Abstract The multi-frequency light curves of BL Lacertae during 1997.5 - 1999.5 have been modeled by four outbursts, each having a 3-stage evolution in the (Sm, νm) plane with distinct rising-plateau-decaying phases. It is shown that the observed light curves can be well fitted for the eight frequencies from 350GHz to 4.8 GHz. The main characteristics of the model-fitting are: (1) the outbursts are found to have very flat spectra with an optically thin spectral index α (defined as Sν ∝ ν-α) of about 0.15. This is consistent with the results previously obtained by Valtaoja et al. (1992); (2) it is found that there is no spectral flattening between the rising-plateau phase and the decay phase. In other words, the optically thin spectral index does not change from the rising-plateau phase to the decay phase. These features are in contrast to the 3-stage shocked-in-jet model proposed by Marscher & Gear (1985) for submm- IR-optical flares, in which a spectral flattening of Δα = 0.5 is predicted when a transition occurs from the Compton/synchrotron phase (or rising-plateau phase) to the adiabatic phase (or decay phase) with α> ~ 0.5 for the shock being non-radiative. We propose a new model to interpret the fitting results, suggesting that the 3-stage evolution of the mm--cm outbursts in BL Lacertae may be related to the process of shock formation and propagation in a highly collimated jet (for example, a 'parabolic' jet). In particular, during the rising phase, the thickness of the synchrotron-radiating region created by the shock may rapidly increase with time (relative to the jet width) due to the rapid injection of relativistic electrons and a magnetic field, and this leads to the observed behavior that the turnover flux density Sm rapidly increases while the turnover frequency νm decreases. In the decay phase, the emitting plasma enters into a free expansion regime without further injection of relativistic electrons and a magnetic field (for example, when a transition from a collimated regime into a conical regime occurs). The plateau phase is a short period between the two regimes with no distinct features determined.

Keywords radio continuum: galaxies — radio outburst — quasars: individual: BL Lacertae

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