Based on a number of all-sky surveys carried out in the 1990s, the scale factor approach has been used to derive the characteristics of the true normal and millisecond pulsar populations and is based on the sample of pulsars within of the Sun . Within this region, the selection effects are well understood and easier to quantify than in the rest of the Galaxy. These calculations should therefore give a reliable local pulsar population estimate.
Integrating the local surface densities of pulsars over the whole Galaxy requires a knowledge of the presently rather uncertain Galactocentric radial distribution [137, 181]. One approach is to assume that pulsars have a radial distribution similar to that of other stellar populations and to scale the local number density with this distribution in order to estimate the total Galactic population. The corresponding local-to-Galactic scaling is . This implies a population of active normal pulsars and millisecond pulsars in the Galaxy.
Based on these estimates, we are in a position to deduce the corresponding rate of formation or birth-rate required to sustain the observed population. From the diagram in Figure 3, we infer a typical lifetime for normal pulsars of , corresponding to a Galactic birth rate of per - consistent with the rate of supernovae . As noted in Section 2.2, the millisecond pulsars are much older, with ages close to that of the Universe (we assume here ). Taking the maximum age of the millisecond pulsars to be , we infer a mean birth rate of at least 1 per . This is consistent, within the uncertainties, with the birth-rate of low-mass X-ray binaries .
© Max Planck Society and the author(s)