First Stars, Very Massive Black Holes, and Metals

Recent studies suggest that the initial mass function (IMF) of the first stars (Population III) is likely to have been extremely top-heavy, unlike what is observed at present. We propose a scenario to generate fragmentation to lower masses once the first massive stars have formed and derive constraints on the primordial IMF. We estimate the mass fraction of pair-unstable supernovae (SN_γγ), shown to be the dominant sources of the first heavy elements. These metals enrich the surrounding gas up to ≈10^-4 Z_☉, when a transition to efficient cooling-driven fragmentation producing ≲1 M_☉ clumps occurs. We argue that the remaining fraction of the first stars ends up in ≈100 M_☉ VMBHs (very massive black holes). If we further assume that all these VMBHs are likely to end up in the centers of galactic nuclei constituting the observed supermassive black holes (SMBHs), then ≈6% of the first stars contributed to the initial metal enrichment and the IMF remained top-heavy down to a redshift z ≈ 18.5%. Interestingly, this is the epoch at which the cool metals detected in the Lyα forest at z ≈ 3 must have been ejected from galaxies. At the other extreme, if none of these VMBHs has as yet ended up in SMBHs, we expect them to be either (1) en route toward galactic nuclei, thereby accounting for the X-ray-bright off-center sources detected locally by ROSAT, or (2) the dark matter candidate composing the entire baryonic halos of galaxies. For case 1 we expect all but a negligible fraction of the primordial stars to produce metals, causing the transition at the maximum possible redshift of ≳22.1, and for case 2, ~3 × 10⁵, a very negligible fraction of the initial stars produce the metals and the transition redshift occurs at z_f ≳ 5.4. In this paper, we present a framework (albeit one that is not stringently constrained at present) that relates the first episode of star formation to the fate of their remnants at late times. Clearly, further progress in understanding the formation and fragmentation of Population III stars within the cosmological context will provide tighter constraints in the future. We conclude with a discussion of several hitherto unexplored implications of a high-mass-dominated star formation mode in the early universe.