A radiation hydrodynamic model for protostellar collapse. I. The first collapse

Dynamical collapse of a molecular cloud core and the formation of a star are investigated by performing radiation hydrodynamic calculations in spherical symmetry. The angle-dependent and frequency-dependent radiative transfer equation is solved without any diffusion approximations, and the evolution of the spectral energy distribution (SED) is examined. In the present paper, as the first step in a series of our work, evolutions before hydrogen molecules begin to dissociate (the so-called first collapse) are examined for different masses and initial temperatures of the parent cloud cores and for different opacities. Numerical results for a typical case [T-init = 10 K and kappa-(P)(10 K)similar to 0.01 cm(2) g(-1)] show that the radius and mass of the first core are similar to 5 AU and similar to 0.05 M., respectively. These values are independent both of the mass of the parent cloud core and of the initial density profile. The analytical expressions for the radius, mass, and accretion luminosity of the first core are also obtained. The SED contains only cold components of a few times 10 K throughout the first collapse phase, because the opaque envelope veils the first core from observers. We suggest that the molecular cloud cores with luminosities higher than similar to 0.1 L. should contain young protostars deep in the center, even if they show no evidence for the existence of central stars in near-infrared and optical observations.