The Fundamental Plane for early-type galaxies. Dependence on the magnitude range

Studying 3 samples of early-type galaxies, which include approximately 8800 galaxies and cover a relatively ample magnitude range ($<\mathrm{\Delta }M>$ $\sim 5$ $mag$), we find that the coefficients as well as the intrinsic dispersion of the Fundamental Plane depend on the width of the magnitude range within which the galaxies are distributed. We analyse this dependence and the results show that it could be due to the fact that the distribution of galaxies in the space defined by the variables $\log (r_e),<\mu {>}_e,\log (\sigma )$ depends on the luminosity.