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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 2 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 3 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 vB (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 vt (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 4 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 1.50108 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.