Optical Variability of Blazars in the Tomo-e Gozen Northern Sky Transient Survey

We studied the optical variability of 241 BL Lacertae (BL Lacs) and 83 flat-spectrum radio quasars (FSRQs) from the 4LAC catalog using data from the Tomo-e Gozen Northern Sky Transient Survey, with ∼50 epochs per blazar on average. We excluded blazars whose optical variability may be underestimated due to the influence of their host galaxy based on their optical luminosity (L O ). FSRQs with γ-ray photon index greater than 2.6 exhibit very low optical variability, and their distribution of standard deviation of repeated photometry is significantly different from that of the other FSRQs (Kolmogorov–Smirnov test p-value equal to 5 × 10−6). Among a sample of blazars at any particular cosmological epoch, those with lower γ-ray luminosity (L γ ) tend to have lower optical variability, and those FSRQs with a γ-ray photon index greater than 2.6 tend to have low L γ . We also measured the structure function of optical variability and found that the amplitude of the structure function for FSRQs is higher than previously measured and higher than that of BL Lacs at multiple time lags. Additionally, the amplitude of the structure function of FSRQs with high γ-ray photon index is significantly lower than that of FSRQs with low γ-ray photon index. The structure function of FSRQs of high γ-ray photon index shows a characteristic timescale of more than 10 days, which may be the variability timescale of the accretion disk. In summary, we infer that the optical component of FSRQs with high γ-ray photon index may be dominated by the accretion disk.


INTRODUCTION
Blazars are a type of active galactic nucleus (AGN) characterized by a relativistic jet pointed directly at the observer (Blandford & Königl 1979).As one of the most powerful phenomena in the universe, blazars have garnered significant attention in the field of extra-galactic astronomy.Jets of blazars are responsible for producing a wide range of observable energies, the majority of which are in the form of non-thermal radiation.The non-thermal radiation includes synchrotron radiation, which occurs across radio to X-ray frequencies, as well as inverse Compton scattering, which occurs from X-ray to γ-ray frequencies (Konigl 1981).
Blazars can be classified into two primary intrinsic types, namely low-ionization (BL Lacs) and high-ionization (FSRQs, predominantly beamed Fanaroff-Riley class II sources) ( (Giommi et al. 2012); (Fanaroff & Riley 1974)).The distinction between BL Lacs and FSRQs is primarily determined by the presence or absence of emission lines in their optical-IR spectra.Specifically, BL Lacs do not display prominent emission lines in their spectra, whereas FSRQs do display prominent emission lines in their spectra.
In a recent study, (Ghisellini et al. 2017) examined the dependence of the Spectral Energy Distribution (SED) on γ-ray luminosity (L γ ) using Fermi/LAT and other data.The study found that FSRQs exhibit a similar SED across a wide range of L γ , while BL Lacs display decreasing synchrotron peak frequencies with increasing L γ .Furthermore, the nature of blazars at various wavelengths has been discussed by several studies ( (Richards et al. 2011), (Landi et al. 2015), (Acciari et al. 2021), (Kaur et al. 2021), (Kerby et al. 2021)).
Studying the optical variability of blazars is essential for understanding their nature.(Clements et al. 2003) monitored the intra-night optical variability of FSRQ PKS 0736+017 and observed a dramatic flare, with the source brightening by 1.3 magnitudes (R band) in just 2 hours.In a study comparing the intra-night optical variability rates of blazars, (Bachev et al. 2012) found indications for the presence of quasi-periodic micro-oscillations with periods of about an hour.Similarly, (Rani et al. 2013) monitored the intra-night multi-wavelength luminosity of BL Lac object S50716+714 over a period of four years and identified a long-term variability trend (about 350 days) and a shorter time scales (about 60 days).(Pandey et al. 2020) studied the optical variability of BL Lac 1ES 0806+524 in three bands (V RI) using high cadence observations for 153 nights during 2011∼2019, and found a small but significant variation in both V band and R band light curves in only one night.In a recent study, (Goyal 2021) examined the intra-night optical variability of 9 BL Lacs and 5 FSRQs, carrying out a Fourier transform on their light curves, and obtained their power spectral densities.They found that most of the power spectral densities were well fit by simple power-laws with slopes ranging from 1.4 to 4.0, with no significant difference between BL Lacs and FSRQs.These studies highlight the diversity of the optical variability of blazars which may give insights into the physical processes driving their emission.
