The cluster of galaxies A 2163 B at z ∼ 0 . 2 II – Colour gradients , r e – < μ > e relations , and the Photometric Plane . ⋆

We present the structural parameters (half light radius r e , mean surface brightness < µ > e within r e and Sersic index n) in the R, I and K bands for N ∼ 60 galaxies in the cluster A 2163B at z ∼ 0.2. The structural parameters are used to estimate the internal colour gradients of bulge–dominated (n > 2) galaxies. For the first time, we perform a comparative optical/NIR analysis of the log r e –< µ > e relation, also known as Kormendy relation (KR), and derive the so-called Photometric Plane in the K band. Colour gradients are negligible at optical wavelengths, while are significantly negative in the optical-NIR, amounting on average to −0.48 ± 0.06. This result is in agreement with our previous measurements of colour gradients at intermediate redshifts, implying the presence of a metallicity gradient in galaxies of about −0.2 dex per radial decade. We derive unbiased estimates of the slope and of the zeropoint of the log r e –< µ > e relation in the R and K bands, respectively, and analyze the waveband dependence of these quantities by taking into account the role of the CM relation and of the colour gradients. We find that the optical–NIR variation of the KR slope implies that colour gradients do not vary with galaxy size or become less steep for galaxies of larger size. This result is in sharp contrast with what would be expected in the monolithic collapse scenario, while can be well understood in a hierarchical merging framework. Finally, we derive the NIR Photometric Plane (PHP) at z ∼ 0.2, attempting to correct both for the correlations between the uncertainties on the structural parameters and for the selection effects of the samples. We find that the PHP coefficients are consistent with those of the local relation and that its observed dispersion is similar to that of the 'spectroscopic' Fundamental Plane (FP), as discussed by Graham (2002). However, the 2 F. La Barbera et al.: Structural properties of A 2163B intrinsic scatter around the Photometric Plane could be significantly larger with respect to that of the FP, although smaller with respect to that of the KR.