Shadow, ISCO, Quasinormal modes, Hawking spectrum, Weak Gravitational lensing, and parameter estimation of a Schwarzschild Black Hole Surrounded by a Dehnen Type Dark Matter Halo

TL;DR

This work analyzes a Schwarzschild black hole embedded in a static Dehnen-type dark matter halo, characterized by core density $\rho_s$ and core radius $r_s$, and assesses how the DM environment alters observables across multiple fronts. The authors derive and utilize a static spherically symmetric metric with $f(r)$ incorporating DM terms, then compute photon orbits, shadow radius $R_s$, and ISCO, finding DM generally enlarges shadows and ISCOs. They further study quasinormal modes via the 6th-order WKB method, greybody factors, and Hawking spectra for scalar and EM perturbations, showing DM influences the spectra and that scalar and EM perturbations can be distinguished observationally; lensing is analyzed with Gauss–Bonnet corrections, revealing DM-enhanced deflection. Finally, the model is confronted with observational bounds on deviation from Schwarzschild from M87$^*$ and Sgr A$^*$, yielding viable ranges for $r_s$ and $\rho_s$ and supporting the possibility that galactic centers may be surrounded by Dehnen-type DM halos.

Abstract

We consider \s black hole (BH) embedded in a Dehnen-$(1,4,0)$ type dark matter halo (DDM) with two additional parameters - core radius $r_s$ and core density $\rs$ apart from mass $M$. We analyze the event horizon, photon orbits, and ISCO around DDM BHs and emphasize the impact of DDM parameters on them. Our study reveals that the presence of dark matter (DM) favourably impacts the radii of photon orbits, the innermost stable circular orbit (ISCO), and the event horizon. We find the expressions for specific energy and angular momentum for massive particles in time-like geodesics around DDM BH and investigate their dependence on DDM parameters. We display BH shadows for various values of core density and radius that reveal larger shadows cast by a \s BH surrounded by DDM (SDDM) than a \s BH in vacuum (SV). We then move on to study quasinormal modes (QNMs) with the help of the $6th$ order WKB method, the greybody factor using the semi-analytic bounds method, and the Hawking spectrum for scalar and electromagnetic perturbations. Core density and radius are found to have a significant impact on QNMs. Since QNMs for scalar and electromagnetic perturbations differ significantly, we can differentiate the two based on QNM observation. The greybody factor increases with core density and radius, whereas, the power emitted as Hawking radiation is adversely impacted by the presence of DM. We then study the weak gravitational lensing using the Gauss-Bonnet theorem and obtain the deflection angle with higher-order correction terms. Here, we see the deflection angle gets enhanced due to DM. Finally, we use bounds on the deviation from \s, $δ$, reported by EHT for $M87^*$, Keck, and VLTI observatories for $Sgr A^*$ to gauge the viability of our model. Our model is found to be concordant with observations. This leads to the possibility of our galactic center being surrounded by DDM.

Figures (20)

• Figure 1: Variation of event horizon with $\rho_s$ kepping $r_s=0.5M$ shown in left panel and with $r_s$ kepping $\rho_s M^{2}=1.0$ shown in the right panel.
• Figure 2: Variation of photon and shadow radii with $\rho_s$ kepping $r_s=0.5M$ shown in left panel and with $r_s$ kepping $\rho_s M^{2}=1.0$ shown in the right panel.
• Figure 3: BH shadows for different values of $\rho_s$ kepping $r_s=0.5M$ shown in left panel and for different values of $r_s$ kepping $\rho_s M^{2}=1.0$ shown in the right panel.
• Figure 4: Variation of $E$ with $r/M$ for different values of core density keeping $r_s=0.5M$ shown in the left panel and for different values of core radius keeping $\rho_s=1.0/M^2$ shown in the right panel.
• Figure 5: Variation of $L$ with $r/M$ for different values of core density keeping $r_s=0.5M$ shown in the left panel and for different values of core radius keeping $\rho_s=1.0/M^2$ shown in the right panel.