PULSAR STATISTICS - THE BIRTHRATE AND INITIAL SPIN PERIODS OF RADIO PULSARS

We investigate the birthrate and initial spin periods of radio pulsars using the recently revised pulsar distance scale of Cordes et al. Our technique is based upon the model-free approach originally suggested by Phinney & Blandford, which makes no assumptions about pulsar luminosity as a function of period, the beaming fraction, or field decay in radio pulsars. It eliminates the large statistical errors inherent in previous methods by restricting the sample to pulsars with luminosities greater than some minimum value. We verify the validity of our approach, and shortcomings of previous methods, by using Monte Carlo simulations on synthetic populations of pulsars which take into account random errors in the pulsar distance scale. We find that small-number statistics and errors in the pulsar distance scale prohibit us from making any firm statements on the birthrate or initial spin periods of pulsars with luminosities less than 10 mJy kpc2. The birthrate of potentially observable pulsars with luminosities greater than 10 mJy kpc2 is between 0.6 and 2 per 1000 yr. There is no convincing evidence that any of these pulsars are born spinning slowly. We estimate that there are (1.3 +/- 0.2) x 10(4) potentially observable pulsars in the Galaxy with luminosities > 10 mJy kpC2. Application of Biggs's beaming law to our results suggests that a pulsar is born once every 125 to 250 yr in the Galaxy, considerably lower than recent estimates of a supernova rate of 1 per 30 yr, but consistent with earlier estimates of the supernova rate. The local pulsar birthrate is calculated to be between 6 and 1 2 pulsar kpC-2 Myr-1, which is in excellent agreement with Blauuw's estimate of the local production rate of OB stars.