Low- and intermediate-mass close binary evolution and the initial-final mass relation

Using Eggleton's stellar evolution code, we carry out 150 runs of Population I binary evolution calculations with the initial primary mass between 1 and 8M_solar, the initial mass ratio dm/dt C Max [ 0, (r_star/r_lobe - 1 )³ ], qM₁M₂ between 1.1 and 4, and the onset of Roche lobe overflow (RLOF) at an early, middle or late Hertzsprung-gap stage. We assume that RLOF is conservative in the calculations, and find that the remnant mass of the primary may change by more than 40per cent over the range of initial mass ratio or orbital period, for a given primary mass. This is contrary to the often-held belief that the remnant mass depends only on the progenitor mass if mass transfer begins in the Hertzsprung gap. We fit a formula, with an error less than 3.6per cent, for the remnant (white dwarf) mass as a function of the initial mass M_1i of the primary, the initial mass ratio q_i and the radius of the primary at the onset of RLOF. We also find that a carbon-oxygen white dwarf with mass as low as 0.33M_solar may be formed if the initial mass of the primary is around 2.5M_solar.