Between two descriptions of dark matter around a black hole: photon sphere, shadow, and lensing

Abstract

We examine observational discrepancies of two widely used models describing anisotropic (dark) matter distributions around a black hole, focusing on their photon spheres, shadow radii, and lensing observables. The models considered are the vacuum and Einstein cluster dark matter model, characterized by negative and zero radial pressure, respectively. The analysis reveals that these models display contrasting photon sphere behavior. In particular, the Einstein cluster results in a more pronounced deviation in the shadow radius relative to the standard Schwarzschild black hole. Additionally, a distinctive lensing phenomenon associated with the matter halo is identified in both models.

Figures (5)

• Figure 1: The shift function for the EC DM with $M_{DM}=100M_{BH}$. The gray dashed line represents the vacuum DM case, for which $\Phi(r)=0$ everywhere.
• Figure 2: (Top) Photon sphere radius and (Bottom) shadow radius for the EC DM and vacuum DM as functions of the DM mass, shown by solid and dotted lines, respectively.
• Figure 3: (Top) Separation angle between the lensed primary and secondary images as a function of $\alpha$, and (Bottom) their differential time delay, for EC DM (solid lines) and vacuum DM (dotted lines).
• Figure 4: (Top) Angular positions of the primary and secondary images as functions of $\alpha$, and (Bottom) their corresponding time delays, for EC DM (solid lines) and vacuum DM (dotted lines), with $M_{DM}/M_{BH}=100$ and $D_{LS}/a_0=1000$.
• Figure S.1: Illustration of the BH lensing setup.