a) First core lifetime τ_fc as a function of ϵ measured in the simulations (circles). The dashed and thin solid lines represent our analytical predictions (see text). b) First core lifetime as a function of mass accretion rate for all runs. The black dashed line portrays a simple estimate from dimensional arguments (see text). c)–i) Ratio of the mass accretion rate measured in the simulation to various predictions Ṁ_pred from numerical and similarity solutions, as a function of ϵ. c) The hearts represent the similarity solution of Larson (1969) and Penston (1969), the stars are the solution of Shu (1977), while the triangles are from the results of Hunter (1977). In panels d) to f), the Ṁ_pred estimate is obtained from dividing the initial cloud mass M₀ by the free-fall times t_ff1, t_ff2, and t_ff3. g) The hearts represent a modified version of Penston’s formula, which is equivalent, barring a scaling factor, to the prediction using the cloud sound crossing time (diamonds). h) The circles represent the first best fitting formula Ṁ_A we have used to predict the lifetimes. i) The squares show the second mass accretion rate estimate Ṁ_B we have selected for our analysis. The colours in all panels code for different initial temperatures (see legend in panel a)).