Multicolor Optical Monitoring of the BL Lacertae Object S5 0716+714 during the 2012 Outburst

BL Lacertae (BL Lac) objects are the most extreme subclass of active galactic nuclei (AGNs), hosted in massive elliptical galaxies, the emission of which is dominated by a relativistic jet closely aligned with the line of sight. This implies the existence of a parent population of sources with a misaligned jet that has been identified with low-power Fanaroff–Riley type I radio galaxies. The most distinctive characteristic of the class is the weakness or absence of spectral lines that historically hindered the identification of their nature and thereafter proved to be a hurdle in the determination of their distance (Angel & Stockman 1980; Urry & Padovani 1995; Falomo et al. 2014). The spectrum of BL Lac objects, dominated by nonthermal emission over the whole electromagnetic range, together with bright compact radio cores, high luminosity, rapid and large amplitude flux variability at all frequencies, and strong polarization, make these sources become an optimal laboratory for high-energy astrophysics. The broadband spectral energy distributions of BL Lac objects have a double-peaked structure. The low-energy peak at the IR-optical-UV band is explained with the synchrotron emission of relativistic electrons, and the high-energy peak at the GeV–TeV gamma-ray band is due to the inverse Compton scattering (e.g., Dermer 1995; Dermer & Schlickeiser 2002; Bottcher 2007). The hadronic model is an alternative explanation for the high-energy emission from BL Lac objects (e.g., Dermer et al. 2012). According to their differences in synchrotron peak frequency, BL Lac objects can be divided into three categories (Abdo et al. 2010): low-synchrotron-peaked (${\nu }_{\mathrm{peak}}^{s}\lt {10}^{14}\,\mathrm{Hz}$), intermediate-synchrotron-peaked (ISP; ${10}^{14}\,\mathrm{Hz}\lt {\nu }_{\mathrm{peak}}^{s}\lt {10}^{15}\,\mathrm{Hz}$), and high-synchrotron-peaked (${10}^{15}\,\mathrm{Hz}\lt {\nu }_{\mathrm{peak}}^{s}$).

The variabilities of BL Lac objects at frequencies ranging from radio to TeV bands have been detected (e.g., Rani et al. 2013; Liao et al. 2014; Bartoli et al. 2016). The timescales of variabilities are from years to minutes (e.g., Fan 2005; Zhang et al. 2008a; Fan et al. 2009a, 2014; Poon et al. 2009). Brightness changes of a few tenths or hundredths of a magnitude during hours or less are often known as intraday variability (IDV) or microvariability (Wagner & Witzel 1995). Short-term variability (STV) has timescales of days to weeks, even months, and long-term variability ranges from months to years (Gupta et al. 2008a; Dai et al. 2015). IDV has been confirmed as the intrinsic nature of the BL Lac objects and has become a subject of intense activity, as its physical mechanisms are not understood well (e.g., Bai et al. 1998; Zhang et al. 2008b; Fan et al. 2009b; Chandra et al. 2011; Dai et al. 2015; Xiong et al. 2016). The shortest variability (microvariability) timescales are important for understanding the geometry of jets, the magnetic field, and black hole mass, because they provide a possible minimum size of variation sources (e.g., Zhang et al. 2008b; Fan et al. 2009b, 2014; Gupta et al. 2009; Rani et al. 2010; Dai et al. 2015; Xiong et al. 2016). The spectral index (or color behavior) is an important but simple factor to explore the variability mechanism (e.g., Wu et al. 2007; Zheng et al. 2008; Gu & Ai 2011).

