Some Astrophysical Aspects of Pulsars

Extract

In principle the formation rate can be obtained on the basis of a knowledge of a spatial densities and lifetimes. Extreme care is needed, however because of the incompleteness of the available sample because of luminosity effects. Since luminosity and age are correlated it is essential that densities and lifetimes be evaluated for the same sample. Incompleteness affects the very faint pulsars most strongly, but because of their long lifetime the effect on the formation rate is comparatively small. We shall assume that the lifetime of a pulsar in our sample is on the average equal to twice its age. Further we estimate distances (r) from dispersion measures on the basis of a mean electron density n_e of 0.05 cm⁻³ near the Sun. The fluctuations in n_e again may cause systematic errors, but no information is available for an estimate of the magnitude of these.

There are 5 pulsars known with r cosb (b galactic latitude) less than 100 pc. For three of these ages are available from which a harmonic mean life time T of 2.5 × 10⁷ yr is found. Of 19 pulsars with r cos b < 300 pc, eight have ages from which T= 1.1 × 10⁷ yr. Samples with larger r cos b appear to be too incomplete for our purpose. Taking the Galaxy to be a uniform disk with a radius of 14 kpc, we obtain from both samples a formation rate of about one pulsar per 250 yr. It should be stressed that this is the rate for ‘visible’ pulsars. If beaming effects cause only a fraction η to be in principle observable, the formation rate is to be multiplied by η⁻¹.