THE RELATIVE DISTANCES TO THE VIRGO, FORNAX AND COMA CLUSTERS OF GALAXIES THROUGH THE D-N-SIGMA AND THE FUNDAMENTAL PLANE RELATIONS

We derive the relative distances to the Virgo, Fornax and Coma cluster s of galaxies by applying the D-n-sigma and the Fundamental Plane (FP) relations to the data of the homogeneous samples of early-type galaxi es studied by Caon et al., Lucey et al. and Jorgensen et al. The two d istance indicators give consistent results, the relative distance modu li to Fornax and Coma with respect to Virgo being Delta mu(FV) = (0.45 +/- 0.15) mag and Delta mu(CV) = (3.55 +/- 0.15) mag respectively, Th e formal error on Delta mu may be as small as 0.07 mag (similar to 3 p er cent in distance), provided that all the sources of bias are taken into account and a correct statistical approach is used. Unfortunately , much of the actual uncertainty in the relative distance of the clust ers (similar to 12-15 per cent) is due to the existence of systematic departures in the measurements of the velocity dispersions among the v arious data sets, and to the corrections for aperture effects. The abo ve result for the Fornax cluster is supported by the L-sigma-mu relati on and, with lesser accuracy, by the log(m)-log(r(e)) relation. Our va lue of Delta mu(FV) is in fair agreement with the one derived using pl anetary nebulae and SNe Ia, while it is in open contrast to that comin g from surface brightness fluctuations, the luminosity function of gl obular clusters, and the infrared Tully-Fisher relation. In our data C oma appears slightly nearer than indicated by the other distance indic ators, but now a better agreement with the Tully-Fisher relation seems to exist. We show that for the galaxies of the Virgo and Fornax clust ers the residuals of the D-n-sigma relation do not correlate with the effective surface brightness (mu)(e). There is also no correlation of the residuals of the D-n-sigma and FP relations with the total luminos ity of the galaxies, or with the ellipticity, or with the isophotal sh ape parameter alpha(4). Instead, a correlation seems to exist with the maximum rotation velocity of the galaxies, V-m, with the (V/sigma) ra tio, and with the exponent m of the r(1/m) fit to the major axis light profiles of the galaxies. If confirmed, these effects introduce a sys tematic bias in both relations when used as distance indicators.