Accretion tori around rotating neutron stars

II. Oscillations and precessions

¹ Research Centre for Computational Physics and Data Processing, Institute of Physics, Silesian University in Opava, Bezručovo nám. 13, CZ-746 01 Opava, Czech Republic
² Astronomical Institute of the Czech Academy of Sciences, Boční II 1401, CZ-14100 Prague, Czech Republic
³ ORIGINS Excellence Cluster, Boltzmannstr. 2, 85748 Garching, Germany
⁴ Max Planck Institute for Extraterrestrial Physics, Gießenbachstraße 1, 85748 Garching, Germany

^⋆ Corresponding author; monika.matuszkova@physics.slu.cz

Received: 21 March 2024
Accepted: 8 September 2024

Abstract

The four characteristic oscillation frequencies of accretion flows (in addition to the Keplerian orbital frequency) are often discussed in the context of the time variability of black hole and neutron star (NS) low-mass X-ray binaries (LMXBs). These four frequencies are the frequencies of the axisymmetric radial and vertical epicyclic oscillations, and the frequencies of non-axisymmetric oscillations corresponding to the periastron (radial) and Lense-Thirring (vertical) precessions. In this context, we investigated the effect of the quadrupole moment of a slowly rotating NS and provide complete formulae for calculating these oscillation and precession frequencies, as well as convenient approximations. Simple formulae corresponding to the geodesic limit of a slender torus (and test-particle motion) and the limit of a marginally overflowing torus (a torus exhibiting a critical cusp) are presented, and more general approximate formulae are included to allow calculations for arbitrarily thick tori. We provide the Wolfram Mathematica code used for our calculations together with the C++ and PYTHON codes for calculating the frequencies. Our formulae can be used for various calculations regarding the astrophysical signatures of the NS super-dense matter equation of state. For instance, we demonstrate that even for a given fixed number of free parameters, a model that accounts for fluid flow precession matches the frequencies of twin-peak quasiperiodic oscillations observed in NS LMXBs better than a model that uses geodesic precession.