How Quickly Did the Giants Form? Constraining the Formation Timescales of Massive Quiescent Galaxies at Cosmic Noon Using Chemical Evolution Modelling

Massive quiescent galaxies (MQGs; M_ ~ 10¹¹ \, M_) at cosmic noon (z ~ 2) host $α$-enhanced stellar populations ([Mg/Fe] ~ 0.4 - 0.5) at near-solar [Fe/H], implying rapid formation histories that spectral energy distribution (SED) fitting alone constrains poorly. To determine the physical conditions and formation timescales that generate these abundances, we employ a one-zone chemical evolution model with nucleosynthetic yields calibrated against resolved stars in the Sculptor dwarf spheroidal. Comparing our model to a compilation of observed abundances, we find MQGs are consistent with rapid formation timescales of ΔtSF ~ 0.1 - 0.4 \, Gyr. The progenitors must sustain high star-formation efficiencies (approximately the molecular gas depletion time; τ_ ~ 0.05 \, Gyr) and retain most of their metal-enriched ejecta (η~ 0), consistent with high-redshift dusty star-forming galaxies (DSFGs). However, our model favours moderately active progenitors with typical star-formation rates (SFRs) of 200-400 \, M_ \, yr⁻¹, matching recently identified `NIRCam-dark' galaxies more closely than the broader DSFG population. Sustained starbursts (SFR 1000 \, M_ \, yr⁻¹) are disfavoured, since they would form most stellar mass before significant SN Ia enrichment and underproduce the observed [Fe/H]. The same framework also reproduces the central abundances of local early-type galaxies over longer timescales (ΔtSF ~ 0.6 - 1 \, Gyr). Chemical abundances can therefore provide powerful constraints on the formation histories of MQGs, and incorporating them into SED-fitting routines will ensure inferred histories remain consistent with the observed chemistry.