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Cosmic Rays and Plasma Astrophysics
R. L. Lysak, Spring, 2016
I. Discovery of Cosmic Rays; Spectrum and Composition
Discovery of cosmic rays (Longair 1.10)
The late 1800’s was an extremely active period in physics, leading to the observation of
fundamental new particles, the theoretical foundations of electromagnetic theory and the seeds of
quantum mechanics and relativity. Various types of “rays” were found, many using “Crooke’s
tubes,” an evacuated tube in which a high voltage could be applied. Röntgen found in 1895 that
photographic plates near a Crooke’s tube became exposed, even if wrapped in opaque material.
The particles responsible for this exposure were called “X-rays.” In 1897, J. J. Thomsen
measured “cathode rays,” now known as electrons, and determined by deflecting them in electric
and magnetic fields that they were about 2000 times lighter than the hydrogen atom. Becquerel
discovered natural radioactivity in 1896, and Pierre and Marie Curie isolated a number of
radioactive elements. Rutherford classified the radiation according to its ability to penetrate
matter. -rays (now known to be Helium nuclei) were the least penetrating, while -rays
(energetic electrons) were more penetrating. Villard identified an even more penetrating
radiation known as -rays, which are high-energy photons.
Cosmic rays were discovered when experimenters measured the radioactivity at higher
altitudes in order to avoid contamination by the natural radioactivity from the Earth. Wulf
ascended the Eiffel Tower, and noted that the background of -rays did not fall off as quickly as
expected from atmospheric absorption. Hess and Kolhörster made separate manned balloon
flights in 1912-3 and found that the radiation intensity actually increased above a few kilometers
in altitude, first suggesting an extraterrestrial origin. The term “cosmic ray” was introduced by
Millikan in 1925. With the invention of the Geiger-Müller tube in 1929 and the introduction of
coincidence techniques, the identification of cosmic rays as heavy charged particles was made.
This conclusion followed from an experiment in which blocks of lead or gold were placed
between two Geiger counters, and it was noted that very frequently the two counters registered
events at the same time. If the cosmic rays were -rays, the signal in the Geiger counter could
only be due to secondary electrons, which would not penetrate the absorber.
Basic observational facts of the cosmic radiation (Kulsrud 12.1; Longair 15.1-3)
Using the various techniques outlined above, a wealth of information has been gathered
on the spectrum, composition, and isotropy of the cosmic rays. Cosmic rays have been detected
from 107 eV/nucleon to over 1020 eV/nucleon. At lower energies, the interaction of these
particles with the interplanetary magnetic field impedes their propagation to the Earth. Particles
at energies below about 1 GeV/nucleon are in fact modulated by the solar wind, with more
particles being observed during solar minimum than during solar maximum as the Sun goes
through its 11-year solar cycle of magnetic activity. At energies between 109 and 1014
eV/nucleon, the spectrum of the cosmic rays follows a power law distribution, in which the flux
of cosmic ray particles per unit energy (measured in unit of particles per area per time per
steradian per MeV) is proportional to E–s where s ranges from 2.5-2.7. At higher energies, from
1015-1020 eV/nucleon, the spectrum becomes steeper, with the power law index increasing to
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3.08. In the transitional range, 1014-1015 eV/nucleon, the spectrum flattens slightly, producing a
bump or “knee” in the spectrum. The origin of this knee is not well understood. The spectrum
of electrons is somewhat steeper, with a spectral index of 3.3 at energies above 10 GeV. Below
this energy the electrons are modulated by the solar wind. This steepening is likely due to the
energy loss of the electrons due to synchrotron radiation.
The chemical composition of the solar wind is another issue of intense study. It is useful
to compare the composition in the cosmic rays to that in the solar system. The composition of
the solar atmosphere can be directly determined from the lines in the solar spectrum. Additional
information on the solar system abundances come from studies of meteorites, which are believed
to be representative of the composition in the early solar system (as opposed to Earth, for
example, where billions of years of chemical reactions have influenced the composition). These
studies have been combined to come up with a distribution of the various elements in the solar
system. Of course, hydrogen and helium are the most abundant elements, and are primarily
produced in the early formation of the universe. The next three elements, lithium, beryllium and
boron are strongly depleted in the solar system. It should be noted that one might imagine
making 8Be from the combination of two 4He nuclei. However, this isotope is unstable, and so it
requires conditions of high temperature and density for a process called the “triple-” process to
occur, in which three 4He nuclei combine to form 12C. Additional reactions with -particles can
then give successive nuclei such as 16O and 20Ne. Note that this process preferentially produces
nuclei with even atomic numbers, and indeed, the abundances of even-numbered elements are
generally larger than odd-numbered elements.
Nuclear burning in stellar interiors can proceed up to the production of 56Fe, which is the
most stable of the heavy nuclei, having the peak binding energy per nucleon. Above this point,
nuclear fusion is no longer energetically favorable. Heavier elements are thought to be produced
only in supernova explosions, where neutrons can be rapidly added to increase the mass of the
nuclei. Thus, elements heavier than iron are much less abundant in the solar system than the
lighter elements.
The composition measured in cosmic rays has many of the same features, including the
odd-even asymmetry and the peak at iron. However, there are some major differences. The
cosmic rays are much more abundant in lithium, beryllium and boron than the solar system as a
whole. In addition, the elements below iron, such as scandium, titanium, vanadium, chromium
and manganese, are also depleted in the solar system but not so much so in the cosmic rays. The
difference between the abundances of the odd and even elements is also less in the cosmic rays.
As a final point, it should be noted that the abundances of elements heavier than iron are similar
in the cosmic rays as in the solar system.
A curious feature of the cosmic ray composition is the presence of a large flux of 4He at
energies below 60 MeV/nucleon, which is referred to as the “anomalous 4He component.” This
component is strongly modulated with the solar cycle, being stronger during solar minimum. It
has been suggested that these anomalous cosmic rays are produced in the outer heliosphere since
the strength of this component increases with distance from the Sun.
A final fact that should be mentioned about the cosmic rays is that the total energy of the
cosmic rays can be estimated from the knowledge of their spectrum, with the result that the
density of cosmic rays with energies greater than 1 GeV is about 1 eV/cm3. It is interesting to
note that the energy densities of the cosmic microwave background, in starlight, and in
interstellar magnetic fields are also the same order of magnitude. Whether the correspondence of
these four energy densities is a coincidence or whether it has physical significance is a matter of
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debate.
Charged particle motion in magnetic fields (Kulsrud 2.1; Longair 7.1)
When the direction of propagation of the cosmic rays is considered, it should be noted
that low energy cosmic rays are bent by the interplanetary magnetic field and so information
about their source direction is lost. The equation of motion of a charged particle in a magnetic
field is given by the Lorentz force equation:
dp
 qv  B
(1.1)
dt
where the relativistic momentum p  mv and   1/ 1  v 2 / c 2 . Note that since the force is
perpendicular to the velocity, the magnetic field does no work on the charged particle and so its
energy, and therefore , is a constant, since the energy is given by E = γmc2. Then this equation
can be written as
dv
q