The object S5 0716+714 (R.A. = ${07}^{{\rm{h}}}{21}^{{\rm{m}}}53\buildrel{\rm{s}}\over{.} 4$, decl. =$71^\circ {20}^{\prime }{36}^{\prime\prime }$, J2000) is classified as an ISP BL Lac object (${\nu }_{\mathrm{peak}}^{s}={10}^{14.6}\,\mathrm{Hz};$ Abdo et al. 2010). It was discovered in the Bonn-NRAO radio survey of flat-spectrum radio sources with a 4.9 GHz flux greater than 1 Jy (Kuehr et al. 1981). Radio maps detected a compact core-jet structure and an extended emission resembling that of an FR II object (Antonucci et al. 1986; Gabuzda et al. 1998). The source has a featureless optical continuum with a redshift of 0.31 ± 0.08 derived by using the host galaxy as a standard candle (Nilsson et al. 2008). Danforth et al. (2013) used intervening absorption systems to set the redshift range $0.2315\lt z\lt 0.3407$. It is one of the brightest BL Lac objects that is highly variable from radio to gamma-ray bands with a very high duty cycle (DC; Wagner & Witzel 1995). Because of its high power and lack of signs of ongoing accretion or surrounding gas, the source is an ideal candidate to explore multiwavelength nonthermal emission. The flux and spectral variations of S5 0716+714 have been extensively studied over the entire electromagnetic spectrum (Wagner & Witzel 1995; Heidt & Wagner 1996; Wagner et al. 1996; Ghisellini et al. 1997; Sagar et al. 1999; Villata et al. 2000, 2008; Qian et al. 2002; Raiteri et al. 2003; Nesci et al. 2005; Wu et al. 2005, 2007; Foschini et al. 2006; Gu et al. 2006; Montagni et al. 2006; Ostorero et al. 2006; Stalin et al. 2006, 2009; Gupta et al. 2008b, 2009, 2012; Zhang et al. 2008b; Anderhub et al. 2009; Vittorini et al. 2009; Rani et al. 2010, 2014; Carini et al. 2011; Chandra et al. 2011, 2015; Zhang et al. 2012; Dai et al. 2013; Larionov et al. 2013; Hu et al. 2014; Liao et al. 2014; Bhatta et al. 2015, 2016; Dai et al. 2015; Wierzcholska & Siejkowski 2015, 2016; Agarwal et al. 2016; Man et al. 2016; Li et al. 2017). In the observations of Poon et al. (2009), the object showed four fast flares with amplitudes ranging from 0.3 to 0.75 mag. Typical timescales of microvariability ranged from 2 to 8 hr. Strong bluer-when-brighter (BWB) chromatism was found on internight timescales. However, a different spectral behavior was found on intranight timescales. A possible time lag of ∼11 minutes between the B and I bands was found on one night. The observations from Chandra et al. (2011) suggested that S5 0716+714 showed night-to-night and intranight variabilities at various timescales. Wu et al. (2007) found that the source showed two strong flares with variation amplitudes of about 0.8 and 0.6 mag, respectively, in the V band; strong BWB correlations were found for both internight and intranight variations; no apparent time lag was observed between the V- and R-band variations; and the observed BWB chromatism may be mainly attributed to the larger variation amplitude at shorter wavelengths. Man et al. (2016) found that variations in the R and B bands lagged approximately 1.5 minutes behind those in the I band for the object. But, from the results of Carini et al. (2011), there are no significant lags between the B- and I-band flux variations. During nearly continuous multiband observations, Bhatta et al. (2016) found that the source displayed pronounced variability and BWB spectral evolution. The results from Hu et al. (2014) showed a strong BWB trend on intranight timescales and a mild BWB trend on internight timescales for the source. Dai et al. (2013, 2015) found that BWB chromatism was observed in long, intermediate, and short timescales. Stalin et al. (2006) and Agarwal et al. (2016) found no evidence of spectral changes with source brightness on either internight or intranight timescales for S5 0716+714, even when the target was in a flaring state.

In order to further explore the characteristics of IDV and STV timescales and spectral properties on both intranight and internight timescales, we monitored the source in multicolor optical bands during the 2012 outburst. Due to the high temporal resolution and long time spans on intraday timescales, more accurate results can be obtained. This paper is organized as follows. The observations and data analysis are described in Section 2. Section 3 presents the results. Discussion and conclusions are reported in Section 4.

