The pulsar distance scale

2.4 The pulsar distance scale

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. As shown in Figure 6

, pulses emitted at lower radio frequencies travel slower through the interstellar medium, arriving later than those emitted at higher frequencies.

Figure 6: Pulse dispersion shown in this Parkes observation of the 128 ms pulsar B1356–60. The dispersion measure is 295 cm^–3 pc. The quadratic frequency dependence of the dispersion delay is clearly visible. Figure provided by Andrew Lyne.

Quantitatively, the delay $Δt$ in arrival times between a high frequency $νhi$ and a low frequency $νlo$ pulse can be shown [229 ] to be

where the dispersion measure

is the integrated column density of electrons, $ne$ , 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 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 [357 , 391 ]. A recent model of this kind, known as NE2001 [88

, 89

], provides distance estimates with an average uncertainty of $∼$ 30%.

Because the electron density models are only as good as the scope of their input data allow, one should be mindful of systematic uncertainties. For example, studies of the Parkes multibeam pulsar distribution [201 , 227 ] suggest that the NE2001 model underestimates the distances of pulsars close to the Galactic plane. This suspicion has been dramatically confirmed recently by an extensive analysis [122 ] of pulsar DMs and measurements of Galactic H $α$ emission. This work shows that the distribution of Galactic free electrons to be exponential in form with a scale height of $1830+120 −250$ pc. This value is a factor of two higher than previously thought. A revised version of the NE2001 model which takes into account these and other developments is currently in preparation [83 ].