The optical variability of FSRQs is a topic of much debate among researchers.One viewpoint is that FSRQs, dominated by accretion disks, should exhibit smaller optical variability than jet-dominated BL Lacs (Wiita 2005).Conversely, others suggest that FSRQs are a mixture of various types, including optically violently variable quasars, highly polarized quasars, core-dominated quasars, and superluminal motion sources, with some objects exhibiting optical variation of up to 50% in one day ( (Penston & Cannon 1970); (Fan 2005)).(Bonning et al. 2012) conducted observations on 9 FSRQs and revealed that in multiple bands (BV RJ), the fractional variability amplitude of 3C 273 was one magnitude lower than that of other FSRQs, providing support for the aforementioned bipolarity.
In a study by (Bauer et al. 2009a), the statistical variability of blazars, which included 276 FSRQs and 86 BL Lacs, and nearly 23000 quasars were analyzed using data from the Palomar-QUEST Survey (Djorgovski et al. 2008).The authors investigated the overall variability of BL Lacs and FSRQs using the structure function and found that different objects exhibit varying degrees of variability details on timescales up to a few years.
Utilizing the Tomo-e Gozen Northern Sky Transient Survey data, we have investigated the optical variability of blazars in this work.Compared to the previous work of (Bauer et al. 2009a), our study has a larger ample size (with redshift) and a larger number of measurements per object, with an average of ∼50 epochs per blazar compared to an average of 6 epochs in (Bauer et al. 2009a).Moreover, we have used the latest catalog, the 4LAC catalog (Ajello et al. 2020), to classify blazars.
In Section 2, we provide a concise description of the data used in this study.Our investigation into the variability of blazars, utilizing the standard deviation of repeated photometry and the structure function, is presented in Section 3. In Section 4, we discuss the differences between this study and previous studies and outline its limitations.Our conclusions are summarized in Section 5.The calculations and interpretations presented in this work are based on a cosmological model defined as a Flat Lambda Cold Dark Matter (ΛCDM) cosmology.Specifically, we adopt a flat universe assumption with Hubble constant H 0 = 70 km s −1 Mpc −1 and a matter density parameter Ω m = 0.3.

Tomo-e Gozen observation of Fermi Blazar
The Tomo-e Gozen Camera (Sako et al. 2018) is a wide-field camera which deploys 84 CMOS sensors and covers about 30% of the entire focal plane (9 degree in diameter) of the 1.05-m Kiso Schmidt telescope (Takase et al. 1977).The camera has a peak photoelectric conversion efficiency of 0.72 at a wavelength of 500 nm; the efficiency falls to 0.36 at wavelengths of 380 and 710 nm.(Figure 1(e)).Since the CMOS sensor can read out the signal pixel by pixel, the read out speed is fast -much more rapid than that of traditional astronomical CCDs.We typically operate the camera in a high-speed mode, reading out all 84 sensors at a rate of 2 frames per second.
In the Tomo-e Gozen project, most of the observation time is used for Northern Sky Transient Survey (Tominaga et al. in preparation).The integration time for a single image is 0.5 seconds, but we combine frames in groups of 12 (or 18 since August 14, 2020): each frame is stacked with 11 (or 17) other images in its group after we have removed the maximum value at each pixel position to avoid cosmic rays.The effective exposure time for our measurements is therefore 6 seconds.In our all-sky survey mode, the area covered each night is about 12,000 square degrees, and a sub-region with low atmospheric extinction (above 40 degrees in elevation) is observed 2-3 times during the night1 By making multiple observations of targets each night in this way, we are exploring short-timescale transients such as supernovae and blazars.
