Examples of the profiles of the gas density (top), visual extinction from the surface (middle) and temperature (bottom). The negative time is for the pre-stellar phase, and a time of zero is when the protostar is formed. For visualisation purposes, 50 of the 100 gas parcels in the sampling are shown. The values of n_gas(r) estimated by Eq. (1) and the T_d(r) estimated by Eq. (9) are the final values of n_gas(t) in Eq. (10) and T_d(t) in Eq. (13) at a given location r. These profiles have L_* = 10⁵ L_⊙, n_in = 10⁷ cm⁻³, r_flat=0.05 pc and a = 0.5 μm.