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More adventures in Inverse-Compton

Had to do some back pedaling on implementing Inverse-Compton.  The Klein-Nishina effects are not as important for most observations, and there was some strangeness in the fast cooling regime.   The main issue was that the cooling frequency was not suppressed as one would expect and this was due to stupidity in the way I originally implemented it.  Here are some new results for physical parameters E = 10^52 ergs, p=2.5, theta_0= 0.2 rad, theta_0bs=0, n= 5, e_e=1, e_b = 0.01, and ksi_n=1.  We tested in the fast cooling regime using the standard expression for Y (Full derivation to follow) and in the slow cooling regime using an approximation of the formula derived in Beniamini et. al. 2015 (arxiv:1504.04833v2).


The red line is the minimum accelerated electron emitted frequency, the dashed line is the IC suppressed cooling frequency, and the blue line is the un-suppressed cooling frequency.
 We originally had a debate about whether the fast cooling spectrum should have the same peak value as the unscattered spectrum, but eventually arrived at the conclusion that it should because the Inverse-Compton effects reduce the overall energy of the spectrum, and the flux in Jansky is not an accurate depiction of that.  using nuF_nu to approximate the energy spectrum, we can see that the overall energy is down in both cases, and that the spacing between the fluxes drops off by the expected 1+Y for values measured above the un-suppressed cooling break.  Next step is to verify the effects of the IC parameter as a function of time, and to make sure that the parameter transitions smoothly between the fast and slow cooling cases.

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