Interpretation of parabolic arcs in pulsar secondary spectra

Abstract

Pulsar dynamic spectra sometimes show organized interference patterns: these patterns have been shown to have power spectra that often take the form of parabolic arcs, or sequences of inverted parabolic arclets whose apexes themselves follow a parabolic locus. Here, we consider the interpretation of these arc and arclet features. We give a statistical formulation for the appearance of the power spectra, based on the stationary phase approximation to the Fresnel–Kirchoff integral. We present a simple analytic result for the power spectrum expected in the case of highly elongated images and a single‐integral analytic formulation appropriate to the case of axisymmetric images. Our results are illustrated in both the ensemble‐average and snapshot regimes. Highly anisotropic scattering appears to be an important ingredient in the formation of the observed arclets.