The Spectral Shape of Synchrotron Radiation 

thank you for your lesson, very clear

So how would you get the spectral index if units are energy not frequency ?

Could this be applied to a black hole, or quasar/blazar? Where the size (or mass) determines the energy frequency and the visibility of the celestial object? Like light, only being visible within a small piece of its spectrum, size (mass) within space (size of the objects center) determining the visible nature of the celestial object?

Thanks for uploading this!