**Publication date:** Jan 2008

**Abstract:**

We discuss the non-geodesic corrections to the formulae for orbital and

epicyclic frequencies given by the presence of a neutron star magnetic

field. In this paper we focus on the „Lorentzian“ corrections arising if

specific charge of a test particle is considered. This corrections are

valid for a slightly charged accreting matter. We consider a magnetic

field generated by an intrinsic static dipole magnetic moment of a

slowly rotating neutron star on the background of the Schwarzschild

geometry.We calculate relevant orbital and epicyclic frequencies in a

fully general relativistic form using the equations governing

perturbations of the circular motion. The nongeodesic corrections are

rather high in the vicinity of the central compact object. 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). This correction

implies an influence of a test particle charge on the effective position

of the innermost marginally stable circular orbit (EISCO) and

constraints a restriction to the specific charge under an evidence for

the orbital motion close to the central compact object. A dipole

magnetic field influences the radial epicyclic frequency and the

position of EISCO. It also cancels the equality of orbital and vertical

epicyclic frequencies present in spherically symmetric Schwarzschild

geometry. However, these corrections become substantial only for a

specific charge values which implying shift of the innermost stable

circular orbit inconsistent with the present astrophysical view of

LMXBs. Hence, in the lowest approximation realitic for observed neutron-

star binary system with QPOs, the influence of the eventual specific

charge of the accreted matter should enter the orbital QPO models in the

form of a slightly lowered radial epicyclic frequency and slightly

shifted ISCO.

**Authors:**

Bakala, Pavel; Sramkova, Eva; Stuchlik, Zdenek; Török, Gabriel;