Stellar population

A stellar population is an ensemble of stars described by its formation times, initial masses, composition and present stellar evolution states. Number fractions must be distinguished from mass-weighted fractions. Shared formation times can correlate the states of components of a binary star even when their initial masses have independence.

The event rate per unit initial stellar mass and per unit delay after star formation. An extended star formation history produces a rate $R(t)=\int \mathrm{SFR}(t-\tau )\Psi (\tau )d\tau$. Measuring rates versus age in old populations constrains progenitor channels only after accounting for stellar lifetimes, age spreads and selection.

A Population III star is a first-generation star formed from essentially metal-free primordial gas. Limited cooling generally raises its characteristic fragmentation mass and favors a more top-heavy initial mass function than in enriched star formation.

A Population II star is an old metal-poor star formed from gas enriched by earlier stellar generations. Metal and dust cooling let enriched gas fragment to lower masses than primordial gas under otherwise comparable conditions.

Integrated spectra can confuse older stellar populations with more metal-rich ones because both can redden the light and change absorption lines. Line strengths depend on stellar metallicity, temperatures, ages, and abundance ratios. Weak metal lines in a young population dominated by hot bright stars need not indicate low stellar metallicity.

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.

If a population forms at a constant number rate for duration $T$ and every birth object is retained in the census, its present ages are uniform on $[0,T]$. A fixed initial mass function with finite mean birth mass also makes constant mass-based star formation rate equivalent to constant number rate.