Search for Intra-day Optical Variability in $\gamma$-ray--loud Blazars S5 0716+714 and 3C 273

We present the photometric observations of blazars S5 0716+714 and 3C 273 with high temporal resolution (30--60s) in the $I$ or $R$ bands. The observations were performed with the 1.02 m optical telescope from 2007 March 07 to 2012 May 16. The $F$-test, one-way ANOVA test, and ZDCF cross-correlation zero lag test are used to search for intra-day variability (IDV). Four and five reliable IDVs survive three tests for S5 0716+714 and 3C 273, respectively. IDVs are found for S5 0716+714 and 3C 273. A flare on 2008 May 08 has $\Delta I \approx$ 0.06$\pm$0.01 mag in a duration of 0.54 hours for S5 0716+714. A flare on 2011 May 10 shows $\Delta R \approx$ 0.05$\pm$0.01 mag in a duration of 0.40 hours for 3C 273. Sharp dips appear on 2011 May 9 for 3C 273, and show $\Delta R \approx$ 0.05$\pm$0.01 mag. Under the assumptions that the IDV is tightly connected to black hole mass $M_{\bullet}$, and that the flare durations are representative of the minimum characteristic timescales, we can estimate upper bounds to $M_{\bullet}$. In the case of the Kerr black holes, $M_{\bullet} \la 10^{8.91} M_{\odot}$ and $M_{\bullet} \la 10^{9.02} M_{\odot}$ are given for S5 0716+714 and 3C 273, respectively. These mass measurements are consistent with those measurements reported in the literatures. Also, we discuss the origins of optical variations found in this work.


INTRODUCTION
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 non-thermal emission, etc (e.g., Urry & Padovani 1995). These significant properties are mostly generated by a relativistic jet with a small viewing angle 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 IR-optical-UV to soft X-ray bands, and the high energy peak is in MeV-GeV-TeV γ-ray regime (e.g., Ghisellini et al. 1998;Abdo et al. 2010b). The usual classification between 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 < 5Å and EW > 5Å, respectively, in the rest frame for optical emission lines, such as Hβλ4861, [Oii]λ3727, [Mgii]λ2798 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;Xiong et al. 2017;Yuan et al. 2017;Li et al. 2017;Feng et al. 2017). The variation timescales of blazars are divided into three classes. Intra-day variability (IDV) or micro-variability 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. 2009Gupta et al. , 2012Dai 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 also Man et al. (2016) 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. 2010a,c;Kalita et al. 2015;Xiong et al. 2017;Yuan et al. 2017). 3C 273 was observed for more than 100 years (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 IDV and LTV. Soldi et al. (2008) suggested complicacy of the radiation mechanisms of the multi-wavelength 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 details. 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, subsection 4.1 is for S5 0716+714, and subsection 4.2 is for 3C 273. Section 5 is for discussions and conclusion.

OBSERVATIONS AND DATA REDUCTION
The photometric observations of S5 0716+714 and 3C 273 were performed with the 1.02m optical telescope at Yunnan Observatories of Chinese Academy of Sciences from 2007 March 07 to 2012 May 16. Before 2009, the Princeton CCD chip (1024 × 1024 pixels) of the 1.02m optical telescope covers a field of view (FOV) of ∼ 6.5 × 6.5 arcmin 2 , and the spatial scale is 0.38 aresec 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 f /13.3 Cassergrain focus. The FOV of the CCD is ∼ 7.3 × 7.3 arcmin 2 , and the projected angle on the sky of each pixel corresponds to 0.21 arcsec in both dimensions. The readout noise is 6.33 electrons, and the gain is 2.0 eletrons/ADU. During the observations, standard Johnson-Cauisns broadband filters were used (e.g., Feng et al. 2017).
In order to improve the observation efficiency and detect the optical variations with the shorter timescales, only one band (I or R) was observed in each night. 648 I band CCD images of S5 0716+714 were obtained in six nights. For 3C 273, we observed fourteen 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 seconds for S5 0716+714 and 30 to 80 seconds 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 full width at half maximum (FWHM) is consistent for different stars. The values of FWHMs for most images are less than 2 arcsec. Thus, our bias and flat-field corrections are reliable. Aperture photometry was performed with APPHOT task. S5 0716+714 and 3C 273 are point-like sources, and our extraction aperture is determined by 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 most observable night (except S5 0716+714 on 2008 May 08), 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 08, 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) There are several comparison stars which 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), andSmith 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 response 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 ∆m i,j (T m ) = star i (T m ) − star j (T m ), where star i and star j are the instrumental magnitudes of the ith and jth comparison stars on the observation night series label T m , respectively. We find the mean value ∆m i,j of the same star pairs is nearly constant on the different nights for six pairs, i.e., | ∆m i,j (T m ) − ∆m i,j (T n ) |≤ 0.005 mag except for very few matching | ∆m i,j (T m ) − ∆m i,j (T n ) |≤ 0.01 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) 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, wether 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 (M ag i = BL − star i + std i , 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 (M ag ij = M ag i − M ag j ), and shift the differential magnitude of the corresponding comparison stars to zero (std ij = star i − star j − std i + std j ). Depending on the variations of std ij , we exclude some preternatural data points of M ag ij . The threshold value is set as | std ij |≤ 0.01 mag. Then the left M ag ij (M ag) 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.
The final errors of the target are calculated from two components. The first component is the Poisson errors σ p of 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 σ = σ 2 p + σ 2 s , and are listed in Table 2.

