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 three 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 R 1/4 model parameters for the effective radii ( R e,4 ) and the mean surface brightness within this radius (Σ e,4 ) and using central velocity dispersion (CVD) measurements (σ 0 ), gave a relation described by R e, 4 ∝σ 0 1.10±0.14 Σ e,4 −0.55±0.09 . Using Sersic R 1/ n light‐profile model parameters and the projected infinite‐aperture velocity dispersion (σ tot, n ), derived from application of the Jeans equation to the observed intensity profiles, gave an ‘improved’ FP described by the relation R e, n ∝σ tot, n 1.37±0.16 Σ e, n −0.76±0.05 . This result, based on independent data, supports the previous finding by Graham & Colless 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 R e,4 ∝σ 0 1.19±0.21 Σ e,4 −0.60±0.11 and R e, n ∝σ tot, n 1.72±0.24 Σ e, 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 seven ellipticals that had published CVD measurements. Treating the range of structural and dynamical profiles present in this sample produced a FP given by the relation R e, n ∝σ tot, n 2.03±0.78 Σ e, n −1.07±0.30 , in tantalizing agreement with the plane expected from the virial theorem, but with discouragingly large errors caused by the small sample size. Similarly to Virgo, the perpendicular rms residual about this plane is 0.050 dex. The FP was also constructed with the purpose of using it as a distance indicator, achieved by minimizing the distance‐dependent quantity log R against the distance‐independent quantities Σ and log σ. 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, whereas 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 three‐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.