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Astron. Astrophys. 339, 41-51 (1998)

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3. Results and discussion

3.1. Spectral index variations

We have seen that there is a reddening of the colour indices when the source becomes fainter. We can generally relate this effect to the host galaxy contribution to the total light, nevertheless it could be an intrinsic characteristic of the emission mechanism and, for this reason, we have performed a further analysis. We have decomposed the observed spectral flux distribution in terms of the host galaxy plus a typical synchrotron power law [FORMULA] of constant slope. To separate the two components, the UBVRI data were grouped daily (since we have never seen intra-night variations), corrected for the interstellar reddening, and then transformed in fluxes using the relations reported by Bessell (1979).

The correction for the galactic interstellar reddening was performed using the colour excess [FORMULA] (Lockman & Savage 1995). From [FORMULA] we have evaluated the UBVRI extinction coefficients with the formula of Cardelli et al. (1989) assuming [FORMULA]=3.1 (Rieke and Lebofsky, 1985).

The spectral slopes with only the interstellar correction are plotted in Fig. 9 with respect to the V flux (top panel) and we can note that the slope is steeper when the flux is lower.

[FIGURE] Fig. 9. Spectral slope vs V flux with only the interstellar correction (top), and with the host galaxy subtraction (bottom)

We considered the host galaxy component due to a typical elliptical galaxy assuming as free parameters its V magnitude and the colour indices (U-B), (B-V), (V-R) and (V-I). The UBVRI fluxes of each night (corrected by the host galaxy contribute) were interpolated with a power law distribution [FORMULA] and the corresponding slopes compared. We found that the best fit is obtained considering a host galaxy with V=15.0, (U-B)=0.6, (B-V)=1.0, (V-R)=0.6 and (V-I)=1.4. The power-law distribution (see Fig. 9, low panel) has a mean spectral slope [FORMULA]=0.85[FORMULA]0.07. This value of [FORMULA] can be considered typical of the X-ray selected BL Lac objects (see Pian et al., 1994) and the colour indices are in agreement with the typical colour indices of elliptical galaxies (see, e. g., Arimoto & Yoshi, 1987).

The brightness distribution of the underlying galaxy of Mkn 421 has been studied by multiaperture photometry (see, e.g., Kinman 1978, Mufson et al. 1980, Makino et al. 1987, Kikucki & Mikami 1987) and direct imaging (Hickson et al. 1982). These studies show that the typical V magnitude of the galaxy with an aperture of 10 arcsec is [FORMULA]14.8, in substantial agreement with our estimate.

In conclusion, our data show that the optical spectral index ([FORMULA]) variations can be easily explained as the host galaxy contribution to the total light. However, this cannot exclude that an intrinsic variability of the spectral slope could be present, but it must have a small amplitude.

3.2. Frequency dependent polarization

Polarization observations at different wavelengths together with flux measurements offer valuable information in trying to understand the behaviour of BL Lacs. Polarization is important when the synchrotron emission hides the effects of possible other components in the spectrum, especially the host galaxy and the accretion disk emissions. Besides, polarization gives information about the magnetic field structure in the source.

Fig. 6 shows the presence of a strong frequency dependent polarization (FDP) in Mkn 421. This is a common phenomenon in BL Lacs (see, e. g., Valtaoja et al. 1991), but the synchrotron radiation produced by an homogeneous plasma causes frequency independent polarization. For this reason many mechanisms have been proposed in order to explain the observed FDP. The most important is the dilution by the thermal, unpolarized light of the host galaxy, that decreases the degree of polarization toward longer wavelengths. Dilution can also be caused by the hotter thermal radiation emitted by the accretion disk around the central black hole (Malkan & Sargent 1982, Smith et al. 1986). In this case the observed degree of polarization should decrease toward shorter wavelengths. In Mkn 421 the degree of polarization decreases toward longer wavelengths and, then, FDP cannot be strictly related to accretion disk dilution.

Fig. 10 (top panel) shows the behaviour of the FDP slope with respect to the magnitude and we can note that the slope is greater when the source is brighter. We have then scaled the linear polarization levels taking into account the host galaxy, with the following transformation:


where [FORMULA] is the true polarization level, [FORMULA] is the observed polarization, [FORMULA] the total magnitude and [FORMULA] the galaxy magnitude derived in Sect. 3.1. Then we have computed the FDP slopes and the new values are reported in Fig. 10 (bottom panel). We see that dilution by host galaxy emission can explain the FDP only when the source is faint. Moreover we note again that the FDP is greater when the source is brighter. For this reason an intrinsic source of FDP is needed.

[FIGURE] Fig. 10. FDP slope vs V magnitude without correction (top), and with the host galaxy subtraction (bottom)

The intrinsic FDP in BL Lacs may be explained either considering two different emitting regions, in the so-called two component models (see, e. g., Smith et al. 1986, Brindle et al. 1986, Ballard et al. 1990), or by a single component if we consider an inhomogeneous jet model (Bjornsson 1985). Although both the models are controversial and more observations are required, we can note that they can explain the FDP observed in Mkn 421.

