On the stability of very massive primordial stars
  The stability of metal-free very massive stars ($Z$ = 0; $M = 120 - 500 \msol$) is analyzed and compared with metal-enriched stars. Such zero-metal stars are unstable to nuclear-powered radial pulsations on the main sequence, but the growth time scale for these instabilities is much longer than for their metal-rich counterparts. Since they stabilize quickly after evolving off the ZAMS, the pulsation may not have sufficient time to drive appreciable mass loss in Z = 0 stars. For reasonable assumptions regarding the efficiency of converting pulsational energy into mass loss, we find that, even for the larger masses considered, the star may die without losing a large fraction of its mass. We find a transition between the $\epsilon$- and $\kappa$-mechanisms for pulsational instability at $Z\sim 2\E{-4} - 2\E{-3}$. For the most metal-rich stars, the $\kappa$-mechanism yields much shorter $e$-folding times, indicating the presence of a strong instability. We thus stress the fundamental difference of the stability and late stages of evolution between very massive stars born in the early universe and those that might be born today. 
I. Baraffe (Ecole Normale Superieure, Lyon), A. Heger and S. E.   Woosley (University of California, Santa Cruz)