and Cosmology

2.4 Kinematics of the Galaxy
center (if the gas follows the Galactic rotation), so that
the largest radial velocity will occur for gas closest to
the tangent point, which will be identified with v r,max (l).
Figure 2.19 shows the observed intensity profile of the
12 CO line as a function of the Galactic longitude, from
which the rotation curve for R < R 0 can be read off.
With the tangent point method, applied to the 21-cm
line of neutral hydrogen or to radio emission lines
of molecular gas, the rotation curve of the Galaxy
inside the Solar orbit can be measured.
Rotation Curve for R>R 0 . The tangent point
method cannot be applied for R > R 0 because for linesof-sight
at π/2 R 0 does
not decline outwards (see Fig. 2.20) as we would expect
from the distribution of visible matter in the Milky
Way. Both the stellar density and the gas density of
the Galaxy decline exponentially for large R – e.g., see
(2.34). This steep radial decline of the visible matter
density should imply that M(R), the mass inside R, is
nearly constant for R R 0 , from which a velocity profile
like V ∝ R −1/2 would follow, according to Kepler’s
law. However, this is not the case: V(R) is virtually constant
for R > R 0 , indicating that M(R) ∝ R. Thus, to
get a constant rotational velocity of the Galaxy much
more matter has to be present than we observe in gas
and stars.
The Milky Way contains, besides stars and gas,
an additional component of matter that dominates
the mass at R R 0 but which has not yet been
observed directly. Its presence is known only by its
gravitational effect – hence, it is called dark matter.
In Sect. 3.3.3 we will see that this is a common phenomenon.
The rotation curves of spiral galaxies are flat
at large radii up to the maximum radius at which it can
be measured; spiral galaxies contain dark matter.
63
Fig. 2.19. 12 CO emission of molecular gas
in the Galactic disk. For each l, the intensity
of the emission in the l − v r plane is plotted,
integrated over the range −2 ◦ ≤ b ≤ 2 ◦
(i.e., very close to the middle of the plane).
Since v r depends on the distance along each
line-of-sight, characterized by l, thisdiagram
contains information on the rotation
curve of the Galaxy as well as on the spatial
distribution of the gas. The maximum
velocity at each l is rather well defined and
forms the basis for the tangent point method