To ensure the accuracy of photometric measurements in the Northern Sky Transient Survey, we adopted SDSS standard stars given by (Ivezić et al. 2007) and observed with the Tomo-e Gozen camera.Following the standard data reduction procedures such as dark and bias subtraction and flat-field correction, we performed aperture photometry using an aperture diameter of 16.6 arcseconds, compared to a typical Full Width at Half Maximum (FWHM) of 7 arcseconds.The magnitude zero point in our unfiltered images was calculated using G-band data from the Gaia satellite DR2 (Gaia et al. 2018).We evaluated the photometric uncertainty of the survey by determining the standard deviation of repeated photometry across all observations for stars measured at least 10 times, in the following manner.We initially select all objects that are suitable for determining the magnitude zero point (zeromag), based on various factors, such as their magnitude, parallax, and the absence of other surrounding objects in the Pan-STARRS1 (Kaiser et al. 2002) and Gaia catalogs.Subsequently, we calculate the zeromag for each object in a frame and then use the median value as the overall zeromag of the frame.During this process, the standard deviation in zeromag calculated for different objects is approximately 0.03 mag.The zeromag error along with other errors (such as flat error, etc.) results in a systematic error of 0.01 to 0.02 mag, and the overall photometric uncertainty of the Northern Sky Transient Survey is presented in Figure 1(a).
We chose as our initial source for candidate blazars the Fourth LAT AGN Catalog (4LAC), derived from the first eight years of data collected by the Fermi Gamma-ray Space Telescope within the energy range from 50 MeV to 1 TeV (Ajello et al. 2020).The observational footprint of the Tomo-e Gozen camera covers nearly 60% of the 4FGL survey's area, and its detection capability down to mag 18.5 is able to identify 44.6% of the blazar sources listed in the 4LAC.Figure 1(b) shows the number of blazars observed and the histogram of the number of detections of each blazar observed by the Northern Sky Transient Survey from 08-31-2019 to 11-04-2022. Figure 1(c) depicts a histogram of the time lag τ (days) in the rest frame between two observations of the same blazar.The sparsity of observational data in the τ ∼ 100 − 250 range can be attributed to the seasonal visibility of objects, the climate of the Kiso Observatory, and instrument adjustments of Tomo-e Gozen.Similarly, the scarcity of observational data in the τ > 400 range can be attributed to the limitation of the survey period.Figure 1(d), which displays a histogram of the mean Tomo-e Gozen magnitude in repeated photometry for BL Lac and FSRQ blazars.The distribution of magnitudes for BL Lac blazars in this study ranges from magnitude 14-18, with a peak value of approximately magnitude 17.3.Similarly, FSRQ blazars have magnitudes distributed in the range of magnitude 15-18, with a peak value of approximately magnitude 17.3.To facilitate the visual understanding of our analyzed dataset, we display example light curves of four well-observed FSRQ objects in Figure 2.

Sample selection & variability measurement
The luminosity relationship between blazars and their host galaxies has a significant impact on our study.When the luminosity of the blazar is not greater than that of the host galaxy, the continuous spectrum emitted by the galaxy can overwhelm the emission lines from the AGN core of the blazars.This phenomenon can also lead to an increase in the radiation photon index from the jet, resulting in a redder spectrum.Consequently, this overlap in spectral features can lead to the misclassification of certain FSRQs as members of the BL Lac class, thereby introducing ambiguity and potential errors.
The assessment of variability of blazars is also complicated by the presence of their host galaxies.First, the optical emission from the host galaxy merges with that from the blazar, making it challenging to isolate the blazar's variability.This is also particularly notable when the blazar's luminosity is not significantly higher than that of the host galaxy, leading to potential underestimation of the blazar's relative variability.Second, since we used a fixed photometric aperture size (16.6 arcseconds in diameter), variations in seeing can cause variations of the galaxy flux within the aperture, possibly resulting in an overestimation of the blazar's absolute variability.
