Propagation in the Galaxy 2: electrons, positrons, antiprotons As we mentioned in the previous lecture the results of the propagation in the Galaxy depend on the particle interaction cross section. If the average amount of matter an 1 GeV cosmic ray sees is 10.8 g/cm 2 and the proton mean free path is 100 g/cm 2 only 10% of the protons would interact. For Fe nuclei, whose cross section is about 15 times higher 80% of the nuclei would interact, so the flux of Fe is affected much more than the proton flux. Of course, Fe nuclei are contained in the Galaxy much longer, which increases the effects. Electrons and positrons have much higher electromagnetic interaction cross sections. Proton- proton cross section at relatively low energy is 30 mb (1 mb = 10-28 cm 2 ) while the basic Thomson cross section is 665 mb.
The interaction cross section is measured in barns (1 barn = 10-24 cm 2 ). The most used unit is a milibarn, which is barn/1,000. Electrons and positrons have much higher electromagnetic interaction cross sections. Proton- proton cross section at relatively low energy is 30 mb (1 mb = 10-27 cm 2 ) while the basic Thomson cross section is 665 mb. Definition of the average interaction length the amount of matter in which a particle interacts once. It starts again with the Avogadro number. The number of atoms per volume is n = N A A. In a compound material n i = N A w i /A i.
The average interaction length is E) = ( n i i )) -1 In case of air the average interaction length is (mb) If a proton air cross is 308 mb the average interaction length is 79 g/cm 2. The cross section increases with energy and the interaction length decreases with energy. The energy dependence can not be faster than ln 2 E. This is the (Marcel) Froissart's bound on the interaction cross section.
Energy loss processes for electrons and positrons The force between two point charges at a distance R from each other (the Coulomb force) is This is the basic force between two charged particles. Ionization loss: The energy loss on excitation and ionization of atoms of a charged particle moving through matter is (in units of MeV/(g.cm 2 )) is which comes to about 2 MeV for electrons in air or water. Note the inverse proportion on the particle mass M. Z and A are the average charge and mass of the medium, so energy loss in Hydrogen is smaller than in air or water.
Compton scattering is a process in which a photon hits one of the atoms electrons and transfers energy to it. For electron energy loss the inverse process, Inverse Compton scattering is very important in astrophysics. is the differential cross section for Compton scattering where k and k' are the photon energies before and after the scattering and q is the primary photon energy in terms of the electron mass. In the case of Inverse Compton scattering the cross section is the same where k is replaced by the photon energy in the electron frame with an account for the angle between the electron and the photon.
For photon energy much larger than the electron mass
Bremsstrahlung: Charged particles interact with the electromagnetic field of the nuclei of matter and produce gamma rays. The energy loss is The radiation length X 0 gives the average amount of matter for bremsstrahlung energy loss For air this amount is 37 g/cm 2 and it is close to that for water. In Hydrogen this amount is 61 g/cm 2. r e is the classical radius of the electron = e 2 /m e c 2 = 2.82x10-13 cm
Synchrotron radiation: Charged particles lose energy in propagation in magnetic fields. For electrons moving randomly in a magnetic field the energy loss is The characteristic frequency of the radiated photons is Synchrotron loss is inversely proportional to the square of the particle mass.
Production of electron positron pairs is the opposite process to bremsstrahlung and their cross sections are closely related. The total cross section is The energy distribution of the pair particles at high gamma ray energy (top) and at threshold (bottom). In order to produce two electrons the energy in the CM should be higher than 2 m e.
Production of electrons and positrons in the Galaxy depends on the models of cosmic ray containment in the Galaxy. The classical model is called the leaky box model where the cosmic rays move with certain mean free path and have probability p to escape from the Galaxy at every step. The models include interactions of the propagated cosmic rays with galactic matter and production of neutral mesons (mostly 0 ). The neutral pions decay to 2 gamma rays that propagate in the Galaxy and generate electron positron pairs. The electrons and the positrons also propagate and lose energy. One has to take into account the energy losses in propagation and the probability to escape from the Galaxy to calculate the fluxes that are detected at Earth. Have in mind that positrons are only produced in propagation while a fraction of the electrons maybe accelerated at the sources of cosmic rays. Positrons also annihilate in propagation. For this reason one expects higher electron flux.
Positron production in proton interactions in one gram of interstellar matter (by R.J. Protheroe). Comparison with other calculations.
Comparison of Protheroe's calculation to older set of data. We will discuss the new measurements in the next lecture.
Comparison of measurements to the calculation for three different models of electron and positron propagation. This is also an old data set. The ratio of e + /e - is supposed to decrease with increasing energy unless there are positrons from the decay of dark matter. In such a case there would be a peak at ½ M DM particle.
Production of antiprotons Antiprotons are generated in collisions of accelerated cosmic rays with galactic matter. Lets consider the production in pp collisions pp -> p + p + p + p bar The center of mass energy in the case the particle 2 is at rest is s 1/2 = (m 2 1 + m 2 2 + 2m 2 E Lab 1 ) 1/2 It is obvious that in the center of mass the energy should exceed the sum of the masses of the produced particles for the interaction to be possible. In this particular case the sum of all masses is 4m p = 3.75 GeV. We can now use the definition of the CM energy to calculate what is the energy threshold for cosmic ray protons to produce proton-antiproton pair. The minimum energy is 6.54 GeV. At this energy the production of proton-antiproton pair with 0 momentum is possible, i.e. all secondary particles are at rest. In practice one need higher energy to generate the collision.
Energy dependence of the antiproton production cross section in pp interactions.
Why are we interested in positrons and antiprotons? This is philosophical question related to cosmology. Why do we have such huge asymmetry between baryons and antibaryons in the Universe. We should have equal amounts of matter and antimatter after the Big Bang, but cannot see antimatter except for positrons and antiprotons. If we are able to see many more antiprotons than the number produced in the Galaxy this would be a sign that we have antimatter astrophysical objects, probably in antimatter galaxies. The big experiment AMS-2 that is at the space station now (Anti Matter Search) is looking for such signals (antiprotons and anti-helium) as well as for ordinary cosmic rays. The first results from AMS-2 will come out this year.