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Recent discoveries of copious amounts of dust in quiescent galaxies (QGs) at high redshifts (z ≳ 1 − 2) challenge the conventional view that these objects have a negligible interstellar medium (ISM) in proportion to their stellar mass. We made use of theSIMBAhydrodynamic cosmological simulation to explore how dust and cold gas evolve in QGs and are linked to the quenching processes affecting them. We applied a novel method for tracking the changes in the ISM dust abundance across the evolutionary history of QGs identified at 0 < z ≲ 2 in both cluster and field environments. The QGs transition from a diversity of quenching pathways, both rapidly and slowly, and they exhibit a wide range of times that elapsed between the quenching event and cold gas removal (from ∼650 Myr to ∼8 Gyr). Contrary to some claims, we find that quenching modes attributed to the feedback from active galactic nuclei (AGNs) do not affect dust and cold gas within the same timescales. Remarkably, QGs may replenish their dust content in the quenched phase primarily due to internal processes and marginally by external factors such as minor mergers. Prolonged grain growth on gas-phase metals appears to be the key mechanism for dust re-formation, which is effective within ∼100 Myr after the quenching event and rapidly increases the dust-to-gas mass ratio in QGs above the standard values (δ_DGR ≳ 1/100). Consequently, despite heavily depleted cold gas reservoirs, roughly half of QGs maintain little evolution of their ISM dust with stellar age within the first 2 Gyr following the quenching. Overall, we predict that relatively dusty QGs (M_dust/M_⋆ ≳ 10⁻³ − 10⁻⁴) arise from both fast and slow quenchers, and they are prevalent in quenched systems of intermediate and low stellar masses (9 < log(M_⋆/M_⊙) < 10.5). This strong prediction poses an immediate quest for observational synergy between, for example, theJames WebbSpace Telescope (JWST) and the Atacama Large Millimetre Array (ALMA). 

The physical mechanisms that link the termination of star formation in quiescent galaxies and the evolution of their baryonic components, stars, and the interstellar medium (ISM; dust, gas, and metals) are poorly constrained beyond the local Universe. In this work, we characterise the evolution of the dust content in 545 quiescent galaxies observed at 0.1 < z < 0.6 as part of the hCOSMOS spectroscopic redshift survey. This is, to date, the largest sample of quiescent galaxies at intermediate redshifts for which the dust, stellar, and metal abundances are consistently estimated. We analyse how the crucial markers of a galaxy dust life cycle, such as specific dust mass (M_dust/M_⋆), evolve with different physical parameters, namely gas-phase metallicity (Z_gas), time since quenching (t_quench), stellar mass (M_⋆), and stellar population age. We find morphology to be an important factor in the large scatter inM_dust/M_⋆(∼2 orders of magnitude). Quiescent spirals exhibit strong evolutionary trends of specific dust mass withM_⋆, stellar age, and galaxy size, in contrast to the little to no evolution experienced by ellipticals. When transitioning from solar to super-solar metallicities (8.7 ≲ 12 + log(O/H)≲9.1), quiescent spirals undergo a reversal inM_dust/M_⋆, indicative of a change in dust production efficiency. By modelling the star formation histories of our objects, we unveil a broad dynamical range of post-quenching timescales (60 Myr < t_quench < 3.2 Gyr). We show thatM_dust/M_⋆is highest in recently quenched systems (t_quench < 500 Myr), but its further evolution is non-monotonic, as a consequence of different pathways for dust formation, growth, or removal on various timescales. Our data are best described by simulations that include dust growth in the ISM. While this process is prevalent in the majority of galaxies, for ∼15% of objects we find evidence of additional dust content acquired externally, most likely via minor mergers. Altogether, our results strongly suggest that prolonged dust production on a timescale of 0.5 − 1 Gyr since quenching may be common in dusty quiescent galaxies at intermediate redshifts, even if their gas reservoirs are heavily exhausted (i.e. cold gas fraction < 1 − 5%).