Search for Intra-day Optical Variability in γ-Ray-loud Blazars S5 0716+714 and 3C 273

Blazars are a special subclass of radio-loud active galactic nuclei (AGNs) and show significant properties, such as rapid and strong variability from radio to γ-ray bands, high and variable polarization, prominent nonthermal emission, etc. (e.g., Urry & Padovani 1995). These significant properties are mostly generated by a relativistic jet with a small viewing angle that is ≲10° (e.g., Blandford & Königl 1979; Urry & Padovani 1995). Spectral energy distributions (SEDs) of blazars generally show a double-peak profile in broadband continuum from radio to γ-ray bands. Broadband observations show that the low energy peak is from infrared (IR)–optical–ultraviolet (UV) to soft X-ray bands, and the high energy peak is in the MeV–GeV–TeV γ-ray regime (e.g., Ghisellini et al. 1998; Abdo et al. 2010a). The usual classification between flat-spectrum radio quasars (FSRQs) and BL Lacs is basically on the basis of rest-frame equivalent widths (EWs) of optical emission lines. One of the defining features of BL Lacs is their weak or absent emission lines (Urry & Padovani 1995). BL Lacs and FSRQs have EW < 5 Å and EW > 5 Å, respectively, in the rest frame for optical emission lines, such as Hβλ4861, [Oii]λ3727, Mgiiλ2798, etc. (e.g., Stickel et al. 1991; Urry & Padovani 1995; Ghisellini et al. 2011; Sbarrato et al. 2012; Ghisellini & Tavecchio 2015).

Blazars show violent variability across the entire electromagnetic spectrum on different timescales from minutes to years. Timescales and amplitudes of variations, and shapes of light curves (LCs), could shed light on some intrinsic properties of blazars, e.g., the sizes of emission regions, the masses of black holes, and the radiation mechanism (e.g., Miller et al. 1989; Xie et al. 2002; Liu & Bai 2015; Guo et al. 2016; Feng et al. 2017; Li et al. 2017; Xiong et al. 2017; Yuan et al. 2017). The variation timescales of blazars are divided into three classes. Intra-day variability (IDV) or microvariability shows flux changes from minutes to less than one day (Wagner & Witzel 1995). Short-term variability shows variations from days to weeks, and long-term variability (LTV) shows variations from months to years (e.g., Gupta et al. 2012; Li et al. 2017). Several models were proposed to explain the variability of blazars, such as the shock-in-jet model (Marscher & Gear 1985; Qian et al. 1991) and the disk instability model (Kawaguchi et al. 1998). The IDVs in blazars seem to be important since the IDV timescales are likely related to the central supermassive black boles in blazars (Liu & Bai 2015; Feng et al. 2017). However, it is difficult to measure the masses of black holes in blazars due to the Doppler boosted emission from the jets of blazars.

S5 0716+714 is a typical BL Lac object discovered in 1979 (Kühr et al. 1981). Wagner & Witzel (1995) found that the source is always in active states, and also similar results were reported in some works (e.g., Nesci et al. 2002; Hu et al. 2014). Thus, S5 0716+714 may be a good candidate for IDV researches. The optical IDV was studied extensively (e.g., Gupta et al. 2009, 2012; Dai et al. 2015; Hong et al. 2017; Li et al. 2017). Rani et al. (2010) reported a variation timescale as short as 15 minutes, and Man et al. (2016) also obtained a variation timescale of 17.6 minutes. Other variation timescales from tens of minutes to a few hours were reported in several works (e.g., Gupta et al. 2009; Dai et al. 2015; Li et al. 2017; Yuan et al. 2017). The variability of 3C 273, the first quasar discovered in 1963 (Smith & Hoffleit 1963), was extensively investigated from radio to γ-rays (e.g., Xie et al. 1999; Fan et al. 2009; Abdo et al. 2010b, 2010c; Kalita et al. 2015; Xiong et al. 2017; Yuan et al. 2017). 3C 273 was observed for more than 100 yr (e.g., Vol’vach et al. 2013), and optical variability on various timescales was reported. Fan et al. (2009) reported the IDV timescales from 13 to 245 minutes for 3C 273. The variation timescales from 23.9 to 744 days were also found (Fan et al. 2014). Dai et al. (2009) studied the spectrum variability, and the bluer-when-brighter behavior was obtained for the IDV and LTV. Soldi et al. (2008) suggested complicacy of the radiation mechanisms of the multiwavelength emission for 3C 273. The photometry with high temporal resolution shorter than minutes may give more information for 3C 273 and more constraints on its central supermassive black hole.

