The nature of millisecond pulsars with helium white dwarf companions

We examine the growing data set of binary millisecond pulsars that are thought to have a helium white dwarf companion. These systems are believed to form when a low- to intermediate-mass companion to a neutron star fills its Roche lobe between central hydrogen exhaustion and core helium ignition. We confirm that our own stellar models reproduce a well-defined period-companion mass relation irrespective of the details of the mass transfer process. With magnetic braking, this relation extends to periods of less than 1 d for a 1 M-circle dot giant donor. With this and the measured binary mass functions, we calculate the orbital inclination of each system for a given pulsar mass. We expect these inclinations to be randomly oriented in space. If the masses of the pulsars were typically 1.35 M-circle dot, then there would appear to be a distinct dearth of high-inclination systems. However, if the pulsar masses are more typically from 1.55 to 1.65 M-circle dot, then the distribution of inclinations is indeed indistinguishable from random. If it were as much as 1.75 M-circle dot, then there would appear to be an excess of high-inclination systems. Thus, with the available data, we can argue that the neutron star masses in binary millisecond pulsars recycled by mass transfer from a red giant typically lie around 1.6 M-circle dot and that there is no preferred inclination at which these systems are observed. Hence, there is reason to believe that pulsar beams are either sufficiently broad or show no preferred direction relative to the pulsar's spin axis which is aligned with the binary orbit. This is contrary to some previous claims, based on a subset of the data available today, that there might be a tendency for the pulsar beams to be perpendicular to their spin.