Log-parabolic spectra and particle acceleration in blazars

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Curved broad-band spectral distributions of non-thermal sources like blazars are described well by a log-parabolic (LP) law where the second degree term measures the curvature. LP energy spectra can be obtained for relativistic electrons by means of a statistical acceleration mechanism whose probability of acceleration depends on energy. In this paper we compute the spectra radiated by an electron population via synchrotron (S) and Synchro-Self Compton(SSC) processes to derive the relations between the LP parameters. These spectra were obtained by means of an accurate numerical code. We found that the ratio between the curvature parameters of the S spectrum to that of the electrons is equal to about 0.2 instead of 0.25, the value foreseen in the delta approximation. Inverse Compton spectra are also intrinsically curved and can be approximated by a log-parabola only in limited ranges. The curvature parameter, estimated around the SED peak, may vary from a lower value than that of the S spectrum up to that of emitting electrons depending on whether the scattering is in the Thomson or in the Klein-Nishina regime. We applied this analysis to computing the SSC emission from the BL Lac object Mkn 501 during the large flare of April 1997. We fit simultaneous BeppoSAX and CAT data and reproduced intensities and spectral curvatures of both components with good accuracy. The large curvature observed in the TeV range was found to be mainly intrinsic, and therefore did not require a large pair production absorption against the extragalactic background. We regard this finding as an indication that the Universe is more transparent at these energies than previously assumed by several models found in the literature. This conclusion is supported by recent detection of two relatively high redshift blazars with H.E.S.S.