X-rays from IC scattering

(no. X-rays produced from starlight per )

(no. X-rays produced from 3K per )

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So we want to find out which is more important to the production of X-rays via the Inverse Compton process, starlight or the 3K microwave background.

This is done by finding the ratio of the number of X-rays produced by the two sources of photons, and this is given by the energy density (the amount of energy per cubic metre) multiplied by the energy distribution of cosmic ray particles per unit volume, multiplied by the square of the gamma factor (again, because this is proportional to the power emitted in the IC process).

This reduces to the ratio of the energy densities multiplied by the square root of the ratio of the gamma factors.