The Star Formation Histories of Red-Sequence Galaxies, Mass-to-Light
  Ratios and the Fundamental Plane
  This paper addresses the challenge of understanding the typical star
formation histories of red sequence galaxies, using linestrength indices and
mass-to-light ratios as complementary constraints on their stellar age
distribution. We construct simple parametric models of the star formation
history that bracket a range of scenarios, and fit these models to the
linestrength indices of low-redshift cluster red-sequence galaxies. For giant
galaxies, we confirm the downsizing trend. We find, however, that this trend
flattens or reverses at sigma < 70 km/s. We then compare predicted stellar
mass-to-light ratios with dynamical mass-to-light ratios derived from the
Fundamental Plane (FP), or by the SAURON group. For galaxies with sigma ~ 70
km/s, models with a "frosting" of young stars and models with exponential star
formation histories have stellar mass-to-light ratios that are larger than
observed dynamical mass-to-light ratios by factors of 1.7 and 1.4,
respectively, and so are rejected. The SSP model is consistent with the FP, and
requires a modest amount of dark matter (20-30%) to account for the difference
between stellar and dynamical mass-to-light ratios. A model in which star
formation was "quenched" at intermediate ages is also consistent with the
observations. We find that the contribution of stellar populations to the
"tilt" of the FP is highly dependent on the assumed star-formation history: for
the SSP model, the tilt of the FP is driven primarily by stellar-population
effects. For a quenched model, two-thirds of the tilt is due to stellar
populations and only one third is due to dark matter or non-homology.
