1 Introduction

Blazars are an interesting and violent subclass of active galactic nuclei (AGN), grouping together (although somewhat artificially from a physical point of view) radio-loud quasars and BL Lacertae objects. These sources have in common flat cm-wave radio spectrum, high and variable polarization, and pronounced variability of the flux density at all frequencies. The superluminal motion observed in these sources together with brightness temperatures in excess of the 10¹² K inverse Compton limit (Kellermann & Pauliny-Toth 1968) indicate highly beamed emission from relativistic jets oriented towards the line of sight of the observer. Using modern-day very long baseline interferometry (VLBI) techniques we can resolve the jet-like structures in blazars on angular scales down to $\sim$0.1 milliarcsec (mas).

Relativistic jets also offer an explanation for radio-to-infrared variability of blazars. Marscher & Gear (1985) studied the strong 1983 outburst in 3C 273 and managed to fit the flaring spectra with self-absorbed synchrotron emission. They explained successfully the time-evolution of the flare as being due to a shock wave propagating in the relativistic jet. The Marscher & Gear model (hereafter MG-model) has three stages of shock evolution based on the dominant cooling mechanisms of the electrons: 1) the Compton scattering loss phase, 2) the synchrotron radiation loss phase and 3) the adiabatic expansion loss phase. MG-model is a simple, analytical model, which describes well the general behaviour of the radio outbursts in AGN (but see the critíque of Björnsson & Aslaken 2000). The model was generalized by Marscher et al. (1992) to include the effects of bending in jets and turbulence on the light curves.

Hughes et al. (1985, 1989a, 1989b, 1991) proposed a similar shock model based on a numerical code simulating a piston-driven shock. Their model succesfully explains the lower frequency variability, but it does not incorporate radiative energy losses of the electrons, which are important at high frequencies and in the earliest stages of the shock evolution. Valtaoja et al. (1992b) presented a generalized shock model describing qualitatively the three stages of the shock evolution (growth, plateau and decay) without going into details, thus providing a framework for comparison between the theory and observations. Total flux density (TFD) monitoring campaigns, which provide nearly fully sampled flux curves at radio wavelengths, and VLBI images, which allow us to map the parsec-scale structure of the blazar jets, are the two main observational tools for constraining theoretical models.

In VLBI observations of blazars, bright knots of emission referred to as "components'' are seen. These components line up to form jet-like features appearing in various forms from very straight to heavily bent structures. The so-called "core'' is the point where the jet becomes visible. The core is presumed stationary (see Bartel et al. 1986), but most of the other VLBI components move outward in the jet at apparent superluminal speeds. However, in some sources there are also stationary components other than the core. These may be due, for example, to interactions between the jet and the surrounding interstellar medium.

According to the shocked jet models, moving components in the VLBI maps are interpreted as shocks propagating down the jet. However, there has been a dearth of conclusive evidence linking VLBI components with radio flux variations; only a relatively small number of individual sources have been investigated thus far. One of the first studies linking TFD variations with moving knots in the VLBI maps was carried out by Mutel et al. (1990). They found that each of four major TFD outbursts of BL Lac between 1980 and 1988 can be associated with the emergence of a new superluminal component. Abraham et al. (1996) estimated the ejection times of seven VLBI components in 3C 273 and noticed that all ejections were related to increases in the single-dish flux density at frequencies higher than 22 GHz. Türler et al. (1999) also studied 3C 273 by decomposing multi-frequency light curves into a series of self-similar flares. They found good correspondence between the ejection times of the VLBI components and the beginning times of the flares. Krichbaum et al. (1998) have reported a correlation between mm-VLBI component ejections and local minima in the 90 GHz total flux density curve of PKS 0528+134. For 3C 345, which is one of the best observed sources with VLBI at 22 GHz, Valtaoja et al. (1999) were able to associate VLBI components with individual millimetre flares. Similar correlations were also found for PKS 0420-014 (Britzen et al. 2000) and for 3C 279 (Wehrle et al. 2001).

In our study, we compare for the first time two large data sets: multi-epoch VLBA images of 42 blazars (Jorstad et al. 2001a) detected at 0.1-3 GeV by EGRET and TFD data from the mm-wave Mets $\ddot{\rm a}$hovi Radio Observatory quasar monitoring program. A description of our data is given in Sect. 2. Our aim is to establish connections between TFD variations and structural changes in the jets. The results from the analysis, as we will show in Sect. 3, strongly support the shocked jet model.

The VLBI core is the dominant component in almost all the cases studied. The core region was usually also highly variable, being responsible for most of the observed TFD variability in these sources. Variations in the VLBI core flux are reported in the literature quite often (see, e.g., the results of the recent VLBA monitoring of 3C 279 by Wehrle et al. 2001). Since the core is usually assumed to be the apex of the jet, the implicit assumption is that a core flare results from a change in the jet flow parameters. However, according to our study, these variations are rather related to moving VLBI components that blend with the radio core. This will be discussed in Sect. 4.

 

 

Table 1: List of sources in our sample. Here z is the redshift and N is the total number of VLBA observations.

Source	Other desig.	Class	z	Epochs	22 GHz	43 GHz	N
0202+149		HPQ	0.833	1995-97	-	+	4
0219+428	3C 66A	BLO	0.444	1995-97	+	+	7
0234+285	CTD 20	HPQ	1.207	1995-97	+	-	4
0235+164	AO 0235+164	BLO	0.94	1995-96	-	+	6
0420-014	OA 129	HPQ	0.915	1995-97	+	+	8
0446+112		GAL	1.207	1995-97	-	+	4
0458-020		HPQ	2.286	1995-97	-	+	5
0528+134		LPQ	2.07	1994-97	+	+	11
0716+714		BLO	>0.2	1995-97	+	-	9
0804+499	OJ 508	HPQ	1.43	1996-97	+	-	3
0827+243		LPQ	2.046	1995-97	+	+	6
0836+710		HPQ	2.17	1995-97	+	+	7
0851+202	OJ 287	BLO	0.306	1995-96	-	+	7
0954+658		BLO	0.367	1995-96	+	-	3
1101+384	Mkn 421	BLO	0.031	1995-97	+	-	8
1156+295	4C 29.45	HPQ	0.729	1995-97	+	-	5
1219+285	ON 231	BLO	0.102	1995-97	+	-	3
1222+216	4C 21.35	LPQ	0.435	1996-97	+	-	2
1226+023	3C 273	LPQ	0.158	1993-95	+	+	5
1253-055	3C 279	HPQ	0.538	1993-97	+	+	10
1510-089		HPQ	0.361	1995-97	-	+	5
1606+106		LPQ	1.226	1994-97	+	+	5
1611+343	DA 406	LPQ	1.401	1994-97	+	+	11
1633+382	4C 38.41	LPQ	1.814	1994-96	+	-	6
1741-038		HPQ	1.054	1995-97	+	-	2
2230+114	CTA 102	HPQ	1.037	1995-97	-	+	7
2251+158	3C 454.3	HPQ	0.859	1995-96	-	+	12