# Epicyclic oscillations in the Hartle-Thorne external geometry

## TL;DR

This paper analyzes the orbital and epicyclic frequencies in the external spacetime of rotating neutron stars described by the Hartle-Thorne metric, with applications to understanding high-frequency QPOs in X-ray binary systems.

## Contribution

It provides a systematic analysis of epicyclic motions in Hartle-Thorne spacetime using realistic neutron star models and universal relations, enhancing QPO modeling accuracy.

## Key findings

- Epicyclic frequencies depend on neutron star parameters and quadrupole moments.
- Results support models explaining QPOs with frequency ratios near 3:2 or 5:4.
- The approach allows direct application across different neutron star configurations.

## Abstract

The external Hartle-Thorne geometry, which describes the space-time 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 space-times, 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 which is accreting matter from its binary companion. In these systems, twin high-frequency quasi-periodic oscillations 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 $f_\mathrm{rot}$.