Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity

We present analytic formulae that approximate the evolution of stars for a wide range of mass M and metallicity Z. Stellar luminosity, radius and core mass are given as a function of age, M and Z, for all phases from the zero-age main sequence up to, and including, the remnant stages. For the most part we find continuous formulae accurate to within 5 per cent of detailed models. These formulae are useful for purposes such as population synthesis that require very rapid but accurate evaluation of stellar properties, and in particular for use in combination with N-body codes. We describe a mass-loss prescription that can be used with these formulae, and investigate the resulting stellar remnant distribution.