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; $M_\star \sim 10^{11} \, \mathrm{M_\odot}$) at cosmic noon ($z \sim 2$) host $α$-enhanced stellar populations ($\mathrm{[Mg/Fe]} \sim 0.4 - 0.5$) 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 $Δt_\mathrm{SF} \sim 0.1 - 0.4 \, \mathrm{Gyr}$. The progenitors must sustain high star-formation efficiencies (approximately the molecular gas depletion time; $τ_\star \sim 0.05 \, \mathrm{Gyr}$) and retain most of their metal-enriched ejecta ($η\sim 0$), consistent with high-redshift dusty star-forming galaxies (DSFGs). However, our model favours moderately active progenitors with typical star-formation rates (SFRs) of $200-400 \, \mathrm{M_\odot \, yr^{-1}}$, matching recently identified `NIRCam-dark' galaxies more closely than the broader DSFG population. Sustained starbursts ($\mathrm{SFR} \gtrsim 1000 \, \mathrm{M_\odot \, yr}^{-1}$) 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 ($Δt_\mathrm{SF} \sim 0.6 - 1 \, \mathrm{Gyr}$). 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.