Calculating distance to a pulsar

How do we determine the distance to a pulsar?

Background

Pulsars are rapidly spinning and highly magnetic neutron stars that emit regular pulses of electromagnetic radiations e.g. Crab Nebula Pulsar in Orion constellation.

Need

Pulsars have been found in different star clusters and sometimes in other galaxies. By measuring the distance to the pulsar we can
indirectly know the distance to the star cluster that can help us in better understanding the cluster.

Idea

Dispersion is a phenomenon where the velocity of transmission of the waves in a ‘dispersive’ medium is dependent on the frequency of the wave. Suppose in a medium, higher the frequency faster the signal travels, then a single emission composing of a multitude of frequencies when observed from a distance would result in a skewed image with frequency components emitted at a single instant arriving at different times. This difference in arrival times as a function of frequency helps us to estimate the travel-time and thus distance to the source.

Concept

Pulsars usually emit radio waves at regular interval. The electromagnetic waves travel the entire distance through the intergalactic medium to reach earth. However, the intergalactic medium is dispersive in nature. Thus the velocity of a wave is dependent on its frequency. Hence a source emitting a broadband of frequencies when observed from a fixed yet unknown distance would render a smeared image.

The idea is that, pulsars periodically emit short bursts of signals. We can use these short blips or bursts to then align the waveforms. In removing the effect of the dispersion, we estimate the duration that the wave has travelled before reaching Earth. Thus, we obtain an estimate of the distance to the pulsar. This distance estimate can then be verified against the values calculated using other standard methods.

Reference
Kraus, J.D., Radio Astronomy, 2nd Ed., Cygnus-Quasar Books, Powell, Ohio 1986