Some effects of galaxy structure and dynamics on the Fundamental Plane

We examine the effects on the Fundamental Plane (FP) of structural departures from an R¼ galaxy light profile. We also explore the use of spatial (i.e., volumetric) as well as projected galaxy parameters. We fit the Sersic R1/n law to the V-band light profiles of 26 E/S0 Virgo galaxies, where n is a shape parameter that allows for structural differences amongst the profiles. The galaxy light profiles show a trend of systematic departures from a de Vaucouleurs R¼ law, in the sense that n increases with increasing effective half-light radius Re. This results in Re, and the associated mean surface brightness within this radius, having systematic biases when constructed using an R¼ law. Adjustments to the measured velocity dispersion are also made, based upon the theoretical velocity dispersion profile shapes of the different R1/n light profiles, constructed assuming spherical symmetry and isotropic pressure support. We construct the FP for the case when structural homology is assumed (specifically, an R¼ law is fitted to all galaxies) and central velocity dispersions, σ0, are used. The plane we obtain is Re ∝ σ01.33±0.10Σe−0.79±0.11 where Σe is the mean surface brightness within the projected effective radius Re. This agrees with the FP obtained by others, and departs from the virial theorem expectation R ∝ σ2Σ− We find that allowing for broken structural homology through fitting R1/n profiles (with n a free parameter), but still using central velocity dispersions, actually increases the departure of the observed FP from the virial plane — the increase in effective radius with galaxy luminosity (and n) is overbalanced by an associated decrease in the mean surface brightness. In examining the use of spatial quantities and allowing for the different velocity dispersion profiles corresponding to the observed light profiles, we find that use of the spatial velocity dispersion at the spatial half-light radius decreases the departure of the observed FP from the virial plane. (Use of the spatial half-light radius and mean surface brightness term has no effect on the FP, as they are constant multiples of their projected values.) Through use of the Jeans hydrodynamical equation, we convert the projected central aperture velocity dispersion, σ0, into the infinite aperture velocity dispersion, σtot,n (which is equal to one-third of the virial velocity dispersion). Using both the R1/n fit and σtot,n we obtain Re,n ∝ σtot,n1.44±0.11Σe,n−0.93±0.08. Making the fullest allowance for broken structural homology thus brings the observed FP closer to the virial plane, with the exponent of the surface brightness term consistent with the virial expectation.