MULTICOLOR OPTICAL MICROVARIABILITY IN S5 0716+714

The light curves for the individual nights are displayed in Figure 1, panels (A)–(E), in time order. The I-band data is plotted with an offset of 0.2 mag so it can be displayed on the same plot as the B-band data. B observations are the diamonds, I observations are the circles. The magnitudes shown are differential magnitudes (source minus comparison) and times are UT. Significant variability was detected from night to night during the course of the observations. Between the first two nights the source was observed, it increased in brightness by 0.10 mag in B and 0.06 mag in I. From night 2 to night 3, the source decreased in brightness by 0.35 mag in B and 0.28 mag in I. Between nights 3 and 5, the source brightened by 0.74 mag in B and 0.68 mag in I.

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Below we discuss the variability amplitudes and timescales observed on individual nights.

2003 March 5. On this night, we observed a 0.072 mag increase in brightness in B and 0.063 in I over the first 2.65 hr of observing, followed by a decline in brightness of 0.069 mag in B and 0.077 in I over 1.90 hr. There is evidence of smaller amplitude events superposed on this overall variation. The two most convincing of these is the event centered on UT 7.756, which has a depth of 0.02 mag in B and 0.02 in I and a duration of 0.66 hr. The second event is centered on UT 9.53, with duration of 0.39 hr and an amplitude of 0.011 in B and 0.011 in I.

2003 March 6. The variability this night was characterized by rapid increases and decreases in brightness. The source displayed a rise of 0.154 mag in B and 0.122 in I over 1.8 hr, followed by a decline in brightness of 0.130 mag in B and 0.103 in I over 1.54 hr, followed by a brightness increase of 0.139 in B and 0.126 in I over 2.42 hr.

2003 March 7. This night's observations began with a well-defined outburst with an amplitude of 0.043 mag in B and 0.045 mag in I, lasting for 1.67 hr and centered on UT 4.45. The source next brightened by 0.187 mag in B and 0.161 mag in I over 2.55 hr. At the end of the observation, there appears to be a well-defined outburst in the B band, with an amplitude of 0.018 mag lasting for 0.79 hr, though there is no obvious counterpart in the I band.

2004 March 8. This night begins with an event centered on UT 3.38 which lasted for 1.5 hr, with an amplitude of 0.031 mag in I and 0.020 mag in B, which is marginally significant given the error bars on B. The source next increased in brightness by 0.050 mag in I and 0.037 mag in B over 0.69 hr, followed by a steady decline in brightness of 0.160 mag in I and 0.124 mag in B over 3.43 hr. Superposed on this decline is evidence of small amplitude events of amplitude 0.01–0.02 mag which are clearly seen in both filters. The night's observation ends with another well-defined event with an amplitude of 0.050 mag in I and 0.036 mag in B and a duration of 1.18 hr.

2004 March 9. The night begins with a decline of 0.08 mag in B and 0.053 mag in I over the first 3.0 hr. Toward the end of this overall decline, there is a rapid decline of 0.065 mag in both filters, followed by an outburst centered on UT 6.5 with an amplitude of 0.05 mag in both filters. The source then rapidly brightens by 0.04 mag in both filters, remains at a constant level for 0.5 hr, then begins a gradual decline for about 1 hr. At the very end of this decline, another sharp drop in brightness occurs with an amplitude of 0.07 mag in both filters, followed by a recovery lasting to the end of the observations.

2003 March 5. A plot of the flux in the I band versus the flux in the B band (F_I versus F_B) and a plot of the ratio of the flux in the B band to the flux in the I band versus the flux in the B band (F_B/I versus F_B) are shown in Figures 2(A) and (B). The flux units in B and I are arbitrary. The plot of F_I versus F_B shows a linear relationship between F_I and F_B with a Spearman correlation coefficient of 0.93 and a confidence factor of 1.4 × 10⁻¹⁷. The F_B/I versus F_B plot shows a counterclockwise hysteresis loop. We have connected the points in time to show this more clearly. As the source increases in brightness in the B band, it appears to stay within a confined range of F_B/I. As it reaches and passes the peak of the variation, F_B/I increases, then as the source fades, F_B/I again remains confined in a narrow range, although higher than on the rising branch. A smaller loop is evident on the right-hand edge of the plot, this loop is in a clockwise direction and corresponds to the dip in the light curve centered on UT 7.75.

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We define the significance of these loops in terms of a measure of their width in relation to the error bars. Since the loops are not circular, we choose and average of the long and short axis of these loops scaled to 1 error bar (σ). For this night, we find the loops range in significance from 2.5σ for the smallest loops to 4.9σ for the largest loop.

