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4 Discussions

4.1 Long-term optical variability

Present light curves (Fig. 3) in combination with the optical light curves given by Wagner et al. (1996) and by Ghisellini et al. (1997) are used to decipher behaviour of the long-term optical variability of the blazar. The 8 months (in 1990/1991 winter) long relative light curve given by Wagner et al. (1996) shows a variation of about 2.5 mag in R passband. The source remained in "low'' state for about 50 days starting from $\rm JD=2448150$.Then, after a slight brightening, it declined to a minimum intensity level around $\rm JD=2448270$. After that it brightened ($\sim$2.5 mag in R) rapidly to reach a maximum intensity level around $\rm JD=2448300$. On the other hand, over the 5 months (November 1994 to April 1995) observational period, the light curve in R passband given by Ghisellini et al. (1997) shows that the source brightened after $\rm JD=2449720$, remained bright for $\sim$50 days, and then faded rapidly to reach a minimum intensity level around $\rm JD=2449800$. Thus in the long-term optical variability of the blazar, events with rapid brightening as well as fading (only one in both cases) have been observed in the above mentioned two R passband light curves. It has to be noted that the durations of both events are almost the same about 30 days.

The average calibrated B,V,R and I magnitudes of the blazar during present observations are $\sim$14.7, 14.2, 13.8 and 13.3 respectively. A comparison of these numbers and the present light curve (Fig. 4) with optical light curves given by Ghisellini et al. (1997) indicates that during the entire period ($\sim$30 days) of our campaign, the blazar was in a relatively low state without any rapid large amplitude ($\ge$ 1 mag) brightening or fading as the exhibited maximum variations are only $\sim$0.2 mag in all four passbands.

4.2 Inter-night variability

As seen from Fig. 3, the blazar remained moderately active during the 4-weeks of monitoring, the observed variations often being much larger than the rms scatter of the relative magnitudes of the pair of comparison stars, which is found to be $\sim$0.014 mag for all the four passbands. Table 3 lists the date, amplitude and duration of those outbursts whose profiles are clearly defined. There seems to be a weak correlation between amplitude and duration of the flares in the sense larger the amplitude longer its duration. For shorter duration flares, the rising and decaying times appear approximately equal and profiles are symmetric with no indications of a "plateau'' longer than one day. Similar behaviour has also been noticed by Ghisellini et al. (1997). For the largest outburst, the profile is asymmetric with rising time about one day and decaying time about 3 days.

Table 3:  Clearly defined outbursts of the blazar S5 0716+71

{ccc} \hline 
 Date & Amplitude & Duration \\  
 March 94 & (mag...
 ... 2 \\  ~7 & 0.20 & 4 \\  18 & 0.24 & 4 \\  26 & 0.12 & 2 \\  \hline\end{tabular}

From the DLCs of all 4 passbands, it appears that the blazar outbursts are superposed on a constant base level emission. This behaviour differs from those observed during the extended optical monitoring campaigns of Wagner et al. (1996) and Ghisellini et al. (1997) when the base levels were found to either drop from a "high'' to a "low'' state or vice-versa by almost a factor of 2 or so within about a day (see also Quirrenbach et al. 1991). The quasi-periodicity of the optical light curve with a characteristic time scale of 1 day, which was then found to persist for a week is not clearly evident during our observations, only some indication of it is present during the first week (Fig. 3). A rigorous comparison of the present data with the earlier dataset would be difficult, because the location of this blazar restricted the monitoring from India during the month of March to just 4-6 hours per night, at most, thereby leaving large gaps in the light curves. It is clear, nonetheless, that in all four passbands the blazar exhibited variations of up to $\sim$0.2 mag between two consecutive nights, as measured relative to both comparison stars. Furthermore, the light curves in the four passbands are tightly correlated, indicating that the spectrum of the flaring component is not much different from that of the "base'' emission. Recall that a close similarity of the light curves at R, V and B during the quasi-periodic variations was also noticed during the 1990 campaign (Quirrenbach et al. 1991; Wagner et al. 1996). However, the campaign by Ghisellini et al. (1997) indicates that in the "low'' optical state of the blazar, the (B-R) spectral index responds to fast optical variations occurring on day-like time scales, the spectrum becoming bluer with increasing brightness in R.

4.3 Flux-optical spectral index correlation

In order to study the correlation between flux and optical spectral index ($\alpha_{BI}$) defined by the BVRI values of present observations, we plot the standard R magnitude and $\alpha_{BI}$ against time in Fig. 4. We determined the R values from the compressed DLCs presented in Fig. 3 and the calibrated R magnitude of star 1 given in Table 1. The spectral index $\alpha_{BI}$ has been calculated by a least-square linear fit procedure, after dereddening the observed calibrated flux of the blazar in BVRI passbands. For this, following Ghisellini et al. (1997), the reddening corrections were taken as AB = 0.30, AV = 0.23, AR = 0.19 and AI = 0.14 magnitudes. The regression coefficients of the linear fit are always $\sim$1. The values of $\alpha_{BI}$ obtained in this way vary from 0.81 to 1.01 with a mean value of 0.84 $\pm$ 0.043, and do not have any significant correlation with the flux (see Fig. 4). Ghisellini et al. (1997) have also obtained a similar result. However, the values of their spectral index, $\alpha_{BR}$ have some what larger range (from 0.81 to 1.15) and higher mean value, 0.94.

