3.3 The Population of Normal and Millisecond Pulsars 

The most recent analysis to use the scaling function approach to derive the characteristics of the true normal and millisecond pulsar populations is based on the sample of pulsars within 1.5 kpc from the Sun [107]. The rationale for this cut-off is that, within this region, the selection effects are well understood and easier to quantify by comparison with the rest of the Galaxy. These calculations should give reliable estimates for the local pulsar population .

  

Figure 10: The corrected luminosity distribution (solid histogram with error bars) derived from a sample of 84 normal pulsars within 1.5 kpc of the Sun [107]. The observed distribution is shown by the dashed line. The difference between the observed and derived distributions below 10 mJy kpc highlights the severe under-sampling of low-luminosity pulsars in the observed population.

The luminosity distribution obtained from this analysis is shown in Fig.  10 . These calculations lead to a local surface density of pulsars kpc for luminosities greater than 1 mJy kpc . Using Biggs' [33] beaming model, the mean surface density of active pulsars with luminosities above 1 mJy kpc is pulsars kpc . Applying the same techniques to the sample of millisecond pulsars, and assuming a mean beaming fraction of 75% [90], the local surface density of millisecond pulsars with luminosities above 1 mJy kpc is kpc .

These estimates of the local surface density of active pulsars allow us to deduce the likely distance to the nearest neutron star to Earth. This number is of interest to those building gravitational wave detectors, since it determines the likely amplitude of gravitational waves emitted from nearby rotating neutron stars. According to Thorne [153], currently planned detectors will be able to detect neutron stars with ellipticities greater than

where P is the rotation period of a neutron star at a distance d from the Earth. For the combined millisecond and normal pulsar populations, with a surface density of pulsars kpc , the nearest neutron star is thus likely to be < 40 pc. Future detections of such sources would be able to determine whether neutron stars have such ellipticities. One of the best known candidates is the nearby 5.75 ms pulsar J0437-4715 [81] which, at a distance of pc [136], is the closest known millisecond pulsar to the Earth.

Integrating the local surface densities of pulsars over the whole Galaxy requires a knowledge of the presently rather uncertain Galactocentric radial distribution [108, 80]. One approach is to assume that pulsars have a radial distribution similar to that of other stellar populations. The corresponding scale factor is then 1000 250 kpc [129]. With this factor, we estimate there to be 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 . From the P - diagram in Fig.  5, we infer a typical lifetime for normal pulsars of yr, corresponding to a Galactic birth rate of per 60 yr -- consistent with the rate of supernovae [159]. Different techniques yield consistent results [107]. As noted in § 2.4, the ages of the millisecond pulsars are much older -- close to that of the Universe yr. Taking the maximum age of the millisecond pulsars to be yr, we infer a mean birth rate of at least yr . Given the uncertainties involved, this agrees satisfactorily with the birth-rate of low-mass X-ray binaries [98].

Binary and Millisecond Pulsars D. R. Lorimer (dunc@mpifr-bonn.mpg.de) http://www.livingreviews.org/lrr-1998-10 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de