3.4 The population of relativistic 3 The Galactic Pulsar Population3.2 Correcting the observed pulsar

3.3 The population of normal and millisecond pulsars 

3.3.1 Luminosity distributions and local number estimates 

The most recent use of the scale factor approach to derive the characteristics of the true normal and millisecond pulsar populations is based on the sample of pulsars within 1.5 kpc of the Sun [152Jump To The Next Citation Point In The Article]. 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 .


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Figure 17: Left: The corrected luminosity distribution (solid histogram with error bars) for normal pulsars. The corrected distribution before the beaming model has been applied is shown by the dot-dashed line. Right: The corresponding distribution for millisecond pulsars. In both cases, the observed distribution is shown by the dashed line and the thick solid line is a power law with a slope of -1. The difference between the observed and corrected distributions highlights the severe under-sampling of low-luminosity pulsars.

The luminosity distributions obtained from this analysis are shown in Fig.  17 . For the normal pulsars, integrating the corrected distribution above 1  tex2html_wrap_inline9333 and dividing by tex2html_wrap_inline9335 yields a local surface density, assuming Biggs' beaming model [32] of tex2html_wrap_inline9337 pulsars tex2html_wrap_inline9339 . The same analysis for the millisecond pulsars, assuming a mean beaming fraction of 75% [122], leads to a local surface density of tex2html_wrap_inline9341 pulsars tex2html_wrap_inline9339 for luminosities above 1  tex2html_wrap_inline9333 .

3.3.2 Galactic population and birth-rates 

Integrating the local surface densities of pulsars over the whole Galaxy requires a knowledge of the presently rather uncertain Galactocentric radial distribution [153, 107]. One approach is to assume that pulsars have a radial distribution similar to that of other stellar populations and scale the local number density with this distribution to estimate the total Galactic population. The corresponding local-to-Galactic scaling is tex2html_wrap_inline9347  [200]. With this approach we estimate there to be tex2html_wrap_inline9349 active normal pulsars and tex2html_wrap_inline9351 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 - tex2html_wrap_inline9123 diagram in Fig.  7, we infer a typical lifetime for normal pulsars of tex2html_wrap_inline9357 yr, corresponding to a Galactic birth rate of tex2html_wrap_inline9359 per 60 yr - consistent with the rate of supernovae [253]. As noted in §  2.4, the millisecond pulsars are much older, with ages close to that of the Universe tex2html_wrap_inline9361 (we assume here tex2html_wrap_inline9363 Gyr [104]). Taking the maximum age of the millisecond pulsars to be tex2html_wrap_inline9361, we infer a mean birth rate of at least tex2html_wrap_inline9367 . This is consistent, within the uncertainties, with the birth-rate of low-mass X-ray binaries [135Jump To The Next Citation Point In The Article].

3.3.3 Implications for gravitational wave detectors 

The estimates of the local surface density of active pulsars allow us to deduce the likely distance of the nearest neutron star to Earth. For the combined millisecond and normal pulsar populations, with a surface density of tex2html_wrap_inline9369 pulsars tex2html_wrap_inline9339, the nearest neutron star is thus likely to be tex2html_wrap_inline9373 . 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 [213]. According to Thorne [244Jump To The Next Citation Point In The Article], currently planned detectors will be able to detect neutron stars with ellipticities greater than tex2html_wrap_inline9375, where P is the rotation period in ms and d is the distance in kpc. The recent probable detection of free precession in the radio pulsar B1828-11 [221] does indicate that ellipticities exist in neutron stars so that nearby objects may be continuous sources of gravitational radiation.

Thus, in order to detect small ellipticities, nearby sources with short spin periods are required. One of the best candidates is the nearby 5.75-ms pulsar J0437-4715 [108Jump To The Next Citation Point In The Article]. At a distance of tex2html_wrap_inline9383  [208Jump To The Next Citation Point In The Article] this is currently the closest known millisecond pulsar to the Earth. The closest known neutron star is RX J185635-3754 discovered in the ROSAT all-sky survey [261]. Multi-epoch HST observations show that this isolated neutron star is located at a distance of tex2html_wrap_inline9387  [260]. In keeping with other radio-quiet isolated neutron stars, the period of this pulsar is likely to be several seconds [176].

3.4 The population of relativistic 3 The Galactic Pulsar Population3.2 Correcting the observed pulsar

image Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de