Radio Wave Propagation through a Medium Containing Electron Density Fluctuations Described by an Anisotropic Goldreich‐Sridhar Spectrum

Abstract

We study the propagation of radio waves through a medium possessing density fluctuations that are elongated along the ambient magnetic field and described by an anisotropic Goldreich-Sridhar power spectrum. We derive general formulae for the wave phase structure function D, visibility, angular broadening, diffraction pattern length scales, and scintillation timescale for arbitrary distributions of turbulence along the line of sight and specialize these formulae to idealized cases. In general, D (?r)5/3 when the baseline ?r is in the inertial range of the turbulent density spectrum, and D (?r)2 when ?r is in the dissipation range, just as for an isotropic Kolmogorov spectrum of fluctuations. When the density structures that dominate the scattering have an axial ratio R 1 (typically R ~ 103), the axial ratio of the broadened image of a point source in the standard Markov approximation is at most ~R1/2, and this maximum value is obtained in the unrealistic case that the scattering medium is confined to a thin screen in which the magnetic field has a single direction. If the projection of the magnetic field within the screen onto the plane of the sky rotates through an angle ?? along the line of sight from one side of the screen to the other, and if R-1/2 ?? 1, then the axial ratio of the resulting broadened image of a point source is 2(8/3)3/5/?? 3.6/??. The error in this formula increases with ?? but reaches only ~15% when ?? = ?. This indicates that a moderate amount of variation in the direction of the magnetic field along the line of sight dramatically decreases the anisotropy of a broadened image. When R 1, the observed anisotropy will in general be determined by the degree of variation of the field direction along the sight line and not by the degree of density anisotropy. Although this makes it difficult to determine observationally the degree of anisotropy in interstellar density fluctuations, observed anisotropies in broadened images provide general support for anisotropic models of interstellar turbulence. Regions in which the angle ? between the magnetic field and line of sight is small cause enhanced scattering due to the increased coherence of density structures along the line of sight. In the exceedingly rare and probably unrealized case that scattering is dominated by regions in which ? (?r/l)1/3, where l is the outer scale (stirring scale) of the turbulence, D (?r)4/3 for ?r in the inertial range. In a companion paper (Backer & Chandran) we discuss the semiannual modulation in the scintillation time of a nearby pulsar for which the field direction variation along the line of sight is expected to be moderately small.