**Publication date:** Feb 2010

**Abstract:**

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 rMISCOmin =

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.

**Authors:**

Bakala, Pavel; Šrámková, Eva; Stuchlík, Zdeněk; Török, Gabriel;