Re-calibrated analytic stellar evolution formulae for the main sequence: Extension to massive stars and variations in [alpha/Fe]

Analytic formulae are an efficient way to approximate the evolution of a star of a given mass and chemical composition, and are widely used in the literature to compute large grids of evolutionary models for stellar population synthesis. Such formulae rely on calibration to detailed stellar evolution models, and existing versions are based on a sparse, limited grid in comparison to modern simulations. By calibrating against the latest generation of single-star evolution models calculated within the Binary Population and Spectral Synthesis framework, we revise and extend pre-existing equations to include the evolution of massive (M 50,) stars and changes in chemical abundances in the form of variations in. We introduce additional terms which allow for a better approximation of the main-sequence lifetimes, and the luminosities and radii at the beginning and end of the main sequence. These revised equations describe the main-sequence age, zero-age and terminal-age radius and luminosity with mean errors of less than 10 per cent or 0.05 dex, for all except the terminal age radius, which shows RMS errors of 20 per cent and 0.1 dex. For enriched stellar populations, we advise using a matched-iron value for metallicity in the equations, consistent with the expectation that iron is the dominant opacity source affecting the evolution of main-sequence stars.