Geodesic Model of HF QPOs Tested for Black Holes in Spacetimes Reflecting the Effect of Surrounding Dark Matter

Abstract

Using the simple but robust model of a shell of dark matter (DM) around a Schwarzschild black hole (BH), represented by the mass ratio of the shell and BH ΔM/M, the shell extension Δr s and its inner radius r s, we study the influence of DM on the spacetime structure and geodesic motion, and provide a classification of the BH+DM shell spacetimes according to the properties of the stable circular geodesics governing Keplerian disks. We focus our attention on the epicyclic motion around circular geodesics that can be related to observational phenomena in X-ray radiation from Keplerian accretion disks, assumed to be influenced by the DM shell only gravitationally. We give the frequencies of the orbital and epicyclic motions and discuss their properties in terms of the parameters governing the DM shell. Using the frequencies in relevant variants of the standard geodesic model of high-frequency quasiperiodic oscillations (HF QPOs), we test the role of DM by fitting the HF QPO data from some microquasars and active galactic nuclei with supermassive BHs where no variant of the geodesic model applied in the standard vacuum BH background is able to explain the data. We thus provide a robust review of the applicability of the geodesic model of HF QPOs, and also provide limits on the amount of DM around a BH. We demonstrate that the geodesic model could be well applied to most observations of active galactic nuclei, with strong restrictions on the amount of invisible matter around BHs.

Testing alternative spacetimes by high-frequency quasi-periodic oscillations observed in microquasars and active galactic nuclei

“…• BHs in DM (dirty BHs) [103], tested (non-rotating case) for QPOs in [104] • BHs in perfect fluid DM (PFDM) [85,105] • BHs in cold DM halo [106] • BHs in scalar field DM halo [106] • Hayward BHs in PFDM [107] • BHs in quintessence [108][109][110][111] Note that the special model of BH spacetime modified roughly by any kind of DM was tested by HF QPOs recently in [104,112].…”