Optical Signatures of a Schwarzschild Black Hole in a Dehnen-Type Dark Matter Halo

TL;DR

This work addresses how a Schwarzschild-like black hole embedded in a Dehnen-type DM halo alters optical signatures in gravitational lensing and shadows. It combines analytic weak-field deflection via the Gauss–Bonnet theorem with numerical strong-field ray tracing, and extends the analysis to plasma environments (uniform and SIS) to study frequency-dependent effects. Key results show that DM-halo parameters $\rho_s$ and $r_s$ raise the photon-sphere radius, deflection angles, and shadow size, while plasma further modulates these observables; photon rings and magnifications shift accordingly. Using EHT data for M87$^*$ and Sgr A$^*$, the study constrains DM-halo scale radius and density as well as plasma parameters, highlighting the joint influence of DM halos and plasma on SMBH optical signals and offering a pathway to probe DM via black-hole environments.

Abstract

In this paper, the optical effects that occur near a Schwarzschild-like black hole (BH) with a Dehnen-type $(1,4,2)$ dark matter (DM) halo are explored. We first derive the photon sphere radius and obtain an analytical expression for the deflection angle in the weak-field regime by applying the Gauss-Bonnet theorem (GBT). For the strong-field regime, we perform ray-tracing calculations to examine the behavior of light trajectories and determine the corresponding number of orbits. We further compute the BH shadow and gravitational lensing in a plasma medium and provide constraints arising from the DM halo parameters. We also extend our analysis to weak gravitational lensing within plasma environments, considering both uniform and singular isothermal sphere (SIS) distributions. We find the analytical expressions for the deflection angle in the presence of plasma and examine the resulting effects on image magnification. The overall results highlight how DM halo properties and plasma characteristics jointly alter observable lensing signatures.

Figures (13)

• Figure 1: The radial profile of $f(r)$ is plotted for various values of $\rho_{s}$ (left) with $r_{s}$=0.5 and $r_{s}$ (right) with $\rho_{s}$= 0.04.
• Figure 2: Dependence of the photon sphere radius $r_{\text{ph}}$ on the dark matter halo density $\rho_s$ (left panel) and the characteristic scale $r_s$ of the halo (right panel). The figures illustrate how $r_{\text{ph}}$ varies with different values of $\rho_s$ and $r_s$ in the BH model.
• Figure 3: The deflection angle $\hat{\alpha}$ is plotted as a function of the impact parameter $b/M$ for photons.
• Figure 4: The plots demonstrate ray tracing around a BH with the DM halo, for a fixed value of $r_s=0.5$. The colored curves indicate distinct intervals of the impact parameter $b$. e.g., the gray curve corresponds to $3\le b<5$, the red to $5\le b<5.5$, and the blue to $5.5\le b<10$. The dashed black rings mark the location of the photon sphere.
• Figure 5: The plots demonstrate ray tracing around a BH with the DM halo, for a fixed value of $\rho_s=0.03$. The colored curves indicate distinct intervals of the impact parameter $b$. e.g., the gray curve corresponds to $3\le b<5$, the red to $5\le b<5.5$, and the blue to $5.5\le b<10$. The dashed black rings mark the location of the photon sphere.