Formation of Primordial Protostars
  The evolution of collapsing metal free protostellar clouds is investigated for various masses and initial conditions.   We perform hydrodynamical calculations for spherically symmetric clouds taking account of radiative transfer of the molecular hydrogen lines and the continuum, as well as of chemistry of the molecular hydrogen.   The collapse is found to proceed almost self-similarly like Larson-Penston similarity solution.   In the course of the collapse, efficient three-body processes transform atomic hydrogen in an inner region of $\sim 1 M_{\sun}$ entirely into molecular form.   However, hydrogen in the outer part remains totally atomic although there is an intervening transitional layer of several solar masses, where hydrogen is in partially molecular form.   No opaque transient core is formed although clouds become optically thick to H$_{2}$ collision-induced absorption continuum, since H$_{2}$ dissociation follows successively.   When the central part of the cloud reaches stellar densities ($\sim   10^{-2} {\rm g cm^{-3}}$), a very small hydrostatic core ($\sim   5 \times 10^{-3} M_{\sun}$) is formed and subsequently grows in mass as the ambient gas accretes onto it.   The mass accretion rate is estimated to be $3.7 \times 10^{-2} M_{\sun}   {\rm yr^{-1}} (M_{\ast}/M_{\sun})^{-0.37}$, where $M_{\ast}$ is instantaneous mass of the central core, by using a similarity solution which reproduces the evolution of the cloud before the core formation. 
Kazuyuki Omukai and Ryoichi Nishi (Kyoto University)