  This analysis uses spectra of ~16,000 nearby SDSS quiescent galaxies to track
variations in galaxy star formation histories along and perpendicular to the
Fundamental Plane (FP). We sort galaxies by their FP properties (sigma, R_e,
and I_e) and construct high S/N mean galaxy spectra that span the breadth and
thickness of the FP. From these spectra, we determine mean luminosity-weighted
ages, [Fe/H], [Mg/H], and [Mg/Fe] based on single stellar population models
using the method described in Graves & Schiavon (2008). In agreement with
previous work, the star formation histories of early-type galaxies are found to
form a two-parameter family. The major trend is that mean age, [Fe/H], [Mg/H],
and [Mg/Fe] all increase with sigma. However, no stellar population property
shows any dependence on R_e at fixed sigma, suggesting that sigma and not
dynamical mass (M_dyn ~ sigma^2 R_e) is the better predictor of past star
formation history. In addition to the main trend with sigma, galaxies also show
a range of population properties at fixed sigma that are strongly correlated
with surface brightness residuals from the FP, such that higher surface
brightness galaxies have younger mean ages, higher [Fe/H], higher [Mg/H], and
lower [Mg/Fe] than lower-surface brightness galaxies. These latter trends are a
major new constraint on star-formation histories.
