1D Models of Middle-Aged PWNe Remain Reliable Despite 50% Apparent Size Increase in 2D Reverberation Simulations

The study generates a representative PWN-SNR population using supernova kinetic energy, ejecta mass, ambient density, and pulsar spin-down power drawn from observed distributions. Early evolution follows a semi-analytical prescription before switching to a 1D Lagrangian hydro code that tracks the reverse-shock interaction. Within the region of interest containing most Galactic systems, large diversity in expansion histories collapses to a common relaxed state consistent with the Sedov-Taylor solution. Two-dimensional axisymmetric simulations optimized for computational cost reveal that Rayleigh-Taylor and Kelvin-Helmholtz instabilities grow from initial seed perturbations yet do not measurably alter the volume-integrated energy or magnetic-field evolution tracked in 1D. Apparent projected size can increase by up to 50% due to mixing, an effect relevant for morphological comparisons with CTA and ASTRI data. These results directly strengthen predictions that middle-aged PWNe dominate the unresolved Galactic TeV background and set the injection spectrum for cosmic-ray electrons and positrons observed at Earth. Future multi-dimensional runs incorporating radiative cooling and anisotropic pulsar winds will test whether the 10% flux uncertainty floor remains valid once CTA begins survey operations.