors and/or nucleosynthetic traces. Observationally, the three most iron-deficient stars yet known were discovered with [Fe/H] = −5.6, −5.4, and −4.8 (HE1327−2326, Frebel et al. 2005; HE0107−5240, Christlieb et al. 2002; HE0557−4840, Norris et al. 2007) among candidates identified by the Hamburg/ ESO (HES) survey (Christlieb et al. 2001). Thanks to recent large-scaled surveys (HK survey, Beers et al. 1992, and HES survey) and high-dispersion spectroscopy (HDS) observations with large telescopes, the number of extremely metal-poor (EMP) stars with [Fe/H]  −3 that have the detailed surface abundances revealed now amounts to ∼150 (see, e.g., SAGA database; Suda et al. 2008). Nevertheless, the above three stars are only detected in the metallicity range below [Fe/H] < −4, to which we refer collectively as hyper metal-poor (HMP) stars. The HMP stars and their scarcity have drawn wide interest, and have been studied by many authors, but their origin has yet to be fully clarified (e.g., Prantzos 2003; Karlsson 2005; Tumlinson 2007b). Among the stars born in the early universe, only low-mass stars are currently observed in the Galactic halo, which we refer to as “EMP survivors.” Massive stars have already ended their lives, and yet, may have left their imprints on the low-mass survivors. On the basis of the observations, Komiya et al. (2007, 2009, hereafter referred to as Papers I and II, respectively) discuss the characteristics of the stars with [Fe/H]  −2.5, L79

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Then we discuss the origin of the very small abundances of iron for HMP stars in the hierarchical formation scenario. As for the HMP stars, the central issues explored in the literature have been the origin of their peculiar abundance patterns (see, e.g., Tumlinson 2007b). The observed abundance patterns of the light elements in these stars, from lithium, carbon through aluminum, have been investigated in detail in relation to asymptotic giant branch (AGB) nucleosynthesis with binary mass transfer to a low-mass survivor (Suda et al. 2004; Nishimura et al. 2009; Campbell & Lattanzio 2008), or the stellar winds from rapidly rotating massive stars (Maynet et al. 2006). In these scenarios, however, the very low-iron abundance remains an open question. There are other scenarios that propose HMP stars as second generation stars, formed from the gas polluted by the peculiar ejecta of some Population III supernovae (Umeda & Nomoto 2003; Iwamoto et al. 2005), or in combination with other supernova (Limongi et al. 2003; Karlsson 2006). However, these scenarios may not work without specially tailored mechanism(s) to form stars that incorporate these ejecta (see, e.g., Suda et al. 2004). Note that Tumlinson (2006) and Salvadori et al. (2006) investigate the formation history of EMP stars in the hierarchical model, and Tumlinson (2007a) study such models with IMFs varying due to the influence of the cosmic microwave background and with the binary contribution included as well. However, none of these studies offered explanations for the distinction between the EMP and HMP stars and for the origin of the low-iron abundances of the HMP stars. In this Letter, we investigate two possible iron sources. Suda et al. (2004) proposed HMP stars as low-mass Population III stars with their surface iron pollution arising from the accretion of interstellar matter (ISM). We follow the surface abundance changes for individual Population III and EMP survivors by ISM accretion along with the metal enrichment by supernovae and through the merging history, to estimate the “pollution limit” for the most metal-poor stars. This is the first computations of the expected surface metal pollution where the structure formation and the chemical enrichment of the Galaxy are fully taken into account. Another possible source of iron is the prepollution of gas before it is incorporated into the mini-halos. It is proposed that the first stars are so massive to explode as pair instability supernovae (PISNe), and for such energetic supernovae, the blast wave may sweep out the gas from their host mini-halos (Bromm et al. 2003; Kitayama & Yoshida 2005; Machida et al. 2005), and pollute the inter-halo gas with metal ejecta. HMP stars will be formed out of this prepolluted gas in the halos that collapse later. We also present a model including prepollution to explore observational constraints on the first supernovae. 2. COMPUTATION METHODS We first calculate the merger trees of a halo of mass 1012 M in the Λ cold dark matter universe (ΩM = 1 − ΩΛ = 0.3, Ωb = 0.045, h = 0.7, σ8 = 0.9) using the N-branch tree method with accretion, formulated by Somerville & Kolatt (1999). Figure 1 shows one realization of the merger trees. We set the lower mass limit, Mh,l , of mini-halos at the virial temperature, Tvir = 103 K, for which H2 molecules cool the primordial gas to form stars (Tegmark et al. 1997). We then follow the star formation and chemical evolution along all the branches of merger trees. Stars are generated in each halo according to the probability specified by the IMF, and with the star formation efficiency (SFE), set equal to the average value

