Some effects of galaxy structure and dynamics on the Fundamental Plane.   II. A Virgo-Fornax distance modulus
  The influence of broken structural homology, and the implied broken dynamical homology, is examined for the Fundamental Plane (FP). A bisector method of linear regression was applied, in 3-dimensions, to derive the best FP and a bootstrapping procedure has been used to estimate the associated uncertainties. For 25 E and S0 Virgo galaxies, the `standard' FP, constructed using R^{1/4} model parameters for the effective radii (R_{e,4}) and the mean surface brightness within this radius (Sigma_{e,4}) and using central velocity dispersion measurements (sigma_0), gave a relation described by R_{e,4}~sigma_{0}^{1.10+/-0.14}Sigma_{e,4}^{-0.55+/-0.09}. Using Sersic R^{1/n} light profile model parameters and the computed velocity dispersion within an aperture of infinite radius (sigma_{tot,n}) gave an `improved' FP described by the relation R_{e,n}~sigma_{tot,n}^{1.37+/-0.16}Sigma_{e,n}^{-0.76+/-0.05}. Upon removal of the known S0 galaxies from the sample, the above planes were observed to change to R_{e,4}~sigma_{0}^{1.19+/-0.21}Sigma_{e,4}^{-0.60+/-0.11} and R_{e,n}~sigma_{tot,n}^{1.72+/-0.24}Sigma_{e,n}^{-0.74+/-0.09}. The perpendicular rms residuals about these planes are 0.084 and 0.050 dex, respectively. A similar analysis of the Fornax cluster produced a FP given by the relation R_{e,n}~sigma_{tot,n}^{2.03+/-0.78}Sigma_{e,n}^{-1.07+/-0.30}, in tantalizing agreement with the plane expected from the virial theorem, but with discouragingly large errors due to the small sample size of only 7. Similarly to Virgo, the perpendicular rms residuals about this plane is 0.050 dex. A Virgo-Fornax distance modulus was computed using Working-Hotelling confidence bands. The `standard' FP parameters gave a value of 0.45+/-0.16 mag, where as the `improved' FP parameters gave a value of 0.25+/-0.12 mag. 
Alister W. Graham