Interpretation of parabolic arcs in pulsar secondary spectra

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.