Per unit solid angle problem in cosmic particles' fluxes When it comes to measuring cosmic particles' fluxes people draw graphs in terms of “per unit solid angle”. What do they mean by that? Is that the average value of the flux divided by the total solid angle observed? It is obvious that fluxes in general are not isotropic, so from each direction we should expect different amounts of the incoming particles.
For example, 
 
Another question is how to treat this theoretically. Let's say I'm making a theoretical prediction on the flux and want to compare it to the experimental results. Such experiments as PAMELA or AMS-02 are being run in space, so the actual detector position is changing from time to time. At one time it might be oriented in the direction of the higher incoming flux than at the other moment. In that case how should I make my calculations and treat "per unit solid angle" problem?
 A: The solid angle enters due to how one measures incident particles.  It relates to the angular area subtended by the detector field-of-view (FOV).  In particle telescopes, one can define a geometric factor, which derives from the optics of the instrument and is used to convert particle counts to a physical unit like number flux (also sometimes called intensity) with units like # s-1 sr-1 m-2 eV-1 (i.e., number of particles per unit time, per unit solid angle, per unit area, per unit energy).

What do they mean by that? Is that the average value of the flux divided by the total solid angle observed?

No, it is related to the fact that the detector does not observe all $4 \pi$ steradians of the sky at any given instant.  So if you only observe part of the sky, how do you convert the number of particles you see to something independent of your FOV?  It's how we convert counts to a physical unit like flux to determine the total rate of incident particles from any arbitrary direction over any arbitrary area at any given time.

It is obvious that fluxes in general are not isotropic, so from each direction we should expect different amounts of the incoming particles.

No, but that is not really the issue.  Again, it's related to how we measure things and how we estimate particle fluxes.  In your specific example, there does not appear to be any directional information, which suggests it is an omnidirectional average (i.e., average over all look directions, thus there is no information about isotropy vs. anisotropy).

At one time it might be oriented in the direction of the higher incoming flux than at the other moment. In that case how should I make my calculations and treat "per unit solid angle" problem?

Again, the units are not dependent on the incident number of particles.  It does not matter what direction a detector looks, it should still have the same geometric factor, which informs the user how to convert between raw counts to a physically significant unit system like flux.
