The statistics of radio pulsars: A spark model

We use Monte Carlo techniques to relate a theoretical pulsar emission model to the observed distributions of pulse period, magnetic field strength, distance, and luminosity of radio pulsars. We assume that the radio luminosity of pulsars is proportional to the gap potential and current flow from the polar cap. The current is assumed to be nonuniform and clustered in sparks, but only those sparks swept by the line of sight contribute to the observed radio luminosity. We test our model by using the Ruderman-Sutherland vacuum gap potential and find that the simulated distributions are consistent with those observed, with the exception of the period distribution. The model predicts more long-period pulsars than are observed. This discrepancy may result from the model itself, a reduced sensitivity of surveys to long-period pulsars, or the nondipole spin-down of pulsars.