Our optical observations were carried out using the 60 cm BOOTES-4 auto-telescope that is located at the Lijiang Observatory of the Yunnan Observatories of the Chinese Academy of Sciences, where the longitude is $100^\circ {01}^{\prime }51^{\prime\prime} {\rm{E}}$ and the latitude is $26^\circ {42}^{\prime }32^{\prime\prime}$ N, with an altitude of 3193 m. The telescope's main objective is to observe gamma-ray bursts and blazars. Further details about it are given in Table 1. During our observations, the telescope was equipped with standard Johnson UBV and Cousins RI filters. The optical observations in the B, V, R, and I bands were in a corresponding cyclic mode. Time resolutions for most of the nights are less than 6 minutes, and time spans on a night are more than 5 hr (Table 2). The time intervals between the V and R bands range from 30 to 131 s, and most of the nights have time intervals less than 50 s. The typical exposure times in the B, V, R, and I bands are 60, 40, 40, and 40 s, respectively. Thus, our observations with high temporal resolution (few minutes) can be considered quasi-simultaneous measurements. All images have been prereduced with the CCDRED package, and observing data were processed using the photometric tool DAOPHOT in the IRAF⁶ software package. The flat-field images were taken at dusk and dawn when possible. The bias images were taken at the beginning and end of the observation. In order to determine aperture radius, we used different aperture radii (1.5 × FWHM, 1.7 × FWHM, 2 × FWHM, 2.5 × FWHM, and 3 × FWHM) to carry out aperture photometry for all observations per night. We found that the low-aperture radius had a better mean signal-to-noise ratio (S/N) on a night, i.e., 1.5 × FWHM had the best mean S/N on a night. Moreover, we plotted the aperture radii (from 1 × FWHM to 4 × FWHM) versus magnitudes for different frames on a night. The results showed that the change rate of increasing brightness was rapid from 1 × FWHM to 1.7 × FWHM and quickly slowed after 1.7 × FWHM. When the aperture radius was near 3 × FWHM, the brightness stayed almost constant. So, considering the best S/N and constant brightness, we made a compromise, i.e., the aperture radius of 1.7 × FWHM was selected. In order to obtain pure skylight background, the target and other objects should be excluded from the sky annulus. The inner radius and width of the sky annulus were 5 × FWHM and 2 × FWHM, respectively. After correcting the flat field and bias, aperture photometry was performed, and instrumental aperture magnitudes were obtained. The finding chart of S5 0716+714 was taken from the website.⁷ From the above finding chart, we chose the marked 3 and 5 stars as comparison stars, because their magnitudes were similar to that of the blazar and the differential magnitude between the 3 and 5 stars was the smallest variation among the comparison stars. Following Zhang et al. (2004, 2008a), Fan et al. (2014),  and Bai et al. (1998), the source magnitude was given as the average of the values derived with respect to the two comparison stars ($\tfrac{{m}_{3}+{m}_{5}}{2}$, where m₃ is the blazar magnitude obtained from standard star 3 and m₅ is the blazar magnitude obtained from standard star 5). The magnitudes of the comparison stars in the field of S5 0716+714 were taken from Villata et al. (1998) and Ghisellini et al. (1997). The observing uncertainty on each night was the rms error of the differential magnitude between the two comparison stars. The rms errors of the photometry on a certain night were calculated from the two comparison stars in the usual way,

$$\begin{eqnarray}&&\sigma =\sqrt{\sum \displaystyle \frac{{({m}_{i}-\overline{m})}^{2}}{N-1}},\,\,i=1,2,3,\ldots ,\,N,\end{eqnarray} \tag{ 1 }$$

where ${m}_{i}={({m}_{3}-{m}_{5})}_{i}$ is the differential magnitude of stars 3 and 5, $\overline{m}=\overline{{m}_{3}-{m}_{5}}$ is the average differential magnitude over the entire data set, and N is the number of observations on a given night. The actual number of observations for S5 0716+714 is 13 nights obtaining 683 B-band, 871 V-band, 874 R-band, and 878 I-band data points. The results of the observations are given in Tables 3–6 for filters B, V, R, and I, respectively.

Table 1.  Details of Telescopes and Instruments

Telescope	60 cm BOOTES-4
CCD model	SBIG 1001 E
Chip size	1024 × 1024 pixels
Pixel size	$24.6\times 24.6$ $\mu {\rm{m}}$
Scale	$1\buildrel{\prime\prime}\over{.} 07$ pixel−1
Field	${18}^{\prime }\times {18}^{\prime }$
Gain	1.75 ${e}^{-}$ ADU−1
Readout noise	16 ${e}^{-}$ rms
Binning used	1 × 1
Typical seeing	15

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In order to quantify the IDV of the object, we have employed three statistical analysis techniques: the C-test, F-test, and one-way analysis of variance (ANOVA) (e.g., de Diego 2010; Goyal et al. 2012; Hu et al. 2014; Agarwal & Gupta 2015; Dai et al. 2015; Xiong et al. 2016). The blazar is considered variable (V) if the light curve satisfies the criteria of the C-test, F-test, and ANOVA. The blazar is considered probably variable (PV) if only one of the above three criteria is satisfied. The blazar is considered nonvariable (N) if none of the criteria are met. Romero et al. (1999) introduced the variability parameter, C, as the average value between C₁ and C₂,

$$\begin{eqnarray}&&{C}_{1}=\displaystyle \frac{\sigma (\mathrm{BL}\mbox{--}\mathrm{StarA})}{\sigma (\mathrm{StarA}\mbox{--}\mathrm{StarB})},{C}_{2}=\displaystyle \frac{\sigma (\mathrm{BL}\mbox{--}\mathrm{StarB})}{\sigma (\mathrm{StarA}\mbox{--}\mathrm{StarB})},\end{eqnarray} \tag{ 2 }$$

