Scintillation of Radio Sources: The Role of Caustics

Abstract

Scintillation of a radio source can be treated relatively simply by making the stationary phase point (SPP) approximation to the Fresnel-Kirchhoff integral, but the range of validity of the SPP approximation is not well determined. We identify three idealized models for the phase variation for which there are accurate approximations (exact results), and we compare these exact results with the SPP approximations to them. For two of the models—the coherent wave (CW) model and the single-phase pulse model—the integral can be evaluated in closed form, involving infinite sums that can be truncated without loss of accuracy, and for the third model the integral is determined accurately using fast Fourier transforms. We find that for the majority of observer positions the SPP method gives excellent results. However, near a caustic the SPP approximation breaks down and can be positively misleading. We find that for moderate screen strengths the putative caustic lines are the loci of regions where the intensity oscillates rapidly. The conventional caustic behavior is exhibited only as an envelope of rapid diffractive fluctuations for sufficiently large phase variations, with amplitude 0 103 rad. We discuss a suggested application of the single phase pulse to extreme scattering events and compare our exact results with existing models that are based on geometric optics. We also suggest that the CW model might be applied to the highly localized, anisotropic turbulence inferred for intraday variable sources and for the secondary spectra in pulsars.