Gravitational lensing in plasma: Relativistic images at homogeneous plasma

Abstract

We investigate the influence of plasma presence on relativistic images formed by Schwarzschild black hole lensing. When a gravitating body is surrounded by a plasma, the lensing angle depends on a frequency of the electromagnetic wave due to refraction properties, and the dispersion properties of the light propagation in gravitational field in plasma. The last effect leads to a difference, even in uniform plasma, of the gravitational deflection angle in plasma from the vacuum case. This angle depends on the photon frequency, which resembles the properties of the refractive prism spectrometer. Here we consider the case of a strong deflection angle for the light, traveling near the Schwarzschild black hole, surrounded by a uniform plasma. Asymptotic formulas are obtained for the case of a very large deflection angle, exceeding 2. We apply these formulas for calculation of position and magnification of relativistic images in a homogeneous plasma, which are formed by the photons performing one or several revolutions around the central object. We conclude that the presence of the uniform plasma increases the angular size of relativistic rings or the angular separation of point images from the gravitating center. The presence of the uniform plasma increases also a magnification of relativistic images. The angular separation and the magnification become significantly larger than in the vacuum case, when the photon frequency goes to a plasma frequency.

The Milky Way’s Supermassive Black Hole: How Good a Case Is It?

“…However, the shadow of a black hole is not a very clean observable, and inclinations and accretion phenomena may cause the disappearance (or washiness) of a shadow as well. In 2013, Tsupko & Bisnovatyi-Kogan gave a first detailed analysis of how the images from the surroundings of black holes change in the presence of plasma (Tsupko and Bisnovatyi-Kogan, 2013). This may imply that suitable observing frequencies may lie even above 230 GHz to avoid that the images are severly washed out.…”

Frequency-dependent effects of gravitational lensing within plasma

“…Following Tsupko & Bisnovatyi-Kogan (2013), we assume the plasma is a static, inhomogeneous medium such that V t = √ −g tt , V α = 0. This static condition simplifies the effective photon energyhω = −pt √ −g tt .…”

“…As we proceed through the derivations of the main equations, we keep theh factors, but the numerical calculations are performed withh = 1. We follow the method and notation of Synge (1960), and review the derivation of Tsupko & Bisnovatyi-Kogan (2013) to find the generalized trajectories of photons in the presence of an isotropic, inhomogeneous plasma distribution, though more general possibilities exist (Perlick 2000). Let us assume spherical symmetry and adopt the line element…”

“…Lensing effects modified by plasma surrounding galaxy scale lenses were also investigated by Er & Mao (2014), requiring observations at MHz frequencies. In this work we will study ray-tracing under the influence of both gravitational lensing and refractive plasma effects following Tsupko & Bisnovatyi-Kogan (2013), and examine frequency-dependent orbits for light rays. Deflection by both gravity and plasma was discussed by Muhleman & Johnston (1966) for the case of radio waves passing by the Sun, using the product of the gravitational and plasma refractive indices to derive a weak ⋆ E-mail: rogers@physics.umanitoba.ca field approximation.…”

Sachs equations for light bundles in a cold plasma

“…The exact formula for the bending angle in a plasma whose density depends only on the radial coordinate was calculated on the Schwarzschild spacetime and in the equatorial plane of the Kerr spacetime by Perlick [13]. For further discussions of plasma effects in strong gravitational fields see Bisnovatyi-Kogan and Tsupko [14,15,16], Morozova, Ahmedov and Tursunov [17], Er and Mao [18], Rogers [19,20,21] and Perlick, Tsupko and Bisnovatyi-Kogan [22,23].…”