The intrinsic luminosity and initial period of pulsars

The observed properties of pulsars are modeled on the assumption that they evolve by emitting magnetic dipole radiation and have exponentially decaying magnetic fields. The models are constructed by using Monte Carlo techniques to generate a Galactic sample of pulsars having particular distributions of initial periods, magnetic dipole moments, and positions. By choosing a relationship between the radio luminosity L(r), the period (P), and the P derivative, it is determined which pulsars of the generated sample could be detected by one of the major pulsar surveys. Detailed account is taken of known selection effects in these surveys. Models in which the size of the pulsar emission cone is dependent on the period are considered. The properties of the detectable pulsars are compared with the properties of the observed pulsars, and the initial distributions and luminosity relation of the model are adjusted until a satisfactory agreement is obtained. A crucial point is that the observed relation between L(r) and P, P derivative is affected by selection effects and does not apply to the actual pulsar population. It is found that the best fits are obtained with models in which the pulsars are injected with relatively long periods, about 0.5 sec.