vB
(1.2)
dt m
A first point to note is that there is no acceleration in the direction of the magnetic field, and so
the component of velocity parallel to B is constant. If we assume that the magnetic field does
not change in time, a little bit of algebra reveals that
d 2v
  2 v 
(1.3)
dt 2
where the perpendicular subscript means that we are only considering the perpendicular
components. Here we have introduced the gyrofrequency
qB

(1.4)
m
which is the frequency at which the particle gyrates around the magnetic field. For example, if
the magnetic field is in the z direction, the velocity can be written as
v x  v sin  t   
v y  v cos  t   
v z  v
(1.5)
where v v|| and  are constants determined by the initial conditions. Integrating these equations
to find the position, we have
x  x0  a cos  t   
y  y0  a sin  t   
z  z0  vt
(1.6)
Thus, the particle’s path is a helix with its axis along the magnetic field and a radius given by
v
mv p
a  

(1.7)

qB
qB
This quantity is called the gyroradius. It is customary in cosmic ray studies to write the
gyroradius in terms of a rigidity R  p c / q , which is essentially the perpendicular energy per
charge, and is commonly expressed in gigavolts. Note that in the non-relativistic limit, where
p  2mE , electrons have a smaller gyroradius than protons of the same energy. On the other
hand, in the relativistic limit, p = E/c and the gyroradius is just proportional to the energy in
perpendicular motion of the particle, regardless of mass.
These considerations indicate that if a cosmic ray particle has a gyroradius small in size
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compared with the solar system, it is not possible to determine the direction from which this
particle originated. The gyroradius of a 1012 eV proton in the interplanetary field of about 1 nT
(i.e., 10–9 T) is about 20 AU (1 AU is the distance from the Sun to the Earth, which is 1.50108
km). Thus, particles below this energy will be strongly deflected by the magnetic field and their
direction will be lost. However, it is found that the anisotropy of the cosmic rays is very small
up to an energy of about 1016 eV. At this energy, the particles have a gyroradius of 10 parsecs in
the 0.1 nT galactic magnetic field. The isotropy of the cosmic rays can be further influenced by
scattering processes, as we shall see later. At higher energy, the anisotropy of the cosmic rays
becomes larger. More of these particles come from the general direction of the north galactic
pole rather than in the plane of the galaxy. This suggests an extragalactic origin for these cosmic
rays. It is interesting to note that this direction is toward the center of the local supercluster of
galaxies, indicating that these highest energy cosmic rays may be produced throughout this
supercluster.