The evolution of short‐period binary pulsars: a systematic study

We present evolutionary sequences for low‐mass close binary systems in which a low‐mass (1.0–1.5 M⊙) secondary star transfers mass to a neutron star. Roche lobe filling occurs when the secondary is a turn‐off main‐sequence star (having a small helium core). We assume loss of angular momentum owing to gravitational wave radiation and magnetic braking. We have found that the loss (and the mechanism of loss) of mass and angular momentum from the system is the main factor determining the value of the bifurcation period ( P bif ). The bifurcation period separates the formation of the converging systems from the diverging systems. Variations in the initial chemical composition, and in the initial mass of the secondary, lead only to minor changes in P bif . We have also investigated how changes in the chemical composition influence the initial orbital period ( P i ) versus final orbital period ( P f ) relation. The initial chemical composition has a more significant effect on this relation for shorter P i than for longer P i . We have found systematic differences for the P f versus white dwarf mass relation for various chemical compositions. For converging systems, we have found that there is a boundary orbital period ( P b ) such that if P i  <  P b , a system will evolve through the period gap (there are no low‐mass X‐ray binaries with orbital periods between one and three hours) with a Roche lobe overflowing secondary, but the accretion on to the neutron star is forbidden owing to the ‘propeller effect’. The systems will end their evolution as ultra‐short period and very bright, low‐mass X‐ray binaries. If P b  <  P i  <  P bif , then short orbital period millisecond binary pulsar systems will be formed.