For S5 0716+714 and 3C 273, we carried out observations in the I or R bands from 2007 March 7 to 2012 May 16, and the observations were performed with high temporal resolution (30–60 s). Thus, we can investigate IDVs on shorter variation timescales in detail. The structure of this paper is as follows. Section 2 gives observations and data reduction; Section 3 presents search for IDVs. Section 4 presents results, Section 4.1 is for S5 0716+714, and Section 4.2 is for 3C 273. Section 5 is for discussions and conclusion.

The photometric observations of S5 0716+714 and 3C 273 were performed with the 1.02 m optical telescope at Yunnan Observatories of Chinese Academy of Sciences from 2007 March 7 to 2012 May 16. Before 2009, the Princeton charge-coupled device (CCD) chip (1024 × 1024 pixels) of the 1.02 m optical telescope covers a field of view (FOV) of ∼6.5 × 6.5 arcmin², and the spatial scale is 038 per pixel. For this CCD, the readout noise and gain are 3.9 electrons and 4.0 electrons/ADU, respectively. After 2009, the telescope was equipped with a new Andor DW436 CCD (2048 × 2048 pixels) camera at a f/13.3 Cassergrain focus. The FOV of the CCD is ∼7.3 × 7.3 arcmin², and the projected angle on the sky of each pixel corresponds to 021 in both dimensions. The readout noise is 6.33 electrons, and the gain is 2.0 electrons/ADU. During the observations, standard Johnson–Cousins broadband filters were used (e.g., Feng et al. 2017).

In order to improve the observation efficiency and to detect the optical variations with the shorter timescales, only one band (I or R) was observed in each night. In six nights, 648 I-band CCD images of S5 0716+714 were obtained. For 3C 273, we observed 14 nights and obtained 2305 CCD frames (611 in the I band and 1694 in the R band). Table 1 lists the complete observation log. The flat-field images were taken at twilight or dawn, and the bias frames were taken at the beginning and/or at the end of observations. Depending on the filters and weather conditions, the exposure times were set from 30 s for S5 0716+714 and 30–80 s for 3C 273. All the CCD images were reduced by the standard IRAF procedures. For each night, the median of all the bias images was used to generate a master bias. Then, target images and flat-field images were subtracted by the master bias. After the bias correction, master flat-field images were generated by taking the median of all flat-field images in each band, and the target images were corrected by the master flat-field image. Before photometric reduction, we checked each image carefully. In the whole FOV, the background is nearly uniform, and the FWHM is consistent for different stars. The values of FWHMs for most images are less than 2″. Thus, our bias and flat-field corrections are reliable. Aperture photometry was performed with the APPHOT task. S5 0716+714 and 3C 273 are point sources, and our extraction aperture is determined by the FWHM. For each source, we chose 26 different aperture radii from 1.0 to 2.5 FWHM. Comparing the results of different aperture radii shows that the LCs are generally consistent with each other. The best signal-to-noise ratio (S/N) would be obtained with an aperture radius of 1.6 FWHM.

During our observations, several comparison stars are always located in the target FOV. For the most observable night (except S5 0716+714 on 2008 May 8), we can choose the same four comparison stars to calibrate the relevant target and characterize the uncertainties in the observations. Star2, star5, and star6 are always located in the FOV of 0716+714 on 2008 May 8 and are used in data reduction. Figure 1 shows the comparison stars star2, star3, star5, and star6 for S5 0716+714, and starC, starE, starG, and star1 for 3C 273. The magnitude calibration is performed as follows.

