Probing geometrically perturbed strange stars with minimal decoupling using millisecond pulsar timing observations

Abstract

We construct a gravitationally decoupled anisotropic strange star model using the minimal geometric deformation approach with a MIT bag equation of state and an additional source sector controlled by a deformation parameter $\beta$ and a radial perturbation scale $\Psi$ through $g(r)=\sin(\Psi r^{2})$. The resulting Einstein system is consistently split into seed and $\theta$-sectors and matched to an exterior Schwarzschild geometry. The model is constrained by high-mass pulsars: PSR J0740+6620 $(2.08\pm0.07\,M_\odot)$, PSR J1810+1744 $(2.13\pm0.04\,M_\odot)$, PSR J1959+2048 $(2.18\pm0.09\,M_\odot)$, and PSR J2215+5135 $(2.28^{+0.10}_{-0.09}\,M_\odot)$. It reproduces these objects with predicted radii $R \approx 11.3$--$12.9$ km. The maximum mass reaches $M_{\max} \approx 2.28\,M_\odot$ for $\beta = 3\times 10^{-3}$ and $\Psi \approx 0.03\,\text{km}^{-2}$, while for $\beta = 10^{-3}$ the configuration yields $M_{\max} \approx 2.12\,M_\odot$ with $R \approx 12.2$ km. The central density lies in $\rho_c \approx (2.4$--$3.1)\times 10^{-4}\,\text{km}^{-2}$, decreasing smoothly to $\rho_s \approx 2.0\times 10^{-4}\,\text{km}^{-2}$. The anisotropy increases from zero at the center to $\Delta \approx (0.25$--$0.45)\times 10^{-4}\,\text{km}^{-2}$ near the surface, generating additional outward support that enhances compactness by $\sim 15\%$. The compactness parameter spans $C \approx 0.17$--$0.22$, safely below the Buchdahl limit, while the surface redshift reaches $z_s \approx 0.25$--$0.38$. The condition $dM/d\rho_c > 0$ is satisfied throughout, confirming dynamical stability. Overall, $\beta$ enhances the maximum mass by up to $\sim 15\%$, while $\Psi$ introduces controlled oscillatory structure without violating observational constraints, producing stable ultra-compact stars consistent with current pulsar data.