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 \nuis

t = k_\mathrm{DM} \times \left(\frac{\mathrm{DM}}{\nu^2}\right)

where the dispersion constant k_\mathrm{DM}is given by

 k_\mathrm{DM} = \frac{e^2}{2 \pi m_\mathrm{e}c} \simeq 4.149 \mathrm{GHz}^2\mathrm{pc}^{-1}\mathrm{cm}^3\mathrm{ms},[10]

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

\mathrm{DM} = \int_0^d{n_e\;dl}

with units of parsecs per cubic centimetre (1pc/cm3 = 30.857×1021 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 \Delta Tbetween a high frequency \nu_{hi}and a low frequency \nu_{lo}component of a pulse will be

\Delta t = k_\mathrm{DM} \times \mathrm{DM} \times \left( \frac{1}{\nu_{\mathrm{lo}}^2} - \frac{1}{\nu_{\mathrm{hi}}^2} \right)

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.