Cosmic ray electrons and positrons from discrete stochastic sources

Understand

The distances that galactic cosmic ray electrons and positrons can travel are severely limited by energy losses to at most a few kiloparsec, thereby rendering the local spectrum very sensitive to the exact distribution of sources in our galactic neighbourhood.

• However, due to our ignorance of the exact source distribution, we can only predict the spectrum stochastically.
• We argue that even in the case of a large number of sources the central limit theorem is not applicable, but that the standard deviation for the flux from a random source is divergent due to a long power law tail of the probability density.
• Instead, we compute the expectation value and characterise the scatter around it by quantiles of the probability density using a generalised central limit theorem in a fully analytical way.