Protostar Formation in Supersonic Flows: Growth and Collapse of Spherical Cores

We present a unified model for molecular core formation and evolution, based on numerical simulations of converging, supersonic flows. Our model applies to star formation in GMCs dominated by large-scale turbulence, and contains four main stages: core building, core collapse, envelope infall, and late accretion. During the building stage, cores form out of dense, post-shock gas, and become increasingly centrally stratified as the mass grows over time. When the shock radius defining the core boundary exceeds $R\approx 4 a (4\pi G \rho_{mean})^{-1/2}$, where $a$ is the isothermal sound speed, a wave of collapse propagates from the edge to the center. During the building and collapse stages, density profiles can be fit by Bonnor-Ebert profiles with temperature 1.2 - 2.9 times the true value. As found previously for initially static equilibria, outside-in collapse leads to a Larson-Penston density profile $\rho \approx 8.86 a^2/(4 \pi G r^2)$. The third stage, consisting of an inside-out wave of gravitational rarefaction leading to $\rho\propto r^{-3/2}$, $v\propto r^{-1/2}$, is also similar to that for initially-static spheres, as originally described by Shu. We find that the collapse and infall stages have comparable duration, $\sim t_{ff}$, consistent with estimates for observed prestellar and protostellar (Class 0/I) cores. Core building takes longer, but does not produce high-contrast objects until shortly before collapse. The time to reach core collapse, and the core mass at collapse, decrease with increasing inflow Mach number. For all cases the accretion rate is $\gg a^3/G$ early on but sharply drops off; the final system mass depends on the duration of late-stage accretion, set by large-scale conditions in a cloud.