Slowly rotating Tolman VII solution

TL;DR

This paper models a slowly rotating Tolman VII fluid sphere, calculating key physical parameters and comparing them with neutron star data, demonstrating the model's accuracy within 10% for realistic compactness ranges.

Contribution

The study extends the Tolman VII solution to include slow rotation effects and compares its predictions with neutron star data, showing high accuracy.

Findings

Moment of inertia and quadrupole moment computed for various configurations.

Ellipticity behavior changes at a critical tenuity value.

Relative errors within 10% when compared to realistic neutron star models.

Abstract

We present a model of a slowly rotating Tolman VII (T-VII) fluid sphere, at second order in the angular velocity. The structure of this configuration is obtained by integrating the Hartle-Thorne equations for slowly rotating relativistic masses. We model a sequence in adiabatic and quasi-stationary contraction, by varying the tenuity parameter $R/R_{\mathrm{S}}$, where $R$ is the radius of the configuration and $R_{\mathrm{S}}$ is its Schwarzschild radius. We determined the moment of inertia $I$, mass quadrupole moment $Q$, and the ellipticity $\varepsilon$, for various configurations. Similar to previous results for Maclaurin and polytropic spheroids, in slow rotation, we found a change in the behaviour of the ellipticity when the tenuity reaches a certain critical value. We compared our results of $I$ and $Q$ for the T-VII model with those predicted by the universal fittings proposed for realistic neutron stars. For the relevant range of compactness, we found that relative errors are within $10\%$, thus suggesting the T-VII solution as a very good approximation for the description of the interior of neutron stars.