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

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.