Sources of scatter in the fundamental plane and the Dn-sigma relation

On the basis of new photometric data for early-type galaxies in the Coma Cluster we have determined the relation log rₑ_ = α log σ + bₑ_+ c known as the fundamental plane (FP). The scatter in the FP is equivalent to 11% uncertainty on distances. The residuals for the FP show no dependence on other available photometric and geometric parameters. Analysis of a nearby sample of ellipticals indicates that differences in dynamical structure for these galaxies may cause a scatter in the FP equivalent to 10% uncertainty on the distances. Thus, it may be possible to decrease the scatter by using the mean velocity dispersion within half the effective radius instead of the central velocity dispersion. The scatter in the Dₙ_-σ relation for the Coma Cluster galaxies is 17%, much higher than the 11% scatter for the FP. The residuals depend on the mean surface brightness. A similar result was obtained by Lucey, Bower, & Ellis, who used a linear fit in a restricted interval in ₑ_ in order to incorporate the effect in the distance determination. The Dₙ_-σ relation is an approximation to the FP, as first noted by Dressler et al. and Phillips. We find that the dependence on ₑ_ can be understood (without restrictions in ₑ_) as originating from this approximation. The FP projects into a slightly tilted and bended surface in the log Dₙ_-log σ-ₑ_ space. The available data in literature support this interpretation. Under the assumption that the FP is linear and the galaxies follow a de Vaucouleurs r¹/4^ law, the Dₙ_-σ relation can cause systematic errors of the order 10%-15% on distance determinations. It is possible that some existing discrepancies between distances determined from the Dₙ_-σ relation and from the Tully-Fisher method or the surface brightness fluctuation method are caused by the systematic errors of the Dₙ_-σ relation. There is no evidence that the large-scale motions in the universe derived by Lynden-Bell et al. on the basis of the Dₙ_-σ relation are severely affected by the systematic errors. We conclude that the FP is to be preferred as a distance indicator.