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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. [ABSTRACT FROM AUTHOR]

We present a full general relativistic analytic solution for a radiation-pressure-supported equilibrium fluid torus orbiting a rotating neutron star (NS). We applied previously developed analytical methods that include the effects of both the NS's angular momentum and quadrupole moment in the Hartle-Thorne geometry. The structure, size, and shape of the torus are explored, with a particular focus on the critically thick solution – the cusp tori. For the astrophysically relevant range of NS parameters, we examined how our findings differ from those obtained for the Schwarzschild space-time. The solutions for rotating stars display signatures of an interplay between relativistic and Newtonian effects where the impact of the NS angular momentum and quadrupole moment are almost counterbalanced at a given radius. Nevertheless, the space-time parameters still strongly influence the size of tori, which can be shown in a coordinate-independent way. Finally, we discuss the importance of the size of the central NS which determines whether or not a surrounding torus exists. We provide a set of tools in a Wolfram Mathematica code, which establishes a basis for further investigation of the impact of the NSs' super-dense matter equation of state on the spectral and temporal behaviour of accretion tori. [ABSTRACT FROM AUTHOR]

We examine the influence of quadrupole moment of a slowly rotating neutron star (NS) on the oscillations of a fluid accretion disk (torus) orbiting a compact object the spacetime around which is described by the Hartle‐Thorne geometry. Explicit formulae for non‐geodesic orbital epicyclic and precession frequencies, as well as their simplified practical versions that allow for an expeditious application of the universal relations determining the NS properties, are obtained and examined. We demonstrate that the difference in the accretion disk precession frequencies for NSs of the same mass and angular momentum, but different oblateness, can reach up to tens of percent. Even higher differences can arise when NSs with the same mass and rotational frequency, but different equations of state (EoS), are considered. In particular, the Lense‐Thirring precession frequency defined in the innermost parts of the accretion region can differ by more than one order of magnitude across NSs with different EoS. Our results have clear implications for models of the LMXBs variability. [ABSTRACT FROM AUTHOR]