Nucleosynthesis, Reionization, and the Mass Function of the First Stars

We critique the hypothesis that the first stars were very massive stars (VMSs; M > 140 M_☉). We review the two major lines of evidence for the existence of VMSs: (1) that the relative metal abundances of extremely metal-poor Galactic halo stars show evidence of VMS enrichment and (2) that the high electron-scattering optical depth (τ_e) to the cosmic microwave background found by the Wilkinson Microwave Anisotropy Probe (WMAP) requires VMSs for reionization in a concordance ΛCDM cosmology. The yield patterns of VMSs exploding as pair-instability supernovae are incompatible with the Fe-peak and r-process abundances in halo stars. Models including Type II supernovae and/or "hypernovae" from zero-metallicity progenitors with M = 8-40 M_☉ can better explain the observed trends. We use the nucleosynthesis results and stellar evolution models to construct an initial mass function (IMF) for reionization. With a simple metal transport model, we estimate that halo enrichment curtails metal-free star formation after ~10⁸ yr at z ~ 20. Because the lifetime-integrated ionizing photon efficiency of metal-free stars peaks at ~120 M_☉ and declines at higher mass, an IMF with an approximate lower bound at M ~ 10-20 M_☉ and no VMS can maximize the ionizing photon budget and still be consistent with the nucleosynthetic evidence. An IMF devoid of low-mass stars is justified independently by models of the formation of primordial stars. Using a semianalytic model for H I and He II reionization, we find that such an IMF can reproduce τ_e ≃ 0.10-0.14, consistent with the range from WMAP, without extreme astrophysical assumptions, provided that metal-free star formation persists 10⁷-10⁸ yr after star formation begins. Because stars in the mass range 50-140 M_☉ are the most efficient sources of ionizing photons but are expected to collapse to black holes without releasing metals, this IMF effectively decouples early metal enrichment and early ionization. Such an IMF may allow the unique properties of the zero-metallicity IMF to persist longer than they would in the pure VMS case and to contribute significantly to the global ionizing photon budget before halo self-enrichment and/or interhalo metal transport truncates metal-free star formation. We conclude, on the basis of these results, that VMSs are not necessary to meet the existing constraints commonly taken to motivate them.