A&A 367, 277-281 (2001)
Y. Lu 1,2 - G. Zhao1 - L. C. Deng1 - M. R. Cen2 - Y. C. Liang1
1 - Beijing Astronomical Observatory, Datun Rd. 20A, Chaoyang, Beijing 100012, PR China
2 - The Department of Physics, Normal University of Central China, Wuhan, Hubei 430079, PR China
Received 11 August 2000 / Accepted 18 December 2000
A model of supernova-driven chemical evolution of the Galactic halo proposed by Tsujimoto et al. (1999) (TSY) is used to investigate the observations of the first generation stars (FGS). We assume in this paper that a star with a metallicity is truly a FGS. We obtain FGS probabilities with the Miller-Scalo form of the stellar initial mass function and limit our model parameters to values consistent with the observed metallicity distributions of metal-poor stars in the range of . We find a metallicity distribution function (MDF) of the long-lived halo field stars for against the iron abundance in agreement with the observations. If the star formation in the halo is confined to individual gas clouds with masses from 1 107to , our model suggests that the probability of identifying FGS in the halo is about 6.14 10-5 to 6.14 10-6.
Key words: galaxy: evolution - galaxy: halo-stars: abundance - stars: formation - supernovae: general
In the standard big bang cosmology, the amount of heavy elements synthesized in the universe is as small as (Z = mass fraction of heavy elements); hence the material from which the FGS were formed consists of pure hydrogen and helium (Wagoner et al. 1967). It is expected that the physical processes leading to the formation of the primordial stars are very different from those for Pop I stars formed from the gas with solar abundance. The initial mass function (IMF) of the primordial stars, for example, might be different from the Salpeter's IMF. However, the IMF of stars is key to modeling the evolution of galaxies; the IMF shape, together with the lower and upper bounds of stellar mass, largely influences the resulting abundance pattern of heavy elements ejected through supernova explosions, the total amount of mass contained in stellar remnants, the star formation rate and the chemical evolution models (Tinsley 1980).
The observational and theoretical state of FGS is not clear, leading to some confusion. In this work, we define a FGS as a star with a metallicity ratio of (Beers 1999). A chemical evolution model allows us to theoretically analyse such metallicity distribution among generations of stars. Observational uncertainties and large number of parameters required by such models make their use eqivocal for very metal-poor stars (VMPS, i.e. halo stars). However, they can be used to determine a model for the evolving system using the most recent data and current hypotheses. In conventional chemical evolution models, the abundance pattern of stars is the same as the homogeneous gas cloud in which such stars are formed. The star formation rate (SFR) is assumed to be proportional to some power of the gas density (Tinsely 1980; Schmidt 1959). This has been successfully used to assess the chemical compositions of nearby stars and HII regions (Pagel & Patchett 1975; Matteucci & Greggio 1986; Yoshii et al. 1996).
Recent observations of VMPS in the Galactic halo imply that abundances pattern with may indicate a preceding single or multiple supernova event (SNe) (McWilliam et al. 1995; Ryan et al. 1996). This suggests that conventional chemical evolution models cannot be applied to the Galactic halo. Thus, the abundance patterns of the VMPS or FGS is not expected to follow the predictions of the conventional models. Audouze & Silk (1995) have attempted to explain the observed abundance patterns of VMPS. Shigeyama & Tsujimoto (1998, ST98) and Tsujimoto & Shigeyama (1998, TS98) proposed that the formation of VMPS is triggered by a single supernova remnant (SNR), and that the stars formed thus retain the abundance pattern of the SN. Following ST98 and TS98, Tsujimoto et al. (1999, hereafter TSY) developed a model for the early epochs of Galactic chemical evolution, suggesting that the metal-free Pop III stars could form in primordial gas clouds of the Galactic halo. If the stellar IMF exists in the form of Salpeter, we expect one FGS to be found per 103-104 halo stars.
This paper aims to determine what stellar IMF properties are allowable which still fit the observational constraints using the TSY model. In Sect. 2, we discuss the characteristics of the Miller-Scalo IMF (Miller & Scalo 1979). The chemical evolution model and assumptions are described in Sect. 3. In the last section we present the results and discussion.
