Revisiting Vaidya-Tikekar stellar model in the linear regime

TL;DR

This paper develops new solutions for relativistic star models using the Vaidya-Tikekar metric ansatz, analyzing how the curvature parameter affects star properties and correlates with observational data of pulsars.

Contribution

It introduces a new class of solutions in the linear regime of the Vaidya-Tikekar model, linking curvature parameters with physical properties and observational data of pulsars.

Findings

Curvature parameter influences mass-radius relationship.

Correlation between curvature, bag constant, and pulsar data.

Potential for parameter fine-tuning based on observations.

Abstract

We obtain a new class of solutions by revisiting the Vaidya-Tikekar stellar model in the linear regime. Making use of the Vaidya and Tikekar metric ansatz [J. Astrophys. Astron. {\bf3} (1982) 325] describing the spacetime of static spherically symmetric relativistic star composed of an anisotropic matter distribution admitting a linear EOS, we solve the Einstein field equations and subsequently analyze physical viability of the solution. We probe the impact of the curvature parameter $K$ of the Vaidya-Tikekar model, which characterizes a departure from homogeneous spherical distribution, on the mass-radius relationship of the star. In the context of density-dependent MIT Bag models, we show a correlation between the curvature parameter, the bag constant and total mass and radius of some of the well-known pulsars viz., 4U 1820-30, RX J1856-37, SAXJ 1808.4 and Her X-1. We explore the possibility of fine-tuning these parameters based on current observational data.