Pulse Broadening due to Multiple Scattering in the Interstellar Medium

Abstract

It has been observed that the pulses received from pulsars are broadened at low frequencies, and this effect is thought to be due to multipath propagation in the interstellar medium. In this paper the pulse broadening is investigated in the limit of strong multiple scattering, in which ray optics is applicable. Two cases are considered: the scattering medium is assumed either to be concentrated in a small fraction of the line of sight near the pulsar, or to extend over the whole line of sight. Analytical solutions for the probability density function are found for these two cases, with the aid of the theory of Wiener integrals of Kac and Blane-Lapierre & Fortet. Both solutions are characterized by a slow rise to a decay which rapidly becomes exponential. The relation between this exponential decay time constant and the r.m.s. broadening of the angular size of the source is found, and compared with that expected on the basis of the ‘thin-slab’ model in which the scattering medium is effectively confined to a plane approximately midway between source and observer.