3.2 Correcting the observed pulsar 3 The Galactic Pulsar Population3 The Galactic Pulsar Population

3.1 Selection Effects in Pulsar Searches 

The most prominent selection effect at play in the observed pulsar sample is the inverse square law, i.e.  for a given luminosity Popup Footnote, the observed flux density falls off as the inverse square of the distance. This results in the observed sample being dominated by nearby and/or bright objects. Beyond distances of a few kpc from the Sun, the apparent flux density of most pulsars falls below the flux thresholds tex2html_wrap_inline1939 of the a survey. Following [56], we may parameterise the survey threshold by:


In this expression, tex2html_wrap_inline1941 is a correction factor tex2html_wrap_inline1943 which reflects losses to hardware limitations, SNR tex2html_wrap_inline1945 is the threshold signal-to-noise ratio (typically 7-10), tex2html_wrap_inline1947 and tex2html_wrap_inline1949 are the receiver and sky noise temperatures, G is the antenna gain, tex2html_wrap_inline1953 is the number of polarisations observed, tex2html_wrap_inline1955 is the observing bandwidth, tex2html_wrap_inline1957 is the integration time, W is the observed pulse width and P is the pulse period.

It follows from this equation that the sensitivity decreases as W /(P - W) increases. Also note that if W > P, the pulsed signal is smeared into the background emission and is no longer detectable. The observed pulse width W is in fact broader than the intrinsic value for a number of reasons: finite sampling effects; pulse dispersion, as well as scattering due to the presence of free electrons in the interstellar medium. As discussed above, the dispersive smearing scales as tex2html_wrap_inline1969, where tex2html_wrap_inline1971 is the observing frequency. This can largely be removed by dividing the pass-band into a number of channels and applying successively longer time delays to higher frequency channels before summing over all channels to produce a sharp ``de-dispersed'' profile Popup Footnote . The smearing across the individual channels, however, still remains and becomes significant at high dispersions when searching for short-period pulsars. Multi-path scattering results in a one-sided broadening due to the delay in arrival times which scales roughly as tex2html_wrap_inline1973, which can not be removed by instrumental means.

Dispersion and scattering become most severe for distant pulsars in the inner Galaxy as the number of free electrons along the line of sight becomes large. The strong frequency dependence of both effects means that they are considerably less of a problem for surveys at observing frequencies > 1400 MHz [46Jump To The Next Citation Point In The Article, 82Jump To The Next Citation Point In The Article] compared to the usual 400 MHz search frequency. An added bonus for such observations is the reduction in tex2html_wrap_inline1949, since the spectral index of the non-thermal emission is about -2.8 [91]. Pulsars themselves have steep radio spectra. Typical spectral indices are -1.6 [110, 99], so that flux densities are an order of magnitude lower at 1400 MHz compared to 400 MHz. Fortunately, this can usually be compensated somewhat by the use of larger receiver bandwidths at higher radio frequencies. For example, the 1380 MHz system at Parkes has a bandwidth of 270 MHz compared to their 430 MHz system, where 32 MHz is available.

In the past, the main disadvantage in surveying at high frequencies has been the sky coverage rate which scales with the solid angle of the telescope beam. The current generation of high-frequency pulsar searches at Parkes and Jodrell Bank tackles this problem by installing multi-beam receivers in these telescopes. At Parkes, a 13 beam system [7] has been installed for use in neutral hydrogen surveys. The system is also being used for pulsar searches and can cover the sky at the same rate as the recent Parkes low-frequency 430 MHz survey [111, 107Jump To The Next Citation Point In The Article]. Together with a 4-beam system being installed at Jodrell Bank, the sensitivity of these systems is about 7 times better than previous surveys at 1400 and 1520 MHz [46, 82] and should thus discover several hundred new pulsars. Indeed, the Parkes survey has recently begun and has already discovered over 100 new pulsars. For an update, and more information, see Fernando Camilo's multibeam page [8].

3.2 Correcting the observed pulsar 3 The Galactic Pulsar Population3 The Galactic Pulsar Population

image Binary and Millisecond Pulsars
D. R. Lorimer (dunc@mpifr-bonn.mpg.de)
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de