Probing the Schwarzschild black hole immersed in a dark matter halo through astrophysical tests

TL;DR

This paper explores how dark matter halos around Schwarzschild black holes influence astrophysical phenomena, using geodesic and QPO data to constrain dark matter parameters and test deviations from general relativity.

Contribution

It introduces a method combining weak and strong field tests to constrain dark matter halo parameters around black holes using astrophysical observations.

Findings

Dark matter effects are observable near supermassive black holes.

QPO frequencies can probe deviations caused by dark matter halos.

Constraints on halo parameters are derived from observational data.

Abstract

We investigate a recently derived Schwarzschild-like black hole immersed in a Dehnen-type $(\alpha,\beta,\gamma)=(1,4,5/2)$ dark matter (DM) halo. We obtain constraints on the two model parameters, i.e., the halo core radius $r_s$ and the DM density parameter $\rho_s$ in both the weak and the strong field regimes. In the weak field, we model test particle geodesics and match the predicted perihelion shift to Mercury (Solar System) and the orbit of the S2 star data. We obtain upper limits on $r_s$ and $\rho_s$ and highlight that the DM halo effects become observable only around supermassive BHs. In the strong field, we analyse twin high frequency quasiperiodic oscillations (QPOs) from four microquasars (e.g., GRO~J1655-40, GRS~1915+105, XTE~J1859+226, and XTE~J1550-564). Because QPO frequencies depend only on the local spacetime curvature, they can serve as a probe of halo-induced deviations from general relativity. Our MCMC analysis produces posterior distributions for model parameters, revealing close agreement between the theoretical QPO frequencies and the observations for GRS 1915+105 and GRO J1655-40. The same analysis also yielded best-fit values and upper bounds for each parameter. Our combined geodesic and QPO analysis demonstrates that timelike orbits and epicyclic oscillations can act as sensitive probes of DM halos around BHs, offering a pathway to distinguish Dehnen-type profiles from alternative DM distributions in future analysis and observations.