Spectral evolution of the Crab PWN spectrum (as seen with Fermi LAT) during the 2011 April flare (adopted from Buehler et al. 2012; ApJ, 749, 26).

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Simulation of spectral evolution due to synchrotron cooling with steady the state spectrum characterized by photon index of 2.2 and harder injected (during a finite time) spectrum characterized by photon index of 1.2 (Kargaltsev et al. in prep.).