The galactic distribution, birthrate, and luminosity evolution of pulsars

The radial distribution of galactic pulsars is analyzed and used to obtain expressions for the pulsar birth rate, luminosity function, and the evolution of pulsar luminosity. Pulsars are shown to exist in a ring-like structure about 7-8 kpc across, with the majority of the population between 5 and 10 kpc from the galactic center. From data on 190 pulsars, it is estimated that there exist 62,000 + or - 15,000 pulsars with luminosities between 3 x 10 to the 26th and 3 x 10 to the 29th erg/sec in the galaxy, assuming an orientation coefficient of 0.11. From this, an upper limit to the pulsar birth rate of 0.027 + or - 0.009/year or one every 37 + 18 or - 9 years is derived. An expression relating pulsar luminosity to age is presented which may be used for all but young pulsars (age less than 10,000 years). From this expression, it is seen that the true age of pulsars with a luminosity greater than or equal to 3 x 10 to the 16th erg/sec will be 3.6 + or - 0.4 million years, in agreement with both the kinematic and spindown ages.