SEARCH FOR IDVs
The variability amplitude (Amp) on a given night can be calculated by the definition of Heidt & Wagner (1996): where M ag max and M ag min are the maximum and minimum magnitudes within the LC, respectively, and σ can use the standard deviation of Std. Table 1 lists Amp of the LCs, in which IDVs are detected. Two standard statistical methods are used to investigate IDVs: the F -test and 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 one-way ANOVA test, the IDVs are tested further with cross-correlation analysis.
The F -test have been widely used in detection of IDVs (e.g., Hu et al. 2014;Xiong et al. 2017;Feng et al. 2017). The value of F is calculated by comparing the variances of two samples, and is defined as where V ar(M ag) is the variance of the calibrated magnitude of the blazar, and V ar(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 in details the one-way ANOVA, 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 AN OV A (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 IDV, the LC is considered to have IDV. The results of one-way ANOVA and the critical values on the basis of grouping 7 data points are listed in Table 1 3C 273). We will give further studies with cross-correlation analyses between the variations of the target and Std for these three nights.
In order to avoid the illusive IDVs caused by the comparison stars, 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 from the F -test and 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 equal population rather than equal binwidth 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 Figure 6). Finally, four and five reliable IDVs survive the ZDCF cross-correlation zero lag test for S5 0716+714 and 3C 273, respectively.

