7.4. GALAXIES 445
rotating around the center of the galaxy. The Sun is 3× 104 ly from the nucleus, it moves at
300km/s and has a period of 2× 108 years.
The halo of the Milky Way is spherically-shaped, centered onthe nucleus of the galaxy,
and has the radius of 10^5 ly. The halo consists of less gas and roughly 120 globular clusters,
each of which has hundreds of thousands of stars and moves in an elliptical orbit around the
nucleus of the galaxy. The halo does not rotate with the disk.
6.Galaxy clusters.Galaxies are not uniformly distributed in the Universe, butaggregate
in clusters of different size. Clusters of galaxies are the largest known astronomical systems
bound by gravitational attraction. They form dense regionsin the large scale structure of our
Universe. The clusters are associated with much larger, non-gravitationally bounded groups,
called superclusters.
The great regular clusters of galaxies are spherically-shaped, have roughly thousands of
galaxies, almost all of which are ofEandS0 types. The regular clusters of galaxies are
typically 5× 106 ly in radius, and have no clear outer boundaries. Clusters are locked as
their galaxies held together by mutual gravitational attraction. However, their velocities are
too large, exceeding 10^3 km/s, for them to remain gravitationally bound by their mutual at-
tractions. It implies the presence of either an additional invisible mass component, or an
additional attractive force besides the Newtonian gravity. This is the so called dark matter
phenomenon. Astronomical observations manifest that there are large amounts of intergalac-
tic gas which is very hot between 10^7 ∼ 108 K. The total mass of the gas is greater than
that of all galaxies in the cluster. The wind of intergalactic gas streaming through these fast
moving galaxies is strong enough to strip away their interstellar gas. This explains why theE
andS0 types of galaxies have less gas because their gas has been swept out by intergalactic
winds.
The other galaxy clusters are irregular. They have various sizes ranged from thousands
of members to a few tens of members. The smaller clusters are also called galaxy groups.
For example, our galaxy is a member of a galaxy group known as the local group which
possesses about 40 galaxies. The irregular clusters lack spherical symmetry in shape and
contain a mixture of all types of galaxies.
7.4.2 Galaxy dynamics
Galaxies are mainly either spiral or elliptical. Each galaxy possesses a compact core, known
as galactic nucleus, which is supermassive and spherical-shaped. Thus, the galactic dynamic
model is defined in an annular domain:
r 0 <r<r 1 ,wherer 0 is the radius of galaxy nucleus andr 1 the galaxy radius. In the following we develop
models for spiral and elliptical galaxies, and provide their basic consequences on galactic
dynamics.
1.Spiral galaxies.Spiral galaxies are disc-shaped, as shown in Figure7.6. We model the
galaxy in a disc domain as
(7.4.1) D={x∈R^2 |r 0 <|x|<r 1 },