where (BL–StarA), (BL–StarB), and (StarA–StarB) are the differential instrumental magnitudes of the blazar and comparison star A, the blazar and comparison star B, and comparison stars A and B, respectively. Here σ is the standard deviation of the differential instrumental magnitudes. The adopted variability criterion requires $C\geqslant 2.576$, which corresponds to a 99% confidence level. Despite the very common use of C-statistics, de Diego (2010) pointed out that it has severe problems. The F-test is considered to be a proper statistics to quantify the IDV (e.g., de Diego 2010; Joshi et al. 2011; Goyal et al. 2012; Hu et al. 2014; Agarwal & Gupta 2015; Xiong et al. 2016). The value of F is calculated as

$$\begin{eqnarray}&&{F}_{1}=\displaystyle \frac{\mathrm{Var}(\mathrm{BL}\mbox{--}\mathrm{StarA})}{\mathrm{Var}(\mathrm{StarA}\mbox{--}\mathrm{StarB})},{F}_{2}=\displaystyle \frac{\mathrm{Var}(\mathrm{BL}\mbox{--}\mathrm{StarB})}{\mathrm{Var}(\mathrm{StarA}\mbox{--}\mathrm{StarB})},\end{eqnarray} \tag{ 3 }$$

where Var(BL–StarA), Var(BL–StarB), and Var(StarA–StarB) are the variances of the differential instrumental magnitudes. The F-value from the average of F₁ and F₂ is compared with the critical F-value, ${F}_{{\nu }_{\mathrm{bl}},{\nu }_{* }}^{\alpha }$, where ${\nu }_{\mathrm{bl}}$ and ${\nu }_{* }$ are the number of degrees of freedom for the blazar and comparison star, respectively ($\nu =N-1$), and α is the significance level set as 0.01 (2.6σ). If the average F-value is larger than the critical value, the blazar is variable at a confidence level of 99%. De Diego (2010) reported that the ANOVA is a powerful and robust estimator for microvariations. It does not rely on error measurement but derives the expected variance from subsamples of the data. The one-way ANOVA test divides the data into many groups. Then, it compares the variances between intergroups and intragroups. From Appendix A3 of de Diego (2010), the statistics

$$\begin{eqnarray}&&F=\displaystyle \frac{{\displaystyle \sum }_{j=1}^{k}{\displaystyle \sum }_{i=1}^{{n}_{j}}{(\bar{{y}_{j}}-\bar{y})}^{2}/(k-1)}{{\displaystyle \sum }_{j=1}^{k}{\displaystyle \sum }_{i=1}^{{n}_{j}}{({y}_{{ij}}-\bar{{y}_{j}})}^{2}/(N-k)}=\displaystyle \frac{{{SS}}_{{\rm{G}}}/(k-1)}{{{SS}}_{R}/(N-k)},\end{eqnarray} \tag{ 4 }$$

where y_ij represents the ith observation (with $i=1$, 2, ..., n_j ) on the jth group (with $j=1$, 2, ..., k), $\bar{y}$ is the mean of the whole data set, $\bar{{y}_{j}}$ is the mean on the jth group, k is the number of groups, and N is the number of the whole data set. The ${{SS}}_{{\rm{G}}}$ and ${{SS}}_{R}$ are  the between-groups and within-groups sum of squares, respectively. Considering the time of exposure, we bin the data in a group of five observations (see de Diego 2010 and Xiong et al. 2016 for details). If the measurements in the last group are less than 5, then it is merged with the previous group. The critical value of ANOVA can be obtained by ${F}_{{\nu }_{1},{\nu }_{2}}^{\alpha }$ in the F-statistics, where ${\nu }_{1}=k-1$, ${\nu }_{2}=N-k$, and α is the significance level set at 0.01. If the F-value from Equation (4) exceeds the critical value ${F}_{{\nu }_{1},{\nu }_{2}}^{\alpha }$, the blazar is variable at a confidence level of 99%. In order to further quantify the reliability of variability, the value of S_x can be calculated as (e.g., Hu et al. 2014)

$$\begin{eqnarray}&&{S}_{x}={m}_{i}-\overline{m},\,\,\,x=V,R,I,\end{eqnarray} \tag{ 5 }$$

where m_i and $\overline{m}$ are same as in Equation (1). The variability amplitude (Amp) can be calculated by (Heidt & Wagner 1996)

$$\begin{eqnarray}&&\mathrm{Amp}=100\times \sqrt{{({A}_{\max }-{A}_{\min })}^{2}-2{\sigma }^{2}} \% ,\end{eqnarray} \tag{ 6 }$$

where A_max and A_min are the maximum and minimum magnitude, respectively, of the light curve for the night being considered, and σ is the rms error. When estimating the variability amplitude, we only consider the nights detected as variability.

