Evolution of Neutron-star, Carbon-oxygen White-dwarf Binaries

We consider the evolution of neutron-star (ns), carbon-oxygen white-dwarf (co) binaries, using both the Bethe & Brown (1998) schematic analytic evolutions and the Portegies Zwart & Yungelson (1998) numerical population syntheses. The scenario in which the circular neutron-star, carbon-oxygen white-dwarf binaries (ns, co)c have gone through common envelope evolution is considered. In conventional common envelope evolution for the (ns, co)c it is easy to see that the observed ratio a (ns, co)c/(ns, co)e should be ∼ 50 because: (i) The formation rate of the two types of binaries is, within a factor 2, the same. (ii) The magnetic fields in the (ns, co)c binaries will be brought down by a factor of ∼ > 100 by He accretion in the neutron-star, He-star phase following common envelope evolution just as the inferred pulsar magnetic field strengths in the (ns, ns) binaries are brought down (Brown 1995). The magnetic fields are not, however, brought down to the ∼ 5× 10 G of four of the five (ns, co)c binaries. In the earlier literature, the five observed (ns, co)c binaries were evolved through common envelope, but now a concensus is arising that common envelope evolution is avoided, as we shall discuss. Accepting this, we see that the present discrepancy between observed (ns, co)c binaries (none) and the predicted ∼ 50 is great. We show that the introduction of hypercritical accretion, which sends the neutron star into a black hole, is helpful in explaining this discrepancy. One of our main purposes in these evolutions is to compare the schematic, analytic and numerical population syntheses. We show there to be excellent agreement between these two approaches and we outline why this results. a The lower suffix e (c) denotes the eccentric (circular) binaries. Circularization implies here common envelope evolution. Subject headings: binaries: close – stars: neutron – white dwarfs – stars: evolution – stars: statistics