In order to minimize the potential for errors in our analysis, we attempt to select objects in which the luminosity contributed by the central engines (blazars) in our sample will be greater than the luminosity contributed by their host galaxies.A previous study (Urry et al. 2000) employing the Hubble Space Telescope to examine the host galaxies of BL Lac objects, spanning redshifts from 0.1 to 1.3, revealed an absolute magnitude for these galaxies of M B = −21.4± 0.6 AB mag (after adjustments for bandpass, Hubble constant, and conversion from Vega to AB system).Hence the bright end of blazar host galaxies within a 2σ range is M B = −22.6AB mag.This finding is consistent with bright end of the luminosity function of galaxies, as reported by the SDSS survey (Blanton et al. 2003), which is around -22.8 AB mag (in the g-band).Consequently, we will exclude candidates whose optical luminosity L O (including blazar and host galaxy) is lower than the K-corrected optical luminosities of any hypothetical host galaxy type (including elliptical, Sc, Sa, and starburst galaxies) corresponding to an absolute magnitude of M B = -23 AB magnitudes.We present in Figure 3 the K-corrected optical luminosity,L g , of different types of hypothetical galaxies as a reference for galaxy evolution at various redshifts; we define L g as where L ′ g is the optical luminosity of galaxies with absolute magnitude M B =-23 AB mag before K-correction and k g (z) is the K-correction factor for galaxies with where ν 1g and ν 2g are the starting and ending frequencies, respectively, for the Gaia G-band, and R g (ν) represents its quantum efficiency.Similarly, ν 1B and ν 2B are designated as the initial and terminal frequencies for the Gaia B-band, with R B (ν) denoting its quantum efficiency.f ν (ν) is the spectral density of flux of each galaxy template provided by Kinney et al. (1996).

Optical luminosity of Blazers
The optical luminosity of Blazars without K correction, L ′ O , was calculated using redshift data from the 4LAC database, average magnitude data from the Tomo-e Gozen survey.and the astropy.cosmology.luminositydistance method (Robitaille et al. 2013).Power-law fitting was performed on the flux of each object in the Pan-STARRS g, r, i bands (Kaiser et al. 2002) to determine its photon index Γ O in the optical band, which was then used to perform K-correction and yield the optical luminosity L O in the following manner: where Here, ν 1t and ν 2t are the starting and ending frequencies of the Tomo-e Gozen band and R t (ν) represents Tomo-e Gozen's quantum efficiency (see Figure 1(e)).
In order to assess the variability of blazars, we first calculated the standard deviation in repeated photometry (light curve).To obtain the intrinsic standard deviation σ of blazars, we subtracted the photometric uncertainty, which is shown in Figure 1(a), from this initial standard deviation σ ′ .σ = σ ′2 − magerr(mag) 2 (5) A total of 241 BL Lacs and 83 FSRQs were included in the original sample.To ensure accurate observations of optical luminosity and avoid interference from the stellar component of host galaxies, our study excluded blazars located below any of the lines in Figure 3 and made the final sample of 120 BL Lacs and 78 FSRQs for more detailed investigation.

Standard deviation of repeated photometry
The distribution of photon indices of γ-ray2 and optical wavelengths3 , and their relationship to the standard deviation of repeated photometry, are shown in Figure 4.The distribution of optical photon indices for BL Lacs and FSRQs, while overlapping in range, demonstrates a significant difference with a KS-test p-value of 2.6e-5, possibly indicating multiple emission mechanisms.The peak of the optical photon index distribution for FSRQs is notably lower, which may be attributed to the bluer color of their accretion disks.Conversely, the γ-ray photon index distribution shows a pronounced difference between the two classes, with FSRQs typically exhibiting higher values than BL Lacs, as indicated by a KS-test p-value of 6.6e-31.This disparity is likely due to the differences in the peak of the inverse Compton scattering between the two.The photon index of BL Lacs at γ-ray and optical wavelengths is positively correlated, whereas those of FSRQs display an anti-correlation.Furthermore, FSRQs with a γ-ray photon index greater than ∼2.6 (highlighted by the yellow region in the left panel of Figure 4) present a smaller standard deviation in repeated photometry measurements compared to those with a lower γ-ray photon index.Further discussion of this trend is presented in section 3.2.
