Upperpanel: source function as proposed by Ulrich (1976) and Hueso & Guillot (2005). The radius is normalized to the centrifugal radius r_c, and the source term is normalized to the mean surface mass flux () such that its surface integral gives unity. Lower panel: cumulated mass accretion rate (normalized by the total mass accretion rate), Ṁ, integrated within radius r. The values of Ṁ_tot and r_c are to be specified as functions of time according to the initial conditions of the prestellar core envelope.