The IMF is assumed to
be a time invariant mass spectrum with a power law of the form
Miller & Scalo 1979; Tinsley 1980; Scalo 1986; Kroupa et al. 1993), where
is the number of star in the mass
interval m to
is a lower mass limit of stars, and
is the upper mass limit of stars. Normally, the IMF is
derived from the observed present-day mass function (PDMF) in the
solar neighborhood, which is assumed to be independent of
time (Scalo 1986). The derivation of the IMF from PDMF is
difficult, involving assumptions about
the star formation rate during the lifetime of the Galaxy
(Tinsley 1980; Scalo 1986). For stars with lifetimes longer than
the age of the Galaxy (
), the IMF is derived by
assuming an average star formation rate in the past, whereas for
stars with lifetimes negligible relative to the age of the Galaxy
), the IMF is derived by assuming a present-time
star formation rate and taking into account the stellar lifetimes
(). Given the uncertainties in both theory and
observation, the IMF variations can be
parameterized, and the proposed IMF can be tested by means
of a detailed chemical evolution model. This method has been
adopted in many cases (Yoneyama 1972; Hutchins 1976; Carlberg 1981;
Kashlinsky & Rees 1983; Palla et al. 1983; Silk 1983;
Haiman et al. 1996; Uehara et al. 1996; Tegmark et al. 1997; Omukai &
Nishi 1998; Nakamura & Umemura 1999). Globular clusters (GCs) are
to have a IMF similar to the Miller-Scalo form, with a typical lower
mass limit of
(Padoan et al. 1997,
PNJ). It is worth noting that halo field stars, associated with
type II supernovae, indicate an origin common to that of GCs
(Wheeler et al. 1989). Based on the chemical evolution model of
TSY, we use the Miller & Scalo IMF to model observations of
Galactic halo stars. This IMF can be
approximated by a half-Gaussian distribution in ,
We assume that the star-forming process is confined in isolated clouds, which may explain the recent observation of abundance patterns in metal-poor stars (TS98; ST98; TSY). In our model, a fraction, , of the cloud mass has been turned into Pop III stars at time t=0; the massive stars of the same population have exploded as Pop III SNs, which in turn initiate the chemical evolution in a given cloud. All stars of subsequent generations are assumed to form from the SNR shells around the radiative shock front. The mass fraction of each shell that is converted into stars is taken as a constant, . Following TSY, when stars form as above, the star formation rate (SFR) can be given by
|Figure 1: The relation between the duration of star formation in a cloud and a probability of observing Pop III stars as a fraction of their number among all the long-lived stars with . a) stands for Salpeter's IMF, and b) is for Miller-Scalo's IMF|
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|of present model||of TSY model|
|1 105||6.14 10-3||2.53 10-2|
|1 106||6.14 10-4||2.53 10-3|
|1 107||6.14 10-5||2.53 10-4|
|1 108||6.14 10-6||2.53 10-5|
Figure 2 shows the predicted stellar [Fe/H] distribution function for
compared to the data obtained by Ryan & Norris (1991).
|Figure 2: The frequency distribution of the long-lived halo field stars for against the iron abundance, compared with the observations of Ryan & Norris (1991). The star corresponds to the observational data. The solid circle is a calculation from the present model, and the solid triangle corresponds to the model of TSY|
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|Figure 3: The mass fraction of the gas evolves with time. a) The TSY model, b) the present model|
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|Figure 4: The model curves of the metallicity of ISM over time. The solid line a) corresponds to the TSY model, and the solid line b) is the present model curve|
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Based on a new model for Galactic chemical evolution (TSY), but using the Miller-Scalo form of the primordial IMF, our results are similar to those of the TSY model. However, the probability of detecting the metal-free Pop III stars is smaller because the Miller-Scalo IMF is enhanced in the massive end compared with the Salpeter IMF at time t=0. This can be infered from the longer star-formation duration (Fig. 1) and the smaller fraction of the cloud mass turned into Pop III stars at time t=0 in the frame of Miller-Scalo IMF. From Table 1, we find that the probability of detecting the metal-free Pop III stars with the Miller-Scallo IMF is about 0.24 times that found with the Salpeter IMF. In another words, we find only one Pop III star in a sample of 4 104 halo stars here.
In order to reproduce the observed [Fe/H] distribution function of stars, we also need to decrease the mean value of heavy-element yields (about -0.35 dex) from SN. This is different from the TSY model. Usually, theoretical metallicity distributions of stars are constructed as a function of metallicity , whereas observations of stellar abundances are usually expressed in terms of [Fe/H], since the abundance of iron is the most easily measured. For halo stars, , because not all elements are deficient by the same factor. The chemical evolution models adopted in our paper is parameterized by the "effective yield", which is a measure of the efficiency of the enrichment process. The yield determined from observed [Fe/H] values is not the effective yield of metals, but rather that of iron. Following the argument of Lambert (1989) and Kurucz (1979), we also assumed that the effective yield of metals will be 0.35 dex higher, so that [Fe/H] is .
If the form of the primordial IMF is the Miller-Scalo form, finding the very first generation of star is difficult as found above. Note that the definition of FGS implies a very specific set of requirements for pollution of stellar atmospheres (either by intrinsic or extrinsic mechanisms) and the IMF: (i) Pollution of a stellar atmosphere with metallic species subsequent to a star's formation cannot be effective (see the confined values of ), else we would never measure a star's atmospheric metal abundance satisfying the definition of FGS; (ii) The IMF must extend to include low stars with sufficiently long main-sequence lifetimes that might be identifiable at present. In the case of top-heavy stellar IMF in the galaxy at early times, no metal-free stars can be found. In conclusion, metal-free Pop III stars are sure to be found eventually if the star formation history in the Galactic Halo is the same as that assumed by TSY, and by increasing the sample of observed stars with the lowest metal abundances.
We thank R. Cayrel for his important comments and T. Tsujimoto for a useful discussion and friendly help to our paper. This work is partially supported by the National Natural Science Foundation of China.