Population synthesis of Galactic middle-aged pulsar wind nebulae I. Detection prospects for current and future instruments

Pulsar wind nebulae (PWNe) constitute the largest population of Galactic very-high-energy (VHE; $E > 100$ GeV) $\gamma$-ray sources and are key laboratories for studying particle acceleration and pulsar--supernova remnant (SNR) interactions. However, realistic population-level predictions have so far lacked any detailed treatment of the reverberation phase, when the nebula is compressed by the SNR reverse shock, significantly altering its dynamics and radiative spectrum. We employ the hybrid \texttt{TIDE+L} framework, which combines a thin-shell dynamical model with a Lagrangian treatment of the SNR structure during reverberation, allowing self-consistent evolution of thousands of PWNe across all stages up to $10^5$ yr. Each source is evolved under distributions of pulsar spin-down, SNR, and environmental properties, and the resulting $\gamma$-ray fluxes are used to estimate the detectability by current and next-generation $\gamma$-ray observatories while accounting for their sensitivity and sky coverage. The model predicts that the upcoming Cherenkov Telescope Array Observatory (CTAO) will detect an order of magnitude more PWNe than those firmly detected in the TeV range, confirming its dominant contribution to the forthcoming TeV population census. Our results demonstrate that realistic modeling of reverberation is important for predicting the Galactic TeV PWNe population.