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

TL;DR

This work analyzes a Schwarzschild black hole embedded in a Dehnen-type dark matter halo with parameters $(r_s, ρ_s)$, deriving both weak-field and strong-field constraints on the halo. Using perihelion precession data for Mercury and S2, and twin HF QPOs from four microquasars, the authors perform geodesic analyses and an MCMC-based QPO modeling study to constrain the halo parameters and assess model viability. They show that DM halo effects are amplified around supermassive BHs and that epicyclic frequencies respond predictably to halo parameters, enabling discrimination between Dehnen-type halos and other DM distributions. The results demonstrate that timelike orbits and QPOs are potent probes of BH+DM systems and provide a framework for future observational tests of DM halo profiles in strong gravity regimes.

Abstract

We investigate a recently derived Schwarzschild-like black hole immersed in a Dehnen-type $(α,β,γ)=(1,4,5/2)$ 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 $ρ_s$ 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 $ρ_s$ 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.

Figures (4)

• Figure 1: Parameter space between the dimensionless halo radius $r_{s}$ and the dimensionless dark‐matter density $\rho_{s}$. The shaded region indicates the observationally allowed values of $(r_{s},\,\rho_{s})$ from Mercury (left) and S2 star (right) measurements.
• Figure 2: The radial profile of the frequencies $\nu_\theta$ and $\nu_r$ measured by a distant observer is shown as a function of $r/M$ for different values of $\rho_s$ and $r_s$.
• Figure 3: Posterior probability distributions for the black hole mass ($M$), the dimensionless QPO radius ($r/M$), and the dark matter halo density ($\rho_s$) and halo radius ($r_s$) - obtained with the FR model. Vertical red dashed lines mark the 95 % credible upper limits on $\rho_s$ and $r_s$.
• Figure 4: Comparison between model predictions and observational data for HF QPOs in X-ray binary systems. Dots, triangles and stars represent the model frequencies (upper and lower, respectively) calculated using best-fit parameters obtained from MCMC analysis (see Table \ref{['table:best-fit2']}). The blue error boxes show the corresponding observational data, including uncertainties in both mass and QPO frequency (see Table \ref{['Table 1']}). Each source is labeled accordingly.