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Low-Energy Cosmic RaysCosmic rays, broadly defined, are charged particles from outside the solar system. Thesecan be electrons, protons, or ions; the latter two dominate the number observed. They arecalled cosmic “rays” because initially it was thought that they are a type of photon. Study oflow-energy cosmic rays tells us about the composition and density of the interstellar mediumand, importantly, about the formation and dispersal of heavy elements in the galaxy. Studyof the highest energy cosmic rays, which we will discuss in the next lecture, may revealnew physics and even if it doesn’t, it tells us a lot about acceleration processes and theintergalactic medium.The observation of cosmic rays has challenges quite different from the observation ofphotons. Ask class: what are some of the differences? A major one is that, being chargedparticles, cosmic rays are deflected by magnetic fields. These fields can be in the intergalacticor interstellar medium, or in the solar system itself. This deflection limits the availableangular resolution for high energy cosmic rays, and renders any angular resolution impossiblebelow a certain energy, since the average deflection angle exceeds 180◦. Another difference isthat many nuclei are radioactive. If the half-life is comparable to or less than the propagationtime in the rest frame of the nucleus, such radioactive nuclei will decay. This means thatby measuring isotopic composition one has a clock indicating how long the cosmic rays havebeen propagating. A third difference is that because nuclei are complex particles (unlikephotons), a collision can split the nucleus (this is called “spallation”). By knowing thespallation cross section at a given energy, one therefore has an indication of the total columndepth of material traversed. A fourth difference has to do with the information available:for a photon, the information is its energy, direction, and polarization. For a cosmic ray,the information is the energy and the type of particle, although type of particle is tough tomeasure at high energies.The energy spectra of cosmic raysThe general spectrum of cosmic rays, from 1 GeV per nucleon on up, is an amazinglygood power law (see Figure 1). The number flux between energies E and E+dE is N(E)dE =KE−xdE, with x = 2.5 − 2.7 over most of the range. Around a total energy of 1015eV,the spectrum becomes slightly steeper (higher x), and around 1018−19eV it becomes slightlyshallower again. These are therefore referred to as the “knee” and the “ankle” of the cosmicray distribution.Below about 1 GeV per nucleon, the number flux drops dramatically below the extendedpower law. Ask class: assuming that there is no true drop in the population, what effectmight explain this? At a low enough energy, the solar wind and its associated magnetic fieldFig. 1.— The cosmic ray energy spectrum, with energy on the horizontal axis in units of eV. Fromhttp://cosmic.phys.columbia.edu/images/crspectrum.gifis able to prevent the propagation of charged particles. This is therefore an artifact. Ofcourse, there also has to be a real cutoff at some point (a power law extended indefinitelywould mean an infinite number of particles!), but this means that, as always in astronomy,one has to be cautious about inferences based on raw data. There is always an interpretationinvolved.This leads us again into the issue of propagation through a region with magnetic fields.Ask class: given two otherwise identical particles, which is affected more, one with moremomentum or one with less? The one with less momentum. Ask class: given two otherwiseidentical particles, which is affected more, one with more charge or one with less? The onewith more charge. In both cases, it’s a question of the gyroradius of the particle in themagnetic field. In fact, it turns out that there is a quantity called the rigidity, R = pc/ze(where p is the relativistic three-momentum and ze is the charge), which uniquely determinesthe dynamics of a charged particle in a magnetic field. For two particles with the samevelocity and hence the same Lorentz factor, R = (A/z)(mpγvc/e), so the rigidity dependsonly on A/z. Ask class: what is the approximate value of A/z, for elements less massivethan iron? About 2, so different particles with the same energy per nucleon behave similarly.The elemental abundance of cosmic raysThis is where contact is made with the synthesis of elements in stars, particularly heavyelements and those formed in r-process neutron capture in supernovae. The net result is thatelemental abundances are not very different from those of typical abundances in the SolarSystem. The major difference is that light elements (lithium, beryllium, and boron) aredramatically overabundant in cosmic rays compared to the Solar System, and that cosmicrays of elements somewhat lighter than iron are somewhat overabundant. Both of theseexcesses are thought to be due to spallation. Another way to get at the properties of cosmicrays is to look at different isotopes of the same element. The cross section for spallation isnot going to be very different between different isotopes, so this gives a better idea of theoriginal composition before any spallation. In addition, as mentioned earlier, many isotopes(especially those produced only by spallation) are radioactive, so they act as clocks. Aparticularly good clock is10Be, which has a half-life of 3.9 × 106yr, which is comparable totypical diffusion times through the disk of the Galaxy. There tends to be an overabundanceof neutron rich isotopes in cosmic rays compared to their abundance in the Solar System,but the overabundance factor isn’t huge: e.g.,25Mg/24Mg is about 1.6 times greater than inthe Solar System.The isotropy and energy density of cosmic raysThe local magnetic field in the interplanetary medium is about 10−5G. This meansthat protons with γ = 103, i.e., energies of about 1 TeV, have gyroradii that are rg=3 × 1011γ(B/10−4G) = 3 × 1014cm, or about 20 AU. Therefore, protons with energies thisgreat or greater can maintain their directions once in the Solar region.In addition, highly relativistic particles interact with the Earth’s atmosphere to producean air shower, as discussed earlier in the course. The shower is composed of relativistic parti-cles that themselves preserve the original direction fairly well, so ground-based observationscan determine the direction of the cosmic ray with reasonable accuracy, as well as its


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