In Figure 5, we present a histogram that shows the standard deviation observed in repeated photometric measurements of blazars, specifically focusing on those observed more than five times.Our analysis reveals a notable distinction in the variability patterns of BL Lacs and FSRQs.The standard deviation for BL Lacs predominantly clusters within the 0.0 to 0.2 magnitude range.Conversely, the standard deviation for FSRQs demonstrates a more uniform distribution across different magnitude bins.
Further scrutiny, employing the Kolmogorov-Smirnov (KS) test, accentuates the disparity in the distribution patterns of FSRQs based on their gamma-ray photon indices.FSRQs characterized by high gamma-ray photon indices (exceeding 2.6) manifest a statistically significant divergence in their distribution when compared to two groups: FS-RQs with lower gamma-ray photon indices (resulting in a p-value of 3.8E-6 ) and the general population of FSRQs (yielding a p-value of 2.3E-3 ). Figure 2 provides detailed illustrations of these relationships for several well-observed objects.The FSRQ 3C232, which has a high γ-ray photon index, displays notable stability throughout our nearly three-year observation period.Another largely quiescent object is 4C+21.35,which has a relatively low γ-ray photon index; it exhibits slight fluctuations during the initial stage of our observations (before MJD 59000) before becoming quiet in subsequent observations.On the other hand, OI275 and Ton599, both of which have relatively low γ-ray photon indices, display dramatic variations during our observation period.The maximum optical luminosity of these two objects can exceed the minimum optical luminosity by more than ten times.
Figure 6 presents the relationship between redshift and K-corrected4 γ-ray luminosity (L γ ) for FSRQs and BL Lacs.Despite the inevitable selection bias in the data due to sensitivity limitations and volume effects, the limited dataset still reveals a noticeable trend: blazars with lower optical variability (reddish symbols) tend to cluster in regions of lower γ-ray luminosity (L γ ) across different cosmological epochs.

FSRQs
Bl Lacs The analysis of blazars by (Ghisellini et al. 2017) primarily utilized L γ as the distinguishing characteristic.While this approach offers a straightforward method of categorization, it could overlook a critical aspect: the potential diversity in physical properties of blazars at different redshifts, despite having similar L γ .This oversight is significant, considering that the properties and surrounding environment of an AGN are intricately linked to its redshift.Consequently, relying solely on L γ for classification, without considering the redshift, might lead to a skewed understanding of blazar properties.
To quantitatively analyze the relationship between luminosity and redshift, we introduce a new metric: the relative luminosity index (R L ).
where the term k(z) represents the unified K-correction coefficient5 and D L denotes the luminosity distance, which is also dependent on the redshift.
Figure 7 delineates the correlation between the optical variability of FSRQs and BL Lacs and their respective R L values.The red solid line in the figure indicates a linear regression fit to the data.The optical variability of both FSRQs and BL Lacs shows a positive correlation with their relative luminosity index (R L ).For FSRQs, this correlation is weak and not statistically significant, with a Pearson correlation coefficient of r=0.19 and a confidence level of p=0.09.In contrast, for BL Lacs, the correlation is moderate and statistically significant, with a Pearson correlation coefficient of r=0.46 and a confidence level of p=1.6e-7.

