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In the three-dimensional parameter space defined by velocity dispersion,effective radius (R_e), and effective surface brightness (I_e), early-typegalaxies are observed to populate a two-dimensional fundamental plane (FP) withfinite thickness. In Paper III of this series, we showed that the thickness ofthe FP is predominantly due to variations in the stellar mass surface density(Sigma_*) inside the effective radius R_e. These variations representdifferences in the dark matter fraction inside R_e (or possibly differences inthe initial mass function) from galaxy to galaxy. This means that galaxies donot wind up below the FP at lower surface brightness due to the passive fadingof their stellar populations; they are structurally different. Here, we showthat these variations in Sigma_* at fixed dynamical mass (M_dyn) are linked todifferences in the galaxy stellar populations, and therefore to differences intheir star formation histories. We demonstrate that the ensemble of stellarpopulation and Sigma_* variations through the FP thickness can be explained bya model in which early-type galaxies at fixed M_dyn have their star formationtruncated at different times. The thickness of the FP can therefore beinterpreted as a sequence of truncation times. Galaxies below the FP haveearlier truncation times for a given M_dyn, resulting in lower Sigma_*, olderages, lower metallicities in both [Fe/H] and [Mg/H], and higher [Mg/Fe]. Weshow that this model is quantitatively consistent with simple expectations forchemical enrichment in galaxies. We also present fitting functions forluminosity-weighted age, [Fe/H], [Mg/H], and [Mg/Fe] as functions of the FPparameters velocity dispersion, R_e, and I_e. These provide a new tool forestimating the stellar population properties of quiescent early-type galaxiesfor which high-quality spectra are not available.

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