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Tidal deformability of a star in the presence of an external tidal field provides an important avenue to our understanding about the structure and properties of neutron stars. The deformation of the star is characterized by the tidal Love number (TLN). In this paper, we propose a technique to measure the TLN of a particular class of compact stars. In particular, we analyze the impact of anisotropy and compactness on the TLN.

In this paper, we develop a new relativistic compact stellar model for a spherically symmetric anisotropic matter distribution. The model has been obtained through generating a new class of solutions by invoking the Tolman ansatz for one of the metric potentials grr and a physically reasonable selective profile of radial pressure. We have matched our obtained interior solution to the Schwarzschild exterior spacetime over the bounding surface of the compact star. These matching conditions together with the condition of vanishing the radial pressure across the boundary of the star have been utilized to determine the model parameters. We have shown that the central pressure of the star depends on the parameter p0. We have estimated the range of p0 by using the recent data of compact stars 4U 1608-52 and Vela X-1. The effect of p0 on different physical parameters e.g., pressure anisotropy, the subliminal velocity of sound, relativistic adiabatic index etc. have also been discussed. The developed model of the compact star is elaborately discussed both analytically and graphically to justify that it satisfies all the criteria demanded a realistic star. From our analysis, we have shown that the effect of anisotropy becomes small for higher values of p0. The mass-radius (M-R) relationship which indicates the maximum mass admissible for observed pulsars for a given surface density has also been investigated in our model. Moreover, the variation of radius and mass with central density has been shown which allow us to estimate central density for a given radius (or mass) of a compact star.

We present a model of compact astrophysical object under General Theory of Relativity using the anisotropic extension of Tolman IV solution. The anisotropy function, derived from the model, remains well behaved throughout the interior of the star. The model satisfies several necessary conditions for a physically realistic compact star. Physical viability of the model is verified specifically by plugging in the estimated parameter values of the Low Mass X-ray Binary (LMXB) candidate 4U 1608–52. Our stability analysis of this star, by using various criteria for stability, provides satisfactory results. In connection to anisotropy, we compute the Tidal Love Number (TLN) for the compact stellar model and compare the calculated values with existing literature.