Probing black holes surrounded by Dust field in Quantum Fluctuation Modified Gravity with twin-peak QPOs

Abstract

We study a static, spherically symmetric black hole solution surrounded by a dust field within quantum fluctuation modified gravity, in which the quantum-fluctuation parameter $α$ and the dust-field strength parameter $K$. The horizon structure reveals the two parameters acting in opposite directions: strengthening $K$ draws the inner and outer horizons together until they merge into a single extremal horizon, while a larger $α$ restores the Schwarzschild limit; the same opposing trend extends to the effective potential and the characteristic circular-orbit radii -- the innermost stable circular orbit, the marginally bound orbit, and the marginal circular orbit -- which shift inward with $K$ and outward with $α$, and to the Keplerian and radial epicyclic frequencies of massive test particles. From these frequencies we build three twin-peak quasi-periodic oscillation models -- relativistic precession, warped-disk, and epicyclic-resonance -- along with their $3{:}2$, $4{:}3$, and $5{:}4$ resonance radii, all following the same $K$-$α$ trend. Testing all three models against twin-peak QPO data from two stellar-mass (GRO~J1655$-$40, XTE~J1550$-$564) and two intermediate-mass (M82~X$-$1, NGC~1313~X$-$1) sources through a Markov Chain Monte Carlo analysis places best-fit constraints, at the $2σ$ level, of $K\in(0,0.5)$ and $α\in(0.3,0.6)$ across all sources and models.