Hydrodynamical Collapse of First Stars: Are They Very Massive?

We investigate the collapse of metal-free protostellar clouds within a spherically symmetric hydrodynamical scheme including the transfer of radiation and the chemistry of the primordial gas. We find that the cloud collapses on a time-scale of $\sim 10^{5-6}$ yr due to cooling from the H2 formed through 3-body reactions. In this phase luminosities $>10^{32}$ erg/s are emitted. For most of the collapse time the evolution is self-similar, even when the central regions become optically thick. Later, a small mass hydrostatic core develops surrounded by a massive accreting envelope. Core formation occurs when the central temperature is about 20,000 K: the central collapse halts when the compressional heating overcomes the cooling from H2 dissociation. The initial core mass is 0.003 Msun but it grows at an enormous rate $\sim 0.1$ Msun/yr. In this phase the accretion luminosity is $>10^{36}$ erg/s and is emitted mainly in IR continuum; a similar luminosity is radiated in IR lines from the H2 envelope. Such radiation field is unable to stop accretion, due to the small opacity of the infalling gas, despite the large luminosities. The mass transfer onto the core continues and its rate decays as $t^{-0.3-0.4}$. This fate is similar among clouds with different initial configurations, including those resulting from 3D simulations of primordial objects. The mass inflow upon the core is a key difference in a comparison with the present-day star formation where the inflow rate is at least 1000 times smaller: in primordial stars the fast mass growth is unimpeded by radiation effects, but in present-day protostars these might be most relevant. We discuss implications of the results and detectability of this pristine cosmic star formation activity. [abridged]