Evolutionary-state selection by stellar lifetimes

Given a birth-mass distribution and age distribution, an evolutionary state occupies the mass-age set where its starting lifetime has elapsed and its ending lifetime has not. The state number fraction is the probability measure of this set. Initial mass function tail coordinates and the probability integral transform can turn these weighted regions into simple geometric areas.

A phase bounded by mass-dependent lifetimes ${\tau }_a(M)$ and ${\tau }_b(M)$ occupies ${\tau }_a(M)<t<{\tau }_b(M)$, clipped to the population age range. Its boundaries can be mapped into uniform probability coordinates to evaluate evolutionary-state fractions.