Initial Mass Function for Zero-Metal Stars

The initial mass function (IMF) for the zero-metal stars is derived based on the opacity-limited fragmentation theory. If a pregalactic cloud is born just after the decoupling epoch, the fragments evolve isothermally due to the two-photon cooling of aromic hydrogen. The IMF formed in such a cloud has a peak around intermediate mass. The slope toward the massive part of the IMF is steeper than a Salpeter-like IMF. The mass at the peak of the IMF is four to ten solar masses, depending on the assumed mass-luminosity relation for protostars. In the cloud which is born in the low-temperature region, the fragments evolve isothermally due to the cooling by molecular hydrogen. The density fluctuations in the fragments are amplified in isobaric condition by the thermochemical instability, and those with about 10 solar masses become bound by self-gravitation before the opacity eventually quenches the instability.