On magnetic-field-induced non-geodesic corrections to relativistic orbital and epicyclic frequencies

We discuss non-geodesic corrections to orbital and epicyclic frequencies of charged test particles orbiting a non-rotating neutron star with a dipole magnetic field. Using a fully relativistic approach we consider the influence of both the magnetic attraction and repulsion on the orbital and epicyclic motion. The magnetic repulsion introduces a rather complex and unusual behaviour of the circular orbital motion that is well defined down to the radius where the vertical epicyclic frequency loses its meaning. We demonstrate that for the intensity of the magnetic interaction appropriately restricted, the stable circular orbits extend down to the magnetic innermost stable circular orbit (MISCO) that is located well under the geodetic innermost stable circular orbit (GISCO) and even can reach the region under the photon circular orbit. The lowest stable circular orbit at r^MISCO_min = 2.73M, associated with the highest possible orbital frequency \nu _{K}^{\max} = 3284\, Hz (1.5 \, {\it M}_{\odot}/\it M) , corresponds to the critical value of the particle-specific charge and the neutron star magnetic dipole moment product (\tilde{q} \mu )_crit = 1.87 M^2 . For the magnetic attraction acting above the GISCO, the situation is much more simple and we demonstrate that the most significant correction arises for the radial epicyclic frequency and consequently for the location of the MISCO when the strong magnetic attraction pushes its location far behind the location of GISCO. We show that the Lorentz force also naturally violates the equality of the orbital and vertical epicyclic frequencies implied by the spherical symmetry of the background Schwarzschild geometry giving rise to the new effect of nodal precession of the orbital motion plane. Finally, we apply the magnetic attraction corrections on the relativistic precession model of the twin-peak high-frequency quasiperiodic oscillations observed in the galactic low mass x-ray binaries, showing possible high relevance of the modified radial epicyclic frequency.