The DC is calculated as (Romero et al. 1999; Stalin et al. 2009; Hu et al. 2014)

$$\begin{eqnarray}&&\mathrm{DC}=100\displaystyle \frac{{\displaystyle \sum }_{i=1}^{n}{N}_{i}(1/\bigtriangleup {T}_{i})}{{\displaystyle \sum }_{i=1}^{n}(1/\bigtriangleup {T}_{i})} \% ,\end{eqnarray} \tag{ 7 }$$

where $\bigtriangleup {T}_{i}=\bigtriangleup {T}_{i,\mathrm{obs}}{(1+z)}^{-1}$, z is the redshift of the object, and $\bigtriangleup {T}_{i,\mathrm{obs}}$ is the duration of the monitoring session of the ith night. Note that since the monitoring durations on different nights for a given source were not always equal, the computation of DC has been weighted by the actual monitoring duration $\bigtriangleup {T}_{i}$ on the ith night. The value of N_i will be set to 1 if IDV is detected, otherwise N_i = 0 (Goyal et al. 2013).

3.1. Variability

The analysis results on IDV are shown in Table 7. From Table 7, it can be seen that IDV is found on seven nights with at least two bands detected as IDV on a night. The light curves detected as IDV are given in Figure 1, which shows the variability of various shapes. For the seven nights, we also check the color variations on intraday timescales. However, the results from three statistical tests do not show significant color variations on intraday timescales. The rest of the nights are considered PV, except for the I band on 6 February. On 27 January, the brightness first increases and then decreases along the arc. On 28 January, the brightness first increases and then decreases, and finally increases. On 29 January, the brightness first decreases and then increases along the symmetrical arc. On 30 January, the brightness changes are similar to those of 29 January but not along the symmetrical arc. On 1 and 8 February, the brightness continues to increase, while on 4 February, the brightness continues to decrease. The corresponding changes of magnitude and change rate are seen in Table 8. When calculating the change rate, we first determine increasing or decreasing time points and then use the slope from error-weighted linear regression analysis as the change rate. The results from Table 8 show that the average change rate is $\langle \mathrm{CR}\rangle =0.035\pm 0.009$ Mag/h during the ascent and $\langle \mathrm{CR}\rangle =0.035\pm 0.014$ Mag/h during the descent. The average change rates between the ascent and descent are equal. However, different cases are found on certain nights. The corresponding times of variation range from 47 to 274 minutes. On 29 January, the increasing and decreasing change rates are close. The correlations between variability amplitude and source average brightness are shown in Figure 2. Although Figure 2 shows trends/tendencies of larger amplitude with brighter magnitude for the I and R bands, the analysis of the nonparametric Spearman rank indicates that there are no significant correlations between variability amplitude and source average brightness for different wavebands (significance level ${P}_{I}=0.1$, ${P}_{R}=0.1$, ${P}_{V}=0.8$, and ${P}_{B}=0.7$). The variability amplitude is from 12.81% to 33.22%, and the average value is 19.92% ± 5.87% (Table 7 and Figure 2). Making use of Equation (7), we calculate the DC of the IDV. The DC is 44% for S5 0716+714 (98%, if PV cases are also included).

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Table 7.  Results of IDV Observations of S5 0716+714

