Dust and PAHs in late-stage galaxy evolution: Imprints of TP-AGB dust injection, grain growth and AGN feedback in high-z quiescent galaxies with JWST and ALMA
A major unknown in late-stage galaxy evolution is what regulates the cold interstellar medium (ISM) after quenching, a question central to interpreting molecular gas, dust, and stellar content in quiescent galaxies (QGs) now probed by ALMA and JWST to $z\sim7$. We present the first semi-analytic model that follows the coupled post-quenching evolution of dust, cold gas, and polycyclic aromatic hydrocarbons (PAHs), using flexible star-formation histories and a framework tracking small and large carbonaceous and silicate grains. At $z\sim1$, we find that QGs of similar mass ($M_\star\sim8\times10^{10} M_\odot$), stellar-population age ($\sim2$ Gyr), and cold gas fractions ($f_{\rm gas}\sim1$-$10\%$), span $2$-$3$ dex in $M_{\rm dust}/M_\star$ and $M_{\rm dust}/M_{\rm gas}$, ranging from star-forming-like ratios to highly depleted dust states. The diversity arises from delayed dust injection by thermally pulsing asymptotic giant branch (TP-AGB) stars and ISM grain growth, which sustain dust enrichment for up to $\sim2.5$ Gyr after quenching. Without these channels, the pre-quenching $M_{\rm dust}$ falls below $10\%$ of its initial value within $\lesssim0.5$-$1$ Gyr, and twice as fast when AGN feedback is active. The imprint of post-quenching dust processing persists in substantial reservoirs of small carbonaceous grains, with PAH fractions of $\sim2$-$3\%$, even if the cold-dust budget falls below typical ALMA continuum detection limits ($M_{\rm dust}/M_\star\lesssim10^{-4}$). Such signatures may remain detectable with JWST/MIRI at $\mu$Jy depths, probing chemically enriched dust phases in otherwise ALMA-faint galaxies. Altogether, dust and PAHs provide independent probes of distinct stages of ISM evolution in QGs, rather than simply tracing the residual cold ISM of the preceding star-forming phase.