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Previous studies of the stellar mean metallicity and [Mg/Fe] values ofmassive elliptical (E)~galaxies suggest that their stars were formed in a veryshort timescale which cannot be reconciled with estimates from stellarpopulation synthesis (SPS) studies and with hierarchical-assembly. Applying thepreviously developed chemical evolution code, GalIMF, which allows anenvironment-dependent stellar initial mass function (IMF) to be applied in theintegrated galaxy initial mass function (IGIMF) theory instead of an invariantcanonical IMF, the star formation timescales (SFT) of E galaxies arere-evaluated. The code's uniqueness lies in it allowing the galaxy-wide IMF andassociated chemical enrichment to evolve as the physical conditions in thegalaxy change. The calculated SFTs become consistent with the independent SPSresults if the number of type Ia supernovae (SNIa) per unit stellar massincreases for more massive E~galaxies. This is a natural outcome of galaxieswith higher star-formation rates producing more massive star clusters, spawninga larger number of SNIa progenitors per star. The calculations show E~galaxieswith a stellar mass $\approx 10^{9.5} M_\odot$ to have had the longest meanSFTs of $\approx2\,$Gyr. The bulk of more massive E~galaxies were formed faster(SFT$\,\approx 1\,$Gyr) leading to domination by M~dwarf stars and largerdynamical mass-to-light ratios as observed, while lower-mass galaxies tend tolose their gas supply more easily due to their shallower potential andtherefore also have similarly-short mean SFTs. This work achieves, for thefirst time, consistency of the SFTs for early-type galaxies betweenchemical-enrichment and SPS modelling and leads to an improved understanding ofhow the star formation environment may affect the total number of SNIa per unitstellar mass formed.

Downsizing revised: Star formation timescales for elliptical galaxies with an environment-dependent IMF and number of SNIa