A MODEL FOR THE SPECTRAL VARIABILITY OF BL LACERTAE OBJECTS AT HIGH-FREQUENCIES

The average amplitude of variability of BL Lac objects is larger at higher frequencies, and the spectra in the X-ray range show a hardening with increasing intensity. This is shown to be a natural consequence of the relativistic jet model proposed by Ghisellini, Maraschi, & Treves, where higher frequencies are produced nearer to the jet core. Time-dependent properties are computed assuming that a perturbation travels at fixed speed down the jet, producing enhancements of constant amplitude of the relativistic particle density and of the magnetic field, in a slab or self-similar cone geometry. The time-dependent spectral intensities due to synchrotron radiation and first-order Compton scattering are computed numerically, and approximate analytic formulae are given. The evolution of the spectral shape with time and the light curves at fixed frequencies are presented and discussed in detail. The results are compared with observations. Finally, we estimate the expected intrinsic amplitude assuming that the perturbation is due to a planar relativistic shock wave. Using the results obtained by Lind & Blandford, the dependence of the observed amplitude on the viewing angle and on the shock and fluid velocities is discussed.