3.3. Optical-radio comparison

A visual comparison between polarimetric, optical and radio light curves around the outburst is reported in Fig. 11. Although we have missed the beginning of the optical outburst, this comparison suggests that the radio emission has a lag respect to the optical. If we consider the decline we can estimate a temporal lag of almost 1-2 months, the same is true if we consider the optical maximum and the radio peak. The polarization flare is obviously related to the optical and radio outburst but we have missed the beginning and, therefore, we cannot have a quantitative comparison of the events. We can only argue that the polarization flare seems to decay faster than the optical and radio ones.

[FIGURE] Fig. 11. Radio (22 GHz) and optical (V) flux curves, and optical polarization around the great 96-97 outburst

We have analysed the correlation between the optical and radio behaviour on the 1996-97 outburst of Mkn 421 using the discrete correlation function and the modified mean deviation method. The discrete correlation function (DCF) is analogous to the classical correlation function (which requires evenly sampled data) except that it can work with unevenly sampled data (see Edelson & Krolik 1988). The value of [FORMULA] for which DCF has the maximum is the best estimate of the lag. The optical-22 GHz cross correlation function is shown in Fig. 12. The figure shows a peak at [FORMULA] 45 days. Fig. 13 reports the optical-37 GHz cross correlation function, with a peak at [FORMULA] 30 days.

[FIGURE] Fig. 12. Optical-22 GHz cross correlation, [FORMULA]=9 days

[FIGURE] Fig. 13. Optical-37 GHz cross correlation, [FORMULA]=14 days

Another method used in this study is a modification of the mean variance method (MMD) introduced by Hufnagel & Bregman (1992) and recently performed by Edelson et al. (1995). The value of [FORMULA] for which MMD has the minimum is the best estimate of the lag. Fig. 14 shows the result for the optical-22 GHz and the lag is confirmed. The minimum is around [FORMULA] 60 days, but the curve is quite broad and a range between 30 an 60 days is reasonable. The optical-37 GHz comparison is reported in Fig. 15, and in this case the lag is of 20-30 days.

[FIGURE] Fig. 14. Optical-22 GHz mean dispersion, [FORMULA]=15 days

[FIGURE] Fig. 15. Optical-37 GHz mean dispersion, [FORMULA]=5 days

The 37 GHz radio data have a poor sampling and a low S/N ratio, then it is impossible to find a clear correlation between 22 and 37 GHz.

3.4. Where does the outburst originate?

The origin of the radio flux can be explained by the shock-in-jet-models discussed, e. g., in Marscher & Gear (1985), Hughes et al. (1989), Valtaoja et al. (1992). According to these models, the radio outbursts are caused by shocks in the relativistic jets, and an enhancement of the polarization level is expected.

It is usually expected that there should be little correlation between the optical and radio behaviour in BL Lacs. This is partly due to the fact that the optical variations typically occur more rapidly than the radio variations and, therefore, this was taken as support for the idea that the optical emission is generated in a much smaller volume than the radio emission. In some inhomogeneous synchrotron source models for blazars, however, the radio and optical emission may be strictly correlated. For some combinations of the jet geometry and particle outflow acceleration, the radio and optical emission could come from the same region, in the outer part of the jet (Ghisellini et al., 1985). For a different choice of the jet geometry and particle flow, the optical emission could come from the inner part of the jet while the radio emission is produced in the outer regions.

Many attempts to search for correlations between the optical and radio emissions in BL Lacs yielded no clear indication of a connection between the emission at the two frequencies, while different radio frequencies are well correlated, with a time delay of the emission at longer wavelengths with respect to the shorter ones (see, e.g., Hufnagel & Bregman 1992). However, other authors confirmed the correlation between some optical and radio flux variations and suggested that sometimes the optical variations precede the radio outbursts (see, e.g., Valtaoja et al. 1987, Tornikoski et al. 1994b). The radio delays can be easily explained by source opacity arguments, and one might even expect radio and optical variations to be simultaneous above the frequency where the source turns transparent (for an example see Tornikoski et al. 1994a).

Although our radio data on Mkn 421 are affected by large uncertainty, the statistical analysis we performed shows quite clearly the optical-radio correlation for the great 1996-97 outburst, with the radio emission which lags of 30-60 days respect to the optical emission. The lag is shorter than the outburst temporal scale ([FORMULA]5 months), therefore the radio and optical emissions probably came from the same physical region, such as might be expected at a shock front in the jet.

