The Analytical Solution to the Temporal Broadening of a Gaussian-Shaped Radio Pulse by Multipath Scattering from a Thin Screen in the Interstellar Medium

The radio pulse from a pulsar can be temporally broadened by multipath scattering in the interstellar medium and by instrumental effects within the radio telescope. The observed pulse shape is a convolution of the intrinsic one with the impulse responses of the scattering medium and instrumentation. Until recently, common methods used to model the observed shape make assumptions regarding the intrinsic pulse shape and impulse responses, compute the convolution numerically, and solve for the pulse width and scattering timescale iteratively. An analytical solution is shown to exist for the specific case of the temporal broadening of a Gaussian-shaped pulse by a thin scattering screen. The solution is applied to multi-frequency observations of PSR B1834-10 to characterize the frequency dependence of its intrinsic pulse width and scattering timescale.