\includegraphics [height=12cm,clip]{}
\end{figure} Figure 4:   The light curve in the R passband (lower panel) is compared with the corresponding optical spectral index $\alpha_{BI}$ (upper panel)

4.4 Intra-night variability

An important issue in the variability studies concerns the shape(s) of the profiles of the flares. For some of the densely monitored blazars, the large individual optical flares seen on the time-scale of $\approx$1 day are characterized by exponential growth and decay profiles, as, e.g., in the cases of the intra-day variable blazars PKS 2155-304 (Urry et al. 1993) and S5 0954+658 (Wagner et al. 1993). In contrast, the individual flares on day-like time scale recorded in 1990 and 1994-95 optical monitoring of the present blazar S5 0716+71 are well described by linear profiles (cf. Wagner et al. 1996; Ghisellini et al. 1997). Since any dichotomy of this nature can signify fundamentally different emission processes, we have made an attempt to determine the shapes of the individual optical flares of S5 0716+71 recorded during our campaign.

As seen from Figs. 1 and 2, the blazar showed on 3 nights prominent optical flares with rates $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... per hour, sustained over a minimum of two hours (see also, Fig. 5). Note that the positive bump peaking around $19^{\rm h}$ UT on the DLCs of March 4 is clearly related to the variation of the comparison star 1 (Fig. 1) and hence we have ignored the affected portion of the blazar DLC from subsequent analysis. Since all three flares indicate a linear temporal variation on the magnitude scale, we have fitted least-square regression lines to these flaring segments of the DLCs. These best-fit lines are shown in Fig. 5 and their slopes are given in Table 4, together with the regression coefficients. It is interesting that for each flare the slopes are essentially the same for the different passbands. The difference in the slopes is always $\le 1 \sigma$. It is therefore not statistically significant. Moreover, the regression coefficients for the linear fits are $\geq$ 90% in all cases, excepting the I-band profile on March 18 which is noisy, as evident from the DLC of the comparison stars (Fig. 1). Thus, at least over the few hours spanned by these observations, all the three prominent events of intra-night variability can be described by linear trends on magnitude scale (which, therefore, corresponds to an exponential intensity variation). Similar linear intra-night magnitude variations in B and R bands have been noticed by Ghisellini et al. (1997) on two occasions. Unfortunately, none of the flaring segments of the present DLCs encompass the intensity turnover point (which is not unexpected considering the modest durations of these DLCs). Therefore, the question of linear vis-a-vis exponential variation cannot yet be settled conclusively, though an exponential intensity variation seems to be consistent with all the prominent intra-night flares recorded in the present as well as Ghisellini et al. (1997) optical observations of S5 0716+71. It would be of great interest to enquire if the shapes (linear/exponential) of the outbursts of a given blazar depend on the time-scale of the outburst and whether they vary from one occasion to another.

\includegraphics [angle=-90,width=14.5cm,clip]{}\end{figure} Figure 5: DLCs relative to the comparison star 1 in the R and I passbands for those three nights when the blazar intensity varied by $\protect\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
 ...skip\halign{\hfil$\scriptscriptstyle ... per hour for a minimum of 2 hours. The data for the remaining 2 passbands have not been plotted as the temporal coverage was not so dense as in R and I, due to lower sensitivity of the CCD. Note that the positive bump seen in the profiles of March 4 near 19 UT is clearly due to a variation of the comparison star (see Fig. 1) and therefore has been ignored in the computation of the best fit-line

Table 4:  Slopes and regression coefficients ($\gamma$) of the least-square linear fits to the intra-night magnitude variations

{ccc ccc} \hline 
 Date& Filter &\multicolumn{2}{c}{DLC1} &\mult...
 ...m$\space 0.006 & 0.78 &$-$0.010 $\pm$\space 0.008 & 0.37 \\  \hline\end{tabular}

4.5 Search for ultra-rapid fluctuations

Since on many nights in the present campaign, a fairly dense temporal coverage was achieved simultaneously in the different passbands, it is possible to look for any ultra-rapid fluctuations on time scales shorter than $\sim$1 hour. In particular, such events can provide important clues to relativistic beaming of the AGN's optical radiation (e.g., Guilbert et al. 1983). Indeed, based on the 1990 campaign substantial flickering of this blazar on time scales as short as $\sim$15 min was inferred from the structure function analysis of the optical light curve (Wagner et al. 1996). A close look at Fig. 1 reveals many events of ultra-rapid fluctuations, often occurring in more than one passband simultaneously. Table 5 provides a log of such individual events which were detected during almost every observing run. However, it turned out that practically each one of these fluctuations is due to one of the comparison stars, since the simultaneous DLC relative to the other comparison star does not show the corresponding fluctuation. The only exception is a 0.15 mag jump seen at $\sim$16.5 UT on March 3; however, its reality is uncertain since the feature is a single data point seen only on the V-band DLC (Fig. 1). Thus, the availability of differential light curves using multiple comparison stars serves as a powerful discriminator and a safeguard against serious misinterpretation of the data. It may be noted that the amplitudes of these ultra-rapid fluctuations are typically of order of a few percent and thus the present optical data of 1994 do not exclude the possibility of the blazar exhibiting lower level ultra-rapid variations, similar to those inferred by Wagner et al. (1996) from the statistical analysis of the 1990 light curves of this blazar.

Table 5:  Rapid intensity fluctuation events seen on the DLCs, and the comparison stars most likely responsible for the events

{cc clc} \hline 
 Date&UT & Amplitude & \multicolumn{1}{c}{Filte...
 ...\ 26 &15.5 &0.06 &$R,I$& 2 \\ 28 &$\sim$15 &0.05 &$R$& 2 \\  \hline\end{tabular}

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