**Publication date:** Jun 2019

**Abstract:**

The external Hartle─Thorne geometry, which describes the spacetime

outside a slowly rotating compact star, is characterized by the

gravitational mass M, angular momentum J, and quadrupole moment Q of the

star and gives a convenient description, which, for the rotation

frequencies of more than 95% of known pulsars, is sufficiently accurate

for most purposes. We focus here on the motion of particles in these

spacetimes, presenting a detailed systematic analysis of the frequency

properties of radial and vertical epicyclic motion and of orbital

motion. Our investigation is motivated by X-ray observations of binary

systems containing a rotating neutron star that is accreting matter from

its binary companion. In these systems, twin high-frequency quasi-

periodic oscillations (QPOs) are sometimes observed with a frequency

ratio approaching 3:2 or 5:4, and these may be explained by models

involving the orbital and epicyclic frequencies of quasi-circular

geodesic motion. In our analysis, we use realistic equations of state

for the stellar matter and proceed in a self-consistent way, following

the Hartle─Thorne approach in calculating both the corresponding values

of Q, M, and J for the stellar model and the properties of the

surrounding spacetime. Our results are then applied to a range of

geodetical models for QPOs. A key feature of our study is that it

implements the recently discovered universal relations among neutron-

star parameters so that the results can be directly used for models with

different masses M, radii R, and rotational frequencies f

_{rot}.

**Authors:**

Urbancová, Gabriela; Urbanec, Martin; Török, Gabriel; Stuchlík, Zdeněk; Blaschke, Martin; Miller, John C.;