Date	Band	C	F	${F}_{C}(99)$	FA	${F}_{A}(99)$	V/N	A (%)	Ave (mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
2012 Jan 27	I	3.69	13.60	1.53	52.89	1.98	V	17.12	13.18
2012 Jan 27	R	4.25	18.08	1.53	58.32	1.98	V	18.23	13.72
2012 Jan 27	V	3.66	13.38	1.53	36.13	1.98	V	18.10	14.13
2012 Jan 27	B	2.78	7.75	1.53	8.02	1.98	V	27.92	14.63
2012 Jan 28	I	4.00	15.99	1.73	27.60	2.44	V	15.61	13.31
2012 Jan 28	R	3.93	15.46	1.73	48.93	2.44	V	12.85	13.94
2012 Jan 28	V	2.93	8.60	1.73	31.00	2.44	V	25.09	14.30
2012 Jan 28	B	2.73	7.44	1.74	28.37	2.45	V	17.13	14.80
2012 Jan 29	I	1.81	3.33	1.75	5.09	2.45	PV	⋯	12.95
2012 Jan 29	R	2.60	6.76	1.75	24.43	2.46	V	13.96	13.43
2012 Jan 29	V	3.06	9.37	1.74	26.68	2.45	V	12.81	13.91
2012 Jan 29	B	2.26	5.12	1.74	14.55	2.45	PV	⋯	14.41
2012 Jan 30	I	3.76	14.15	1.75	57.76	2.46	V	13.60	13.06
2012 Jan 30	R	4.43	19.62	1.75	49.74	2.46	V	16.46	13.60
2012 Jan 30	V	3.79	14.33	1.75	42.76	2.46	V	17.16	14.03
2012 Jan 30	B	2.75	7.56	1.75	40.27	2.46	V	18.20	14.52
2012 Jan 31	I	1.86	3.46	1.79	6.01	2.54	PV	⋯	12.99
2012 Jan 31	R	1.69	2.85	1.79	6.41	2.54	PV	⋯	13.51
2012 Jan 31	V	2.31	5.33	1.79	5.78	2.54	PV	⋯	13.92
2012 Jan 31	B	1.82	3.31	1.78	4.85	2.53	PV	⋯	14.39
2012 Feb 01	I	6.90	47.66	1.87	164.48	2.66	V	17.07	12.72
2012 Feb 01	R	8.26	68.23	1.86	77.19	2.65	V	22.05	13.22
2012 Feb 01	V	4.53	20.54	1.86	123.93	2.65	V	18.06	13.63
2012 Feb 01	B	1.96	3.86	1.86	72.58	2.65	PV	⋯	14.11
2012 Feb 02	I	1.36	1.86	1.87	24.90	2.66	PV	⋯	12.45
2012 Feb 02	R	1.37	1.87	1.87	11.81	2.66	PV	⋯	12.92
2012 Feb 02	V	0.82	0.68	1.88	12.49	2.73	PV	⋯	13.30
2012 Feb 02	B	0.77	0.62	1.86	12.21	2.65	PV	⋯	13.74
2012 Feb 03	I	2.08	4.33	2.42	22.41	3.90	PV	⋯	12.47
2012 Feb 03	R	1.95	3.80	2.42	17.45	3.90	PV	⋯	12.99
2012 Feb 03	V	1.68	2.84	2.42	8.02	3.90	PV	⋯	13.38
2012 Feb 03	B	1.81	3.26	2.51	3.62	3.99	PV	⋯	13.86
2012 Feb 04	I	5.36	28.77	1.71	92.85	2.34	V	19.55	12.74
2012 Feb 04	R	3.64	13.26	1.71	77.16	2.34	V	26.53	13.29
2012 Feb 04	V	2.57	6.62	1.71	30.70	2.34	V	28.24	13.72
2012 Feb 04	B	1.36	1.86	1.71	17.71	2.34	PV	⋯	14.20
2012 Feb 05	I	1.25	1.58	1.95	15.88	2.89	PV	⋯	12.71
2012 Feb 05	R	1.21	1.49	1.95	7.92	2.89	PV	⋯	13.21
2012 Feb 05	V	0.95	0.94	1.95	4.20	2.89	PV	⋯	13.52
2012 Feb 05	B	1.43	2.06	1.92	13.76	2.85	PV	⋯	14.13
2012 Feb 06	I	0.78	0.61	2.26	1.00	3.53	N	⋯	12.40
2012 Feb 06	R	0.90	0.80	2.26	5.29	3.53	PV	⋯	12.86
2012 Feb 06	V	0.79	0.62	2.26	4.51	3.53	PV	⋯	13.21
2012 Feb 07	I	1.22	1.54	1.79	41.82	2.53	PV	⋯	12.52
2012 Feb 07	R	1.44	2.07	1.78	15.88	2.53	PV	⋯	13.06
2012 Feb 07	V	1.21	1.45	1.76	5.87	2.55	PV	⋯	13.44
2012 Feb 08	I	2.74	7.52	1.63	92.30	2.21	V	29.27	12.31
2012 Feb 08	R	2.97	8.84	1.63	110.20	2.21	V	33.22	12.81
2012 Feb 08	V	1.89	3.58	1.63	27.82	2.22	PV	⋯	13.21

Note. Column (1) is the date of observation, column (2) is the observed band, column (3) is the value of the C-test, column (4) is the average F-value, column (5) is the critical F-value with 99% confidence level, column (6) is the F-value of ANOVA, column (7) is the critical F-value of ANOVA with 99% confidence level, column (8) is the variability status (V: variable; PV: probable variable; N: nonvariable), and columns (9) and (10) are the variability amplitude and daily average magnitudes, respectively.

