and Cosmology

2. The Milky Way as a Galaxy
64
Fig. 2.20. Rotation curve of the Milky
Way. Inside the “Solar circle”, that is at
R < R 0 , the radial velocity is determined
quite accurately using the tangent point
method; the measurements outside have
larger uncertainties
The nature of dark matter is thus far unknown; in
principle, we can distinguish two totally different kinds
of dark matter candidates:
• Astrophysical dark matter, consisting of compact
objects – e.g., faint stars like white dwarfs, brown
dwarfs, black holes, etc. Such objects were assigned
the name MACHOs, which stands for “MAssive
Compact Halo Objects”.
• Particle physics dark matter, consisting of elementary
particles which have thus far escaped detection
in accelerator laboratories.
Although the origin of astrophysical dark matter would
be difficult to understand (not least because of the
baryon abundance in the Universe – see Sect. 4.4.4 – and
because of the metal abundance in the ISM), a direct
distinction between the two alternatives through observation
would be of great interest. In the following
section we will describe a method which is able to
probe whether the dark matter in our Galaxy consists of
MACHOs.
2.5 The Galactic Microlensing Effect:
The Quest for Compact
Dark Matter
In 1986, Bohdan Paczyński proposed to test the possible
presence of MACHOs by performing microlensing
experiments. As we will soon see, this was a daring idea
at that time, but since then such experiments have been
carried out. In this section we will mainly summarize
and discuss the results of these searches for MACHOs.
We will start with a description of the microlensing effect
and then proceed with its specific application to the
search for MACHOs.
2.5.1 The Gravitational Lensing Effect I
Einstein’s Deflection Angle. Light, just like massive
particles, is deflected in a gravitational field. This is one
of the specific predictions by Einstein’s theory of gravity,
General Relativity. Quantitatively it predicts that
a light beam which passes a point mass M at a distance
ξ is deflected by an angle ˆα, which amounts to
ˆα = 4 GM
c 2 ξ
. (2.71)
The deflection law (2.71) is valid as long as ˆα ≪ 1,
which is the case for weak gravitational fields. If we
now set M = M ⊙ , R = R ⊙ in the foregoing equation,
we obtain
ˆα ⊙ ≈ 1 . ′′ 74
for the light deflection at the limb of the Sun. This deflection
of light was measured during a Solar eclipse in
1919 from the shift of the apparent positions of stars