The Faber-Jackson relation for early-type galaxies: Dependence on the magnitude range

TL;DR

This study investigates how the parameters of the Faber-Jackson relation for early-type galaxies vary with the magnitude range and luminosity, revealing that these parameters are significantly affected by selection effects and the distribution shape.

Contribution

It demonstrates that the Faber-Jackson relation parameters depend on magnitude range and luminosity, highlighting the importance of considering these factors in comparative studies.

Findings

Faber-Jackson parameters vary systematically with magnitude range.

Fluctuations in slope are statistically significant and not due to chance.

Selection effects and distribution shape influence the relation's parameters.

Abstract

We take a sample of early-type galaxies from the Sloan Digital Sky Survey (SDSS-DR7, $\sim$ 90 000 galaxies) spanning a range of approximately 7 $mag$ in both $g$ and $r$ filters and analyse the behaviour of the Faber-Jackson relation parameters as functions of the magnitude range. We calculate the parameters in two ways: i) We consider the faintest (brightest) galaxies in each sample and we progressively increase the width of the magnitude interval by inclusion of the brighter (fainter) galaxies (increasing-magnitude-intervals), and ii) we consider narrow-magnitude intervals of the same width ($\Delta M = 1.0$ $mag$) over the whole magnitude range available (narrow-magnitude-intervals). Our main results are that: i) in both increasing and narrow-magnitude-intervals the Faber-Jackson relation parameters change systematically, ii) non-parametric tests show that the fluctuations in the values of the slope of the Faber-Jackson relation are not products of chance variations. We conclude that the values of the Faber-Jackson relation parameters depend on the width of the magnitude range and the luminosity of galaxies within the magnitude range. This dependence is caused, to a great extent by the selection effects and because the geometrical shape of the distribution of galaxies on the $M - \log (\sigma_{0})$ plane depends on luminosity. We therefore emphasize that if the luminosity of galaxies or the width of the magnitude range or both are not taken into consideration when comparing the structural relations of galaxy samples for different wavelengths, environments, redshifts and luminosities, any differences found may be misinterpreted.