Cosmological simulation predicts that the first stars could be between a few solar masses, all the way to a hundred or more solar masses. However, as of now, there is no unmistakable evidence of the results of pair instability supernova in observed low-metallicity stars. Recent simulations found that fragmentation happens frequently during the accretion phase, potentially resulting in low-mass zero-metallicity; still, no truly zero-metallicity stars have been discovered in the galaxy.
In the talk, I will discuss fragmentation conditions in primordial accretion flows, with a focus on the cooling function of zero-metallicity gas and its thermal stability. Fast H_2 cooling is the key component leading to fragmentation in the simulation. However, the H_2 roto-vibrational line becomes optically thick around n~1e10 cm^-3, and an optical depth approximation is needed to model the attenuated cooling in this regime. I provide a fitting function for the optical depth of molecular hydrogen based on the accretion disk structure. Based on this cooling function, I will argue that inner disk is resistant to fragmentation. Fragments, if any, should initially formed at the outer disk. The dynamical influence of fragments on the accretion flow would be an important factor that governs the mass of the first stars.
