and Cosmology

3. The World of Galaxies
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the potential well, and therefore the mass. Both methods
reveal that ellipticals are also surrounded by a dark halo.
The weak gravitational lens effect, which we will discuss
in Sect. 6.5.2 in a different context, offers another
way to determine the masses of galaxies up to very large
radii. With this method we cannot study individual galaxies
but only the mean mass properties of a galaxy
population. The results of these measurements confirm
the large size of dark halos in spirals and in ellipticals.
Correlations of Rotation Curves with Galaxy Properties.
The form and amplitude of the rotation curves
of spirals are correlated with their luminosity and their
Hubble type. The larger the luminosity of a spiral, the
steeper the rise of v(R) in the central region, and the
larger the maximum rotation velocity v max . This latter
fact indicates that the mass of a galaxy increases with
luminosity, as expected. For the characteristic values of
the various Hubble types, one finds v max ∼ 300 km/s
for Sa’s, v max ∼ 175 km/s for Sc’s, whereas Irr’s have
amuchlowerv max ∼ 70 km/s. For equal luminosity,
v max is higher for earlier types of spirals. However,
the shape (not the amplitude) of the rotation curves
of different Hubble types is similar, despite the fact that
they have a different brightness profile as seen, for instance,
from the varying bulge-to-disk ratio. This point
is another indicator that the rotation curves cannot be
explained by visible matter alone.
These results leave us with a number of obvious questions.
What is the nature of the dark matter? What are
the density profiles of dark halos, how are they determined,
and where is the “boundary” of a halo? Does the
fact that galaxies with v rot 100 km/s have no prominent
spiral structure mean that a minimum halo mass
needs to be exceeded in order for spiral arms to form?
Some of these questions will be examined later, but
here we point out that the major fraction of the mass of
(spiral) galaxies consists of non-luminous matter. The
fact that we do not know what this matter consists of
leaves us with the question of whether this invisible
matter is a new, yet unknown, form of matter. Or is the
dark matter less exotic, normal (baryonic) matter that
is just not luminous for some reason (for example, because
it did not form any stars)? We will see in Chap. 4
that the problem of dark matter is not limited to galaxies,
but is also clearly present on a cosmological scale;
furthermore, the dark matter cannot be baryonic. A currently
unknown form of matter is, therefore, revealing
itself in the rotation curves of spirals.
3.3.4 Stellar Populations and Gas Fraction
The color of spiral galaxies depends on their Hubble
type, with later types being bluer; e.g., one finds B −
V ∼ 0.75 for Sa’s, 0.64 for Sb’s, 0.52 for Sc’s, and 0.4
for Irr’s. This means that the fraction of massive young
stars increases along the Hubble sequence towards later
spiral types. This conclusion is also in agreement with
the findings for the light distribution along spiral arms
where we clearly observe active star-formation regions
in the bright knots in the spiral arms of Sc’s. Furthermore,
this color sequence is also in agreement with the
decreasing bulge fraction towards later types.
The formation of stars requires gas, and the mass
fraction of gas is larger for later types, as can be measured,
for instance, from the 21-cm emission of HI, from
Hα and from CO emission. Characteristic values for the
ratio 〈 〉
M gas /M tot are about 0.04 for Sa’s, 0.08 for Sb’s,
0.16 for Sc’s, and 0.25 for Irr’s. In addition, the fraction
of molecular gas relative to the total gas mass is smaller
for later Hubble types. The dust mass is less than 1% of
the gas mass.
Dust, in combination with hot stars, is the main
source of far-infrared (FIR) emission from galaxies.
Sc galaxies emit a larger fraction of FIR radiation than
Sa’s, and barred spirals have stronger FIR emission than
normal spirals. The FIR emission arises due to dust being
heated by the UV radiation of hot stars and then
reradiating this energy in the form of thermal emission.
A prominent color gradient is observed in spirals:
they are red in the center and bluer in the outer regions.
We can identify at least two reasons for this trend. The
first is a metallicity effect, as the metallicity is increasing
inwards and metal-rich stars are redder than metal-poor
ones, due to their higher opacity. Second, the color gradient
can be explained by star formation. Since the gas
fraction in the bulge is lower than in the disk, less star
formation takes place in the bulge, resulting in a stellar
population that is older and redder in general. Furthermore,
it is found that the metallicity of spirals increases
with luminosity.
Abundance of Globular Clusters. The number of
globular clusters is higher in early types and in more