Some effects of galaxy structure and dynamics on the Fundamental Plane
Authors: Alister Graham & Matthew Colless
Abstract:
We examine the effects on the Fundamental Plane (FP) of structural departures
from an 
galaxy light
profile. We also explore the use of spatial (i.e. volumetric) as well as
projected galaxy parameters. We fit the Sersic
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 law,
in the sense that n increases with increasing effective half-light
radius 
.
This results in ,
and the associated mean surface brightness within this radius, having
systematic biases when constructed using an
law.
Adjustments to the measured velocity dispersion are also made, based
upon the theoretical velocity dispersion profile shapes of the different
light profiles,
constructed assuming spherical symmetry and isotropic pressure support.
We construct the FP for the case when structural homology is assumed
(specifically, an
law is fitted to all galaxies) and central
velocity dispersions, 
,
are used. The plane we obtain is
,
where 
is the mean
surface brightness within the projected
effective radius .
This agrees with the FP obtained by others and departs from the virial theorem
expectation 
.
We find that allowing for broken structural homology through fitting
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 over-balanced 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
decreased the departure of the observed FP from the virial plane.
(Use of the spatial half-light radius and mean surface brightness term had 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,
,
into the infinite aperture velocity dispersion,
(which is equal to one-third of the virial velocity dispersion).
Using both the fit and
we obtain
.
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.