Plasma effects on gravitational lensing and shadow observables of a Kerr-like black hole in a dark matter halo

Abstract

Plasma, as a medium around the black hole for light propagation, is known to visibly alter the shape of its shadow and the observables, which could impact the interpretation of the Event Horizon Telescope results. In this study, we examine how dark matter and non-magnetized, pressureless plasma influence the shadow of a Kerr-like black hole. We analyze the null-geodesics in the presence of both homogeneous and inhomogeneous plasma profiles and show how their influence on photon orbits affects the resulting black hole shadow. Our findings indicate that increasing the black hole's spin generally enlarges both the shadow radius and deformation. Additionally, the viewing angle decreases the shadow radius while reducing deformation as the observer moves farther from the equatorial plane. For this model, astrophysically reasonable amounts of dark matter show no significant impact on the photon trajectories. However, we observe that increasing plasma density increases both the shadow radius and deformation for homogeneous plasma, while it decreases them for inhomogeneous plasma. The emission rate also depends significantly on the model of plasma chosen, with homogeneous plasma causing significantly more emission as plasma strength increases. We also study the constraints obtained from comparing theoretical shadow radii with EHT observations of M87* and Sgr A*, which allows us to infer reasonable plasma distribution properties and frequencies in our theoretical model.

Figures (13)

• Figure 1: Variation of the inner $(r_{h-})$ and outer ($r_{h+}$) horizons as a function of the black hole spin $a$. Note the derivative of both curves going to infinity at the intersection.
• Figure 2: Panel (a) shows $r_h$ and $a_{extr}$ with varying $\rho_e$; and panel (b) shows $r_{h+}$ and $r_{h-}$ with varying $\rho_e$. Note that both graphs are on a horizontal log scale. Also, $\rho_e \in (0, 9E-9]$ is scaled in BH units with $M=1$.
• Figure 3: Panel (a) shows the variation of $r_{p+}$ and $r_{p-}$ as a function of $a$ for different plasma models, while ${\omega_c^2}/{\omega_0^2}$ is kept at 0.5; Panel (b) shows the variation of $r_{p+}$ and $r_{p-}$ as a function of ${\omega_c^2}/{\omega_0^2}$ for different plasma models, while $a$ is kept at 0.99.
• Figure 4: Variations of deflection angle as a function of $a$ (Panel (a)), $\eta$(Panel (b)), and ${\omega_c^2}/{\omega_0^2}$ (Panel (c)) for different plasma models. In all cases, $\rho_e = 6.9 E 6 M_\odot / kpc^3$, $r_e = 91.2 kpc$, and $\alpha =.16$
• Figure 5: Shadow shape for various values of black hole spin $a$ and inclination angles $\theta_0$ for no plasma, inhomogeneous plasma and homogeneous plasma profiles. Panels (a)-(c): $\theta_0 = \pi/2$; panels (d)-(f): $\theta_0 = \pi/12$. In all cases, $\rho_e = 6.9 E 6 M_\odot / kpc^3$, $r_e = 91.2 kpc$, $\alpha =.16$, and $\omega_c^2/\omega_0^2 = .5$