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 p art we find continuous formulae accurate to within 5 per cent of detailed m odels. 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.