COLLAPSE AND FRAGMENTATION OF MOLECULAR CLOUD CORES .1. MODERATELY CENTRALLY CONDENSED CORES

The high frequency of detection of binary companions to pre-main-sequence stars and suspected protostars supports the hypothesis that binary stars are formed through the fragmentation of collapsing molecular cloud cores. Observations show that molecular cloud cores are centrally condensed, typically prolate in shape, and often contain significant angular momentum. A second-order accurate radiative hydrodynamics code has been used to calculate the self-gravitational collapse of protostellar clouds with initial properties similar to the observed molecular cloud cores. The initial clouds have exponential density profiles, with central densities a factor of 20 higher than the boundary density, and uniform angular velocity. Exponential density profiles are flatter at the center and steeper in the outer regions than the power-law profiles used to model molecular cloud cores. Depending on the initial ratios of thermal (alpha(i)) and rotational (beta(i)) to gravitational energy and the initial axis ratio, such clouds may either (a) collapse to slightly higher densities and then re-expand to a diffuse, ellipsoidal equilibrium state, (b) collapse toward stellar densities while retaining a single density maximum, or (c) collapse and fragment into a binary or higher order system of protostellar cores moving on highly eccentric orbits. For a 2:1 initial axis ratio, the critical values are about alpha(i) < 0.54-0.42beta(i) for (b) to occur and alpha(i) < 0.45-0.36beta(i) for (c), while for a 1.5:1 initial axis ratio, the values are alpha(i) < 0.62-0.48beta(i) for (b) and alpha(i) < 0.33-0.26beta(i) for (c). These critical values for alpha(i) are significantly lower than those derived by Miyama, Hayashi, & Narita for initially uniform density clouds, indicative of the increased resistance to fragmentation in centrally condensed cloud cores.