Properties of luminous red galaxies in the Sloan Digital Sky Survey

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.