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We examine the colour–magnitude relation of brightest cluster galaxies (BCGs) in the Sloan Digital Sky Survey (SDSS). The colour–magnitude and colour–velocity dispersion relations of the BCGs are flatter in slope, by factors of 2 or more, than those of non-BCG early-type galaxies of similar luminosity , while their colours at the half-light radius are mag redder. We investigate and compare radial colour gradients (which are usually negative) in these BCGs and a sample of 37 000 early-type galaxies, using a gradient estimator based on the ratio of de Vaucouleurs effective radii in g and r passbands, . The mean colour gradient of BCGs is flatter (by 23 per cent) than for other E/S0 galaxies of similar luminosity. The colour gradients in early-type galaxies are stronger at intermediate luminosity than at low or the highest luminosities, and tend to decrease with increasing velocity dispersion (σ). In non-BCG E/S0s, colour gradients increase for larger effective radii (up to 10–12 kpc), and are negatively correlated with , the mass density and stellar age. However, gradients can be reduced or inverted (positive) for post-starburst galaxies at the youngest ages. In BCGs, these trends are absent and the mean colour gradient remains at a relatively low level ( by our measure) whatever the other properties of the galaxies. The redder half-light radius colours of the BCGs can be explained by their slightly greater ages combined with flatter radial colour gradients. We discuss possible explanations in terms of spheroidal galaxies initially having a colour gradient positively correlated with luminosity and positively correlated with large radius and/or low density. Subsequently, elliptical-elliptical ‘dry’ mergers progressively reduce colour gradients, towards a low but non-zero value. This has occurred a greater number of times during the formation histories of the most massive E/S0s, and to by far the greatest degree in the BCGs. [ABSTRACT FROM AUTHOR]

We select a sample of 70 378 E/S0 (early-type) galaxies at 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–σ relation (CσR). Both the CMR and CσR evolve bluewards with increasing redshift, approximately in agreement with passive evolution models with age ∼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 CσR depends on the aperture in which the colour was defined, the slope does not, suggesting that colour gradients are correlated with residuals from the relation. Since these residuals are age indicators, our findings suggest that colour gradients depend on the age of the stellar population. [ABSTRACT FROM AUTHOR]

From a sample of early-type galaxies from the Sloan Digital Sky Survey, we measured the traditional Fundamental Plane in the and z bands. We then replaced luminosity with stellar mass, and measured the ‘stellar mass’ Fundamental Plane. The Fundamental Plane, , steepens slightly as one moves from shorter to longer wavelengths: the orthogonal fit has slope in the g band and 1.47 in z, with a statistical random error of ∼0.02. However, systematic effects can produce larger uncertainties, of the order of ∼0.05. The Fundamental Plane is thinner at longer wavelengths: it has an intrinsic scatter of 0.062 dex in g and 0.054 dex in z. We have clear evidence that the scatter is larger at small galaxy sizes/masses; at large masses, measurement errors account for essentially all of the observed scatter (about 0.04 dex), suggesting that the Plane is rather thin for the very massive galaxies. The Fundamental Plane steepens further when luminosity is replaced with stellar mass to 1.54 or 1.63 when stellar masses are estimated from broad-band colours or from spectra, respectively. The intrinsic scatter also reduces further to 0.048 dex on average. Since colour and stellar-mass-to-light ratio are closely related, this explains why colour can be thought of as the fourth Fundamental Plane parameter. However, the slope of the stellar mass Fundamental Plane remains shallower than the value of 2 associated with the virial theorem. This is because the ratio of dynamical to stellar mass increases at large masses: . This scaling is the edge-on projection of the stellar mass κ-space. The face-on view suggests that there is an upper limit to the stellar density for a given dynamical mass, and this decreases at large masses: . All these trends can be used to constrain early-type galaxy formation models. We also study how the estimated coefficients a and B of the Plane are affected by other selection effects, whether in apparent or in absolute quantities. For example, if low-luminosity objects are missing from the sample, and one does not account for this, then a and B are both biased low from their true values. If objects with small velocity dispersions are missing, then a is biased high, although this matters more for the orthogonal than the direct-fitted quantities. These biases are seen in Fundamental Planes which have no intrinsic curvature, so the observation that a and B scale with L and σ is not, by itself, evidence that the Plane is warped. On the other hand, we show that the Plane appears to curve sharply downwards at the small-size/mass end, and more gradually downwards as one moves towards larger sizes/masses. Whereas the drop at small sizes is real, most of the latter effect is due to correlated errors. [ABSTRACT FROM AUTHOR]