Moreover, recent comparisons of the optical and VLBI polarization position angles for BL Lacs appear to confirm that the optical and radio emissions are sometimes linked (Gabuzda & Sitko 1994, Gabuzda et al. 1996). This observed correspondence could be explained in a natural way if the optical polarization of BL Lac objects is associated with the formation and emergence of new VLBI components. One natural possibility is that the optical polarization originates in compact, highly energetic shocks as they form and emerge from the core (Gabuzda et al. 1996). Since the distance traveled behind the shock front by a relativistic electron before suffering radiative losses would depend on energy, the thickness of the emission region would decrease with increasing frequency. This would naturally produce the optical/radio lag and account for its being shorter than the variability time-scales. However, shock fronts alone cannot solve all the problems with the relativistic jet model, since spectral variability would still be expected. Celotti, Maraschi & Treves (1991) computed simulated light curves that would be expected in the inhomogeneous jet model, approximating the propagation of a shock wave in the jet by a schematic perturbation of given size and amplitude moving at constant speed. They predicted strong spectral variability only above the spectral break and a substantial stability below. If we consider that for Mkn 421 the spectral break is placed in the X-ray region, we can argue that the observed lack of spectral variability in the optical region is therefore in agreement with this model.

Very high resolution VLBI maps of Mkn 421 show an unresolved core and outer components that exhibit apparent superluminal motion along the jet without significant change of position angle (Zhang & Baath 1990, 1991). VLBI observations therefore can be used to study a new component emerging from the core during an outburst and to study its behaviour on its way out. Recent observations (13 March 1997) made with the NRAO VLBA at the frequency of 15 GHz seem to confirm the presence of a new component after the 96/97 outburst (Kellermann et al. 1998).

3.5. Comparison between our data and high-energy flares

Mkn 421 is a well-known variable source in the TeV and X-ray spectral bands. Whipple observations show that the mean [FORMULA]-ray emission has gradually decreased from 1995 to 1997 (Mc Enery et al. 1997). Some well definite rapid flares are superimposed to this trend, with typical time scales of only a few hours or days. On February 1, 1997, for example, the [FORMULA]-ray emission increased by a factor of 5.5 above the average flux with a duration less than a day. The most impressive variation occurred in May 7, 1996, when the flux increased by a factor of 5 in 2.5 hours and Mkn 421 became the most intense source of TeV [FORMULA]-rays ever observed (Mc Enery et al. 1997). This flare was followed by another less pronounced [FORMULA]-ray flare only a few days after (May 15, 1996).

Similar to the TeV [FORMULA]-ray variability, also the X-ray behaviour of Mkn 421 can be described as composed of a series of rapid flares (Schubnell 1997). Up to date, many evidences are available that show how rapid TeV and X-ray flares are strictly correlated, and this fact find a natural explanation if the same non-thermal electrons are responsible for the two emission components, with the [FORMULA]-rays produced by Inverse Compton Scattering (see, e.g. Macomb et al. 1995).

Optical data taken in the same period of the X-ray/TeV flares generally did not show an increase in the optical flux (Schubnell 1997, Fiorucci et al. 1997) or show a correlation with high-energy flares but a less pronounced variation of only one or two tenths of magnitude (Buckley et al. 1996, Weekes et al. 1996).

In Fig. 16 are indicated with vertical lines the dates of the high-energy flares superposed to the optical flux. Our data substantially confirm that in the period of X-ray/TeV flares the optical flux is marginally influenced by the high-energy events. On the other hand, the optical outburst follows the May 1996 flares by almost 5 months, and the February 1997 flare happens during the decline of the outburst.

[FIGURE] Fig. 16. Optical V flux around the outburst and the dates of the X-ray/TeV flares: May 7, 1996, May 15, 1996 and February 1, 1997

At present, there are not clear evidences that can link the long term optical and radio variation with the rapid TeV flares observed in the same period. The different temporal scales of the low-energy and high-energy events suggest that the variations arose from two distinct, spatially separated sources.

In synchrotron emission, photons are produced with energies scaled by the magnetic field intensity:


and the electron cooling time is inversely proportional to the square of the magnetic field:


If we assume that both the maximum Lorentz factor of electrons ([FORMULA]) and the magnetic field intensity (B) decrease with distance along the jet, then the spectra produced closer to the central engine are expected to be shifted to higher frequencies than the spectra produced in the more distant regions. With this assumption the high-frequency synchrotron flares are produced by electrons having a faster cooling time and so they are more rapid than the low-energy flares.

For this reason we suggest that Mkn 421 variability can be explained with the superposition of spectra arising from at least two spatially separated sources, one which is relatively long-lived (weeks, months) and is placed in the outer parts of the jet, another which is short-lived (hours/days) and is closer to the central engine. Probably both sources represent dissipative "events" (shocks/reconnection sites) propagating along the jet at relativistic speeds, but the effects in the spectral energy distribution are different since different are the emission regions.

This effect can explain why Mkn 421 show a much higher amplitude of variability in X-ray and TeV bands than at lower energies within respective spectral components (Sikora et al. 1998): if the rapid flare is produced close to the central engine then it will be probably observed to have high amplitudes only in the high energy tails of the synchrotron and Compton components, and it will have negligible contribution at lower frequencies. On the other hand, if the long flare is produced in the outer regions of the jet then it will be probably observed to have high amplitudes only in the low energy tails of the synchrotron and Compton components.

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© European Southern Observatory (ESO) 1998

Online publication: September 30, 1998