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

Pavel Bakala (1) , Eva Šrámková (1) , Zdeněk Stuchlík (1) , Gabriel Török (1)

1 Faculty of Philosophy and Science

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 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 looses its meaning. We demonstrate that for 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 region under the photon circular orbit. The lowest stable circular orbit at r MISCO min = 2.73M, associated with the highest possible orbital frequency ν max K = 3284 Hz (1.5M ? /M), corresponds to the critical value of the particle specific charge and the neutron star magnetic dipole moment product (µ) crit = 1.87M 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 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 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.

Mots clés: 95.30.Sf; 97.10.Gz; 97.10.Ld; 97.80.Jp

Pavel Bakala, Eva Šrámková, Zdeněk Stuchlík, Gabriel Török. On magnetic-field-induced non-geodesic corrections to relativistic orbital and epicyclic frequencies. Classical and Quantum Gravity, 2010, 27 (4), pp.45001. ⟨10.1088/0264-9381/27/4/045001⟩. ⟨hal-00630001⟩