2010ApJ...715..230O

One ingredient in an empirical birthrate estimate for pulsar binaries is the fraction of sky subtended by the pulsar beam: the pulsar beaming fraction. This fraction depends on both the pulsar's opening angle and the misalignment angle between its spin and magnetic axes. The current estimates for pulsar binary birthrates are based on an average value of beaming fractions for only two pulsars, i.e., PSRs B1913+16 and B1534+12. In this paper, we revisit the observed pulsar binaries to examine the sensitivity of birthrate predictions to different assumptions regarding opening angle and alignment. Based on empirical estimates for the relative likelihood of different beam half-opening angles and misalignment angles between the pulsar rotation and magnetic axes, we calculate an effective beaming correction factor, f_b,eff, whose reciprocal is equivalent to the average fraction of all randomly selected pulsars that point toward us. For those pulsars without any direct beam geometry constraints, we find that f_b,eff is likely to be smaller than 6, a canonically adopted value when calculating birthrates of Galactic pulsar binaries. We calculate f_b,eff for PSRs J0737-3039A and J1141-6545, applying the currently available constraints for their beam geometry. As in previous estimates of the posterior probability density function P({R}) for pulsar binary birthrates {R}, PSRs J0737-3039A and J1141-6545 still significantly contribute to, if not dominate, the Galactic birthrate of tight pulsar-neutron star (NS) and pulsar-white dwarf (WD) binaries, respectively. Our median posterior present-day birthrate predictions for tight PSR-NS binaries, wide PSR-NS binaries, and tight PSR-WD binaries given a preferred pulsar population model and beaming geometry are 89 Myr^–1, 0.5 Myr^–1, and 34 Myr^–1, respectively. For long-lived PSR-NS binaries, these estimates include a weak (x1.6) correction for slowly decaying star formation in the galactic disk. For pulsars with spin period between 10 ms and 100 ms, where few measurements of misalignment and opening angle provide a sound basis for extrapolation, we marginalized our posterior birthrate distribution P({R}) over a range of plausible beaming correction factors. We explore several alternative beaming geometry distributions, demonstrating that our predictions are robust except in (untestable) scenarios with many highly aligned recycled pulsars. Finally, in addition to exploring alternative beam geometries, we also briefly summarize how uncertainties in each pulsar binary's lifetime and in the pulsar luminosity distribution can be propagated into P({R)}.