Evolution of Neutron-Star, Carbon-Oxygen White-Dwarf Binaries

At least one, but more likely two or more, eccentric neutron-star, carbon-oxygen white-dwarf binaries with an unrecycled pulsar have been observed. According to the standard scenario for evolving neutron stars which are recycled in common envelope evolution we expect to observe $\text{gsim}50$ such circular neutron star-carbon oxygen white dwarf binaries, since their formation rate is roughly equal to that of the eccentric binaries and the time over which they can be observed is two orders of magnitude longer, as we shall outline. We observe at most one or two such circular binaries and from that we conclude that the standard scenario must be revised. Introducing hypercritical accretion into common envelope evolution removes the discrepancy by converting the neutron star into a black hole which does not emit radio waves, and therefore would not be observed.