There is an observed relation, between the brightness & power of relativistic jets, common to Quasars & GRBs:

http://phys.org/news...lack-holes.html

Could the following calculations help explain the same?

So:

By partial fractions:

So the integration yields:

For relativistic jets , and most of the power is radiated early on, at high . So:

But the initial electron energy was also proportional to . So, **the average power of emissions is (calculated to be) constant at all energy scales**:

Perhaps some similar sort of scale invariance, whereby the power emitted by decelerating electrons is quasi-constant, could account, for the observed Jet brightness / power relation.