Accretion disk in the Hartle-Thorne spacetime

TL;DR

This paper analyzes the properties of accretion disks around rotating deformed objects using the Hartle-Thorne metric, calculating orbital parameters and disk luminosities, and comparing results with other metrics and neutron star models.

Contribution

It provides a detailed analysis of accretion disk characteristics in the Hartle-Thorne spacetime, including flux and luminosity, and compares these with Kerr and q-metrics for realistic neutron star parameters.

Findings

Hartle-Thorne and Kerr metrics yield similar flux and luminosity results.

q-metric predicts significantly different accretion disk properties.

Predicted ISCO radii are consistent with neutron star models.

Abstract

We consider the circular motion of test particles in the gravitational field of a rotating deformed object described by the Hartle-Thorne metric. This metric represents an approximate solution to the vacuum Einstein field equations, accurate to second order in the angular momentum $J$ and to first order in the mass quadrupole moment $Q$. We calculate the orbital parameters of neutral test particles on circular orbits (in accretion disks) such as angular velocity, $\Omega$, total energy, $E$, angular momentum, $L$, and radius of the innermost stable circular orbit, $R_{ISCO}$, as functions of the total mass, $M$, spin parameter, $j=J/M^2$ and quadrupole parameter, $q=Q/M^3$, of the source. We use the Novikov-Thorne-Page thin accretion disk model to investigate the characteristics of the disk. In particular, we analyze in detail the radiative flux, differential luminosity, and spectral luminosity of the accretion disk, which are the quantities that can be measured experimentally. We compare our results with those obtained in the literature for the Schwarzschild and Kerr metrics, and the $q$-metric. It turns out that the Hartle-Thorne metric and the Kerr metric lead to similar results for the predicted flux and the differential and spectral luminosities, whereas the q-metric predicts different values. We compare the predicted values of $M$, $j$, and $q$ with those of realistic neutron star models. Furthermore, we compare the values of $R_{ISCO}$ with the static and rotating radii of neutron stars.