Modeling HF-QPOs in microquasars and AGNs: charged particles around black holes with CDM halos

Abstract HF QPOs are among the most intriguing phenomena observed in LMXBs containing BHs or neutron stars. In this work, we investigate charged particles’ dynamics in the nearby of a Schwarzschild-like BH embedded in a uniform magnetic field and surrounded on all sides by CDM. Thereby gaining deeper insight into the influence of magnetic and DM distributions on observable phenomena near compact objects. We first present a modified metric, which incorporates the effects of a CDM, and we explore how both DM and magnetic fields influence the effective potential, stable circular orbits, and escape conditions for ionized particles. Employing a Hamiltonian formalism, we analyze the energy boundaries and ISCO, demonstrating that CDM causes an outward shift of the ISCO, while magnetic fields tend to pull it closer to the event horizon. We compute the fundamental oscillation frequencies – radial, latitudinal, Keplerian, and Larmor – and demonstrate how their variation depends on the combined influence of CDM and magnetic field strength. The resulting frequency structure allows us to identify resonance radii associated with HF QPOs, particularly those in 3:2 ratios observed in microquasars. We assess several theoretical models for QPO generation, including the Epicyclic Resonance (ER0, ER1, ER2, ER3, ER4, ER5), Relativistic Precession (RP0, RP1, RP2), Tidal Disruption (TD), and Warped Disk (WD) models. A comparative fit of observational data from GRS 1915+105, H1743-322, XTE 1550-564, and GRO 1655-40 demonstrates that the ER4 model provides the best match for HF QPOs in the presence of moderate magnetic flux $$B' = {-\,0.01,\,0,\,0.01}$$ B ′ = - 0.01 , 0 , 0.01 . In contrast, for supermassive black holes in some active galactic nuclei (AGNs), the model that best fits the majority of the data depends on the magnetic field strength: ER0 for $$B' = 0$$ B ′ = 0 , and ER5 for $$B' = \pm \, 0.01$$ B ′ = ± 0.01 . Our results highlight the importance of including both magnetic and dark matter (DM) effects in strong-field astrophysics and support the use of HF QPOs as sensitive probes of BH environments. This study opens new perspectives for exploring particle dynamics, accretion disk structure, and observational signatures of DM near compact objects.