Spectral-based k-corrections and implications for the colour-magnitude relation of E/S0s and its evolution

We select a sample of 70 378 E/S0 (early-type) galaxies at 0 < z < 0.36 from the Sloan Digital Sky Survey (SDSS), excluding disc and star-forming galaxies. We estimate g and r magnitudes in the observer-and rest frames directly from the SDSS DR6 spectra; this provides an object-by-object estimate of the k-correction. Observer-frame colours can also be estimated from the imaging photometry. However, in this case, rest-frame colours, and hence k-corrections, must be inferred from fitting to data in other band passes as well as to stellar population synthesis models. There are small (a few 0.01 mag) discrepancies between the spectra and imaging photometry, particularly for galaxies with low signal-to-noise ratios in the spectra and more negative eclass spectral classifications. We correct for these, and then use the k-corrections from the spectra to study the evolution of the rest-frame colour-magnitude relation (CMR) and colour-sigma relation (C sigma R). Both the CMR and CsR evolve bluewards with increasing redshift, approximately in agreement with passive evolution models with age similar to 12 Gyr. The rate of evolution is sensitive to the k-corrections. Using k-corrections from the Coleman, Wu & Weedman (CWW) template spectrum, rather than the observed SDSS spectra, gives a CMR with much more evolution; k-corrections from Blanton & Roweis, which are based on fitting Bruzual & Charlot models with solar abundance ratios to the ugriz colours, give less/no evolution. However, the slope and zero-point of CMR depends on whether colours were defined in fixed physical or angular apertures, a consequence of the fact that the centres of these objects tend to be redder: the relation is steeper for fixed angular apertures. These colour gradients must be accounted for when estimating CMR evolution with fixed angular apertures. On the other hand, although the zero-point of the CsR depends on the aperture in which the colour was defined, the slope does not, suggesting that colour gradients are correlated with residuals from the sigma-M-r relation. Since these residuals are age indicators, our findings suggest that colour gradients depend on the age of the stellar population.