Pulsar Binary Birthrates with Spin-Opening Angle Correlations
Empirical birthrate estimates for pulsar binaries depend on 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. Previous estimates use the average value for only two pulsars, i.e. PSRs B1913+16 and B1534+12. We explore how birthrate predictions depend on assumptions about opening angle and alignment, using empirically-motivated distributions to define an effective beaming correction factor, f_{b,eff}. For most known pulsars, we expect f_{b,eff} to be less than 6. We also calculate f_{b,eff} for PSRs J0737-3039A and J1141-6545, applying the currently available constraints for their beam geometry. Our median posterior birthrate predictions for tight PSR-NS binaries, wide PSR-NS binaries, and tight PSR-WD binaries are 89/Myr, 0.84/Myr, and 34/Myr, respectively. For pulsars with spin period between 10 ms and 100 ms, we marginalized our posterior birthrate distribution P(R) over a range of plausible beaming correction factors. Our predictions are robust, changing little between several alternative misalignment angle distribution models. [ABRIDGED]