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(7.40)

interstellar 7-radiation found by satellites in the 1960s and 1970s. Protons impinging on molecular clouds produce more localized sources of 7-rays. Observations by the COS-B satellite and, subsequently, the Compton Gamma Ray Observatory, were useful as an independent means of tracing the distribution of H2 in giant cloud complexes.

The observed energies of cosmic rays span an enormous range, from 10 to 1014 MeV. Note that a single proton of 1014 MeV has the kinetic energy of a well-hit tennis ball. From about 103 to 109 MeV, the received particle flux, $CR(E), follows a power law: $CR(E) ~ E-2 7. Here, the flux is measured per unit energy E (see Figure 7.1). At higher energies than those shown in the figure, the flux declines as E-3. Conversely, $CR(E) flattens and then turns over as E falls below about 103 MeV. This turnover is an effect of the solar wind, that both sweeps out incoming particles and creates a periodic modulation of the flux in step with the solar activity cycle.

Where do cosmic rays come from and how do they attain such high energies? With regard to the latter issue, all the particles are electrically charged and thus subject to magnetic deflection.

Figure 7.1 The observed particle flux in cosmic rays, as measured per unit solid angle and per unit energy. The flux is plotted as a function of E, the energy per particle. The straight line is a power law with slope —2.7.

3 4 5 Energy log E

3 4 5 Energy log E

Figure 7.1 The observed particle flux in cosmic rays, as measured per unit solid angle and per unit energy. The flux is plotted as a function of E, the energy per particle. The straight line is a power law with slope —2.7.

Indeed, it is the magnetic field within the solar wind that prevents low-energy particles from reaching the Earth. A time-invariant field cannot alter a proton's energy, since the Lorentz force is perpendicular to the velocity vector. A changing magnetic field, however, generates an electric field that can do work. Thus, as E. Fermi pointed out in 1949, cosmic rays could be accelerated by the fields frozen into a turbulent interstellar plasma. Fifteen years earlier, W. Baade and F. Zwicky had proposed that supernovae constitute the basic source of cosmic rays. In recent decades, these two ideas have merged in a fruitful way. It is now believed that cosmic rays with energies up to 109 MeV are produced by particle acceleration within the magnetized shocks created by supernova remnants as they plow through the interstellar medium. More energetic particles are probably extragalactic in origin.

The energy density of cosmic rays within our Galaxy is about 0.8 eV cm-3, close to that associated with a typical interstellar magnetic field of 3 |G. This similarity suggests that the Galactic field is strong enough to contain, at least temporarily, the cosmic rays produced from within. Any charged particle entering a magnetized region executes circular motion. The size of the gyroradius, rB, for a particle of mass m, charge q, and velocity v in a field of magnitude B is

where y is the Lorentz factor (1 — v2/c2)~1/2. Even for a 106 MeV proton in a 3 |G field, rB is only of order 1015 cm, far less than Galactic dimensions. Thus, the orbit is a tight helix, in which the velocity is closely confined in the plane perpendicular to the field, but is unconstrained in the parallel direction (Figure 7.2). Irregularities in the field change the orientation of these helical orbits and lead to a gradual drift of the particles out of the Galaxy. From measurements

Figure 7.2 Helical motion of a cosmic-ray proton in a magnetic field. The gyroradius rB is indicated.

of the isotopic abundances of heavier nuclei, we know that the mean confinement time is of order 107 yr. Diffusion across field lines also accounts for the high degree of isotropy seen in the cosmic rays entering our solar system.

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