  We perform population synthesis modelling of a magnitude-limited sample of
4391 Luminous Red Galaxies selected from the Sloan Digital Sky Survey Data
Release 4 (SDSS DR4). We fit measured spectral indices using a large library of
high resolution spectra, covering a wide range of metallicities and assuming an
exponentially decaying star-formation rate punctuated by bursts, to obtain
median-likelihood estimates for the light-weighted age, metallicity, stellar
mass and extinction for the galaxies. The ages lie in the range 4-10 Gyr,
peaking near 6 Gyr, with metallicities in the range -0.4<[Z/H]<0.4, peaking at
[Z/H] ~ 0.2. Only a few per cent of the spectra are better fit allowing for a
burst in addition to continuous star-formation. The total stellar masses of all
the galaxies are confined to a very narrow range. Our results broadly agree
with those of previous groups using an independent population synthesis code.
We find, however, that our choice in priors results in ages 1-2 Gyr smaller,
decreasing the peak star formation epoch from z=2.3 to z=1.3. We develop a
metal evolution model incorporating stochastic star-formation quenching
motivated by recent attempts to solve the `anti-hierarchical' formation problem
of ellipticals. Two scenarios emerge, a closed box with an effective stellar
yield of 0.26, and an accreting box with an effective stellar yield of 0.10.
Both scenarios require an IMF weighted towards massive stars and characteristic
star-formation quenching times of about 100 Myr, the expected lifetime of
luminous QSOs. The models predict an anti-correlation between the age and mean
metallicity similar to that observed.