1. (1)  
   There are several comparison stars that have been widely used in the previous works. Star2, star3, star5, and star6 for S5 0716+714 have been calibrated in Villata et al. (1998), and Smith et al. (1985) has given the magnitude of starC, starE, and starG for 3C 273. However, the transmittance of different filters might be slightly different, and the responses of different CCDs are also different. Thus, we only adopt the brightness of the brightest star in the FOV to recalibrate other stars. For each night, we measure the mean differential magnitude of every two comparison stars, , where star_i and star_j are the instrumental magnitudes of the ith and jth comparison stars on the observation time series, T_m, respectively. We find the mean value, , of the same star pairs is nearly constant on the different nights for six pairs, i.e., mag except for very few matching mag from 2007 to 2012. Therefore, the mean values are used to calibrate each comparison star. We choose the brightness of star2 and starC as the standard flux of the image for S5 0716+714 and 3C 273, respectively.
2. (2)  
   The brightness of comparison stars are considered to be constant, and the differential magnitude of any two stars should be constant. Theoretically, we can use any star to calibrate the target. Nevertheless, the tracking accuracy of the telescope, weather conditions, moon state, flat-field correction, and other unexpected reasons would influence the calibration of target. To avoid these effects, we calibrate the target by the different comparison stars (, BL is the instrumental magnitude of target, star_i is the instrumental magnitude of the ith comparison star, and std_i is the calibrated magnitude of the ith comparison star). Then, we average any two calibrated results () and shift the differential magnitude of the corresponding comparison stars to zero (). Depending on the variations of std_ij, we exclude some preternatural data points of Mag_ij. The threshold value is set as ∣std_ij∣ ≤ 0.01 mag. Then, the left Mag_ij (Mag) are averaged as the final results. We also calculate the mean value of std_ij (Std), which can be used to estimate the variability and systematic uncertainties of the target. Table 2 exhibits the results of sources and comparison stars.

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The final errors of the target are calculated from two components. The first component is the Poisson errors, σ_p, of the target and comparison stars, and σ_p can be obtained from IRAF. Another component comes from some unexpected reasons mentioned in the previous paragraphs, and we attribute the relevant errors to the systematic uncertainties, σ_s, which can be given by σ_s = ∣Std∣. The final errors are given by and are listed in Table 2.

The variability amplitude (Amp) on a given night can be calculated by the definition of Heidt & Wagner (1996):

where and Mag_min are the maximum and minimum magnitudes within the LC, respectively, and σ can use the standard deviation of Std. Table 1 lists the Amp of the LCs, in which IDVs are detected. Two standard statistical methods are used to investigate IDVs: the F-test and the one-way analysis of variance (ANOVA; e.g., de Diego 2010; Gaur et al. 2012; Hu et al. 2014; Agarwal & Gupta 2015; Feng et al. 2017). If the LCs simultaneously satisfy the criteria of the F-test and the one-way ANOVA test, the IDVs are tested further with a cross-correlation analysis.

The F-test have been widely used in detection of IDVs (e.g., Hu et al. 2014; Feng et al. 2017; Xiong et al. 2017). The value of F is calculated by comparing the variances of two samples and is defined as

where Var(Mag) is the variance of the calibrated magnitude of the blazar, and Var(Std) is the variance of the calibrated comparison stars. The critical value of the F-test can be obtained by the F-statistic. The significance level is set at 0.01. Thus, if the F value is larger than the critical value, the blazar is considered to be variable at the confidence level of 99% (i.e., 2.6σ). Table 1 shows the F values and the critical values. However, the F-test relies on the error of the target and comparison stars. Thus, another robust analysis method is necessary. The one-way ANOVA is a powerful tool to quantify the variability of blazars. de Diego (2010) has investigated the one-way ANOVA in detail and has shown that the one-way ANOVA is a powerful and robust method in the detection of IDVs. The one-way ANOVA does not depend on the error measurement but on the variability of blazars. The critical value of the one-way ANOVA test can be compared to the F-statistic (see de Diego 2010; Feng et al. 2017, for details). The one-way ANOVA tests are performed by grouping the data in sets of 20 individual observations (see description in A.3 in de Diego 2010). The method might be influenced by the intervals of the bins that are used to calculate ANOVA (see A.3 in de Diego 2010). So, we use five different bins of grouping 3, 4, 5, 6, and 7 data points for each night. If the data points in the last bin are less than those in the previous bin within the same LC, we merge them into the previous bin. As all the five groupings for the same LC detect the IDV, the LC is considered to have a IDV. The results of the one-way ANOVA and the critical values on the basis of grouping seven data points are listed in Table 1. For comparison purposes, we also carry out the one-way ANOVA test on the curves of Std of the comparison stars. The test results are listed in Table 1. As the one-way ANOVA test on Std gives a variable result, the IDV of the target seems to be questionable (2007 March 7 and 2008 May 6 for S5 0716+714; 2008 May 8 for 3C 273). We will give further studies with cross-correlation analyses between the variations of the target and Std for these three nights.