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

S5 0716+714
The LC on 2008 May 06 can not survive the ZDCF cross-correlation zero lag test for S5 0716+714. The R-band magnitudes are converted to linear fluxes F using the formula F = 3.08 × 10 −0.4×R+3 Jy, and the I-band magnitudes are converted to linear fluxes F using the formula F = 2.55 × 10 −0.4×I+3 Jy (e.g., Feng et al. 2018). During our observations, S5 0716+714 was active, and the IDVs were detected in 5 out of 6 days. Rising and declining phases were observed on 2007 March 08 and 09, respectively (see Figure 3). On 2007 March 08, it was almost monotonically increasing by ∆I ≈ 0.05±0.01 mag in ≈ 0.09 days. On the following day, S5 0716+714 faded by ∆I ≈ 0.05±0.01 mag in ≈ 0.05 days. The flare of S5 0716+714 on 2008 May 08 can be fitted by a third-order polynomial with a reduced Chi-square χ 2 ν = 0.790 (see Figure 7a).
On 2008 May 07, S5 0716+714 darkens by ∆I ≈ 0.06±0.01 mag in ∼ 0.05 days. On 2008 May 08, we detected successive rising, declining and rising variations with magnitude changes of ∆I ≈ 0.08±0.01 mag (see Figure 3). First, S5 0716+714 brightens slowly by ∆I ≈ 0.08±0.01 mag in 53.4 minutes, and darkens fast by ∆I ≈ 0.07±0.01 mag in 13.2 minutes. Second, a little flare varies by ∆I ≈ 0.04±0.01 mag in 13.6 minutes. Finally, S5 0716+714 brightens fast by ∆I ≈ 0.08±0.01 mag in 6.6 minutes, and darkens by ∆I ∼ 0.04±0.01 mag in 5.4 minutes. From MJD = 595.06049 to 595.03814 (MJD = JD-2454000), S5 0716+714 brightens by ∆I ≈ 0.05±0.01 mag in 19.0 miniutes and darkens by ∆I ≈ 0.07±0.01 mag in 13.2 minutes. This variation has a duration 32.2 minutes that can give the minimum timescale of variations during our observations of S5 0716+714. Amp on 2008 May 07 and 08 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 investigate the LTV.  Figures 4 and 7b). The flare has a basically complete profile, consists of 29 data points, and lasts for 0.40 hours (see Figure 7b). 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 7b). 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 χ 2 ν = 0.504 (see Figure 7b). 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 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 ∆t ob min of variability were generally used to estimate M • for AGNs (e.g., Abramowicz & Nobili 1982;Miller et al. 1989;Xie et al. 2002Xie et al. , 2005Dai et al. 2015;Liu & Bai 2015). Models based on accretion disk were proposed to connect ∆t ob min 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 ∆t ob min is in units of seconds, j = J/J max is the dimensionless spin parameter of a black hole with the maximum possible angular momentum J max = GM 2 • /c, and G being the gravitational constant. Equations (3a) and (3b) 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 (3a). Kaspi et al. (2000) obtained M • = 0.235 +0.037 −0.033 -0.550 +0.089 −0.079 × 10 9 M ⊙ from the reverberation mapping of the Balmer lines, which are consistent with our result. Paltani & Türler (2005) obtained M • = 2.44 +0.51 −0.30 × 10 9 M ⊙ from the reverberation mapping of the Balmer lines and the Lyα and CIV lines, and generally this mass is larger than other measurements in the literatures. Also, this mass is larger than our result. Peterson et al. (2004)  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 accretion disk is not found in multi-wavelength 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 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 accretion disk. Nilsson et al. (2008) used the host galaxy of S5 0716+714 as the "standard candle" to derive its redshift of z = 0.31 ± 0.08 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 ultraviolet-optical regime (Türler et al. 1999). The blue-bump may be attributed to Fe II line, Balmer line and continuum emission (Paltani et al. 1998). If the blue-bump is the thermal emission from accretion disk, equations (3a) and (3b) are not appropriate to estimate M • for 3C 273. For the Kerr black hole, Xie et al. (2002) deduced a formula for accretion disk from Abramowicz & Nobili (1982) M • 1.62 × 10 4 ∆t ob The flare duration of 0.40 hours and equation (4) give M • 10 7.30 M ⊙ for 3C 273. This upper limit of M • is much lower than masses M • = 10 8.37 -10 9.39 M ⊙ obtained in the literatures. It may be not possible that the blue-bump is the thermal emission from accretion disk for 3C 273. Then, it is supported that the flare with a duration of 0.40 hours is produced from the relativistic jets in 3C 273. Equation (3a) gives a reasonable constraint on M • for 3C 273. The shock-in-jet model, the most frequently used model to explain the IDV behaviors which 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 the 1.02 m optical telescope from 2007 March 07 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 fourteen nights. The one-way ANOVA test is carried out on Std of the comparison stars. There are IDVs of Std for 3 out of 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, one-way ANOVA test, and ZDCF crosscorrelation zero lag test for S5 0716+714 and 3C 273, respectively. Optical IDVs with flare durations of 0.54 and 0.40 hours are found for S5 0716+714 and 3C 273, respectively. Based on equation (3a) and ∆t ob min 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 those measurements reported in the literatures, except for M • = 2.44 +0.51 −0.30 × 10 9 M ⊙ for 3C 273 (Paltani & Türler 2005), generally larger than other measurements in the literatures. Sharp dips are found in the LC on 2011 May 9 for 3C 273, and show ∆R ≈ 0.05±0.01 mag. It is supported that these optical IDVs are from emission regions in the jets of S5 0716+714 and 3C 273.   Fig. 3.-LCs of S5 0716+714 (symbols same as Figure 2). Y-axes denote the apparent magnitudes.