Isolated pulsar spin evolution on the P –$P-{\dot P}$diagram

We look at two contrasting spin-down models for isolated radio pulsars and, accounting for selection effects, synthesize observable populations. While our goal is to reproduce all of the observable characteristics, in this paper we pay particular attention to the form of the spin period versus period derivative ($P-{\dot P}$ diagram and its dependence on various pulsar properties. We analyse the initial spin period, the braking index, the magnetic field, various beaming models as well as the pulsar's luminosity. In addition to considering the standard magnetic dipole model for pulsar spin-down, we also consider the recent hybrid model proposed by Contopoulos and Spitkovsky. The magnetic dipole model, however, does a better job of reproducing the observed pulsar population. We conclude that random alignment angles and period-dependent luminosity distributions are essential to reproduce the observed $P-{\dot P}$diagram. We also consider the time decay of alignment angles and attempt to reconcile various models currently being studied. We conclude that in order to account for recent evidence for the alignment found by Weltevrede and Johnston, the braking torque on a neutron star should not depend strongly on the inclination. Our simulation code is publicly available and includes a web-based interface to examine the results and make predictions for yields of current and future surveys.