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 during the accretion phase of protostellar evolution, as a result of the gradient of the 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 (weakly increasing with time) in the early accretion phase; and (2) in the more realistic case including cooling saturation at higher densities, may initially be either weakly increasing or weakly decreasing with time, for the low dust temperature (T_d~ 6 K) and high dust temperature (T_d~ 10 K) cases, respectively. Hence, our results show that the initial decline in seen in isothermal models is definitely not enhanced by non-isothermal effects, and is often suppressed by them. In all our models, 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 in the accretion phase probably needs to appeal to the global molecular cloud structure and possible envelope support, which results in a finite mass reservoir for cores.