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. Studyof low-energy cosmic rays tells us about the composition and density of the interstellarmedium and, importantly, about the formation and dispersal of heavy elements in thegalaxy. Study of the highest energy cosmic rays, which we will discuss in the next lecture,may reveal new physics and even if it doesn’t, it tells us a lot about acceleration processesand the intergalactic medium.The observation of cosmic rays has challenges quite different from the observationof photons. Ask class: what are some of the differences? A major one is that, beingcharged particles, cosmic rays are deflected by magnetic fields. These fields can be in theintergalactic or interstellar medium, or in the solar system itself. This deflection limits theavailable angular resolution for high energy cosmic rays, and renders any angular resolutionimpossible below a certain energy, since the average deflection angle exceeds 180◦. Anotherdifference is that many nuclei are radioactive. If the half-life is comparable to or less thanthe propagation time in the rest frame of the nucleus, such radioactive nuclei will decay.This means that by measuring isotopic composition one has a clock indicating how long thecosmic rays have been propagating. A third difference is that because nuclei are complexparticles (unlike photons), a collision can split the nucleus (this is called “spallation”). Byknowing the spallation cross section at a given energy, one therefore has an indication of thetotal column depth of material traversed. A fourth difference has to do with the informationavailable: for a photon, the information is its energy, direction, and polarization. For acosmic ray, the information is the energy and the type of particle, although type of particleis tough to measure 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. 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 spectrumbecomes slightly steeper (higher x), and around 1018−19eV it becomes slightly shalloweragain. These are therefore referred to as the “knee” and the “ankle” of the cosmic raydistribution.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 magneticfield is 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 magneticfields. Ask class: given two otherwise identical particles, which is affected more, one withmore momentum or one with less? The one with less momentum. Ask class: given twootherwise identical particles, which is affected more, one with more charge or one withless? The one with more charge. In both cases, it’s a question of the gyroradius of theparticle in the magnetic field. In fact, it turns out that there is a quantity called therigidity, R = pc/ze (where p is the relativistic three-momentum and ze is the charge),which uniquely determines the dynamics of a charged particle in a magnetic field. For twoparticles with the same velocity and hence the same Lorentz factor, R = (A/z)(mpγvc/e),so the rigidity depends only on A/z. Ask class: what is the approximate value of A/z, forelements less massive than iron? About 2, so different particles with the same energy pernucleon 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 isthat elemental abundances are not very different from those of typical abundances in theSolar System. The major difference is that light elements (lithium, beryllium, and boron)are dramatically overabundant in cosmic rays compared to the Solar System, and thatcosmic rays of elements somewhat lighter than iron are somewhat overabundant. Both ofthese excesses are thought to be due to spallation. Another way to get at the propertiesof cosmic rays is to look at different isotopes of the same element. The cross section forspallation is not going to be very different between different isotopes, so this gives a betteridea of the original composition before any spallation. In addition, as mentioned earlier,many isotopes (especially those produced only by spallation) are radioactive, so they actas clocks. A particularly good clock is10Be, which has a half-life of 3.9 × 106yr, which iscomparable to typical diffusion times through the disk of the Galaxy. There tends to be anoverabundance of neutron rich isotopes in cosmic rays compared to their abundance in theSolar System, but the overabundance factor isn’t huge: e.g.,25Mg/24Mg is about 1.6 timesgreater than in the Solar System.The isotropy and energy density of cosmic raysThe local magnetic field in the interplanetary medium is about 10−4G. This meansthat protons with γ = 103, i.e., energies of about 1 TeV, have gyroradii that arerg= 3 × 1011γ(B/10−4G) = 3 × 1014cm, or about 20 AU. Therefore, protons with energiesthis great 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 relativisticparticles that themselves preserve the original direction fairly well, so ground-basedobservations can determine the direction of the cosmic ray with reasonable accuracy, aswell as its original energy. Observations of cosmic rays show that the arrival directions arerelatively isotropic, and in fact the lower the energy (down to 1012eV) the more