Two families of astrophysical diverging lens models

Abstract

In the standard gravitational lensing scenario, rays from a background source are bent in the direction of a foreground lensing mass distribution. Diverging lens behaviour produces deflections in the opposite sense to gravitational lensing, and is also of astrophysical interest. In fact, diverging lensing due to compact distributions of plasma has been proposed as an explanation for the extreme scattering events (ESEs) that produce frequency-dependent dimming of extra-galactic radio sources, and may also be related to the refractive radio-wave phenomena observed to affect the flux density of pulsars. In this work we study the behaviour of two families of astrophysical diverging lenses in the geometric optics limit, the power-law and the exponential plasma lenses. Generally, the members of these model families show distinct behaviour in terms of image formation and magnification, however the inclusion of a finite core for certain power-law lenses can produce a caustic and critical curve morphology that is similar to the well-studied Gaussian plasma lens. Both model families can produce dual radial critical curves, a novel distinction from the tangential distortion usually produced by gravitational (converging) lenses. The deflection angle and magnification of a plasma lens varies with the observational frequency, producing wavelength-dependent magnifications that alter the amplitudes and the shape of the light curves. Thus, multi-wavelength observations can be used to physically constrain the distribution of the electron density in such lenses.

The Effects of Plasma Lensing on the Inferred Dispersion Measures of Fast Radiobursts

“…Lens models based on both analytical and numerical approaches have also been explored (e.g. Tuntsov et al 2016;Cordes et al 2017;Er & Rogers 2018). When an electromagnetic wave propagates through a plasma lens, it will be delayed due to two separate effects.…”

“…The exponential models are a family of lenses that include the most well-known model, the Gaussian lens (e.g. Clegg et al 1998;Bannister et al 2016;Cordes et al 2017), as well as the family of powerlaw models (Er & Rogers 2018). These lens families are useful because they can be used as building blocks to construct more complicated density distributions.…”

Magnetized filament models for diverging plasma lenses

“…with the effective potential for plasma lenses in analogy with gravitational lensing (Tuntsov et al 2016;Er & Rogers 2018)…”

“…which agrees with eqs. 49 and 50 in Er & Rogers (2018). In this expression, the power-index h determines how fast the lens convergence changes as a function of radial distance from the lens centre.…”

“…The imaging properties of the spherical Gaussian lens depend on the characteristic scale angle of the lens As and the width of the lens σ. In fact, it can be shown that there exists a critical lens width (Er & Rogers 2018), such that σcrit = As…”