Evolution of low-mass close binary systems with a neutron star: its dependence with the initial neutron star mass

We construct a set of binary evolutionary sequences for systems composed by a normal, solar composition, donor star together with a neutron star. We consider a variety of masses for each star as well as for the initial orbital period corresponding to systems that evolve to ultra-compact or millisecond pulsar-helium white dwarf pairs. Specifically, we select a set of donor star masses of 0.50, 0.65, 0.80, 1.00, 1.25, 1.50, 1.75, 2.00, 2.25, 2.50, 3.00 and 3.50 M-circle dot, whereas for the accreting neutron star we consider initial mass values of 0.8, 1.0, 1.2 and 1.4 M-circle dot. Because the minimum mass for a proto-neutron star is approximately 0.9 M-circle dot, the value of 0.8 M-circle dot was selected in order to cover the whole range of possible initial neutron star masses. The considered initial orbital period interval ranges from 0.5 to 12 d. It is found that the evolution of systems, with fixed initial values for the orbital period and the mass of the normal donor star, heavily depends upon the mass of the neutron star. In some cases, varying the initial value of the neutron star mass, we obtain evolved configurations ranging from ultra-compact to widely separated objects. We also analyse the dependence of the final orbital period with the mass of the white dwarf. In agreement with previous expectations, our calculations show that the final orbital period-white dwarf mass relation is fairly insensitive to the initial neutron star mass value. A new period-mass relation based on our own calculations is proposed, which is in good agreement with period-mass relations available in the literature. As a consequence of considering a set of values for the initial neutron star mass, these models allow finding different plausible initial configurations (donor and neutron star masses and orbital period interval) for some of the best observed binary systems of the kind we are interested in here. We apply our calculations to analyse the case of PSR J0437-4715, showing that there is more than one possible set of initial parameters (masses, period and the fraction beta of matter accreted by the neutron star) for this particular system.