New analytical model of static black hole with a dark matter halo and parametric constraints through quasiperiodic oscillations

TL;DR

The paper addresses how dark matter halos shaped by a Dehnen-type density profile influence Schwarzschild-like black holes. By constructing an analytic BH solution embedded in a $(\alpha,\beta,\gamma)=(1,4,2)$ halo and analyzing curvature, energy conditions, and timelike geodesics, it reveals that increasing halo density or scale shifts stable and unstable circular orbits outward. It extends to rotation via the Newman-Janis method, deriving epicyclic frequencies and applying the RP1 QPO model, then constrains halo parameters with MCMC using microquasar QPO data. The findings show physically viable spacetimes with halo-induced modifications to ISCOs and orbital dynamics, offering a pathway to infer DM halo properties around BHs from QPO observations. This work provides a transferable analytic framework linking DM halos to observable strong-gravity phenomena.

Abstract

A novel analytical Schwarzschild-like black hole (BH) solution is derived. It exhibits a static BH with a dark matter (DM) halo characterized by a Dehnen-type density profile. This solution could represent an alternative perspective on the interaction of black hole-dark matter systems, providing new insights into the fundamental properties of DM halos. We study the properties of the newly derived BH solution by examining its spacetime curvature characteristics and energy conditions, providing insights into how the DM halo influences these fundamental characteristics. Additionally, we analyze the timelike geodesics of test particles in the obtained BH-DM spacetime, highlighting how the presence of the novel Dehnen-type DM halo alters the gravitational dynamics and modifies particle trajectories. Increase of the DM halo's density $ρ_s$ and characteristic scale $r_s$ leads to an outward shift of both stable and unstable circular orbits. Finally, we test our model by fitting it to real data from the microquasars GRO J1655-40, GRS 1915+105, and XTE J1550-564 using a statistical Markov Chain Monte Carlo (MCMC) method. This allows us to find the best estimates for the properties of the DM halo surrounding these systems.

Figures (11)

• Figure 1: Radial profile of metric function $f(r)$ for various values of the characteristic density $\rho_s$ (left panel) and characteristic scale $r_s$ of the DM halo (right panel). Hereafter, we shall set $M=1$, for simplicity.
• Figure 2: The dependence of BH event horizon on the density $\rho_s$ (left panel) and the characteristic scale $r_s$ of the DM halo (right panel).
• Figure 3: The radial $r$ dependence of the Ricci scalar ($R$) (left panel), the Kretschmann scalar ($K$) (middle panel), and the square of the Ricci tensor ($R^2$) (right panel) for a Schwarzschild-like BH in a DM halo for the different values of $\rho_s$ and $r_s$ parameters.
• Figure 4: The radial dependence of the NEC (top left panel), WEC (top right panel), DEC (bottom left panel), SEC (bottom right panel) for various values of $\rho_s$ and $r_s$ parameters.
• Figure 5: The trajectories of the timelike particle in the vicinity of a Schwarzschild-like BH in a DM halo for varying $\rho_s$ and $r_s$ parameters.