Stability, Tidal Deformability, and Statistical Constraints of Anisotropic Compact Stars with a Generalized Polytropic Equation of State : Modelling Observation with Buchdahl Space-Time
An anisotropic compact star model is constructed within the framework of general relativity by combining the Buchdahl space-time with a generalized polytropic equation of state. The model parameters are constrained through Darmois-Israel junction conditions by matching interior geometry smoothly with exterior Schwarzschild space-time. The proposed framework is applied to thirty-eight observed compact star candidates spanning a broad range of masses and radii. Regular and physically acceptable distributions of the energy density, radial pressure, tangential pressure, enclosed mass, anisotropy and gravitational redshift are obtained throughout the stellar interior. Energy density and pressure components are found to decrease outward, while the enclosed mass and gravitational redshift are found to increase monotonically towards the stellar surface. The radial pressure is required to vanish at the boundary, thereby determining the estimated stellar radius. The anisotropy is found to provide an additional outward contribution that supports the stellar configurations against gravitational collapse. The physical acceptability of the model is examined through the Zeldovich condition, radial adiabatic index, causality conditions and Herrera cracking criterion. Hydrostatic equilibrium is achieved through the balance among gravitational, hydrostatic and anisotropic forces. The tidal response is also investigated, and an inverse relation between the estimated mass and dimensionless tidal deformability is obtained. The calculated configurations span \(2.88\lesssim M_{\rm Est}/M_\odot\lesssim3.23\) and yield \(22.55\lesssimΛ\lesssim68.38\). MCMC analysis provides statistically constrained compactness and tidal parameters. Overall, a physically viable description of anisotropic compact stars is obtained.