M_D − Ṁ_* plane for different values of ${\sigma }_{M_0}$. The colored dots in every plot are Monte Carlo simulations of 10⁵ proto- planetary disks with ω = 0.8 and t = 5 Myr, evolving following Eqs. (4), (5), where M₀ follows a lognormal distribution centered on the natural logarithm of 0.1 M_⊙ with a spread of (a) 0.04 dex, (b) 0.22 dex, (c) 0.30 dex, (d) 0.65 dex. The black dots show the “boomerang” shape of the isochrones for a disk population with the same parameters as in the other disk populations, but with ${\sigma }_{M_0}=0$. For the four plots, t_acc,0 follows a lognormal distribution centered on the natural logarithm of 1 Myr, with a spread of 0.26 dex.