I What´s the cosmic ray's energy dependence?

[morenopo2012]

i read that the cosmic rays are almost at the velocity of the light, therefore, if they are relativistic their energy it is expressed as

E = (p²c² + m₀²c⁴)^½

if the cosmic rays have a spectrum energy from 10⁹ GeV to 10²¹ GeV

the difference between a proton with an energy of 10⁹ and another one with an energy of 10²¹ it depends only of the momentum? and if it does, How is this possible?

 

[NFuller]

How is this possible?

What do you mean? It's possible since you are working in the relativistic limit.

 

[mathman]

i read that the cosmic rays are almost at the velocity of the light, therefore, if they are relativistic their energy it is expressed as

E = (p²c² + m₀²c⁴)^½

if the cosmic rays have a spectrum energy from 10⁹ GeV to 10²¹ GeV

the difference between a proton with an energy of 10⁹ and another one with an energy of 10²¹ it depends only of the momentum? and if it does, How is this possible?

m₀ and c are constant, so only p can vary to get variable E.

 

[ChrisVer]

the difference between a proton with an energy of 109 and another one with an energy of 1021 it depends only of the momentum? and if it does, How is this possible?

Yes, it depends only on the momentum. Obviously you have "slow" and "fast" protons. The difference between those is their origin (how they are produced and accelerated to those energies). For example low-energetic protons (from the whole spectrum of CRs), originate mainly from the Sun (they are produced and accelerated in the same way solar winds do). The mechanism that leads to accelerating particles to the ultra-high-energy-cosmic-rays (UHECR) regime is not 100% understood and it may not be just a single one (e.g. some can come from neutron stars -although the neutron stars are not that many- , or they can be accelerated by Supernovae etc)...