ALMA reveals diverse dust-to-gas mass ratios and quenching modes in old quiescent galaxies

Recent discoveries of dust and molecular gas in quiescent galaxies (QGs) up to z3 challenge the long-standing view that the interstellar medium depletes rapidly once star formation ceases, raising key questions of whether dust and gas co-evolve in QGs, and how their depletion links to stellar aging. We present deep Atacama Large Millimeter/submillimeter Array (ALMA) Band~6 continuum and CO (3--2) observations of 17 QGs at z0. 4 in the COSMOS field. Using the dust-to-molecular gas mass ratio (δ ₃₆ₑ) as a key diagnostic, we trace post-quenching evolution of the cold interstellar medium. Our study triples the number of QGs with direct δ ₃₆ₑ estimates, constraining 12 systems with stellar population ages of 5--10 Gyr. For the first time, we show that δ ₃₆ₑ in QGs ranges from 8 below to 2. 5 above the canonical value of δ ₃₆ₑ1/100. Despite uniformly low molecular gas fractions (median f ₇䃒=M ₇䃒/M_4. 1\%), QGs follow diverse evolutionary paths: about half exhibit rapid (700 Myr) exponential dust decline with age, while the rest show mild decline over 2 Gyr, maintaining elevated δ ₃₆ₑ1/100. Our results support simulations predictions of dust and molecular gas evolving independently post-quenching, without a preferred quenching mode. This challenges the use of dust continuum as a H₂ tracer, implying that quenching cannot be robustly linked to interstellar medium conditions when relying solely on dust or gas.