Shadows and Observational Images of a Schwarzschild-like Black Hole Surrounded by a Dehnen-type Dark Matter Halo

TL;DR

This study explores how dark matter halos influence the observable shadow and photon ring of a Schwarzschild-like black hole, using observational constraints and modeling different accretion scenarios.

Contribution

It introduces a detailed analysis of the effects of Dehnen-type dark matter halos on black hole shadows, constrained by EHT data, and examines optical appearances with various accretion models.

Findings

Increased dark matter density and radius enlarge the black hole's photon sphere and shadow.

The peak intensity shifts to higher impact parameters with larger dark matter halos.

Dark matter parameters significantly alter the optical appearance of the black hole.

Abstract

This paper investigates the optical appearance of a Schwarzschild-like black hole (BH) surrounded by a Dehnen-(1, 4, 5/2) type dark matter (DM) halo, with a focus on how the DM halo's density $\rho_{s}$ and radius $r_{s}$ influence the BH's shadow and photon ring. First, the radius $r_h$ of the BH's event horizon and the equation of motion for photons were derived, and observational data from the Event Horizon Telescope (EHT) for M87* were used to constrain the parameters $\rho_{s}$ and $r_{s}$ of the DM halo. Afterward, by varying the values of $\rho_{s}$ and $r_{s}$, key parameters such as the effective potential $V_{eff}$ of photons, the critical impact parameter $b_{ph}$, the radius $r_{isco}$ of the innermost stable circular orbit, and the radius $r_{ph}$ of the photon sphere were calculated for each case. It was found that as $\rho_{s}$ and $r_{s}$ increase, the above mentioned parameters all show an increasing trend. Subsequently, we investigated the optical appearance of the BH illuminated by two types of accretion models: optically and geometrically thin disk models and spherical accretion models. The findings indicate that as $\rho_{s}$ and $r_{s}$ increase, the peak of the received intensity shifts toward a higher impact parameter $b$, resulting in a distinct optical appearance.