The D N − σ and Fundamental Plane Relations as Distance Indicators of Early Type Galaxies in the Virgo and Fornax Clusters

We investigate the properties of early-type galaxies as distance indicators by applying the D n – σ , Fundamental Plane (FP), and log( m ) – log r e relations to a complete and fairly homogeneous sample of galaxies members of the Virgo and Fornax clusters. The relative mean distance of the two clusters can be derived with an accuracy up to ∼ 3% provided that the internal kinematics of the galaxies is taken into account and a correct statistical approach is used. The residuals of the D n – σ and FP relationships do not correlate with many structural and geometrical parameters of the galaxies: the mean effective surface brightness, the total luminosity, the average ellipticity and the Fourier coefficient a 4 of the isophotes, and, the exponent m of the r 1/ m law which parametrizes the shape of the light profiles. On the other hand, the kinematics of the galaxies affect both relations producing residuals that correlate with the maximum rotation velocity V max and the ( V/σ ) ratio. Once confirmed by future more accurate observations, this effect would introduce a sistematic bias in the distance determination of the clusters; a problem difficult to manage if the internal kinematics of the cluster members is unknown.