Some Effects of Galaxy Structure and Dynamics on the Fundamental Plane. II
. A Virgo-Fornax distance modulus
Author: Alister Graham
Abstract:
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 
model parameters for the
effective radii ( 
) and the mean surface brightness within this
radius ( 
) and using central velocity dispersion
(CVD) measurements ( 
), gave a relation described by
.
Using Sersic 
light profile model parameters and the projected, infinite
aperture, velocity
dispersion ( 
), derived from application of the
Jeans equation to the observed intensity profiles, gave an `improved' FP
described by the relation
.
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
.
Upon removal of the known S0 galaxies from the sample of Virgo galaxies,
the above planes were observed to change to
and
.
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
,
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 
against
the distance-independent quantities 
and 
.
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.