and Cosmology

2. The Milky Way as a Galaxy
52
is measured, so the orientation of dust particles cannot
be random, rather it must be coherent on large
scales. Such a coherent alignment is provided by
a large-scale magnetic field, whereby the orientation
of dust particles, measurable from the polarization
direction, indicates the (projected) direction of the
magnetic field.
• The Zeeman effect. The energy levels in an atom
change if the atom is placed in a magnetic field. Of
particular importance in the present context is the fact
that the 21-cm transition line of neutral hydrogen is
split in a magnetic field. Because the amplitude of
the line split is proportional to the strength of the
magnetic field, the field strength can be determined
from observations of this Zeeman effect.
• Synchrotron radiation. When relativistic electrons
move in a magnetic field they are subject to the
Lorentz force. The corresponding acceleration is perpendicular
both to the velocity vector of the particles
and to the magnetic field vector. As a result, the electrons
follow a helical (i.e., corkscrew) track, which is
a superposition of circular orbits perpendicular to the
field lines and a linear motion along the field. Since
accelerated charges emit electromagnetic radiation,
this helical movement is the source of the so-called
synchrotron radiation (which will be discussed in
Fig. 2.11. Distribution of dust in the Galaxy, derived from
a combination of IRAS and COBE sky maps. The northern
Galactic sky in Galactic coordinates is displayed on the left,
the southern on the right. We can clearly see the concentration
of dust towards the Galactic plane, as well as regions
with a very low column density of dust; these regions in the
sky are particularly well suited for very deep extragalactic
observations
more detail in Sect. 5.1.2). This radiation, which is
observable at radio frequencies, is linearly polarized,
with the direction of the polarization depending on
the direction of the magnetic field.
• Faraday rotation. If polarized radiation passes
through a magnetized plasma, the direction of the
polarization rotates. The rotation angle depends
quadratically on the wavelength of the radiation,
Δθ = RM λ 2 . (2.37)
The rotation measure RM is the integral along the
line-of-sight towards the source over the electron
density and the component B ‖ of the magnetic field
in direction of the line-of-sight,
RM = 81 rad
cm 2
∫D
0
dl
pc
n e
cm −3 B ‖
G . (2.38)
The dependence of the rotation angle (2.37) on λ allows
us to determine the rotation measure RM, and
thus to estimate the product of electron density and
magnetic field. If the former is known, one immediately
gets information about B. By measuring the
RM for sources in different directions and at different
distances the magnetic field of the Galaxy can be
mapped.