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 neu tron star. Roche lobe filling occurs when the secondary is a turn-off main-sequence star (having a small helium core). We assume loss of ang ular momentum owing to gravitational wave radiation and magnetic braki ng. We have found that the loss (and the mechanism of loss) of mass an d angular momentum from the system is the main factor determining the value of the bifurcation period (P-bif). The bifurcation period separa tes the formation of the converging systems from the diverging systems . Variations in the initial chemical composition, and in the initial m ass of the secondary, lead only to minor changes in P-bif. We have als o investigated how changes in the chemical composition influence the i nitial orbital period (P-i) versus final orbital period (P-f) relation , The initial chemical composition has a more significant effect on th is relation for shorter P-i than for longer P-i. We have found systema tic differences for the P-f versus white dwarf mass relation for vario us chemical compositions, For converging systems, we have found that t here is a boundary orbital period (P-b) such that if P-i < P-b, a syst em will evolve through the period gap (there are no low-mass X-ray bin aries with orbital periods between one and three hours) with a Roche l obe 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 binar ies. If P-b < P-i < P-bif, then short orbital period millisecond binar y pulsar systems will be formed.