### 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.
Quantitatively, the delay in arrival times between a high frequency and a low frequency
pulse can be shown [229] to be

where the dispersion measure
is the integrated column density of electrons, , 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 emission. This work shows
that the distribution of Galactic free electrons to be exponential in form with a scale height of
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].