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). Requiring a symmetrical treatment of the FP variables, a bisector method of linear regression was applied, in 3-dimensions, to derive the best FP. A bootstrapping procedure has been used to estimate the uncertainties associated with the slope of the FP. For 25 E and S0 Virgo galaxies, the 'standard' FP, constructed using R1/4 model parameters for the effective radii (Re,4) and the mean surface brightness within this radius (Σe, 4) and using central velocity dispersion (CVD) measurements (σ0), gave a relation described by Re,4 ∝ σ0^1.10±0.14 Σe,4^−0.55±0.09. Using Sersic R1/n light profile model parameters and the projected, infinite aperture, velocity dispersion (σtot,n), derived from application of the Jeans equation to the observed intensity profiles, gave an 'improved' FP described by the relation Re,n ∝ σ^1.37±0.16 tot,n Σe,n^−0.76±0.05. This result, based on independent data, supports the previous finding by Graham & Colless (1997a) that assumptions of structural and dynamical homology are partly responsible for the departure of the observed FP from the plane expected by the virial theorem, which predicts R ∝ σ^2 Σ−1. Upon removal of the known S0 galaxies from the sample of Virgo galaxies, the above planes were observed to change to Re,4 ∝ σ 0 ^1.19±0.21Σe,4^−0.60±0.11 and Re,n ∝ σ- tot,n^1.72±0.24Σe,n^−0.74±0.09. The perpendicular rms residuals about these planes are 0.084 and 0.050 dex, respectively. The Fornax cluster was similarly treated, although removal of the S0 galaxies left a sample of only 7 ellipticals which had published CVD measurements. Treating the range of structural and dynamical profiles present in this sample produced a FP given by the relation Re,n ∝ σ tot,n^2.03±0.78Σe,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. Similarly to Virgo, the perpendicular rms residuals about this plane is 0.050 dex. The FP was also constructed with the purpose of using it as a distance indicator, achieved by minimising the distance-dependent quantity logR against the distance-independent quantities Σ and log σ. A Virgo-Fornax distance modulus was computed using Working-Hotelling confidence bands (Feigelson & Babu 1992). 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. However, a full treatment of the uncertainties on the FP slopes, derived through a bootstrapping procedure of the 3-dimensional FP data set, revealed that the analytical expressions for the uncertainties on the estimated distance moduli, given above, should be increased by a factor of ~5.