The Kormendy relation for early-type galaxies Dependence on the magnitude range

Aims. Previous studies have indicated that faint and bright early-type galaxies (ETGs) present different coefficients and dispersions for their Kormendy relation (KR). A recently published paper states that the intrinsic dispersion of the KR depends on the magnitude range within which the galaxies are contained, therefore we investigate here whether the magnitude range also has an influence on the values of the coefficients of the KR: alpha (zero point) and beta (slope). If the values of the KR coefficients depend on the magnitude range, and this fact is not considered when performing comparisons of different galaxy samples, the differences which might be found may be misinterpreted. Methods. We perform an analysis of the KR coefficients for 4 samples of galaxies, which contain an approximate total of 9400 ETGs in a relatively wide magnitude range ( similar to 6 mag). We calculate the values of the KR coefficients in two ways: i) we consider the faintest galaxies in each sample and we progressively increase the width of the magnitude interval by inclusion of the brighter galaxies (increasing magnitude intervals); and ii) we consider narrow magnitude intervals of the same width (Delta M = 1.0 mag) over the whole magnitude spectrum available (narrow magnitude intervals). We also perform simulations of the distribution of galaxies in the log(r(e)) - (e) plane and compare the KR defined by the simulations with that obtained from the real galaxy samples. Results. The main results we find are as follows: i) in both increasing and narrow magnitude intervals the KR coefficients change systematically as we consider brighter galaxies; ii) non-parametric tests show that the fluctuations in the values of slope of the KR are not products of chance variations and that there is evidence of an underlying trend; and iii) this trend suggest a maximum of the slope around absolute magnitude M-B similar to -18 +/- 1. Conclusions. We conclude that the values of the KR coefficients depend on the width of the magnitude range and the brightness of galaxies within the magnitude range. This dependence is due to the fact that the distribution of galaxies in the log(r(e)) - (e) plane depends on luminosity and that this distribution is not symmetrical, that is, the geometric shape of the distribution of galaxies in the log(r(e)) - (e) plane plays an important role in the determination of the values of the coefficients of the KR.