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 about7. 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 about1, we find that QGs of similar mass (M about8 times10 10 M), stellar-population age (about2 Gyr), and cold gas fractions (f gas about1 - 10%), span 2 - 3 dex in M dust/M and M dust/M 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 about2.5 Gyr after quenching. Without these channels, the pre-quenching M dust falls below 10% of its initial value within 0.5 - 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 about2 - 3%, even if the cold-dust budget falls below typical ALMA continuum detection limits (M dust/M 10-4). Such signatures may remain detectable with JWST/MIRI at μ 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.