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
and the dispersion measure DM is the column density of electrons — i.e. the number density of electrons (electrons/cm3) integrated along the path traveled by the photon from the pulsar to the Earth — and is given by
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.