That's almost not a joke - I did particle astrophysics, not astronomy, but for the exact same reason you state, our physics results (we used particle physics as a window to astronomy, or at least we tried to) would end up with broken power law fits.

There's something deeply satisfying using a model so simple to explain a piece of nature. :)

Example: cosmic ray energy spectrum. http://iopscience.iop.org/1367-2630/12/7/075009/downloadFigu...