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Table 8.  Results of Change Rate

Date (UT)	Band	MJD*	Magnitude*	CR (Mag/h)
2012 Jan 27	B	55953.6895	14.743	0.037
		55953.8845	14.517	−0.075
		55953.9619	14.782	⋯
	V	55953.7152	14.248	0.039
		55953.8573	14.066	−0.026
		55953.9668	14.188	⋯
	R	55953.7064	13.825	0.038
		55953.8714	13.642	−0.04
		55953.9671	13.763	⋯
	I	55953.7091	13.291	0.03
		55953.8879	13.119	−0.031
		55953.9744	13.225	⋯
2012 Jan 28	B	55954.6851	14.889	0.034
		55954.8249	14.749	−0.032
		55954.8988	14.828	⋯
	V	55954.6859	14.380	0.037
		55954.8052	14.255	−0.032
		55954.8586	14.322	⋯
	R	55954.6865	13.942	0.031
		55954.8346	13.821	−0.054
		55954.8674	13.882	⋯
	I	55954.6871	13.380	0.029
		55954.8352	13.281	⋯
		55954.9049	13.328	⋯
2012 Jan 29	V	55955.6805	13.831	−0.026
		55955.8317	13.960	0.027
		55955.9753	13.842	⋯
	R	55955.6811	13.429	−0.02
		55955.8405	13.534	0.03
		55955.9718	13.434	⋯
2012 Jan 30	B	55956.6878	14.401	−0.044
		55956.8243	14.584	0.021
		55956.9602	14.462	⋯
	V	55956.6886	13.924	−0.042
		55956.8333	14.096	0.032
		55956.9487	13.976	⋯
	R	55956.6892	13.506	−0.038
		55956.8298	13.671	0.025
		55956.9657	13.569	⋯
	I	55956.6898	12.975	−0.032
		55956.8345	13.111	0.024
		55956.9745	13.013	⋯
2012 Feb 01	V	55958.8348	13.694	0.054
		55958.9539	13.522	⋯
	R	55958.8313	13.285	0.052
		55958.9586	13.136	⋯
	I	55958.8319	12.773	0.043
		55958.9798	12.607	⋯
2012 Feb 04	V	55961.7198	13.616	−0.019
		55961.9772	13.899	⋯
	R	55961.7205	13.185	−0.024
		55961.9778	13.451	⋯
	I	55961.7211	12.636	−0.027
		55961.9718	12.868	⋯
2012 Feb 08	R	55965.6871	12.979	0.039
		55965.9327	12.654	⋯
	I	55965.6911	12.457	0.034
		55965.9430	12.162	⋯

Note. The star symbol stands for increasing/decreasing time points and corresponding magnitudes. When calculating the change rate, we consider the coefficients of correlation $\gt 0.7;$ for CR, the positive and negative signs are increasing brightness and decreasing brightness, respectively.

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Short-term light curves and the color index are given in Figure 3. From Figure 3, we can see that, on the whole, the BL Lac object continues to brighten with a remarkable first brightening and then darkening peak during the short term, and the average color index on each night remains approximately constant during this period. The overall magnitude variabilities are $\bigtriangleup B\,=1\buildrel{\rm{m}}\over{.} 24$, $\bigtriangleup V=1\buildrel{\rm{m}}\over{.} 42$, $\bigtriangleup R=1\buildrel{\rm{m}}\over{.} 3$, and $\bigtriangleup I=1\buildrel{\rm{m}}\over{.} 23$. The magnitude distributions in the B, V, R, and I bands are $14\buildrel{\rm{m}}\over{.} 89\,\lt B\lt 13\buildrel{\rm{m}}\over{.} 65$, $14\buildrel{\rm{m}}\over{.} 45\lt V\lt 13\buildrel{\rm{m}}\over{.} 03$, $13\buildrel{\rm{m}}\over{.} 94\lt R\lt 12\buildrel{\rm{m}}\over{.} 64$, and $13\buildrel{\rm{m}}\over{.} 39\lt I\lt 12\buildrel{\rm{m}}\over{.} 16$, respectively. The average values of the magnitudes and color index are $\langle B\rangle \,=\,14\buildrel{\rm{m}}\over{.} 35\pm 0\buildrel{\rm{m}}\over{.} 31$, $\langle V\rangle \,=\,13\buildrel{\rm{m}}\over{.} 73\,\pm \,0\buildrel{\rm{m}}\over{.} 36$, $\langle R\rangle \,=\,13\buildrel{\rm{m}}\over{.} 33\,\pm \,0\buildrel{\rm{m}}\over{.} 34$, $\langle I\rangle \,=\,12\buildrel{\rm{m}}\over{.} 81\,\pm 0\buildrel{\rm{m}}\over{.} 33$, and $\langle V-R\rangle =0\buildrel{\rm{m}}\over{.} 39\pm 0\buildrel{\rm{m}}\over{.} 04$.

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3.2. Cross-Correlation Analysis and Variability Timescales

Following Giveon et al. (1999), Wu et al. (2007), Liu et al. (2008), Liao et al. (2014), and Xiong et al. (2016), we use the z-transformed discrete correlation function (ZDCF; Alexander 1997) to perform the interband correlation analysis and search for the possible interband time delay. The ZDCF code of Alexander (1997) can automatically set how many bins are given and be used to calculate the interband correlation and autocorrelation function (ACF). In order to achieve statistical significance, the minimal number of points per bin is 10. The results of the ZDCF for all data are given in Figure 4. As an illustration, the results of the ZDCF on four nights are given in Figure 4. They show that there are good interband correlations but no significant time lags.

