On the Nature of Pulsars. III. Analysis of Observations

Abstract

In this paper we formulate statistical methods for the analysis of pulsar observations based upon the magnetic-dipole model presented in the first paper in this series. Applying this formalism to the extant observations, we reach the following tentative conclusions; 1. The observations are consistent with the magnetic-dipole model and a "turnoff" time of about 4 X 106 years. The observed pulsars have an average age of approximately 2 X 106 years. The distribution of periods (in particular, the lack of long-period objects) can be quantitatively understood. 2. If we assume that the pulsar emission is in the form of a rotating pencil beam, then we observe between one4ourth and one-sixth of bright nearby objects. 3. The present birth rate is near 5 X 10-' , or one per 30 years in the Galaxy. 4. The average scale height for the distribution above the plane is about 120 pc. The data, however, suggest that young objects are concentrated to the plane much more strongly than the old ones; this, together with the known anomalous space motion of the Crab object, leads us to conclude tentatively that most pulsars receive a velocity averaging 100 km at birth, and the initial scale height is about 80pc. 5. The derived bfrth rate and scale height are consistent with the statement that all or most stars more massive than about 4 M0 become pulsars at death. The scale height is inconsistent with the progenitors being much less massive objects, and the number of objects is inconsistent with them being much more massive ones. The population identification makes the association of pulsar formation with T 'pe II supernova events very plausible. 6. With these results we consider the evolution of the nuclear region of the Galaxy and conclude that during its early history it might have been a small non thermal source with a total luminosity between that of Seyfert nuclei and QSOs, fluctuating on a time scale of approximately 1 year.