Probing galaxy evolution through the internal colour gradients, the Kormendy relations and the Photometric Plane of cluster galaxies at z ~ 0.2

We present a detailed analysis of the photometric properties of galaxies in the cluster A 2163B at redshift $z \sim 0.2$. R-, I- and K-band structural parameters, (half light radius ${R_{\rm e}}$, mean surface brightness $\mathrm{\langle \mu \rangle_e}$ within ${R_{\rm e}}$ and Sersic index ${n}$) are derived for $N \sim 60$ galaxies, and are used to study their internal colour gradients. For the first time, we use the slopes of optical-NIR Kormendy relations to study colour gradients as a function of galaxy size, and we derive the Photometric Plane at $z\sim 0.2$ in the K band. Colour gradients are negligible at optical wavelengths, and are negative in the optical-NIR, amounting on average to $\rm -0.48 \pm 0.06$. This result is in agreement with our previous measurements of colour gradients at intermediate redshifts, and imply a metallicity gradient in galaxies of ${\sim}0.2~\rm dex$ per radial decade. The analysis of the Kormendy relation suggests that its slope increases from the optical to the NIR, implying that colour gradients do not vary or even do become less steep in more massive galaxies. Such a result is not simply accomodated within a monolithic collapse scenario, while it can be well understood within a hierarchical merging framework. Finally, we derive the first NIR Photometric Plane at $ z \sim 0.2$, accounting for both the correlations on the measurement uncertainties and the selection effects. The Photometric Plane at $ z \sim 0.2$ is consistent with that at $z \sim 0$, with an intrinsic scatter significantly smaller than the Kormendy relation but larger than the Fundamental Plane