2-2
b
Velocity dispersions
Stars
in bound systems must obey the virial theorem. The theorem, together
with the measured velocity distribution, can be used to measure
the
mass distribution in a bound system, such as elliptical galaxies
or globular
clusters. With some exceptions, velocity dispersion estimates
of elliptical
galaxies do not match the predicted velocity dispersion from the
observed
mass distribution, even assuming complicated distributions of
stellar orbits.
As with galaxy rotation curves, the obvious way to resolve the
discrepancy
is to postulate the existence of non-luminous matter.
2-2
c
Galaxy clusters
Galaxy
clusters are particularly important for dark matter studies since
their masses can be estimated in three independent ways:
From the scatter in radial velocities of the galaxies within clusters
From X-rays emitted by hot gas in the clusters. From the X-ray
energy
spectrum and flux, the gas temperature and density can be estimated,
hence
giving the pressure; assuming pressure and gravity balance determines
the
cluster’s mass profile.
Gravitational lensing (usually of more distant galaxies) can measure
cluster
masses without relying on observations of dynamics (e.g., velocity).
Generally, these three methods are in reasonable agreement that
dark matter
outweighs visible matter by approximately 5 to 1.
2-2
d
Gravitational lensing
One of
the consequences of general relativity is massive objects (such
as a
cluster of galaxies) lying between a more distant source (such
as a quasar)
and an observer should act as a lens to bend the light from this
source. The
more massive an object, the more lensing is observed.
Strong lensing is the observed distortion of background galaxies
into arcs
when their light passes through such a gravitational lens. It
has been observed
around many distant clusters including Abell 1689. By measuring
the distortion geometry, the mass of the intervening cluster can
be obtained.
In the dozens of cases where this has been done, the mass-to-light
ratios
obtained correspond to the dynamical dark matter measurements
of clusters.
Lensing can lead to multiple copies of an image. By analyzing
the
distribution of multiple image copies, scientists have been able
to deduce
and map the distribution of dark matter around the MACS J0416.1-2403
galaxy cluster.
Weak gravitational lensing investigates minute distortions of
galaxies,
using statistical analyses from vast galaxy surveys. By examining
the apparent
shear deformation of the adjacent background galaxies, the mean
distribution of dark matter can be characterized. The mass-to-light
ratios
correspond to dark matter densities predicted by other large-scale
structure
measurements. Dark matter does not bend light itself; mass (in
this case
the mass of the dark matter) bends spacetime. Light follows the
curvature
of spacetime, resulting in the lensing effect.
