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

We critique the hypothesis that the first stars were very massive stars (VMS; M > 140 Msun). We review the two major lines of evidence for the existence of VMS: (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 (tau_e) to the CMB found by WMAP requires VMS for reionization in a concordance LambdaCDM cosmology. The supernova yield patterns of VMS are incompatible with the Fe-peak and r-process abundances in halo stars. Models including Type II supernovae and/or ``hypernovae'' from metal-free progenitors with 8 - 40 Msun can better explain the observed trends. With a simple metal-transport model, we estimate that halo enrichment curtails metal-free star formation after ~10^8 yr at z ~ 20. Because the ionizing photon efficiency of metal-free stars peaks at ~120 Msun and declines at higher mass, an IMF with a lower bound at M ~ 10 - 20 Msun 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 semi-analytic model for H I and He II reionization, we find that such an IMF can reproduce tau_e = 0.10 - 0.14, consistent with the range from WMAP. We conclude, on the basis of these results, that VMS are not necessary to meet the existing constraints commonly taken to motivate them.