I've trouble understanding the following graph, taken from Wikipedia: enter image description here

It's supposed to show the cosmic ray flux vs particle energy. I've never seen a "flux" written in these units... Why ${GeV}^{-1}$?

  • 3
    $\begingroup$ Why not? This is a distribution over particle energy. That factor is just saying "per unit of energy". $\endgroup$ Feb 27 at 11:58
  • $\begingroup$ Spectra are dN/dE which is per unit energy. But be aware that in astroparticle research, often that same information is shown multiplied by some E^(-2.7) or some such power law. That is because this spectrum is so extremely steep. So always check the vertical axis units first with those cosmic ray spectrum plots ... $\endgroup$
    – rfl
    Feb 27 at 14:21

1 Answer 1


It is a differential flux. If you wanted to know the total particle rate per unit area, per unit solid angle, per unit time, with units $\rm m^{-2}\,sr^{-1}\,s^{-1}$, you would have to choose an energy interval that you care about and integrate the curve in the figure.

Some authors would write a monstrous differential symbol rather than $F$, like

$$ F = \frac{\mathrm dN}{\mathrm dA\ \mathrm d\Omega\ \mathrm dt\ \mathrm dE} $$

to make explicit that the number of particles observed $N$ depends on your detector’s area $A$, its solid angle acceptance $\Omega$, your experiment’s running time $t$, and your choice of energy window.

The horizontal lines on the diagram are probably integrated over $4\pi$ steradians for all particle energies higher than the intersection of the horizontal line and the blue differential flux curve.


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