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Figure 1. Example of merger trees for a halo of mass 1012 M . The variations of total (dark matter plus baryon) mass, Mh , of halos are plotted against the redshift, z (bottom) and the age, t, of the universe (top) for 1000 branches randomly selected among the total of ∼2 × 105 .

of the Galaxy (= 10−10 yr−1 ). We apply a high-mass IMF, in a log-normal form with median mass Mmd = 10 M and variance ΔM = 0.4, as derived for the EMP stars in Papers I and II. Half of the stars are assumed to be binaries, with the secondary stars having masses drawn from a uniform distribution of mass ratios between the secondary and primary stars. We register all the individual stars, and follow their evolution. The massive stars explode as Type II supernovae, after a lifetime of 107 yr, and eject mass MFe = 0.07 M of iron, which are assumed to mix instantaneously and uniformly in their host clouds. When the host halos merge or accrete matter, the iron abundances are averaged over the newly incorporated mass. Since the baryonic components may orbit within the new combined halos before dissolving into larger systems, we take into account the time necessary for orbit decay according to the results of Lacey & Cole (1993). The stars of mass M  0.8 M survive to the present, those of mass M  0.8 M − ΔMG (ΔMG = 0.01 M ; see Paper I) now on the giant branch. We trace the changes of their surface iron abundances due to ISM accretion, by assuming the Bondi– −3/2  Hoyle accretion rate, M˙ = 4π (GM)2 ρ Vr2 + cs2 , where M is the stellar mass (or the sum of two member masses for binaries), ρ and cs are the gas density and sound velocity of the ISM, and Vr is the relative velocity between the stars (or the barycenter of binaries) and the ambient gas. In the primordial clouds, the gas cools to ∼200 K, with the H2 molecule as the main coolant, and gathers toward the center to form stars. We assume that Vr reduces to become comparable with the sound velocity at this temperature. For the density of the ISM, we assume an isobaric contraction from the virial temperature to this temperature, i.e., ρ = ρvir (Tvir /200 K), where ρvir is the virialized gas density of halos. After the host cloud merges to become part of a larger halo, the stars move with the virial velocity, Vvir , of the larger halo in an ISM with density ρvir . For the binaries, we simply assume that half of the accreted ISM settles onto each member (but see Bate & Bonnel 1997; Ochi et al. 2005). Matter accreted onto the stars is mixed in the surface-convective zone with mass MSCZ = 0.003 M and 0.2 M for dwarfs and giants, respectively (Fujimoto et al. 1995).

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Figure 2. MDF of EMP survivors, predicted by the fiducial model with a highmass IMF (dark shaded histogram) and that by one with the IMF changed into a low-mass IMF for [Fe/H] > −2.5 (light shaded histogram), which are compared with the observed MDF by SAGA database and by Ryan & Norris (1991), matched at [Fe/H]  −3 (solid lines) under the same area coverage and advance of HDS follow-up observations.

3. RESULTS AND DISCUSSION 3.1. Metallicity Distribution Function Figure 2 shows the resulting MDF for our fiducial model without ISM accretion (dark shaded histogram) and the comparison with observations (solid line). The observed MDF for [Fe/H] < −3 is taken from the SAGA database (Suda et al. 2008) of EMP stars studied with HDS, and that for [Fe/H] > −3 is from the kinematically selected samples of halo stars reported by Ryan & Norris (1991), scaled to match the former at [Fe/H] = −3. In our hierarchical scenario, the stars separate into two groups, Population III stars (Z = 0) and EMP stars, born before and after first pollution, respectively. The latter stars well reproduce the observed MDF for −4  [Fe/H]  −2.5. In particular, the cutoff near [Fe/H]  −4 is produced without any artificial change of IMF, as discussed in Paper II. In comparison with observations, we consider not only the shape of the MDF but also the total number of EMP survivors. The effective survey area of the HES survey is 6726 deg2 (Christlieb et al. 2008) and roughly 40% of the selected metalpoor candidates have received medium-resolution spectroscopic follow up (Beers & Christlieb 2005). The faint limiting magnitude (B < 17.5) provides some confidence that almost all of the EMP giants that are present in the survey fields are identified. As for dwarfs, we may take into account the limiting observable distance by adopting the observed number ratio of EMP dwarfs to giants (=0.93). We allow for the fact that 153 stars of [Fe/H] < −3 have had abundances determined by the HDS observations and compiled by the SAGA database, while the HES counts ∼200 candidates of stars with [Fe/H] < −3. The figure shows that our model predicts the number of EMP survivors in a good agreement with the observation. For higher metallicity, the MDF of our fiducial model extends with a similar slope to that for EMP stars. In this figure, we also show the MDF computed by switching the IMF from a high-mass one to a low-mass one with Mmd = 0.22 (Chabrier 2003) at [Fe/H] = −2.5. The resultant MDF (light shaded histogram) exhibits a steep increase of low-mass survivors, while the observed MDF smoothly extends from EMP stars