2003 March 6. The F_I versus F_B and F_B/I versus F_B plots are shown in Figures 2(C) and (D) for this night. The F_I versus F_B plot is linear, with a Spearman correlation coefficient of 0.96 and a confidence factor of 4.2 × 10⁻²⁴. The F_B/I versus F_B plot clearly shows a clockwise hysteresis loop with a significance of 16σ. This clockwise loop describes the dip in the light curve that runs from UT 5.8 to UT 9.3 in Figure 1(B). As the source brightens, F_B/I remains relatively constant, as the peak is passed, F_B/I decreases and remains relatively constant during the declining branch. Then as the source reaches a minimum and begins to increase in brightness again, F_B/I returns to a relatively constant level, nearly identical to the i_B/I values seen at the beginning of the observation.

2003 March 7. Figures 2(E) and (F) display the i_I versus F_B and F_B/I versus F_B plots. The F_I versus F_B plot shows a linear trend followed by a plateau, which is different from the strictly linear behavior the F_I versus F_B plots displayed the first two nights the source was observed. The plateau is coincident with the last two hours of variability seen in Figure 1(C). The Spearman correlation coefficient is 0.91 with a confidence factor of 8.49 ×10⁻²² for the linear portion of this plot. Counterclockwise loops are visible at the beginning and end of the F_B/I versus i_B plots, correlating with the mini-bursts seen at the beginning and end of this nights observation. These loops have a significance of 6.5σ for the loop corresponding to the beginning of the observation and 9.0σ for the loop corresponding to the end of the observation. In addition, a linear trend is visible corresponding to the last two hours of the observation, with F_B/I increasing (becoming bluer) as F_B increases.

2003 March 8. The F_I versus F_B curve (Figure 3(A)) shows a linear relationship over the entire observation, with a Spearman correlation coefficient of 0.96 ×10⁻³⁰. F_B/I versus F_B (Figure 3(B)) shows counterclockwise loops corresponding to mini-bursts and clockwise loops corresponding to dips in brightness. These loops range in significance from 4.5σ to 16σ.

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2003 March 9. Figures 3(C) and (D) show the F_I versus F_B and F_B/I versus F_B plots for this night. The F_I versus F_B plot is linear, with a Spearman correlation coefficient of 0.94 and a significance factor of 3.1 × 10⁻²². F_B/I versus F_B initially shows a slight increase in F_B/I as F_B increases, then exhibits the looping behavior seen in previous nights corresponding to the bursts and dips seen toward the end of this night's observations. The significance of these loops ranges from 24σ to 4σ.

The Z-transformed discrete cross-correlation (ZDCF) program of Alexander (1997) was applied to the observations to search for the presence of any lags. Magnitudes were converted to arbitrary flux and we searched for any lags between the flux in different wavelength bands and between F_B and F_B/I. The resulting plots of correlation coefficient R versus lag are shown in Figures 4(A)–(F) and Figures 5(A)–(D). Table 1 summarizes the results of this analysis. The lag was determined by fitting a Gaussian to the peak in the plot and the quoted errors are the errors on the Gaussian fit. In order for us to consider a lag meaningful, we require that the magnitude of the lag be greater than three times the data spacing, i.e., only lags greater than 0.39 hr (23 minutes) are considered meaningful. Using this criteria, no meaningful lags were found between the B- and I-flux variations for any of the five nights of observations. Three meaningful lags were found between F_B/I and F_B were on the nights of 2003 March 5, 2003 March 6, and 2003 March 7. A lag of 85.8 ± 1.8 minutes with R = 0.61 is seen on the night of 2003 March 5, where F_B/I leads F_B. On UT 2007 March 6, we find F_B leads F_B/I by 31.8 ± 0.02 minutes, with R = 0.44. A lag of 85.8 ± 0.6 minutes with an R = 0.59 was found on UT 2003 March 7, where F_B/I was leading F_B.

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In order to obtain a determination of the significance of these lags, we set out to determine how often such lags might occur by chance. Using a Monte Carlo type methodology, pairs of B and I light curves were simulated using the slopes of the PDS found for a given nights B and I light curves. B/I flux ratios and light curves were determined and the data were sampled consistent with the sampling of the actual observations. The ZDCF algorithm was applied to these time series, and we determined the percentage that any lag with the same or better quality (as defined by the cross-correlation coefficient R) was detected. We also determined the percentage that a lag of the same sign would occur. For 2003 March 5, we find a lag of the same or better quality randomly occurs 10% of the time and a positive lag of the same or better quality occurred 6% of the time. The night of 2003 March 6, we find a lag of the same or better quality randomly occurs 18% of the time and a negative lag of the same quality occurs 10% of the time. On 2006 March 7, we find a lag of the same or better quality randomly occurs 10% of the time and a positive lag of the same or better quality occurs 2% of the time. This leads us to conclude the detected lags are significant.

