Precision photometry of early-type galaxies in the Coma and Virgo clusters: a test of the universality of the colour-magnitude relation - II. Analysis

We have undertaken a detailed comparison of the colours of early-type galaxies in the Virgo and Coma clusters. In Paper I (this issue), we presented our system of homogeneous U,V,J and K photometric measurements for these galaxies. In this paper, we use this data set to investigate the universality of the colour–magnitude correlation. Our work reassesses the anomaly noted by Aaronson, Persson & Frogel. Following these authors, we initially compare the relative distances of the two clusters derived from the L – σ and U – V and V – K colour–magnitude correlations. However, in contrast to their result, we find that all three relations give compatible relative distance moduli: Δmᵤ−ᵥ=4.01±0.20,Δmᵥ−ₖ=3.58±0.23, ΔmḺ−σ=3.62±0.16. A similar result is found by correlating the colours and velocity dispersions with photometric diameters. Again, we find that all three comparisons give consistent distance estimates: Δmᵤ−ᵥ=3.87±0.15, Δmᵥ−ₖ=3.42±0.21, ΔmḎ−σ=3.67±0.11, with a mean relative distance modulus of 3.69±0.08. These results show that the colour–magnitude relation has the same form in both Coma and Virgo. An alternative approach is to compare, the colours of the galaxies directly through the distance- independent correlation between colour and velocity dispersion. We find that the median colours are offset by −0.009±0.012(U−V), 0.005±0.016(V−K) and −0.038±0.012(J−K), with an estimated systematic error of 0.02, 0.03 and 0.04 mag in each case. All of these offsets are therefore consistent with there being no intrinsic difference between the colours of early-type galaxies in Virgo and Coma. We conclude that the colour–magnitude relation has the same form in both clusters, and hence can provide a reliable cosmic distance estimator for clusters of galaxies, giving relative distances accurate to ~ 20 per cent per galaxy.
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\nIn addition, our data constrain the intrinsic scatter of early-type galaxies about the mean colour–magnitude relation. We measure an rms scatter of typically 0.05 mag, of which ~ 0.03 mag can be accounted for by observational error. By examining the correlation of residuals, we show that this intrinsic variation is unlikely to be dominated by differences in the star formation histories of elliptical galaxies. We use the stellar population synthesis model of Bruzual to quantify the implications of this result. First, we present simple time-scale arguments to suggest that the spheroidal components of early-type galaxies are unlikely to have formed below a redshift of 2(q₀=0.5). Secondly, we show that our data are only marginally consistent with the strong bursts of star formation required to explain the spectra of galaxies in moderate-redshift clusters.