Macroscopic approaches to rotating neutron stars

TL;DR

This paper develops a macroscopic model for rotating neutron stars incorporating surface effects and calculates their moments of inertia, revealing significant gravitational and surface influences on their properties and deviations from classical models.

Contribution

It extends the macroscopic neutron star model to include rotation and surface effects, providing new insights into the star's moment of inertia and gravitational radius shifts.

Findings

Moment of inertia depends strongly on effective radius due to gravity and surface effects.

Correlation terms significantly shift the Schwarzschild radius.

Adiabaticity condition fails for high-mass neutron stars like J0740+6620.

Abstract

The macroscopic model for a neutron star (NS) as a perfect liquid drop at equilibrium is extended to rotating systems with a small frequency $\omega $ within the effective-surface (ES) approach. The gradient surface terms of the NS energy density $\cal{E}(\rho)$ [Equation of State] are taken into account along with the volume ones at the leading order of the leptodermic parameter $a/R << 1$, where $a$ is the ES crust thickness and $R$ is the mean NS radius. The macroscopic NS angular momentum at small frequencies $\omega$ is specified for calculations of the adiabatic moment of inertia (MI) within the Kerr metric coordinate approach in the outer Boyer-Lindquist and inner Hogan forms. The NS MI, $\Theta=\tilde{\Theta}/(1-\cal{G}_{t\varphi})$, was obtained in terms of the statistically averaged MI, $\tilde{\Theta}$, and its time and azimuthal-angle correlation, $\cal{G}_{t\varphi}$, as sums of the volume and surface components. The MI $\Theta$ depends dramatically on its effective radius $R$ because of strong gravitation and surface effects. We found the significant shift of the Schwarzschild radius due to the correlation term $\cal{G}_{t\varphi}$. With this term, the adiabaticity condition fails for the NS J0740+6620, with the mass about $M_\odot$ for a strong gravitation, in contrast to the NS J0030+0451 for smaller mass, and many other NSs.