An empirical model for protostellar collapse

We propose a new analytic model for the initial conditions of protostellar collapse in relatively isolated regions of star formation. The model is nonmagnetic and is based on a Plummer-like radial density profile as its initial condition. It fits : the observed density profiles of prestellar cores and class 0 protostars; recent observations in prestellar cores of roughly constant contraction velocities over a wide range of radii; and the lifetimes and accretion rates derived for class 0 and class I protostars. However, the model is very simple, having in effect only two free parameters, so it should provide a useful framework for interpreting observations of prestellar cores and protostars and for calculations of radiation transport and time-dependent chemistry. As an example, we model the prestellar core L1544.