Astrophysical Signatures of Einstein-Skyrme Anti-de Sitter Black Holes: Epicyclic Frequencies and QPO Constraints

TL;DR

This paper investigates the geodesic motion and QPO signatures of Einstein-Skyrme Anti-de Sitter black holes, revealing unique epicyclic frequency behaviors and constraining model parameters through observational data analysis.

Contribution

It provides the first detailed analysis of epicyclic frequencies and QPO constraints for Einstein-Skyrme AdS black holes, linking theoretical predictions with observational data.

Findings

The effective potential shows $ u_r$ overtaking $ u_ heta$ at large radii in AdS.

QPO data constrains the Skyrme charge parameter to around 0.6.

The model's parameters yield consistent black hole masses and radii with independent estimates.

Abstract

We study the geodesic motion and epicyclic oscillations of massive test particles around a static, spherically symmetric black hole (BH) solution of the Einstein--Skyrme (ES) theory in Anti-de Sitter (AdS) spacetime. The lapse function of this BH depends on the Skyrme coupling $\eta$, a charge-like parameter $Q$ inherited from the Skyrme term, and the cosmological constant $\Lambda<0$. We first map out the horizon structure and identify three regimes-non-extremal BH (NEBH), extremal BH (EBH), and naked BH (NBH)-showing that the NEBH $\to$ EBH $\to$ NBH transition is governed by $Q$ rather than $\eta$, which enters $f(r)$ only as a constant shift. We then derive the effective potential (EP), locate the innermost stable circular orbit (ISCO), and compute the radiative efficiency, finding that $\mathcal{E}_{\rm ISCO}>1$ in AdS renders the standard Novikov-Thorne formula negative. The corrected radial epicyclic frequency $\Omega_r$ reveals a distinctive AdS signature: $\nu_r$ grows at large $r$ and overtakes the orbital frequency $\nu_\phi$, causing the periastron precession frequency $\nu_p = \nu_\varphi - \nu_r$ to change sign-a feature absent in asymptotically flat geometries. Adopting the relativistic precession (RP) model for quasi-periodic oscillations (QPOs), we perform a Markov chain Monte Carlo (MCMC) analysis using twin-peak QPO data from XTE~J1550-564, GRO~J1655-40, Sgr~A$^*$, and M82~X-1. The posteriors converge to $Q\approx 0.6$ across all sources, with orbital radii near $r\approx 4.2\,M$ and masses consistent with independent estimates, demonstrating that the ES-AdS BH accommodates the observed frequency pairs within physically motivated parameter ranges.