The effect of non-isothermality on the gravitational collapse of spherical clouds and the evolution of protostellar accretion

We investigate the role of non-isothermality in gravitational collapse and protostellar accretion by explicitly including the effects of molecular radiative cooling, gas-dust energy transfer, and cosmic ray heating in models of spherical hydrodynamic collapse. Isothermal models have previously shown an initial decline in the mass accretion rate \dot{M}, due to a gradient of infall speed that develops in the prestellar phase. Our results show that: (1) in the idealized limit of optically thin cooling, a positive temperature gradient is present in the prestellar phase which effectively cancels out the effect of the velocity gradient, producing a near constant \dot{M} in the early accretion phase; (2) in the more realistic case including cooling saturation at higher densities, \dot{M} may initially be either weakly increasing or weakly decreasing with time, for low (T_d ~ 6 K) and high dust temperature (T_d ~ 10 K) cases, respectively. Hence, our results show that the initial decline in \dot{M} seen in isothermal models is definitely not enhanced by non-isothermal effects, and is often suppressed by them. In all our models, \dot{M} does eventually decline rapidly due to the finite mass condition on our cores and a resulting inward propagating rarefaction wave. Thus, any explanation for a rapid decline of $\dot{M}$ in the accretion phase likely needs to appeal to the global molecular cloud structure and possible envelope support, which results in a finite mass reservoir for cores.