Evolution of first cores and formation of stellar cores in rotating molecular cloud cores

We followed the collapse of cloud cores with various rotation speed and density frustrations using three-dimensional hydrodynamical simulations by assuming a barotropic equation of state and examined the comprehensive evolution paths from the rotation molecule cloud core to stellar core. We found that the evolutionary paths depend only on the angular velocity of initial cloud core Omega(c0). These evolutionary paths agree well with predictions of Saigo and Tomisaka's quasi-equilibrium axisymmetric models and SPH calculations of Bate. Evolutionary paths are qualitatively classified into three types. ( 1) A slowly rotating cloud with Omega(c0) < 0:01/t(ff) = 0:05 (rho(c0)/10(-19) g cm(-3))(1/2) rad Myr(-1) shows spherical-type evolution, where rho(c0) is the initial central density. Such a cloud forms a first core which is mainly supported by the thermal pressure. The first core has a small mass of M-core similar to 0.01 M-circle dot and a short lifetime of a few x 100 yr. After exceeding the H-2 dissociation density rho similar or equal to 5.6 x 10(-8) g cm(-3), it begins the second collapse, and the whole of the first core accretes onto the stellar core/disk within a few free-fall timescales. ( 2) A rotating cloud with 0.01/t(ff) < Omega(c0) less than or similar to 0.05/t(ff) shows disk-type evolution. In this case, the first core becomes a centrifugally supported massive disk with M-core similar to a few x 0.01-0.1 M-circle dot and the lifetime is a few thousand years. The first core is unstable against non-axisymmetric dynamic instability and forms spiral arms. The gravitational torque through spiral structure extracts angular momentum from the central region to the outer region of the first core. And only a central part with r similar to 1 AU begins the second collapse after exceeding dissociation density. However, the outer remnant disk keeps its centrifugal balance after stellar core formation. It seems that this remnant of the first core should control the mass and angular momentum accretion onto the newborn stellar system. ( 3) A rotating cloud with 0.05/t(ff) less than or similar to Omega(c0) tends to fragment into binary or multiple during the first core phase.