Source spectral index Whilst studying the propagation of cosmic rays (CRs) through our galaxy, I was comparing simulated data to data measured by the Alpha Magnetic Spectrometer 02. I am studying the proton flux within CRs and am comparing the two data sets given.
The simulated data comes from a theoretical model depending on several factors; one of these factors is the source spectral index. I have to explain what the importance is of the source spectral index of hydrogen, but I struggle to find its exact meaning and importance here. Could someone maybe help me out?
 A: The AMS-02 team have made a nice post on cosmic rays, wherein they state (emphasis mine),

To examine the energy dependence of the electron flux in a model independent way, the flux spectral index $γ$ is calculated from
$γ = d\left[\log\Phi\right]/d\left[\log E\right]$ over non-overlapping energy intervals which are chosen to have sufficient sensitivity to the spectral index

where $\Phi$ is defined a little earlier as a power-law distribution over energy $E$,
$$  \label{eq:1} \Phi_{e^{-}}(E)= \begin{cases} C(E/20.04\mbox{ GeV})^{\gamma}, & E \leq E_{0}; \\ C(E/20.04\mbox{ GeV})^{\gamma}(E/E_{0})^{\Delta\gamma}, & E > E_{0}. \end{cases} $$
They also identify $\gamma\sim-3$, which is the typical value of cosmic rays (and also why you might see flux density plots scaled by $E^3$).
This definition from the AMS-02 team is also in-line with what you'd find over at Wikipedia,

In astronomy, the spectral index of a source is a measure of the dependence of radiative flux density (that is, radiative flux per unit of frequency) on frequency. Given frequency $\nu$ and radiative flux density $S_\nu$, the spectral index $\alpha$  is given implicitly by
$$ S_\nu\propto \nu ^{\alpha }. $$
Note that if flux does not follow a power law in frequency, the spectral index itself is a function of frequency. Rearranging the above, we see that the spectral index is given by
$$ \alpha \!\left(\nu \right)={\frac {\partial \log S_{\nu }\!\left(\nu \right)}{\partial \log \nu }}. $$
Clearly the power law can only apply over a certain range of frequency because otherwise the integral over all frequencies would be infinite.

A: You are looking for an energy distribution with a power-law exponent, i.e., $f(E) \propto E^{-\gamma}$ where $\gamma$ is the spectral index.
