2005A&A...443..961L

We compute numerical simulations of spherical collapse triggered by a slow increase in external pressure. We compare isothermal models to models including cooling with a simple but self-consistent treatment of the coupling between gas, grains and radiation field temperatures. The hydrostatic equilibrium appears to hold past the marginally stable state, until the collapse proceeds. The last hydrostatic state before collapse has a lower central gas temperature in the centre due to the enhanced coupling between gas, grains and radiation field. This results in slightly lower pressure gradients in the bulk of the envelope which is hence slightly more extended than in the isothermal case. Due to the sensitivity of the collapse on these initial conditions, protostellar infall velocities in the envelope turn out to be much slower in the case with cooling. Our models also compute the radiative transfer and a rather large chemical network coupled to gas dynamics. However, we note that the steady-state chemisorption of CO is sufficient to provide an accurate cooling function of the gas. This justifies the use of post-processing techniques to account for the abundance of observed molecules. Existing observations of infall signatures put very stringent constraints on the kinematics and temperature profile of the class 0 protostar IRAM 04191+1522. We show that isothermal models fail to account for the innermost slow infall motions observed, even with the most hydrostatic initial conditions. In contrast, models with cooling reproduce the general shape of the temperature profile inferred from observations and are in much better agreement with the infall signatures in the inner 3000AU.