The Gaussian plasma lens in astrophysics: Refraction

We present the geometrical optics for refraction of a distant background radio source by an interstellar plasma lens, with specific application to a lens with a Gaussian profile of free-electron column density. The refractive properties of the lens are specified completely by a dimensionless parameter alpha, which is a function of the wavelength of observation, the free-electron column density through the lens, the lens-observer distance, and the diameter of the lens transverse to the line of sight. A lens passing between the observer and a background source, due to the relative motions of the observer, lens, and source, produces modulations in the light curve of the background source. Because plasma lenses are diverging, the light curve displays a minimum in the background source's flux density, formed when the lens is on-axis, surrounded by enhancements above the nominal (unlensed) flux density. The exact form of the light curve depends only upon the parameter alpha and the relative angular sizes of the source and lens as seen by the observer. Other effects due to lensing include the following: (1) the formation of caustic surfaces, upon which the apparent brightness of the background source becomes very large; (2) the possible creation of multiple images of the background source; and (3) angular position wander of the background source. If caustics are formed, the separation of the outer caustics can be used to constrain a, while the separation of the inner caustics can constrain the size of the lens. We apply our analysis to two sources, which have undergone extreme scattering events: (1) 0954+658, a source for which we can identify multiple caustics in its light curve, and (2) 1741-038, for which polarization observations were obtained during and after the scattering event. We find general agreement between modeled and observed light curves at 2.25 GHz, but poor agreement at 8.1 GHz. The discrepancies between the modeled and observed light curves may result from some combination of substructure within the lens, an anisotropic lens shape, a lens which only grazes the source rather than passing completely over it, or unresolved substructure within the extragalactic sources. Our analysis also allows us to place constraints on the physical characteristics of the lens. The inferred properties of the lens responsible for the scattering event toward 0954+ 658 (1741-038) are that it was 0.38 AU (0.065 AU) in diameter with a peak column density of 0.24 pc cm(-3) (10(-4) pc cm(-3)), an electron density-within the lens of 10(5) cm(-3) (300 cm(-3)), and a mass of 6.5 x 10(-14) M-. (10(-18) M-.). The angular position wander caused by the lens was 250 mas (0.4 mas) at 2.25 GHz. In the case of 1741-038, we can place an upper limit of only 100 mG on the magnetic field within the lens.