The Gaussian Plasma Lens in Astrophysics: Refraction

Abstract

We consider the geometrical optics for refraction of a distant radio source by an interstellar plasma lens, with application to a lens with a Gaussian electron column density profile. The refractive properties of the lens are specified completely by a dimensionless parameter, alpha, which is a function of the wavelength of observation, the lens' electron column density, the lens-observer distance, and the transverse diameter of the lens. Relative motion of the observer and lens produces modulations in the source's light curve. Plasma lenses are diverging so the light curve displays a minimum, when the lens is on-axis, surrounded by enhancements above the unlensed flux density. Lensing can also produce caustics, multiple imaging, and angular position wander of the background source. If caustics are formed, the separation of the outer caustics can constrain alpha, while the separation of the inner caustics can constrain the size of the lens. We apply our analysis to 0954+654, a source for which we can identify caustics in its light curve, and 1741-038, for which polarization observations were obtained during and after the scattering event. We find general agreement between modelled and observed light curves at 2.25 GHz, but poor agreement at 8.1 GHz. The discrepancies may result from a combination of lens substructure or anisotropic shape, a lens that only grazes the source, or unresolved source substructure. Our analysis places the following constraints on the lenses: Toward 0954+654 (1741-038) the lens was 0.38 AU (0.065 AU) in diameter, with a peak column density of 0.24 pc cm^{-3} (1E-4 pc cm^{-3}) and an electron density of 1E5 cm^{-3} (300 cm^{-3}). The angular wander caused by the lens was 250 mas (0.4 mas) at 2.25 GHz. For 1741-038, we place an upper limit of 100 mG on the lens' magnetic field.