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Astron. Astrophys. 349, 45-54 (1999)

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1. Introduction

Submillimetre-to-radio light curves of blazars show evidence of prominent structures, or flares, apparently propagating from high to low frequencies. A decisive step in the understanding of these flares was done by Marscher & Gear (1985, hereafter MG85). They studied the strong 1983 outburst of 3C 273 by constructing at two epochs a quasi-simultaneous millimetre-to-infrared spectrum after subtracting a quiescent emission assumed to vary on a much longer time scale. They successfully fitted these two flaring spectra with self-absorbed synchrotron emission and showed that their temporal evolution can be understood as being due to a shock wave propagating down a relativistic jet. They identified three stages of the evolution of the shock according to the dominant cooling process of the electrons: 1) the Compton scattering loss phase, 2) the synchrotron radiation loss phase and 3) the adiabatic expansion loss phase.

Another shock model was developed by Hughes et al. (1985) simultaneously to that of MG85. Their piston-driven shock model reproduces well the lower frequency flux and polarization observations of outbursts in BL Lacertae, but fails to describe the observed behaviour in the millimetre domain. A generalization of the three-stage shock model of MG85 was presented by Valtaoja et al. (1992). Their model, based on observations, describes qualitatively the three stages of the MG85 model without going into the details of the physics of the shock. Finally, Qian et al. (1996) proposed a burst-injection model to study the spectral evolution of superluminal radio knots. Their theoretical calculation is able to reproduce well the observed spectral evolution of the C4 knot in 3C 345 (Qian 1996).

To constrain these shock models, we need to extract the properties of the outbursts from the observations. This step is difficult both at high and at low frequencies. At high frequencies because of the brevity of the outbursts that last only a few days to months, thus requiring a very well sampled set of observations in the not easily accessible submillimetre spectral range. At radio frequencies because they very often overlap due to their longer duration, making it difficult to isolate them.

The best observational constraints for the model of MG85 were obtained by Litchfield et al. (1995) for the blazar 3C 279 and by Stevens et al. (1995, 1996, 1998) for PKS 0420-014, 3C 345 and 3C 273, respectively. All these studies are based on isolated outbursts. The method used consists in constructing simultaneous multi-frequency spectra for as many epochs as possible after the subtraction of a quiescent spectrum assumed to be constant with time. The subtraction of a quiescent spectrum is convenient and seems to give good results, but has only weak physical justification. In 3C 273, there was a period of nearly constant flux at millimetre frequencies lasting just more than one year in 1989-1990, which was interpreted as its quiescent state (Robson et al. 1993). At radio frequencies, however, no similar constant flux period was ever observed and there is no evidence that such a state exists at a significant level above the contribution of the jet's hot spot 3C 273A (see Fig. 2 of Türler et al. 1999a).

The different approach presented here to derive the observed properties of the outbursts has the advantage to not rely on the assumption of a quiescent emission. The idea is to decompose a set of light curves covering a large time span into a series of flares. To our knowledge, the first attempt of such a decomposition was made by Legg (1984), who fitted a ten years radio light curve of 3C 120 with twelve self-similar outbursts. Recently, Valtaoja et al. (1999) decomposed the 22 GHz and 37 GHz radio light curves of many active galactic nuclei into several exponentially rising and decaying outbursts. What is new in our approach is that we fit the same outbursts simultaneously to twelve light curves covering more than two decades of frequency from the submillimetre to the radio domain. This adds a new dimension to the decomposition: the evolution of a flare is now a function of both time and frequency. The aim is to obtain both the spectral and temporal properties of a typical flare, from which individual flares differ only by a few parameters.

We use the light curves of 3C 273, the best observed quasar, to have as many observational constraints as possible. The flaring behaviour of 3C 273 was already the subject of several previous studies (e.g. Robson et al. 1993; Stevens et al. 1998). Stevens et al. (1998) obtain results for the first stage of the strong 1995 flare in very good agreement with the predictions of the MG85 shock model. The new approach presented here is however more powerful to constrain the two following stages of the evolution.

We describe below two different approaches. In Sect. 3 we model the light curve of each outburst by an analytic function that can smoothly evolve with frequency, whereas in Sect. 4 we directly model a self-absorbed synchrotron spectrum that evolves with time. The first approach is easier to implement, since it allows us to begin the decomposition with a single light curve before adding the others progressively. The second approach is more physical and gives better constraints to shock models. Our results are discussed in Sect. 5 and summarized in Sect. 6.

Throughout this paper the frequency [FORMULA] is as measured in the observer's frame and "[FORMULA]" refers to the decimal logarithm "[FORMULA]". The convention for the spectral index [FORMULA] is [FORMULA].

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© European Southern Observatory (ESO) 1999

Online publication: August 25, 1999