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

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 $\mathrm{\Psi }$ through $g(r)=\sin (\mathrm{\Psi }{r}^2)$. 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 $(2.08\pm 0.07M_{\odot })$, PSR J1810+1744 $(2.13\pm 0.04M_{\odot })$, PSR J1959+2048 $(2.18\pm 0.09M_{\odot })$, and PSR J2215+5135 $(2.28_{-0.09}^{+0.10}{M}_{\odot })$. It reproduces these objects with predicted radii $R\approx 11.3$–$12.9$ km. The maximum mass reaches $M_{\max }\approx 2.28M_{\odot }$ for $\beta =3\times {10}^{-3}$ and $\mathrm{\Psi }\approx 0.03{\text{km}}^{-2}$, while for $\beta ={10}^{-3}$ the configuration yields $M_{\max }\approx 2.12M_{\odot }$ 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 $\mathrm{\Delta }\approx (0.25$–$0.45)\times {10}^{-4}{\text{km}}^{-2}$ near the surface, generating additional outward support that enhances compactness by $\sim 15\mathrm{\%}$. 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 $dM\mathrm{/}d{\rho }_c>0$ is satisfied throughout, confirming dynamical stability. Overall, $\beta$ enhances the maximum mass by up to $\sim 15\mathrm{\%}$, while $\mathrm{\Psi }$ introduces controlled oscillatory structure without violating observational constraints, producing stable ultra-compact stars consistent with current pulsar data.