Galaxies 203- Most of the dark matter in the Universe, or about two thirds of it, is not associ-
ated with groups and clusters of galaxies, but distributed in the space between
them in the form of massive dark clumps or as a smooth “ocean”. It is as yet
difficult to evaluate this proposal.
Clearly the physics in the Local Universe does not prove the existence of dark mat-
ter, rather it brings in new problems.
9.2 Galaxies
Spiral Galaxies. The spiral galaxies are stable gravitationally bound systems in
which matter is composed of stars and interstellar gas. Most of the observable mat-
ter is in a relatively thin disc, where stars and gas travel around the galactic center
on nearly circular orbits. Visible starlight traces velocity out to radial distances typi-
cally of the order of 10kpc, and interstellar gas out to 20–50kpc. The luminous parts
of galaxies, as evidenced by radiation of baryonic matter in the visible, infrared and
X-ray spectra, account only for훺lum< 0 .01.
By observing the Doppler shift of the integrated starlight and the radiation at
휆= 0 .21m from the interstellar hydrogen gas, one finds that spiral galaxies rotate.
If the circular velocity at radius푟is푣in a galaxy of mass푀, the condition for stability
is that the centrifugal acceleration should equal the gravitational pull:
푣^2
푟=
GM
푟^2
. (9.10)
In other words, the radial dependence of the velocity of matter rotating in a disc is
expected to follow Kepler’s law푣=
√
GM∕푟.
The surprising result for spiral galaxy rotation curves is, that the velocity does not
follow Kepler’s inverse-root law, but stays rather constant after attaining a maximum
at about 5kpc. The most obvious solution to this is that the galaxies are embedded in
extensive, diffuse halos of dark matter. In fact, to explain the observations that푣(푟)≈
constant the radial mass distribution푀(푟)must be proportional to푟and the radial
density profile is
휌(푟)∝푟−^2. (9.11)
Assuming that the disc-surface brightness is proportional to the surface density of
luminous matter, one derives a circular speed which is typically more than a factor of
three lower than the speed of the outermost measured points [5]. This implies that the
calculated gravitational field is too small by a factor of 10 to account for the observed
rotation.
There are only a few possible solutions to this problem. One is that the theory
of gravitation is wrong. It is possible to modify ad hoc Kepler’s inverse square law or
Newton’s assumption that퐺is a constant, but the corresponding modifications cannot
be carried out in the relativistic theory, and a general correlation between mass and
light remains. The modifications would have to be strong at large scales, and this
would greatly enhance cosmic shear, which is inconsistent with measurements.
Another possibility is that spiral galaxies have magnetic fields extending out to
regions of tens of kiloparsecs where the interstellar gas density is low and the gas