Probing neutron star interiors through mass-radius relations and the equation of state using piecewise polytrope

We present a novel framework for probing neutron star interiors by combining piecewise polytropic equations of state with mass-radius constraints. Solving the TOV equations across density regimes, we generate mass-radius curves and compare them with NICER and gravitational wave data. Our analysis highlights how different polytropic segments influence neutron star properties, particularly within the 1.4 − 3.5 M ⊙ range. This approach constrains the pressure-density relation at supranuclear densities and suggests potential exotic matter phases. The results agree and enable more precise interpretation of forthcoming observations, advancing neutron stars as probes of extreme-density physics.