Survival of Protoplanetary Disks in Upper Scorpius from Population Synthesis Models with External Photoevaporation

We present population synthesis models of viscous protoplanetary disks subject to mild external far-ultraviolet (FUV) radiation fields ($F_{\rm UV}=1\text{-}100\,$G$_0$). Our simulations focus on gas disk evolution, exploring stellar masses drawn from an Initial Mass Function and a range of initial disk conditions. We quantify the fraction of surviving disks across $10\,\mathrm{Myr}$ of evolution, track the evolution of gas disk mass and size, and compare our results with observations of protoplanetary disks in the Upper Scorpius region, including the ten targets studied by the AGE-PRO ALMA Large Program. We find that models combining viscous evolution with external photoevaporation yield disk lifetimes of $3\text{-}7\,\mathrm{Myr}$, consistent with observed dispersal timescales, particularly for $10^{-4} \leq \alpha \leq 10^{-2}$. Low-mass stars ($0.1\,$M$_\odot$) are more susceptible to disk dispersal due to their weaker gravitational binding, with their fraction among all surviving disks dropping from $76\%$ at birth to $51\%$ by $10\,\mathrm{Myr}$. The majority of the long-lived disks are those with low viscosity $\alpha < 10^{-3.5}$ and initial characteristic radius $R_c < 125\,\mathrm{AU}$, while the initial disk-to-star mass ratio does not play an important role. The median gas disk mass and radius of the surviving disks exhibit a sharp decline in the first $0.2\,\mathrm{Myr}$ of evolution, followed by a slight increase that reflects survivorship bias. We also explore correlations between gas disk mass and size vs. stellar mass and FUV strength. Our findings highlight the critical role of external photoevaporation in shaping disk populations even at moderate levels of FUV radiation fields.