We use numerical hydrodynamic simulations to investigate prestellar core formation in the dynamic environment of giant molecular clouds ( GMCs ) , focusing on planar post-shock layers produced by colliding turbulent flows .
A key goal is to test how core evolution and properties depend on the velocity dispersion in the parent cloud ; our simulation suite consists of 180 models with inflow Mach numbers { \cal M } \equiv v / c _ { s } = 1.1 - 9 .
At all Mach numbers , our models show that turbulence and self-gravity collect gas within post-shock regions into filaments at the same time as overdense areas within these filaments condense into cores .
This morphology , together with the subsonic velocities we find inside cores , is similar to observations .
We extend previous results showing that core collapse develops in an “ outside-in ” manner , with density and velocity approaching the Larson-Penston asymptotic solution .
The time for the first core to collapse depends on Mach number as t _ { coll } \propto { \cal M } ^ { -1 / 2 } \rho _ { 0 } ^ { -1 / 2 } , for \rho _ { 0 } the mean pre-shock density , consistent with analytic estimates .
Core building takes 10 times as long as core collapse , which lasts a few \times 10 ^ { 5 } yrs , consistent with observed prestellar core lifetimes .
Core shapes change from oblate to prolate as they evolve .
To define cores , we use isosurfaces of the gravitational potential .
We compare to cores defined using the potential computed from projected surface density , finding good agreement for core masses and sizes ; this offers a new way to identify cores in observed maps .
Cores with masses varying by three orders of magnitude ( \sim 0.05 - 50 M _ { \odot } ) are identified in our high- \cal M simulations , with a much smaller mass range for models having low \cal M .
We halt each simulation when the first core collapses ; at that point , only the more massive cores in each model are gravitationally bound , with E _ { th } + E _ { g } < 0 .
Stability analysis of post-shock layers predicts that the first core to collapse will have mass M \propto v ^ { -1 / 2 } \rho _ { 0 } ^ { -1 / 2 } T ^ { 7 / 4 } , and that the minimum mass for cores formed at late times will have M \propto v ^ { -1 } \rho _ { 0 } ^ { -1 / 2 } T ^ { 2 } , for T the temperature .
From our simulations , the median mass lies between these two relations .
At the time we halt the simulations , the M vs . v relation is shallower for bound cores than unbound cores ; with further evolution the small cores may evolve to become bound , steeping the M vs . v relation .