Energy of cosmic particles
The energy of primary cosmic particles varies widely. The figure shows the full energy spectrum. In the range of 1 GeV to about 50 EeV satisfy the spectrum of a law:
This energy is a rather sharp drop in flux by a factor of 1030. The slope of the spectrum (left figure) seems fairly constant with a value of y = -2.7. This suggests that there is a universal gear mechanism. Detailed analysis shows that the dimensionless quantity y is not constant, but varies: -4 < y < -2.7.
In the right graph, the particle flux is multiplied by E3. Slight deviations from y are better mapped this way. Insight in this structure appears to be the key to understanding the origin of cosmic rays. Two areas are under intense investigation: the area around the 'knee' and the area around and beyond the 'ankle'.
The 'knee'
The knee is the area that lies just above an energy of 4 x 1015 eV with a spectral index y ~ -3.1. For energies above 4 x 1017 eV, the spectrum is even steeper: y ~ -3.3. This is called the second knee. It is assumed that the knee structure is a reflection of the rigidity dependent cut-off. The galactic magnetic field is not strong enough to capture cosmic particles when the energy increases. Cosmic particles diffuse out of the galaxy, starting with the lightest (knee) and then losing an increasing fraction upon the second knee, where even the heaviest particles have sufficient energy to escape the magnetic field. This statement is confirmed by measurements showing that in the knee area, the average mass of cosmic rays increases as a function of energy.
Although plausible, this "rigidity dependent cut-off is not beyond all doubt. There are hardly any data available in the important energy region between 1017 and 1019 eV, where the contribution of galactic cosmic rays should end.
The 'ankle' and beyond
For particles with an energy greater than 1-10 x 1018 eV the spectrum flattens again: y takes another value of ~ -2.7. These are known as the 'ankle'. In this area the contribution of extragalactic radiation would dominate.
Above 4 x 1019 eV there is a re-steepening of the spectrum, the spectral index here is -4 to -5. This steepening can be attributed to a phenomenon called the GZK limit. The GZK limit is predicted by Greisen and Kuzmin & Zatsepin. They calculated that cosmic rays with energy greater than 5 x 1019 eV should produce pions by interacting with the microwave background radiation in the universe.
This causes the primary particles to loose energy until it reaches a level below the limit. The fact that the mean free path of cosmic rays is curtailed by this interaction leads to the following conclusion. The chance that cosmic rays with energy above the GZK limit reaches the earth is negligible, unless the source is within a radius of about 50 Mpc. Because particles with such high energies are scarce, the GZK-effect has not been proven scientifically. Recent research (the Auger experiment) does point in that direction.