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In order to avoid the illusive IDVs caused by the comparison stars, a discrete correlation function (DCF; e.g., Edelson & Krolik 1988) is used to study correlations between the LCs of the target and the curves of Std. Correlation analyses are used to test whether the variations of the target follow those of Std, i.e., the illusive variations of the target. No correlations around zero time lags are expected for the relevant variations of the target and Std. If there are correlations around zero time lags, the target has the illusive variations. Correlation analyses are run for the relevant LCs when the target survives the F-test and the one-way ANOVA test (see Table 1). The LCs in Figures 3 and 4 are non-uniformly sampled. The z-transformed discrete correlation function (ZDCF; Alexander 1997) is a binning type of method as an improvement of the DCF technique, but it has a notable feature in that the data are binned by their equal population rather than equal bin widths as in the DCF (e.g., Liu et al. 2011). The ZDCF is more robust than the DCF when applied to unequally sampled LCs (see Liu et al. 2011). The ZDCF results are presented in Figures 5 and 6. For S5 0716+716, there is no correlation on 2007 March 7, but there is a correlation on 2008 May 6. There is no correlation on 2008 May 8 for 3C 273. Thus, the IDVs of these three nights are questionable even if these LCs of the two targets survive the F-test and the one-way ANOVA test. So, these three nights are not considered to have reliable IDVs. Moreover, there is a correlation on 2008 May 6 for 3C 273 (see Figure 6). Finally, four and five reliable IDVs survive the ZDCF cross-correlation zero lag test for S5 0716+714 and 3C 273, respectively.

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The long-term LCs are displayed in Figure 2. Figures 3 and 4 show the LCs that survive the F-test and the one-way ANOVA test for S5 0716+714 and 3C 273, respectively. The details of the IDV LCs are as follows below.

4.1. S5 0716+714

The LC on 2008 May 6 cannot survive the ZDCF cross-correlation zero lag test for S5 0716+714. The R-band magnitudes are converted to linear fluxes of F using the formula Jy, and the I-band magnitudes are converted to linear fluxes of F using the formula Jy (e.g., Feng et al. 2018). During our observations, S5 0716+714 was active, and the IDVs were detected in five out of six days. Rising and declining phases were observed on 2007 March 8 and 9, respectively (see Figure 3). On 2007 March 8, it was almost monotonically increasing by ΔI ≈ 0.05 ± 0.01 mag in ≈0.09 days. On the following day, S5 0716+714 faded by ΔI ≈ 0.05 ± 0.01 mag in ≈0.05 days. The flare of S5 0716+714 on 2008 May 8 can be fitted by a third-order polynomial with a reduced Chi-square (see Figure 7(a)).

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On 2008 May 6, S5 0716+714 darkens by ΔI ≈ 0.06 ±0.01 mag in ∼0.05 days. On 2008 May 8, we detected successive rising, declining, and rising variations with magnitude changes of ΔI ≈ 0.08 ± 0.01 mag (see Figure 3). First, S5 0716+714 brightens slowly by ΔI ≈ 0.08 ± 0.01 mag in 53.4 minutes and darkens fast by ΔI ≈ 0.07 ± 0.01 mag in 13.2 minutes. Second, a little flare varies by ΔI ≈ 0.04 ± 0.01 mag in 13.6 minutes. Finally, S5 0716+714 brightens fast by ΔI ≈ 0.08 ± 0.01 mag in 6.6 minutes and darkens by ΔI ∼ 0.04 ± 0.01 mag in 5.4 minutes. From MJD = 595.06049 to 595.03814 (MJD = JD-2454000), S5 0716+714 brightens by ΔI ≈ 0.05 ± 0.01 mag in 19.0 minutes and darkens by ΔI ≈ 0.07 ± 0.01 mag in 13.2 minutes. This variation has a duration of 32.2 minutes that can give the minimum timescale of variations during our observations of S5 0716+714. Amp on 2008 May 7 and 8 are 10.8% and 9.8%, respectively. The long-term variation amplitude of S5 0716+714 is 0.75 ± 0.01 mag in the I band (see Figure 2). However, the poor sampling and the single color limit us to investigating the LTV.

