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4.4.1 Elliptical Galaxies
The surface brightness radial profiles of elliptical galaxies are in general
reasonably well described by de Vaucouleurs, or , law, first
introduced by [de Vaucouleurs 1948]
|
(4.6) |
where the effective surface brightness is labelled with an additional ``''
because in our model this quantity, unlike the effective radius, will in
general be different for E and D galaxies.
This law has succeeded in reproducing, with a remarkable accuracy, the
profiles of quite a few E galaxies. For instance, [Capaccioli et al. 1990] found
that the fit of the surface brightness radial profile of the nearby
standard elliptical NGC 3379 give residuals smaller than 0.08 mag over
a 10 magnitude range. [Makino et al. 1990], however, found from dynamical
arguments that the law bore little physical significance, though it
is the best-fitting function, and that laws with in the range
3-10 gave almost as good fits for a range of of about 100.
More recently, [Caon et al. 1993] showed that the best-fitting correlates
with the galaxy linear effective radius and luminosity, while [Andredakis et al. 1995]
found that the light profiles of the bulges of disk galaxies, which are also
usually modelled with an law, are in fact best-fitted by
profiles with an correlating with the galaxy morphological type.
Nevertheless, the empirical fitting function given by Equation 4.6
is useful for characterizing the global properties of galaxies, and
by that token in this study elliptical galaxies and bulges of disk galaxies
will both be modelled with laws.
On a magnitude scale, Equation 4.6 becomes
|
(4.7) |
where is the effective surface brightness of Es expressed in
mag/arcsec. This latter quantity can be expressed as function
of and , and thus, via Equation 4.3, of only, obtaining
|
(4.8) |
Values of are given in Table 4.5.
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Mattia Vaccari
2000-12-05