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We investigate prestellar core formation and accretion based onthree-dimensional hydrodynamic simulations. Our simulations represent local$\sim 1$pc regions within giant molecular clouds where a supersonic turbulentflow converges, triggering star formation in the post-shock layer. We includeturbulence and self-gravity, applying sink particle techniques, and explore arange of inflow Mach number ${\cal M}=2-16$. Two sets of cores are identifiedand compared: $t_1$-cores are identified of a time snapshot in each simulation,representing dense structures in a single cloud map; $t_\mathrm{coll}$-coresare identified at their individual time of collapse, representing the initialmass reservoir for accretion. We find that cores and filaments form and evolveat the same time. At the stage of core collapse, there is a well-defined,converged characteristic mass for isothermal fragmentation that is comparableto the critical Bonner-Ebert mass at the post-shock pressure. The core massfunctions (CMFs) of $t_\mathrm{coll}$-cores show a deficit of high-mass cores($\gtrsim 7M_\odot$) compared to the observed stellar initial mass function(IMF). However, the CMFs of $t_1$-cores are similar to the observed CMFs andinclude many low-mass cores that are gravitationally stable. The differencebetween $t_1$-cores and $t_\mathrm{coll}$-cores suggests that the full samplefrom observed CMFs may not evolve into protostars. Individual sink particlesaccrete at a roughly constant rate throughout the simulations, gaining one$t_\mathrm{coll}$-core mass per free-fall time even after the initial massreservoir is accreted. High-mass sinks gain proportionally more mass at latetimes than low-mass sinks. There are outbursts in accretion rates, resultingfrom clumpy density structures falling into the sinks.

Prestellar Core Formation, Evolution, and Accretion from Gravitational Fragmentation in Turbulent Converging Flows