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The zero-crossing time of the ACF is a well-defined quantity and used as a characteristic variability timescale (e.g., Netzer et al. 1996; Alexander 1997; Giveon et al. 1999; Liu et al. 2008). The zero-crossing time is the shortest time it takes the ACF to fall to zero (Alexander 1997). If there is an underlying signal in the light curve with a typical timescale, then the width of the ACF peak near zero time lag will be proportional to this timescale (Giveon et al. 1999; Liu et al. 2008). The width of the ACF may be related to the characteristic size scale of the corresponding emission region (Chatterjee et al. 2012). Another function used in variability studies to estimate the variability timescales is the first-order structure function (SF; e.g., Trevese et al. 1994). There is a simple relation between the ACF and the SF (Giveon et al. 1999). We therefore perform only an ACF analysis on our light curves. The ACF was estimated by the ZDCF. We only analyze the nights detected as IDV. The results of the ACF analysis are given in Figure 5. The results of the ACF analysis on 4 and 8 February are not shown in Figure 5 because all of the ACF values of the two nights are more than zero. Following Giveon et al. (1999), we then use a least-squares procedure to fit a fifth-order polynomial to the ACF, with the constraint that ACF($\tau =0$) = 1. From the fitting results, it is seen that the variability timescales range from 0.054 to 0.134 day.

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3.3. Correlation between Magnitude and Color Index

For the color index, we use the correction factors from Schlafly & Finkbeiner (2011) to correct the Galactic extinction. In order to minimize the bias introduced by the dependence of the color index on the magnitudes, brightness was calculated by averaging the magnitudes of the two bands used to calculate the index (Dai et al. 2015). We concentrate on the V − R index and $(V+R)/2$ magnitude because the V − R index is frequently studied. Figure 6 shows the correlations between V − R index and $(V+R)/2$ magnitude on intraday and short timescales. The results of the analysis of Spearman rank are given in Table 9. The table shows that eight nights have significant correlations between the V − R index and $(V+R)/2$ magnitude, and one night has a significant anticorrelation between the V − R index and $(V+R)/2$ magnitude (significance level $P\lt 0.05$ confidence level). Moreover, four nights have no significant correlations between the V − R index and $(V+R)/2$ magnitude ($P\gt 0.05$). For short timescales, the significant correlation between the V − R index and $(V+R)/2$ magnitude is found (Table 9). Therefore, during the outburst period, most of the nights show a BWB chromatic trend, a weak redder-when-brighter (RWB) trend is found, and a few nights show no correlations between magnitude and color index. The BWB trend appears in short timescales. The spectral index versus the flux in the flare event is given in Figure 7. It is seen that during the flare the spectral index exhibits a clockwise loop for internights.

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Table 9.  Results of Spearman Rank Analysis

Date (UT)	N	r	P
2012 Jan 27	126	0.036	0.69
2012 Jan 28	70	0.38	0.001
2012 Jan 29	69	0.38	0.001
2012 Jan 30	71	0.43	0.0002
2012 Jan 31	66	0.25	0.04
2012 Feb 01	57	0.14	0.32
2012 Feb 02	56	−0.05	0.73
2012 Feb 03	30	0.53	0.002
2012 Feb 04	77	−0.27	0.02
2012 Feb 05	51	0.25	0.07
2012 Feb 06	35	0.41	0.01
2012 Feb 07	65	0.36	0.003
2012 Feb 08	92	0.29	0.006
2012 Jan 28–Feb 08	866	0.56	1 × 10−6

Note. Here N is the number of data, r is the coefficient of correlation, and P is the significance level.

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4.1. Variability

4.2. Spectral Properties

We sincerely thank the referee for valuable comments and suggestions. We acknowledge the support of the staff of the Lijiang 2.4 m and BOOTES-4 telescopes. Funding for the two telescopes has been provided by the Chinese Academy of Sciences and the People's Government of Yunnan Province. This work is financially supported by the National Nature Science Foundation of China (11433004, 11133006, 11673057, 11361140347), the Key Research Program of the Chinese Academy of Sciences (grant no. KJZD-EW-M06), the Strategic Priority Research Program "The Emergence of Cosmological Structures" of the Chinese Academy of Sciences (grant no. XDB09000000), the Chinese Western Young Scholars Program and the Light of West China Program provided by CAS (Y7XB018001, Y5XB091001), and the science and technology project for youth of Yunnan of China (2104FD059). This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.