Formation of Primordial Stars in a Lambda-CDM Universe

Primordial stars are formed from a chemically pristine gas consisting of hydrogen and helium. They are believed to have been born at some early epoch in the history of the Universe and to have enriched the interstellar medium with synthesized heavy elements before the emergence of ordinary stellar populations. We study the formation of the first generation of stars in the standard cold dark matter model. We follow the gravitational collapse and thermal evolution of primordial gas clouds within early cosmic structures using very high-resolution, cosmological hydrodynamic simulations. Our simulation achieves a dynamic range of {approx} 10{sup 10} in length scale. With accurate treatment of atomic and molecular physics, it allows us to study the chemo-thermal evolution of primordial gas clouds to densities up to {rho} {approx} 2 x 10{sup -8}g cm{sup -3} (n{sub H} {approx} 10{sup 16}cm{sup -3}) without assuming any a priori equation of state; a six orders of magnitudes improvement over previous three-dimensional calculations. We implement an extensive chemistry network for hydrogen, helium and deuterium. All the relevant atomic and molecular cooling and heating processes, including cooling by collision-induced continuum emission, are implemented. For calculating optically thick H{sub 2} cooling at high densities, we use the Sobolev method (Sobolev 1960) and evaluate the molecular line opacities for a few hundred lines. We validate the accuracy of the method by performing a spherical collapse test and comparing the results with those of accurate one-dimensional calculations that treat the line radiative transfer problem in a fully self-consistent manner. We then perform a cosmological simulation adopting the standard {Lambda}CDM model. Dense gas clumps are formed at the centers of low mass ({approx} 10{sup 5-6}M{sub {circle_dot}}) dark matter halos at redshifts z {approx} 20, and they collapse gravitationally when the cloud mass exceeds a few hundred solar masses. To examine possible gas fragmentation owing to thermal instability, we compute explicitly the growth rate of isobaric perturbations. We show that the cloud core does not fragment in either the low-density (n{sub H} {approx} 10{sup 10}cm{sup -3}) or high-density ({approx} 10{sup 15}cm{sup -3}) regimes, where gas cooling rate is increased owing to three-body molecule formation and collision-induced emission, respectively. The cloud core becomes marginally unstable against chemo-thermal instability in the low-density regime. However, since the core is already compact at that point and correspondingly the sound-crossing time as well as the free-fall time are short, or comparable to the perturbation growth timescale, it does not fragment. Run-away cooling simply leads to fast condensation of the core to form a single proto-stellar seed. We also show that the core remains stable against gravitational deformation and fragmentation throughout the evolution. We trace in Lagrangian space the gas elements that end up at the center of the cloud, and study the evolution of the specific angular momentum. We show that, during the final dynamical collapse, small angular momentum material collapses faster than the rest of the gas and selectively sinks inwards. Consequently, the central regions have little specific angular momentum, and rotation does not halt collapse. With the large physical dynamic range of our simulation, we, for the first time, obtain an accurate gas mass accretion rate within a 10M{sub {circle_dot}} innermost region around the protostar. The protostar is accreting the surrounding hot (T {approx} 2000K) gas at a rate of M > 10{sup -2}-10{sup -3}M{sub {circle_dot}}/yr. From these findings we conclude that primordial stars formed in early cosmological halos are massive. We carry out proto-stellar evolution calculations using the obtained accretion rate. For a particular gas cloud we simulate, the resulting mass of the first star is M{sub ZAMS} {approx} 60-100M{sub {circle_dot}}, with the exact mass dependent on the actual accretion rate