**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;