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. 
Jason Tumlinson, Aparna Venkatesan, and J. Michael Shull