The bulk of cosmic rays are believed to have a galactic origin, therefore it is important to understand how they are transport in the galaxy and what kind of interactions they suffer.
Galactic Confinement
Let's start by assuming a schematic view of our Milky Way. We can simply it as
One argument to establish the galactic origin of CRs is whether or not the Lamor radius rLof CRs particules is of the order of the size of the Milky Way. The Lamor radius can be expressed as:
rL≃1kpc(1018eVE)(Z1)(BμG)
and so the maximum energy to contain cosmic rays in the Galaxy is:
E<1018eV(1kpch)(BμG)
There are many uncertainties in these numbers but we can assume that the size of the Galactic halo is h∼1−10kpc , and the magnetic field in the halo is about B∼0.1−10μG. Putting this number gives maximum energy of Emax∼1017−1020GeV. Given this result we can assume that lower energy cosmic rays come from own Galaxy, otherwise they would have escaped.
Cosmic-ray interactions
Since we can assume that the majority of CRs are confined in the Milky Way, we can evaluate where and how they will interact during their travel. There are two chiefly process in which a cosmic-ray particle can interact:
Coulomb collisions: They occur when a particle interacts elastically with another particle's Coulomb static electric fields. The Coulomb cross-section for a 1 GeV particle is 10−30cm2 , which means that assuming a target density of n∼1cm−3 the mean Coulomb collision rate (for a particle moving at the speed of light c is given by τ1=nσc∼10−19.5s−1 which correspondes to a 1%collision chance in Hubble time. Therefore Coulomb collision can be neglected.
Spallation processes: It occurs when C, N, O, Fe nuclei impact on interstellar hydrogen. The large nuclei is broken up into smaller nuclei. A clear indication of a spallation comes precisely from the composition comparison with stellar matter.
So spallation is the dominant interaction of CRs in their path through the galaxy, but to know exactly in which regions of the Milky Way this is process takes places we need to know the density of material in the Galaxy.
The interstellar medium
Given the low density of the Galactic halo it is clear that the spallation processes must occur in the Galactic Disk. The Galactic Disk is mostly populated by the Interstellar Medium or ISM. It is mostly composed by Hydrogen in 3 different phases:
Molecular Gas. This phase is the more clumpy as they gathered in molecular clouds that can reach densities of 106cm−3which is still very low for our atmosphere standards (14 times lower). It is composed of hydrogen in molecular form, H2, CO. Sometimes called stars nurseries they are stars forming regions.
By NASA, ESA, N. Smith (University of California, Berkeley), and The Hubble Heritage Team (STScI/AURA); credit for CTIO Image: N. Smith (University of California, Berkeley) and NOAO/AURA/NSF - http://hubblesite.org/newscenter/archive/releases/2007/16/image/a/, Public Domain, https://commons.wikimedia.org/w/index.php?curid=53662647
Atomic Gas. Made up of neutral atomic hydrogen. Astronomers usually refer to atomic Hydrogen as HI(HII is the ionized hydrogen). Neutral hydrogen can be observed by radio telescopes by searching the 21 cm line The maps tracing the HI that is organized in a spiral pattern, like H, and also its structure is quite complex, with overdensities and holes.
Ionized Gas. Is ionized Hydrogen or HII.
The overall density of the ISM is cm. The interstellar gas is not a an static gas, but rather is subject to a turbulent motion.
The Leaky Box model
The Leaky Box model is a very simple model used to describe cosmic-ray confinement. In this simplified phenomenological picture CRs are assumed be accelerated in the galactic plane and to propagate freely within a cylindrical box of size and radius and reflected at the boundaries; the loss of particles is parametrized assuming the existence of a non-zero probability of escape for each encounter with the boundary (Poisson process).
, and also its structure is quite complex, with overdensities and holes.
