Graham, Alister; Colless, Matthew

### Description

We examine the effects on the Fundamental Plane (FP) of structural departures from an R^1/4 galaxy light profile. We also explore the use of spatial (i.e., volumetric) as well as projected galaxy parameters. We fit the Sersic R^1/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 R^1/4 law, in the sense that n...[Show more] increases with increasing effective half-light radius R_e. This results in R_e, and the associated mean surface brightness within this radius, having systematic biases when constructed using an R^1/4 law. Adjustments to the measured velocity dispersion are also made, based upon the theoretical velocity dispersion profile shapes of the different R^1/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 R^1/4 law is fitted to all galaxies) and central velocity dispersions, sigma_0, are used. The plane we obtain is R_e~sigma^1.33+/-0.10 _0Sigma^-0.79+/-0.11 _e, where Sigma_e is the mean surface brightness within the projected effective radius R_e. This agrees with the FP obtained by others, and departs from the virial theorem expectation R~sigma^2Sigma^-1. We find that allowing for broken structural homology through fitting R^1/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, sigma_0, into the infinite aperture velocity dispersion, sigma_tot,n (which is equal to one-third of the virial velocity dispersion). Using both the R^1/n fit and sigma_tot,n we obtain R_e,n~ sigma^1.44+/-0.11_tot,n Sigma^-0.93+/-0.08_e,n . 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.

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