Annu. Rev. Astron. Astrophys. 1994. 32: 531-590
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4.3. Expected Mass of Population III Stars

In all these scenarios, an appreciable fraction of the Universe may go into subgalactic clouds before galaxies themselves form. What happens to these clouds? In some circumstances, one expects them to be disrupted by collisions with other clouds because the cooling time is too long for them to collapse before coalescing. However, there is usually some mass range in which the clouds survive. For example, the range is 106-1011 Msun in the hierarchical clustering scenario. In this case, they could face various possible fates. They might just turn into ordinary stars and form objects like globular clusters. On the other hand, the conditions of star formation could have been very different at early times and several alternatives have been suggested.

Some people argue that the first stars could have been much smaller than at present. Fairly general arguments suggest that the minimum fragment mass could be as low as 0.007 Msun (Low & Lynden-Bell 1976, Rees 1976) and it is possible that conditions at early epochs - such as the enhanced formation of molecular hydrogen (Palla et al 1983, Yoshii & Saio 1986, Silk 1992) - could allow the formation of even smaller objects. One might also invoke the prevalence of high-pressure pregalactic cooling flows (Ashman & Carr 1988, Thomas & Fabian 1990), analagous to the cluster flows observed at the present epoch (Fabian et al 1984) but on a smaller scale. This possibility is discussed detail in Section 9.2.

Other people argue that the first stars could have been much larger than at present. For example, the fragment mass could be increased before metals formed because cooling would be less efficient (Silk 1977). There is also observational evidence that the IMF may become shallower as metallicity decreases (Terlevich 1985), thereby increasing the fraction of high mass stars. Another possibility is that the characteristic fragment mass could be increased by the effects of the microwave background (Kashlinsky & Rees 1983) or by the absence of substructure in the first bound clouds (Tohline 1980).

One could also get a mixture of small and large stars. For example, Cayrel (1987) has proposed that one gets the formation of massive exploding stars in the core of the cloud, followed by the formation of low mass stars where the gas swept up by the explosions encounters infalling gas. Kashlinsky & Rees (1983) have proposed a scheme in which angular momentum effects lead to a disk of small stars around a central very massive star. Salpeter & Wasserman (1993) have a scenario in which one gets clusters of neutron stars and asteroids.

In the baryon-dominated isocurvature scenario, with highly nonlinear fluctuations on small scales, the collapse of the first overdense clouds depends on the effects of radiation diffusion and trapping. Hogan (1993) finds that sufficiently dense clouds collapse very early into black holes with a mass of at least 1 Msun, while clouds below this critical density delay their collapse until after recombination and may produce neutron star or brown dwarf remnants. One of the attractions of this idea is that it allows a baryon density parameter higher than that indicated by Equation (3.1) because the nucleosynthetic products in the high density regions are locked up in the remnants, leaving the products from the low density regions outside (cf Gnedin et al 1994).

It is possible that the first clouds collapse directly to form supermassive black holes (Gnedin & Ostriker 1992). Usually clouds will be tidally spun up by their neighbors as they become gravitationally bound and the associated centrifugal effects then prevent direct collapse. However, just after recombination, Compton drag could prevent this tidal spin-up, especially if the gas becomes ionized or contains dust (Loeb 1993). More detailed numerical hydrodynamical studies of this situation have been presented by Umemura et al (1993), who allow for different ionization histories and for different ratios of baryonic to nonbaryonic density. For a fully ionized gas, the baryonic disk loses angular momentum very effectively and shrinks adiabatically. Even if rotation is important, one could still get a supermassive disk which slowly shrinks to form a black hole due to angular momentum transport by viscous effects (Loeb & Rasio 1993). One might even end up with a supermassive binary system.

While there is clearly considerable uncertainty as to the fate of the first bound clouds, our discussion indicates that they are likely to fragment into stars that are either larger or smaller than the ones forming today. Theorists merely disagree about the direction! One certainly needs the stars to be very different if they are to produce a lot of dark matter. One also requires the clouds to fragment very efficiently. Although this might seem rather unlikely, there are circumstances even in the present epoch where this occurs; for example, in starburst galaxies or cooling flows. This is also a natural outcome of the hierarchical explosion scenario (Carr & Ikeuchi 1985).

We note that there is no necessity for the Population III stars to form before galaxies. It is possible that the Population III clouds just remain in purely gaseous form and become Lyman-alpha clouds (Rees 1986), in which case the formation of the dark-matter-producing stars would need to be postponed until the epoch of galaxy formation. Nevertheless, there is at least the possibility that the Population III stars were pregalactic, and this would have various attractions. For example, it would permit the Universe to be reionized at high redshifts (Hartquist & Cameron 1977), thereby hiding small-scale anisotropies in the microwave background (Gouda & Sugiyama 1992), and it might help to explain why the intergalactic medium appears to be ionized back to redshifts of at least 5 (Schneider et al 1991). Pregalactic stars might also be invoked to explain pregalactic enrichment (Truran & Cameron 1971) and the existence of substantial heavy element abundances in intergalactic clouds at redshifts above 3 (Steidel & Sargent 1988) and in intracluster gas at low redshifts (Hatsukade 1989).

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