$I-$Love$-C$ relation for an anisotropic neutron star

TL;DR

This paper investigates the properties of anisotropic neutron stars using the scalar pressure anisotropy model, analyzing how anisotropy affects key stellar parameters and universal relations, and constrains anisotropy parameters with gravitational wave data.

Contribution

It introduces a detailed study of anisotropic neutron star properties and their impact on universal relations, providing new bounds on stellar parameters using GW170817 data.

Findings

Anisotropy affects mass, radius, and moment of inertia of neutron stars.

The I-Love-C relation weakens with increased anisotropy.

Constraints on stellar radius and moment of inertia are derived from GW data.

Abstract

One of the most common assumptions has been made that the pressure inside the star is isotropic in nature. However, the pressure is locally anisotropic in nature which is a more realistic case. In this study, we investigate certain properties of anisotropic neutron stars with the scalar pressure anisotropy model. Different perfect fluid conditions are tested within the star with the relativistic mean-field model equation of states (EOSs). The anisotropic neutron star properties such as mass ($M$), radius ($R$), compactness ($C$), Love number ($k_2$), dimensionless tidal deformability ($\Lambda$), and the moment of inertia ($I$) are calculated. The magnitude of the quantities as mentioned above increases (decreases) with the positive (negative) value of anisotropy except $k_2$ and $\Lambda$. The Universal relation $I-$Love$-C$ is calculated with almost 58 EOSs spans from relativistic to non-relativistic cases. We observed that the relations between them get weaker when we include anisotropicity. With the help of the GW170817 tidal deformability limit and radii constraints from different approaches, we find that the anisotropic parameter is less than 1.0 if one uses the BL model. Using the universal relation and the tidal deformability bound given by the GW170817, we put a theoretical limit for the canonical radius, $R_{1.4}=10.74_{-1.36}^{+1.84}$ km, and the moment of inertia, $I_{1.4} = 1.77_{-0.09}^{+0.17}\times10^{45}$ g cm$^2$ with 90\% confidence limit for isotropic stars. Similarly, for anisotropic stars with $\lambda_{\rm BL}=1.0$, the values are $R_{1.4}=11.74_{-1.54}^{+2.11}$ km, $I_{1.4} = 2.40_{-0.08}^{+0.17} \times10^{45}$ g cm$^2$ respectively.