Fundamental Astronomy

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18. Galaxies
elliptical, normal spiral and S0 galaxies are in the ranges
re = 1–10 kpc and Ie corresponds to 20–23 magnitudes
per square arc second.
Although de Vaucouleurs’ law is a purely empirical
relation, it still gives a remarkably good representation
of the observed light distribution. However, in the outer
regions of elliptical galaxies, departures may often occur:
the surface brightness of dwarf spheroidals often
falls off more rapidly than (18.8), perhaps because the
outer parts of these galaxies have been torn off in tidal
encounters with other galaxies. In the giant galaxies of
type cD, the surface brightness falls off more slowly
(see Fig. 18.10). It is thought that this is connected with
their central position in clusters of galaxies.
Although the isophotes in elliptical galaxies are ellipses
to a good approximation, their ellipticities and
the orientation of their major axes may vary as a function
of radius. Different galaxies differ widely in this
respect, indicating that the structure of ellipticals is
not as simple as it might appear. In particular, the fact
that the direction of the major axis sometimes changes
within a galaxy suggests that some ellipticals may not
be axially symmetric in shape.
From the distribution of surface brightness, the threedimensional
structure of a galaxy may be inferred as
explained in *Three-Dimensional Shape of Galaxies.
Fig. 18.10. The distribution
of surface brightness
in E and cD galaxies. Ordinate:
surface magnitude,
mag/sq.arcsec; abscissa:
(radius [kpc]) 1/4 . Equation
(18.8) corresponds to
a straight line in this representation.
It fits well with
an E galaxy, but for type cD
the luminosity falls off more
slowly in the outer regions.
Comparison with Fig. 18.11
shows that the brightness
distribution in S0 galaxies
behaves in a similar fashion.
cD galaxies have often been
erroneously classified as S0.
(Thuan, T.X., Romanishin,
W. (1981): Astrophys. J.
248, 439)
The relation (18.8) gives a brightness profile which is
very strongly peaked towards the centre. The real distribution
of axial ratios for ellipticals can be statistically
inferred from the observed one. On the (questionable)
assumption that they are rotationally symmetric, one
obtains a broad distribution with a maximum corresponding
to types E3–E4. If the true shape is not
axisymmetric, it cannot even statistically be uniquely
determined from the observations.
Discs. A bright, massive stellar disc is characteristic
for S0 and spiral galaxies, which are therefore called
disc galaxies. There are indications that in some ellipticals
there is also a faint disc hidden behind the
bright bulge. In the Milky Way the disc is formed by
population I stars.
The distribution of surface brightness in the disc is
described by the expression
I(r) = I0 e −r/r0 . (18.9)
Figure 18.11 shows how the observed radial brightness
distribution can be decomposed into a sum
of two components: a centrally dominant bulge
and a disc contributing significantly at larger radii.
The central surface brightness I0 typically corresponds
to 21–22 mag./sq.arcsec, and the radial scale