to each pulsar can be made from an effect known as
*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 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
and a low frequency
pulse is given [156] by

where the frequencies are in MHz and the dispersion measure DM () 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 (). From Equation (2) it is obvious that a measurement of the delay across a finite
bandwidth yields the DM. 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. Hence,
given the DM, the distance can be estimated from a model of the
Galactic distribution of free electrons.

The electron density model is calibrated from the pulsars with
independent distance estimates and measurements of scattering for
lines of sight towards various Galactic and extragalactic
sources. Independent distance estimates now exist for over 100
pulsars based on 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). Based on
these data, Taylor & Cordes [235] have developed an electron density model which is free from
large systematic trends and can be used to provide distance
estimates with an uncertainty of
30%. However, use of this model to estimate distances to
*individual pulsars*
may result in uncertainties by as much as a factor of two. This
model is currently being refined following recent pulsar
discoveries and independent distance and scattering measurements
(J. Cordes, private communication).

Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
http://www.livingreviews.org/lrr-2001-5
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