Modeling HF-QPOs in Microquasars and AGNs: Charged Particles around Black Holes with CDM Halos

TL;DR

This work modelizes charged-particle dynamics near a Schwarzschild-like BH embedded in a uniform magnetic field and surrounded by a CDM halo using a modified metric that incorporates a Navarro–Frenk–White DM profile. It derives the Hamiltonian framework and epicyclic frequencies (ω_r, ω_θ, ω_φ, ω_L), shows that DM shifts the ISCO outward while the magnetic field pulls it inward, and computes resonance radii for HF QPOs under several models (ER, RP, TD, WD). By fitting HF QPO data from microquasars and AGNs, the study finds ER4 best for microquasars across field strengths, while AGNs favor ER0 or ER5 depending on the magnetic field polarity, highlighting the joint role of DM and MF in shaping QPO phenomenology. The results underscore HF QPOs as powerful diagnostics of BH environments and motivate extensions to rotating spacetimes and more detailed DM distributions to further probe DM near compact objects.

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 ...... 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.

Figures (21)

• Figure 1: Embedding diagram within different values dark-matter parameter ${\bm \kappa}$. The red circle represents the BH event horizon.
• Figure 2: The effective potential in the equatorial plane is shown for various values of $\bm{\kappa}$ and magnetic field strength $B'=0,\pm0.1$. The first row corresponds to $\bm{\kappa}=0$, the second row to $\bm{\kappa}=10$, and the third row to $\bm{\kappa}=20$. The fourth row presents a two-dimensional projection at $z'=0$. The first three rows display three-dimensional representations of the effective potential, while the fourth row provides a comparative $2D$ slice for fixed angular momentum $L'=11$.
• Figure 3: Angular momentum in function of radii $L'_\pm$ (thick), $L'_{ex}$ (dashed) , $\bm{\kappa}=0$ (red), $\bm{\kappa}=10$ (blue), $\bm{\kappa}=20$ (green), within several values of $B'$. Circles representing the point of intersection of $L'_\pm$ and $L'_{ex}$ indication the ISCO position.
• Figure 4: ISCO radius variation on function of magnetic field $B'$ in different values of $\bm{\kappa}$.
• Figure 5: Energy plotted against of angular momentum for distinct values of $\bm{\kappa}$: $\bm{\kappa}=0$ (red), $\bm{\kappa}=10$ (green), and $\bm{\kappa}=20$ (blue). The black curve represents the minimum energy required for a particle tend to infinity, shown for multiple values of $B'$.