Dissecting the Red Sequence. IV. The Role of Truncation in the Two-Dimensional Family of Early-Type Galaxy Star Formation Histories

In the three-dimensional parameter space defined by velocity dispersion, effective radius (R_e), and effective surface brightness (I_e), early-type galaxies are observed to populate a two-dimensional fundamental plane (FP) with finite thickness. In Paper III of this series, we showed that the thickness of the FP is predominantly due to variations in the stellar mass surface density (Sigma_*) inside the effective radius R_e. These variations represent differences in the dark matter fraction inside R_e (or possibly differences in the initial mass function) from galaxy to galaxy. This means that galaxies do not wind up below the FP at lower surface brightness due to the passive fading of their stellar populations; they are structurally different. Here, we show that these variations in Sigma_* at fixed dynamical mass (M_dyn) are linked to differences in the galaxy stellar populations, and therefore to differences in their star formation histories. We demonstrate that the ensemble of stellar population and Sigma_* variations through the FP thickness can be explained by a model in which early-type galaxies at fixed M_dyn have their star formation truncated at different times. The thickness of the FP can therefore be interpreted as a sequence of truncation times. Galaxies below the FP have earlier truncation times for a given M_dyn, resulting in lower Sigma_*, older ages, lower metallicities in both [Fe/H] and [Mg/H], and higher [Mg/Fe]. We show that this model is quantitatively consistent with simple expectations for chemical enrichment in galaxies. We also present fitting functions for luminosity-weighted age, [Fe/H], [Mg/H], and [Mg/Fe] as functions of the FP parameters velocity dispersion, R_e, and I_e. These provide a new tool for estimating the stellar population properties of quiescent early-type galaxies for which high-quality spectra are not available.