**Publication date:** Dec 2007

**Abstract:**

Several models of the X-ray flux modulation observed in the low-mass

X-ray binaries (LMXBs), in particular the neutron star LMXBs, deal with

Keplerian and epicyclic frequencies of geodesic orbital motion. We

discuss non-geodesic corrections to the orbital and epicyclic

frequencies of charged test particles caused by presence of a neutron

star magnetic field. The magnetic field is considered to be generated by

an intrinsic static dipole magnetic moment of a neutron star represented

by the Schwarzschild geometry. We present fully general relativistic

formulae for the orbital and epicyclic frequencies, obtained using the

appropriate equations governing perturbations of the circular motion.

The most significant correction arises for the radial epicyclic

frequency. The zero point of the corrected radial epicyclic frequency

defines radius of the effective innermost stable circular orbit

"(EISCO)." The dipole magnetic field also violates equality of the

orbital and vertical epicyclic frequencies corresponding to the

spherical symmetry of the Schwarzschild geometry.

**Authors:**

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