3.3 The Population of Normal 3 The Galactic Pulsar Population3.1 Selection Effects in Pulsar

3.2 Correcting the observed pulsar sample 

In order to decouple the selection effects from the observed sample, after Phinney & Blandford and Vivekanand & Narayan [126, 162], we define a scaling function tex2html_wrap_inline1979 as the ratio of the total Galactic volume weighted by pulsar density to the volume in which a pulsar could be detected by the surveys:

equation250

In this expression, tex2html_wrap_inline1981 is the assumed pulsar distribution in terms of galactocentric radius R and height above the Galactic plane z . Note that tex2html_wrap_inline1979 is primarily a function of period P and luminosity L such that short period/low-luminosity pulsars have smaller detectable volumes and therefore higher tex2html_wrap_inline1979 values than their long period/high-luminosity counterparts.

This scaling function can be used to estimate the total number of active pulsars in the Galaxy. In practice, this is achieved by calculating tex2html_wrap_inline1979 for each pulsar separately using a Monte Carlo simulation to model the volume of the Galaxy probed by the major surveys [116]. For a sample of tex2html_wrap_inline1997 observed pulsars above a minimum luminosity tex2html_wrap_inline1999, the total number of pulsars in the Galaxy with luminosities above this value is

equation257

Monte Carlo simulations of the pulsar population incorporating the aforementioned selection effects have shown this approximation to be reliable [95]. The factor f in this expression, known as the ``beaming factor'', is the fraction of tex2html_wrap_inline2003 steradians swept out by the radio beam during one rotation. Thus f gives the probability that the beam cuts the line-of-sight of an arbitrarily positioned observer. A naïve estimate of f is 20%; this assumes a beam width of tex2html_wrap_inline2009 and a randomly distributed inclination angle between the spin and magnetic axes [150Jump To The Next Citation Point In The Article]. Observational evidence suggests that shorter period pulsars have wider beams and therefore larger beaming fractions than their long-period counterparts [118Jump To The Next Citation Point In The Article, 106Jump To The Next Citation Point In The Article, 33Jump To The Next Citation Point In The Article, 147Jump To The Next Citation Point In The Article]. It must be said, however, that a consensus on the beaming fraction-period relation has yet to be reached. This is shown below where we compare the period dependence of f as given by a number of models.

  

Click on thumbnail to view image

Figure 9: Beaming fraction plotted against pulse period for four different beaming models: Tauris & Manchester 1998 (TM88; [147]), Lyne & Manchester 1988 (LM88; [106]), Biggs 1990 (JDB90; [33Jump To The Next Citation Point In The Article]) and Narayan & Vivekanand 1983 (NV83 [118]).

Adopting the Lyne & Manchester model, pulsars with periods tex2html_wrap_inline2013 ms beam to about 30% of the sky compared to the Narayan & Vivekanand model in which pulsars with periods below 100 ms beam to the entire sky. Note that, when many of these models were proposed, the sample of millisecond pulsars was < 5; hence their predictions about the beaming fractions of short-period pulsars relied largely on extrapolations from the normal pulsars. A recent analysis of a large sample of millisecond pulsar profiles [90Jump To The Next Citation Point In The Article] suggests that the beaming fraction of millisecond pulsars lies between 50% and unity.



3.3 The Population of Normal 3 The Galactic Pulsar Population3.1 Selection Effects in Pulsar

image 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