Scattering of Pulsar Radiation in the Interstellar Medium

The scattering of pulsar radiation in the interstellar medium is investigated under the assumptions of both ‘ strong ’ and ‘ multiple ’ scattering, and a gaussian spatial autocorrelation function for the scattering irregularities. For a thin screen located midway between the pulsar and the observer it is shown that the frequency autocorrelation function for the resulting scintillations is the Fourier Transform of the pulse broadening function exp $$(-t/\Delta t)$$ arising from multipath propagation. The width of the frequency auto-correlation function to half power $$\Delta f,$$ is thus given by $$2\pi \Delta f \Delta t = 1,$$ and this relationship is fulfilled approximately for all scattering screens. Relationships between $$\Delta f$$ and the decorrelation frequencies used by different observers are established. Measured values of $$\Delta f \,\text{and} \,\Delta t$$ show significant deviations from the theoretical relationship $$\Delta f \propto DM^{-2}$$ where DM is the dispersion measure of the pulsar. These deviations can be explained by a combination of two effects-violations of the assumptions of strong and multiple scattering for nearby pulsars, and regions of anomalously strong scattering along the lines of sight to distant pulsars.