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Figure 3. Effect of surface pollution by the ISM accretion. The resultant surface iron abundance and the redshift at the star formation are plotted for Population III giants (+) and EMP giants (·) with the metallicity of three HMP stars ( with arrow). Histogram in the bottom shows the predicted MDF of Population III (filled boxes) and EMP giants (open boxes), polluted by ISM accretion.

up to [Fe/H]  −1.8. This indicates that there is no significant change from the high-mass IMF as far as the field stars in the Galactic halo are concerned. We also compute a model using the CMB-influenced IMF proposed by Tumlinson (2007a), which results in a similar overproduction of EMP survivors. For [Fe/H] < −4, the fiducial model predicts a large number (∼230) of Population III stars. It is natural to assign these Population III stars to the HMP stars since there are no other observational counterparts in this metallicity range. However, the three HMP stars discovered to date are clearly too few in number. This suggests that the IMF and/or SFE are different for Population III or HMP stars, different from our assumptions in the fiducial model. For primordial gas clouds, it has been argued that a massive star, once formed, can dissociate whole H2 molecules, thereby quenching subsequent star formation (Omukai & Nishi 1999) until it explodes as a supernova (Machida et al. 2005). We compute the model with this effect of suppressing star formation by massive stars with M > 10 M until the first pollution of each mini-halo. The model then predicts ∼42 Population III survivors and ∼22 Population III giants, which are still larger than the detected number of HMP stars. We conclude that low-mass star formation, especially in the binaries, is less efficient for the stars born before first pollution than for the EMP stars. 3.2. Accretion of the ISM and the Origin of HMP Stars We next compute the model with the ISM accretion, as described in the preceding section. Figure 3 shows the stellar surface metallicity, as polluted by accreted iron (horizontal axis), and the redshift of their birth (vertical axis), of individual Population III and EMP stars now on the red giant branch. Their MDF is shown in the bottom panel. In this and the following computations, we include the effect of radiation feedback by massive Population III stars. For dwarf Population III stars, ISM accretion can enrich the surface with metals up to [Fe/H] ∼ −3. When the stars evolve to giants, however, the accreted metals are diluted further by a factor of ∼100, down to [Fe/H] ∼ −5, the similar metallicity to those observed for HMP stars. This supports our interpretation of the observed HMP stars as Population III stars which have undergone surface

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pollution. For the subgiant HE1327−2326, the shallow surface convection zone is shallower and occupied by matter transferred from a binary companion star, for which the accreted iron has been diluted beforehand in the AGB envelope. Our hierarchical model predicts much larger pollution than previous studies which have dealt with the accretion in an evolved Galactic halo (Iben 1983; Frebel et al. 2009). In the mini-halos where the first stars are born, the virial velocity is much smaller than in the halos of larger mass. As a result, the accretion rate can be much higher, reaching up to ∼10−10 M yr−1 , because of strong velocity dependence. The present result shows that such a consideration is necessary, not only for the chemical enrichment of the ISM, but also for the dynamical evolution of the Galaxy, in order to estimate the effect of ISM accretion onto ancient stars. Recently, Carollo et al. (2007) reported an inner/outer-halo structure for the halo of the Galaxy. Most of their sample, however, consists of stars with [Fe/H] > −3 thus the spatial distributions of EMP and HMP stars has yet to be properly established. In our model, Population III and EMP stars are formed in mini-halos at various redshifts, and later follow the merging history without correlation to their metallicity, as seen in Figures 1 and 3. Accordingly, HMP and EMP stars may be spatially distributed more or less homogeneously not only in the outer halo but also in the inner halo.