4.2. 3C 273

3C 273 was observed in the I or R bands on 14 nights, and only 5 nights survive three tests of IDVs. Though the LC on 2008 May 6 survives the F-test and the one-way ANOVA test, it cannot survive the ZDCF cross-correlation zero lag test. Only one night is found to be variable in the I band, and ΔI ≈ 0.04 ± 0.01 mag on 2008 May 7. Other four IDV events are detected in the R band. On 2010 May 18, Amp of 3C 273 is 3.3% in the R band. At the beginning of the LC on 2011 May 7, the source quickly brightens by ΔR ≈0.05 ± 0.01 mag in 0.0185 days (26.6 minutes) and then is almost at a constant level (see Figure 4). For the night of 2011 May 9, it darkens from MJD = 1690.68818 to 1690.70038 and brightens from MJD = 1690.70038 to 1690.70363. This dip shows ΔR ≈ 0.04 ± 0.01 mag in 22.2 minutes. The next dip darkens from MJD = 1690.70363 to 1690.71014 and brightens from MJD = 1690.71014 to 1690.71095. This dip shows ΔR ≈ 0.05 ± 0.01 mag in 10.5 minutes. The next three dips are sharper. The third dip darkens from MJD =1690.81278 to 1690.81453 and brightens from MJD =1690.81453 to 1690.81904. This dip varies by ΔR ≈ 0.05 ±0.01 mag in 9.0 minutes. The fourth dip varies by ΔR ≈0.05 mag ± 0.01 from MJD = 1690.82719 to 1690.83009 and lasts for 4.2 minutes. The fifth dip varies by ΔR ≈0.05 mag ± 0.01 from MJD = 1690.88119 to 1690.88608 and lasts for 7.0 minutes.

The LC on 2011 May 10 has a variation amplitude of ΔR ≈ 0.06 ± 0.01 mag. After MJD = 1691.81, there is a flare with ΔR ≈ 0.05 ± 0.01 mag (see Figures 4 and 7(b)). The flare has a basically complete profile, consists of 29 data points, and lasts for 0.40 hr (see Figure 7(b)). The flare duration can give the minimum timescale of variations during our observations of 3C 273. After this flare, there are seven data points in a darkening phase around MJD = 1691.86, and these points can be fitted linearly with a Pearson’s correlation coefficient, r = 0.963, at the confidence level of 99.95%. (see Figure 7(b)). This darkening phenomenon in 3C 273 is similar to that in Mrk 501 (see Figure 6 in Feng et al. 2017). On 2011 May 10, the flare of 3C 273 can be fitted by a third-order polynomial with (see Figure 7(b)). For a relatively complete flare, the variation timescale could be estimated by the interval between the local minima at the adjacent valleys in the LC (see Feng et al. 2017 for details). This variation timescale is basically consistent with the duration of the flare.

For the long-term LCs of 3C 273 in the I band, a rising phase from 2007 March to 2008 May has ΔI ≈ 0.36 ± 0.01 mag, and a declining phase from 2008 May to 2009 May gives ΔI ≈ 0.54 ± 0.01 mag. For the long-term LCs of 3C 273 from 2009 May to 2012 May, our observational data basically follow the variation trend of the LC from the Small & Moderate Aperture Research Telescope System (SMARTS)⁶ in the R band (Bonning et al. 2012; see Figure 8). The IDV behaviors are found on 2011 May 7, 9, and 10, when 3C 273 is nearly at the brightest of the rising phase from 2010 May to 2011 May. 3C 273 darkens from 2008 May to 2009 May in our observations. A similar darkening trend from MJD ∼500 to 900 appears in the LCs from SMARTS (Bonning et al. 2012).

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We monitored BL Lac object S5 0716+714 and FSRQ 3C 273 with high time resolutions (30–60 s) from 2007 March 7 to 2012 May 16, and IDV behaviors are found in the I or R bands for these two sources. The minimum timescales are 0.54 and 0.40 hr for S5 0716+714 and 3C 273, respectively. Yuan et al. (2017) reported that the minimum timescales of S5 0716+714 and 3C 273 are 0.29 and 0.59 hr, respectively. Our results are consistent with theirs in the order of magnitude. These variability timescales could give upper limits to the sizes of emission regions, , where c is the speed of light, is the observed minimum timescale of variability, δ is the Doppler factor, and z is the redshift of the source. S5 0716+714 is at z = 0.31 (Nilsson et al. 2008; Danforth et al. 2013), and its δ ∼ 10.8 (Savolainen et al. 2010). Thus, D ≲ 4.78 × 10¹⁴ cm for S5 0716+714. The values of z and δ are 0.158 and 16.8 for 3C 273 (Savolainen et al. 2010), respectively, and D ≲ 6.27 × 10¹⁴ cm.

