Macroscopic approaches to rotating neutron stars

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 $\mathcal{E}(\rho )$ in the Equation of State are taken into account along with the volume components at the leading order over 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 used for calculations of the adiabatic moment of inertia (MI) within the Kerr metric approach in the outer Boyer-Lindquist and inner Hogan coordinate forms. The NS MI, $\Theta =\tilde{\Theta }/(1-{\mathcal{G}}_{t\phi })$, was obtained in terms of the statistically averaged MI, $\tilde{\Theta }$, and its time and azimuthal-angle correlation, ${\mathcal{G}}_{t\phi }$, as the sums of volume and surface components. The MI $\Theta$ depends dramatically on the effective radius $R$ due to strong gravitation and surface effects. We found significant additional rotational constraints on the radius $R$ due to the correlation term ${\mathcal{G}}_{t\phi }$ and surface contributions. With these contributions, the adiabaticity condition is better fulfilled for a stronger gravitation in many well-known neutron stars.

Comments: 21 pages, 4 figures. arXiv admin note: text overlap with arXiv:2403.01445