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The broadband SEDs of blazars show two distinct components which in leptonicmodels are associated with synchrotron and SSC emission of highly relativisticelectrons. In some sources the SSC component dominates the synchrotron peak byone or more orders of magnitude implying that the electrons mainly cool byinverse Compton collisions with their self-made synchrotron photons. Therefore,the linear synchrotron loss of electrons, which is normally invoked in emissionmodels, has to be replaced by a nonlinear loss rate depending on an energyintegral of the electron distribution. This modified electron cooling changessignificantly the emerging radiation spectra. It is the purpose of this work toapply this new cooling scenario to relativistic power-law distributedelectrons, which are injected instantaneously into the jet. We will first solvethe differential equation of the volume-averaged differential number density ofthe electrons, and then discuss their temporal evolution. Since any non-linearcooling will turn into linear cooling after some time, we also calculated theelectron number density for a combined cooling scenario consisting of both thelinear and non-linear cooling. For all cases, we will also calculateanalytically the emerging optically thin synchrotron fluence spectrum whichwill be compared to a numerical solution. For small normalized frequencies f <1 the fluence spectra show constant spectral indices. We find for linearcooling a_SYN = 1/2, and for non-linear cooling a_SSC = 3/2. In the combinedcooling scenario we obtain for the small injection parameter b_1 = 1/2, and forthe large injection parameter b_2 = 3/2, which becomes b_1 = 1/2 for very smallfrequencies, again. This is the same behaviour as for monoenergeticallyinjected electrons.

astronomy and astrophysics

Blazar synchrotron emission of instantaneously power-law injected  electrons under linear synchrotron, non-linear SSC, and combined  synchrotron-SSC cooling