3.3. Pre-Enrichment of Metals by PISNe The first stars formed in mini-halos are suggested to be very massive (e.g., Abel et al. 2002; Omukai & Para 2003) and to explode as PISNe with huge explosion energies and with large iron yields (Heger & Woosley 2002; Umeda & Nomoto 2002). We assume that the first stars in the halos of Tvir < 104 K end up as PISNe, following brief lifetime of τ  2 × 106 yr, thus dispersing gas from the host halos and suspending star formation until the next merger. Iron ejecta (MFe = 10 M ) are assumed to mix with gas through the entire Galaxy homogeneously and instantaneously. In addition, we include the re-ionization of ambient gas by massive stars in a statistical manner, and apply the high-mass IMF to the mini-halos in proportion to the fraction of re-ionized gas in the Galaxy. When we assume that all stars formed before first pollution in nonionized mini-halos become PISNe, even with 100% efficiency of the ionization photons (Table 3 of Schaerer 2002), we find that PISNe continue until the gas is enriched up to [Fe/H]  −3.5, causing under- and overproduction of EMP survivors below and above this metallicity, respectively. Consequently, there should be a switchover of the IMF from a very massive one to a high-mass one, somewhere around the metallicities smaller than the observed HMP stars. Figure 4 shows the MDF predicted by the model, when computed with iron pre-enrichment by PISNe up to [Fe/H]cri = −5.6, as well as with ISM accretion taken into account. Only a small number of PISNe participate in the pre-enrichment (∼60 × 10[Fe/H]cri +5.6 in the entire Galaxy). It makes little difference with respect to the fiducial model in other than the presence of pristine iron in the HMP stars, and the resultant MDF very well resembles the observed one. Since the metals from PISNe are mixed later with the metals accreted from the ISM, the prepollution is compatible with the observed absence of the nucleosynthetic signatures of PISNe, as long as the critical metallicity is sufficiently small.

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Figure 4. Effects of metal prepollution by PISNe of the first stars in the minihalos of Tvir < 104 K and [Fe/H]  [Fe/H]cri = −5.6. Shaded histogram and dashed lines denote the MDFs with and without the surface pollution due to ISM accretion. Solid line denotes the observed MFD.

4. SUMMARY We have studied the formation history of HMP and EMP stars by the construction and evolution of cosmologically inspired merger trees. Our approach is unique in the use of a high-mass IMF and the contribution of binaries, as advanced for EMP stars in Papers I and II. We have shown that their peculiar observed MDF is explained in terms of structure formation, without resort to an artificial change of the IMF. In particular, HMP stars with [Fe/H] < −4 are assigned to stars born before the interstellar gas in mini-halos are polluted by their own first supernova. The scarcity of HMP stars suggests that low-mass star formation as low-mass members in the binary systems is less efficient below metallicity [Fe/H]  −4. For higher metallicity, there is no indication of changes in the IMF to a low-mass one as far as the field halo stars are concerned. We demonstrate that the hierarchical structure formation enhances the after-birth accretion of ISM, enriched with metals, sufficiently to pollute the surface of Population III survivors with metals as large as the iron abundances, observed for HMP stars. It is also shown that the prepollution of gas by PISNe, formed in the first collapsed mini-halos, is compatible with the observations as long as PISNe cease to occur below the observed lowest metallicity. Since the pristine metals are mixed with the later accreted ISM, HMP stars should show only the mixed abundance features of iron-group elements from a number of supernovae. In this Letter, we have used quite simplified assumptions, and dealt only with iron. Further elaborations are desirable, in particular for the interactions between the star formation process and the supernovae involved, and for binary formation under metal-deficient conditions. Now that large-scale, deep surveys of halo stars are in progress, we may take advantage of their improved information about the nature of HMP and EMP stars and the evolution of the Galaxy in future studies. A part of this work has been reported in AIPC 1016,77, and IAUS 255, 330. T.S. has been supported by a Marie Curie Incoming International Fellowship under contract PIIF-GA2008-221145. This work is supported partly by JSPS Grand-inaid for Scientific Research (18104003, 18072001, 19740098).

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