Epicyclic motion and accretion disk around a charged black hole in Einstein-ModMax theory with a quintessence field

TL;DR

This work investigates epicyclic motion and high-frequency QPOs for charged particles around a weakly magnetized black hole in Einstein-ModMax theory with a quintessence field. It derives the charged-particle dynamics, computes radial and vertical epicyclic frequencies, and uses the forced-resonance QPO model to connect theory with observations, also examining accretion-disk radiation. A Markov Chain Monte Carlo analysis constrains seven model parameters using QPO data from multiple X-ray binaries, finding tight constraints on mass $M$ and orbital radius $r/M$, with only upper bounds on the ModMax coupling $\nu$, electric coupling $g_{e}$, magnetic coupling $\sigma_{m}$, and dyonic charge $Q/M$, while a mild preference for the quintessence parameter $c$ is noted. Overall, the results suggest consistency with general relativity in the strong-field regime, allowing only small deviations from Einstein-Maxwell theory in the presence of quintessence; disk flux and temperature profiles respond predictably to the model parameters, offering potential observational tests of these beyond-GR effects.

Abstract

We investigate the epicyclic motion of charged test particles and the associated quasi-periodic oscillations (QPOs) around a weakly magnetized black hole surrounded by quintessence within the framework of Einstein-ModMax theory. We analyze the dynamics of charged particles on circular orbits and derive the corresponding radial and vertical epicyclic frequencies. The influence of the nonlinear electrodynamics parameter, magnetic coupling, dyonic charge, and quintessence state parameter on the innermost stable circular orbit and epicyclic frequencies is examined in detail. Using the forced resonance model, we compare the theoretical predictions of high-frequency QPOs with observational data from several X-ray binary systems. A Markov Chain Monte Carlo analysis is employed to constrain the black hole parameters and assess the role of weak magnetization and nonlinear electrodynamics effects. This analysis indicates that QPO observations tightly constrain the black hole mass and orbital radius while placing stringent upper bounds on the ModMax coupling, magnetic interaction, and dyonic charge. In addition, we study the radiative properties of the accretion disk and analyze the effects of the model parameters on the disk flux and temperature profiles. These findings suggest that the observed QPOs are consistent with general relativity in the strong-field regime, allowing only small deviations associated with Einstein-Maxwell theory in the presence of a quintessence field.

Figures (11)

• Figure 1: Effective potential $V_{\mathrm{eff}}$ as a function of radius $r$ for test-particle radial motion with black-hole parameters $M=1$, $c=0.3$, and $\mathcal{L}=10$. (a) For $Q/M=0.8$, $\omega=-0.6$, $c=0.3$, $g_{e}=0.1$, varying $\nu$; (b) for $Q/M=0.8$, $\omega=-0.6$, $c=0.3$, $\nu=0.1$, different values of $g_{e}$; (c) for $Q/M=0.8$, $g_{e}=0.1$, $c=0.3$, $\nu=0.1$, altered values of $\omega$.
• Figure 2: The Keplerian frequency $\Omega_{k}$ is plotted along $r/M$ for $M=1$, $c=0.0009$: a. $Q/M=1$, $\omega =-0.39$ and various values of $\nu$; b. $\nu=1$, $Q=1$, and different values of $\omega$; c. $\omega=-0.39$, $\nu=1$ and several values of $Q/M$.
• Figure 3: The orbital velocity $v$ is plotted along $r/M$ for $M=1$: a. $Q/M=1$, $c=0.0009$, $\omega =-0.39$ and various values of $\nu$; b. $\omega=-0.39$, $c=0.0009$, $\nu=1$ and several values of $Q/M$; b. $\nu=0.1$, $c=0.03$, $Q/M=0.1$, and different values of $\omega$.
• Figure 4: The profile of the fundamental frequencies is plotted against $r/M$ for neutral particles, shown for different values of the dyonic charge $Q/M$.
• Figure 5: The behavior of the fundamental frequencies as functions of $r/M$ for the case of charged particles is plotted. The left and middle panels are plotted for $M = 1$, $Q = 0.1$, quintessence state parameter $\omega = -0.4$, $\nu = 0.5$, and $\sigma_{m} = 3$, with various positive and negative values of the coupling charge $g_{e}$, while the right panel is plotted for $g_{e} = 1.0$ and different values of the magnetic coupling parameter $\sigma_{m}$.