Role of Anisotropy on the Tidal Deformability of Compact Stellar Objects

Shyam Das,Shyamal Pal,Saibal Ray,Bikram Parida

doi:10.3390/ecu2021-09311

Abstract

In this paper, we introduce a framework to study the tidal deformation of relativistic anisotropic compact stars. Anisotropic stresses are ubiquitous in nature and widely used in modelling compact stellar objects. Tidal deformability of astrophysical compact objects is a natural effect of gravity, such as one produced by a companion in a binary system. In general relativity, the existence of this measurable effect of gravity can be quantified by their tidal Love numbers (TLN), which characterize the deformability of a neutron star (NS) from sphericity. The tidal deformability or polarizability parameter of an NS depends on its complex internal structure, and hence, the nature of the compact object can be studied by measuring the TLN. We choose a particular solution, which is the anisotropic generalization of the Tolman IV model, as the interior of the compact stellar object. The physical acceptability of the model has been shown graphically by considering the pulsar 4U 1608-52 with their current estimated mass and radius. By computing the quadrupole moment, we found that the TLN is dependent on anisotropy of the compact object. We graphically analyze the variation of the TLN against anisotropy for different compact objects with a compactness factor. The numerical value of TLN is given for different compact objects for physically acceptable values of the anisotropic parameter.

Highlights

Compact objects are extremely dense astro-physical objects that provide strong gravity and high density, allowing for the study of fundamental physics related to nuclear matter properties
A neutron star placed in a perturbing external gravitational field is deformed and induces a quadrupole moment, which affects the binding energy of the system and increases the rate of emission of gravitational waves during the late stage inspirals
The tidal Love number (TLN), which is the ratio of the induced quadrupole moment to the perturbing tidal gravitational field, can be expressed by a relatively simple analytical formula

Summary

Introduction

Compact objects are extremely dense astro-physical objects that provide strong gravity and high density, allowing for the study of fundamental physics related to nuclear matter properties. The theoretical prediction of the mass and radius of a neutron star (NS) mostly depends on the nature of the nuclear EOS at supra-nuclear densities. In this context, tidal deformability can be used to study their interiors. The tidal response is the astrophysical constraints that can be employed as probes of NS properties It is the astrophysically observable macroscopic property of NS that can be defined as the ratio of the induced multipole moment of a star over the induced tidal field from its companion. We have calculated the TLN, which measures the tidal deformability of the compact object induced by the external field

Physical Features and Tidal Love Number

Results

Conclusions