Direct measurements of the distances to pulsars are notoriously difficult to obtain. There are three basic techniques: neutral hydrogen absorption, trigonometric parallax (measured either with an interferometer or through pulse time-of-arrival techniques) and from associations with objects of known distance (i.e. supernova remnants, globular clusters and the Magellanic Clouds). Together, these provide measurements of (or limits on) the distances to over 100 pulsars. For an excellent review of these measurements and their implications, see .
In the absence of a direct measurement, the distances to most pulsars can be estimated from an effect known as pulse dispersion which arises from the fact that the group velocity of the pulsed radiation through the ionised interstellar medium is frequency dependent: Pulses emitted at higher radio frequencies travel faster through the interstellar medium, arriving earlier than those emitted at lower frequencies. The delay in arrival times between a high frequency (MHz) and a low one (MHz), can be shown  to be
where the dispersion measure DM ( pc) is the integrated column density of free electrons along the line of sight:
Here, d is the distance to the pulsar (pc) and is the free electron density (). Pulsars at large distances have higher column densities and therefore larger DMs than those pulsars closer to Earth so that, from equation 1, the dispersive delay across the bandwidth is greater. Thus, from a measurement of the delay across a finite bandwidth we infer the DM. Hence, the distance can be estimated from a model of the Galactic distribution of free electrons, . Taylor & Cordes  have developed such a model calibrated from the sample of pulsars with independently known distances plus measurements of interstellar scattering for various Galactic and extragalactic sources. The model appears to be free of large systematic trends and can be used to provide distance estimates with an uncertainty of %.
|Binary and Millisecond Pulsars
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