A new look at pulsar statistics - birthrate and evidence for injection

Abstract

We make a statistical analysis of the periods P and period-derivatives of pulsars using a model independent theory of pulsar flow in the 2'-P diagram. Using the available sample of P and P values, we estimate the current of pulsars flowing unidirectionally along the P-axis, which is related to the pulsar birthrate. Because of radio luminosity selection effects, the observed pulsar sample is biased towards low P and high P. We allow for this by weighting each pulsar by a suitable scale factor. We obtain the number of pulsars in our galaxy to be 6.052: x 10^-5 and the birthrate to be 0.048 1:;:; pulsars yr-1 galaxy-1. The quoted errors refer to 95 per cent confidence limits corresponding to fluctuations arising from sampling, but make no allowance for other systematic and random errors which could be substantial. The birthrate estimated here is consistent with the supernova rate. We further conclude that a large majority of pulsars make their first appearance at periods greater than 0.5 s. This 'injection', which runs counter to present thinking, is probably connected with the physics of pulsar radio emission. Using a variant of our theory, where we compute the current as a function of pulsar 'age' . (1/2 PIP), we find support for the dipole braking model of pulsar evolution upto 6 x 10^6 yr of age. We estimate the mean pulsar braking index to be 3.7_C:::.