A structure function analysis was applied to the data from both filters on all five nights. From such an analysis one can derive the slope of the structure function, which is related to the type of process associated with the times series (red noise, white noise, flicker noise, etc.). We found that for the nights of March 5–7, the structure functions resembled each other, displaying a linear rise to a turnover at a lag related to a characteristic variability timescale (Figures 6(A)–(F)). The last two nights, March 8 and 9 (Figures 7(A)–(D)), the structure functions displayed far more complex structure with multiple breaks and plateaus, indicative of several different variability timescales present in the data. Slopes were determined via linear fits in the range between three times the data spacing and 2/3 the length of the data train except for the last two nights, where we measured the slopes on either side of any detected breaks or plateaus. On March 8, we see a slope of in B of 1.36 and 0.98 in I up to timescales of 1 hr. Between 1 and 1.6 hr, the SF is mostly flat, from timescales of 2 hr up to 2.4 hr, the SF has a slope of 1.5 in B and 1.02 in I. On March 9, we see a slope in B of 0.60 up to timescales of 0.8 hr. Between 0.8 and 0.93 hr, the structure function (SF) is mostly flat, from timescales of 0.93 hr up to 1.95 hr, the SF has a slope of 1.68 in B. The structure function plateaus a second time, from 1.95 hr to 2.29 hr, then steepens to a slope of 2.22 from 2.29 to 2.86 hr. After 2.86 hr, it abruptly flattens until 3.24 hr then rises with a slope of 1.03 to timescales of 4.2 hr. In I we see a slope of 0.60 up to timescales of 0.78 hr. From 0.78 to 1.05 hr there is an abrupt decrease and then flattening. From 1.05 hr up to 1.82 hr the structure function has a slope of 1.5. There seems to be a much larger degree of low amplitude, very rapid microvariability on this night, which is contributing to the disparity in the structure function results between the two wavebands. The results are summarized in Table 2.

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The data set we have obtained allows us to determine a differential calibration of the I-band magnitude of comparison star 4 from the sequence of Villata et al. (1998), which is not included in the I-band calibration of the comparison stars in this field of Ghisellini et al. (1997). We determined the I-band magnitude of star 4 with respect to stars 6, 5, and 3 of Ghisellini et al. (1997) for each night, then averaged these values to obtain an magnitude with respect to each comparison star. We then averaged these values to obtain an I-band magnitude for star 4 of 12.645 ± 0.003.

During the course of these observations, complete events with a variety of timescales were observed. Invoking light travel time arguments, we can use the timescales of such events to define upper limits to the size of the emission regions responsible for the variations. The maximum timescale event that was observed was the event on 2003 March 5, which has a timescale of 4.55 hr. The shortest observed events occurred with timescales of 30– 60 minutes and were seen throughout the data; we will take 30 minutes as the lower limit to the shortest timescale variation seen. Invoking light travel time arguments, i.e., R ⩽ δcΔt we find that the regions responsible for the observed microvariability range in size from R ⩽ 5.38 ×10¹³δ cm to R ⩽ 4.90 ×10¹⁴δ cm. Adopting the value of δ = 20 from Nesci et al. (2005), we find this range to be R ⩽ 1.07 ×10¹⁵ cm to R ⩽ 9.8 ×10¹⁵ cm.

Lags observed between F_B and F_B/I and hysteresis loops arise when the information about a variation propagates through the spectral energy distribution. In the model proposed by Kirk et al. (1998) hysteresis loops are expected, and their directionality is a function of the observed frequency and the frequency at which the synchrotron emission component peaks. In this model, one would expect to see only clockwise loops for bursts in S5 07176+1714, since these optical observations are at a frequency far below the peak synchrotron frequency in this source, where the cooling rate for the electrons is much slower than their acceleration rate. However, we see counterclockwise loops for bursts in the observations presented here, opposite what is expected in this model. Inspection of the light curves presented in Figures 1((A)–(E)) shows that the flares are all symmetric, with the exception of the night of 2003 March 5. However, one could easily argue that the observations did not cover the entire flare that night and that if they did one would see a symmetric shape to the flare. If the observed microvariability is the result of local turbulence in the jet and the light crossing time of these turbulent regions is longer than the cooling and particle injection timescales in these regions, symmetric flares (Xilouris et al. 2006) are expected. This leads us to conclude the observed variations are determined by the size of the turbulent regions and not the electron cooling or acceleration timescales intrinsic to those regions.

Table 2 gives the slope(s) of the structure function for each filter on each night. The slopes mostly lie between 1.0 and 2.0 in a region which indicates a fractional noise process (Mandelbrot & Van Ness 1968). This is similar to the result found by Azarnia et al. (2005) who analyzed 10 separate microvariability time series via Fourier analysis. Such a process is expected from turbulent phenomena, thus these results are completely consistent with an interpretation that microvariability arises from turbulent phenomena. The location of the turbulence cannot be determined from these observations, but is most likely within the relativistic jet (Marscher et al. 1992) though there are models within which this turbulence would reside within the accretion disk (Mangalam & Wiita 1993; Chakrabarti & Wiita 1993). No obvious dependencies of the slope on wavelength band are present though we obtained different results between wavebands on the night of March 9th as discussed above. Table 3 gives the variability timescales derived from the turnover or breaks identified within each structure function. The derived timescales are consistent between the two passbands, with the greatest discrepancy again on the night of March 9.