Analytic Model of Spectral Variability of Blazars at High Frequencies. I. Radiative Losses

The evolution of the relativistic electron spectrum in a homogeneous jet due to the injection of fresh relativistic electrons, radiation losses, and particle escape is considered and applied to the interpretation of the spectral variability of blazars at high frequencies. The idea of wide and narrow injected electron spectra is discussed; The synchrotron spectra for wide and narrow injected electron spectra are calculated, taking into account radiation losses and electron escape. It is pointed out that the narrow electron spectrum can give rise to a lag of the emitting spectra between in soft and hard photons that approximately satisfies st v(-1/2) relation, and the wide electron spectrum will produce no peak delay and a largely differing variability of the emitting spectra at high frequencies; the timescale of the spectral delay is also proportional to v(-1/2). In the case of PKS 2155-304, it is concluded that the flares at UV through X-ray wavelengths in 1994 May can be attributed to a sudden injection of high-energy electrons with a narrow spectrum, In the case of Mrk 421, it is suggested that the TeV flare can be attributed to an injection of electrons with a narrow spectrum through synchrotron self-Compton emission and to the X-ray flare as the source of soft photons.