We present the results of fully three-dimensional hydrodynamic simulations of the gravitational collapse of isolated, turbulent molecular cloud cores. Starting from initial states of hydrostatic equilibrium, we follow the collapse of both singular and nonsingular logatropic cores until the central protostar has accreted more than 90% of the total available mass. We find that, in the collapse of a singular core with access to a finite mass reservoir, the mass of the central protostar increases as Macc ∝ t4 until it has accreted ~35% of the total available mass. For nonsingular cores of fiducial masses 1, 2.5, and 5 M☉, we find that protostellar accretion proceeds slowly prior to the formation of a singular density profile. Immediately thereafter, the accretion rate in each case increases to ~10-6 M☉ yr-1, for cores with central temperature Tc = 10 K and truncation pressure Ps = 1.3 × 105kB cm-3 K. It remains at that level until half the available mass has been accreted. After this point, the accretion rate falls steadily as the remaining material is accreted onto the growing protostellar core. We suggest that this general behavior of the protostellar accretion rate may be indicative of evolution from the Class?0 to the Class?I protostellar phase.
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