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2.4 Interstellar dispersion and the pulsar distance scale

From the sky distribution shown in Figure 6View Image it is immediately apparent that pulsars are strongly concentrated along the Galactic plane. This indicates that pulsars populate the disk of our Galaxy. Quantitative estimates of the distance to each pulsar can be made from the measurement of pulse dispersion - the delay in pulse arrival times across a finite bandwidth. Dispersion occurs because the group velocity of the pulsed radiation through the ionised component of the interstellar medium is frequency dependent: Pulses emitted at lower radio frequencies travel slower through the interstellar medium, arriving later than those emitted at higher frequencies. The delay Dt in arrival times between a high frequency n hi and a low frequency n lo pulse is given [185Jump To The Next Citation Point] by
[( )- 2 ( )-2] ( ) Dt = 4.15 ms × -nlo- - -nhi- × --DM----- , (1) GHz GHz cm -3 pc
where the dispersion measure is
integral d DM = ne dl (2) 0
is the integrated free electron column density ne out to the pulsar at a distance d. This equation may be solved for d given a measurement of DM and a model of the free electron distribution.
View Image

Figure 6: The sky distribution of pulsars in Galactic coordinates. The plane of the Galaxy is the central horizontal line. The Galactic centre is the midpoint of this line. Millisecond pulsars are indicated in red. Binary pulsars are highlighted by the open circles. The more isotropic distribution of the millisecond and binary pulsars reflects the differences in detecting them out to large distances cf. the normal population (see Section 3).
In practice, the electron density model is calibrated from the 100 or so pulsars with independent distance estimates and measurements of scattering for lines of sight towards various Galactic and extragalactic sources [310335]. The most recent model of this kind [73Jump To The Next Citation Point74Jump To The Next Citation Point] provides distance estimates with an average uncertainty of ~ 30%.
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