New analytical model of rotating black hole with dark matter halo: constraints from EHT observations and accretion disk

TL;DR

This work constructs a rotating black hole in a Dehnen-type dark matter halo via the Newman-Janis algorithm and analyzes its horizons, shadow, and light-bending properties. By solving the Hamilton-Jacobi equations, the authors map photon orbits and show that the DM halo enlarges the shadow and photon sphere, while a weak-field deflection acquires a DM-enhanced term $\hat{\alpha} \approx \frac{4\tilde{M}^*}{b} \pm \frac{4a\tilde{M}^*}{b^2}$ with $\tilde{M}^*=M+4\pi\rho_s r_s^3$. They constrain DM parameters ($\rho_s$, $r_s$) and BH spin/M using EHT data for Sgr A$^*$ and M87$^*$ via both analytic shadow-size comparisons and MCMC, finding best-fit values consistent with prior DM-halo expectations. Additionally, they explore thin-disk accretion and show that increasing DM strength increases the system mass and reduces radiative flux, illustrating observable signatures of DM halos around SMBHs. Overall, the results indicate that a Dehnen-type DM halo around SMBHs is not excluded by current observations and can be probed with high-resolution shadow and accretion-disk measurements.

Abstract

In this paper, we start from a static black hole (BH) immersed in a Deanne-type dark matter (DM) halo and employ the Newman-Janis algorithm (NJA) to generate the rotating black hole solution with a dark matter halo. Also, we have checked the validity of the obtained space-time. Then we study optical properties of newly obtained rotating BH in DM halo, including the shadow's geometrical shape, deflection angle of light based Ono, Ishihara and Asada (OID) method, photon sphere and the dependence of the shadow radius on DM parameters. Additionally, assuming that spacetime of a supermassive black hole (SMBH) is described by the newly obtained rotating BH solution, we analyze the parameters of the model with shadow size estimates based on the Event Horizon Telescope (EHT) and Gravity collaboration observations of M87* and Sgr A* SMBHs. Then we have used Markov Chain Monte Carlo (MCMC) analysis to constrain DM parameters $ρ_s$, $r_s$ and BH mass M, BH spin a, also we show that best-fit values for the parameters $ρ_s$, $r_s$ are well agreement with previous results which indicate physically reasonability of the our model. Finally, we have analyzed the electromagnetic radiation flux of the rotating BH in the DM halo employing a ray tracing code.

Figures (10)

• Figure 1: Radial dependence $\Delta$ function for different values of the BH parameters $a$, $r_s$, $\rho_s$
• Figure 2: Variation of horizon radius with increase of BH spin parameter $a$ for the selected values of parameters $\rho_s$, $r_s$. Hereafter, we shall for simplicity set $M = 1$.
• Figure 3: BH shadow for various of the BH parameters $r_s$, $\rho_s$, $a$.
• Figure 4: Dependence of the shadow size $R_{sh}$ and photon sphere $r_p$ with respect to different spacetime parameters, here $r_{\pm}$ refers to the prograde and retrograde radii of stable circular orbits.
• Figure 5: The geometry of a quadrilateral embedded in curved space is presented.Ovgun:2018fte