The close correlations between the flares of different bands indicate that the IDV is an intrinsic phenomenon (Wagner & Witzel 1995). Some models were proposed to study the underlying connections between the timescales of variations and the masses of black holes, M_• (e.g., Abramowicz & Nobili 1982; Miller et al. 1989; Xie et al. 2002; Liu & Bai 2015). The observed minimum timescales, , of variability were generally used to estimate M_• for AGNs (e.g., Abramowicz & Nobili 1982; Miller et al. 1989; Xie et al. 2002, 2005; Dai et al. 2015; Liu & Bai 2015). Models based on accretion disk were proposed to connect and M_• for non-blazar-like AGNs (e.g., Abramowicz & Nobili 1982; Miller et al. 1989; Xie et al. 2002). Liu & Bai (2015) proposed a new sophisticated model based on a blob in a relativistic jet to limit M_• for blazars, and the upper limits to M_• are given by

where is in units of seconds, is the dimensionless spin parameter of a black hole with the maximum possible angular momentum of , and G is the gravitational constant. Equations 3(a) and (b) can be applied to the Kerr and Schwarzchild black holes, respectively. For S5 0716+714, we have M_• ≲ 10^8.43 M_⊙ for the Schwarzchild black hole and M_• ≲ 10^8.91 M_⊙ for the Kerr black hole. Liang & Liu (2003) used the optical luminosity to get a mass of M_• = 10^8.10 M_⊙, which is consistent with our results. For 3C 273, we have M_• ≲ 10^9.02 M_⊙ derived with Equation 3(a). Kaspi et al. (2000) obtained – from the reverberation mapping of the Balmer lines, which are consistent with our result. Paltani & Türler (2005) obtained from the reverberation mapping of the Balmer lines and the Lyα and C iv lines, and generally, this mass is larger than other measurements in the literature. Also, this mass is larger than our result. Peterson et al. (2004) also obtained a reverberation-based mass of M_• = (8.86 ± 1.87) × 10⁸ M_⊙, which is consistent with the upper limit of M_• ≲ 10^9.02 M_⊙. Zhang et al. (2019) derived M_• = 10^9.0 ± 0.8 M_⊙ from the correlation between the host bulge stellar mass and the black hole mass and obtained a reverberation-mapped mass of . Sturm et al. (2018) inferred a mass of M_• =(2.6 ± 1.1) × 10⁸ M_⊙ from GRAVITY interferometry observation data of the Paschen-α line for 3C 273. These new measurements are consistent with our result of M_• ≲ 10^9.02 M_⊙. Thus, our estimates of M_• for S5 0716+714 and 3C 273 are consistent with a model in which their optical IDVs are generated from jets.

Except for the jet origin of optical IDVs, an alternative way can explain optical IDVs, e.g., accretion disks (e.g., Agarwal et al. 2016). Though the accretion disk instability can explain some phenomena in the optical–X-ray bands, it cannot explain the radio IDV behaviors (e.g., Wagner & Witzel 1995). Thermal emission from the accretion disk is not found in multiwavelength SEDs of S5 0716+714 (e.g., Liao et al. 2014). The optical emission of S5 0716+714 is from the synchrotron process of relativistic electrons in relativistic jets, and the γ-rays are interpreted as the inverse Compton (IC) scattering of soft photons by the relativistic electrons that produce the optical emission (e.g., Liao et al. 2014). Thus, the ionizing radiation is so weak that broad emission lines are not observable, even though broad emission line region exists in S5 0716+714. Then, its optical spectra will be featureless. Broad emission lines were observed only in a few BL Lac objects (e.g., Celotti et al. 1997; Cao & Jiang 1999). Accretion rates are very low for BL Lac objects (e.g., Cao 2002; Xu et al. 2009). The absence of broad emission lines in most of BL Lac objects may be due to the very weak emission of the accretion disk. Nilsson et al. (2008) used the host galaxy of S5 0716+714 as the “standard candle” to derive its redshift of during its low state. BL Lac object PKS 0537−441 shows an interesting event in the J band with a duration of ∼25 minutes (Impiombato et al. 2011). In both the low and high states, its emission appears to be dominated by a jet, and no evidence of a thermal emission is apparent. Its SEDs are produced by the synchrotron and IC processes within a jet (Pian et al. 2007). For TeV γ-ray BL Lac object Mrk 501, the optical emission is neither the thermal component from accretion disk nor the nonthermal component from a jet (Ahnen et al. 2017). The optical emission is dominated by the host galaxy, and the UV emission is from the jet for Mrk 501. Thus, it is not possible that the optical IDV behaviors are from accretion disk for BL Lac objects with the featureless optical spectra.

