**Dispersion in pulsar timing[**From Wikipedia**]**

Pulsars are
spinning neutron stars that emit pulses at very regular intervals ranging from
milliseconds to seconds. Astronomers believe that the pulses are emitted
simultaneously over a wide range of frequencies. However, as observed on Earth,
the components of each pulse emitted at higher radio frequencies arrive before
those emitted at lower frequencies. This dispersion occurs because of the
ionized component of the interstellar medium, mainly the free electrons,
which make the group velocity frequency dependent. The extra delay added at a
frequency is

where the dispersion constant is given by

,^{[10]}

and the **dispersion measure** *DM* is the column
density of electrons — i.e. the number density of electrons (electrons/cm^{3}) integrated
along the path traveled by the photon from the pulsar to the Earth — and is
given by

with units of parsecs per cubic centimetre (1pc/cm^{3} = 30.857×10^{21} m^{−2}).^{[11]}**This is also referred to as Optical Path Length.**

Typically for
astronomical observations, this delay cannot be measured directly, since the
emission time is unknown. What *can* be measured is the difference in
arrival times at two different frequencies. The delay between a high
frequency and a low
frequency component of a
pulse will be

Re-writing the
above equation in terms of *DM* allows one to determine the *DM* by
measuring pulse arrival times at multiple frequencies. This in turn can be used
to study the interstellar medium, as well as allow for observations of pulsars
at different frequencies to be combined.