The featureless optical spectrum is the typical characteristic of BL Lac objects. On the contrary, quasars show many strong broad emission lines. 3C 273 has strong broad emission lines of the Balmer series and Lyα. The broadband SED of 3C 273 shows a prominent blue bump around the UV–optical regime (Türler et al. 1999). The blue bump may be attributed to the Fe ii line, the Balmer line, and continuum emission (Paltani et al. 1998). If the blue bump is the thermal emission from the accretion disk, Equations 3(a) and (b) are not appropriate to estimate M_• for 3C 273. For the Kerr black hole, Xie et al. (2002) deduced a formula for the accretion disk from Abramowicz & Nobili (1982):

The flare duration of 0.40 hr and Equation (4) give for 3C 273. This upper limit of M_• is much lower than masses of –10^9.39 M_⊙ obtained in the literature. It may be not possible that the blue bump is the thermal emission from the accretion disk for 3C 273. Thus, the flare with a duration of 0.40 hr is likely produced from the relativistic jets in 3C 273. Equation 3(a) gives a reasonable constraint on M_• for 3C 273. The shock-in-jet model, the most frequently used model to explain the IDV behaviors that may be directly related to shock processes in a jet, is based on a relativistic shock propagating down a jet and interacting with a highly nonuniform portion in the jet flow (e.g., Narayan & Piran 2012; Subramanian et al. 2012; Marscher 2014; Saito et al. 2015, and references therein). As the relativistic shock passes through a blob in the jet, an IDV behavior may be produced.

In summary, the photometric observations with high temporal resolution in the I or R bands are used to search for the optical IDV behaviors of S5 0716+714 and 3C 273. The observations were performed with a 1.02 m optical telescope from 2007 March 7 to 2012 May 16. We obtained 687 I-band CCD images in six nights for S5 0716+714. For 3C 273, we obtained 2283 CCD frames (622 frames in the I band and 1661 frames in the R band) in 14 nights. The one-way ANOVA test is carried out on Std of the comparison stars. There are IDVs of Std for 3 out of the 20 nights. The IDVs of the target are not reliable if the one-way ANOVA test gives IDVs for the target and Std. Finally, four and five reliable IDVs survive the F-test, the one-way ANOVA test, and the ZDCF cross-correlation zero lag test for S5 0716+714 and 3C 273, respectively. Optical IDVs with flare durations of 0.54 and 0.40 hr are found for S5 0716+714 and 3C 273, respectively. Based on Equation 3(a) and taken as flare durations, we estimate upper bounds to M_•. M_• ≲ 10^8.91 M_⊙ and M_• ≲ 10^9.02 M_⊙ are given for S5 0716+714 and 3C 273, respectively. Our mass measurements are consistent with most of the measurements reported in the literature, except for for 3C 273 (Paltani & Türler 2005), which is generally larger than other measurements. This supports that these optical IDVs are from the jets, rather than the accretion disks of S5 0716+714 and 3C 273. In addition, sharp dips are found in the LC on 2011 May 9 for 3C 273 and show ΔR ≈ 0.05 ± 0.01 mag.

We are grateful to the anonymous referee for constructive comments leading to significant improvement of this paper. Thanks for the helpful comments from the ApJ statistics editor. H.T.L. and H.C.F. thank the helpful discussions of Prof. Ji-Rong Mao and Dr. Zhi-Xiang Zhang. We thank the financial support of the Key Research Program of the CAS (grant No. KJZD-EW-M06), the National Natural Science Foundation of China (NSFC; grant Nos. 11433004 and 11573067), and the Ministry of Science and Technology of China (2016YFA0400700). We also thank the financial support of the NSFC (grant No. 11273052) and the CAS Interdisciplinary Innovation Team.