FSRQs
Bl Lacs This evidence for a difference between FSRQs and BL Lacs led us to look further into the relationship between the relative luminosity index (R L ) and the dual-band spectral index.For a balanced and methodical analysis, we categorized FSRQs into three distinct groups according to their R L values, with the group boundaries set at log7 and log20.This stratification was designed to ensure an approximately equal number of FSRQs in each category.The same criteria for group classification were applied to BL Lacs, thereby maintaining consistency and comparability in our analytical approach.The FSRQs shown in Figure 2 are located in different zones.Specifically, 3C232 is located in zone 1, while OI275 is in zone 2. On the other hand, 4C+21.35 and Ton599 are both in zone 3. Figure 8 illustrates the distribution of γ-ray photon index and optical photon index for FSRQs and BL Lacs in each zone.Zone 1 FSRQs dominate the high γ-ray photon index group, suggesting that these FSRQs tend to have lower L γ compared to other FSRQs.Conversely, the low γ-ray photon index group does not appear to be dominated by any specific zones of FSRQ, as all three zones exhibit similar tendencies.The optical photon index of the high γ-ray photon index FSRQs is concentrated around 1.5, which is the typical color of a quasar accretion disk (Kishimoto et al. 2008).This suggests that FSRQs dominated by accretion disks differ significantly from those dominated by jets in terms of optical variability and γ-ray photon indices.Notably, zone 2 FSRQs also have optical photon indices concentrated around 1.5, despite their relatively scattered γ-ray photon indices, while zone 3 FSRQs have a relatively concentrated γ-ray photon indices (∼ 2.3) but have relatively scattered optical photon indices.

Structure function
In addition to the standard deviation of repeated photometry, which does not involve the rest frame time interval τ , we also studied the structure function, following the method by (Berk et al. 2004).The structure function can be defined as where m(t) and m(t − τ ) are magnitudes of two measurements of the same object, separated by (rest frame) time τ , and σ SF is uncertainty of the measurements given by ( 8), where magerr(t) represents the blue line in Figure 1(a).
The optical variability of an object can be quantified using the structure function, which depends on the rest frame time interval τ .This function provides insight into the temporal characteristics of the object's variability.A change in the slope of the structure function when plotted again τ may signify a significant timescale relevant to understanding the underlying mechanism of optical luminosity variation.To construct the structure function for a single object, a large number of observation epochs that are widely distributed in time are required.However, due to limited data availability, we constructed structure functions for a class of blazars as a group, combining measurements from objects with similar properties.Figure 9 illustrates the structure functions of FSRQs and BL Lacs.In the process of constructing the structure function for a specific class of blazars, either BL Lacs or FSRQs, a comprehensive approach was adopted to extract and analyze the observational data.The initial step involved the extraction of all available data pairs (magnitudes of one object at two epochs) from the selected blazar class, recording their respective rest frame time lag τ and structure function values.This extensive data set was then combined into a unified set, encompassing observations from various sources.
To facilitate a detailed analysis, the combined data pairs were organized in ascending order based on their τ values.The ordered data set was then equally divided into 20 groups to ensure a balanced representation across varying lag intervals.For each of these groups, a representative data point was generated to populate the structure function graph.The x-coordinate of these data points, indicating the lag value, was calculated as the mean of all lag values within the respective group.Within each group, we computed two y-coordinates: one for the 50th percentile of the SF values, the other for the 75th percentile of the SF values.
In the rest-time time interval τ spanning 10 to 100 days, it is evident that the median (50th percentile) variability of Flat Spectrum Radio Quasars (FSRQs) is lower than that of BL Lacertae objects (BL Lacs), while their 75th percentile variability exceeds that of BL Lacs.This observation suggests that FSRQs exhibit greater internal heterogeneity than BL Lacs.Despite this difference, it's important to note that both BL Lacs and FSRQs have a similar smooth pattern in the intraday timescale.Additionally, contrary to the findings of Emmanoulopoulos and Bauer (2009), no distinct trough in variability was observed in the 70-250 day range.We attribute this discrepancy to the expanded dataset now available and the refined criteria for sample selection in our study.(Bauer et al. 2009a) and (Bauer et al. 2009b).The rest frame interval τ is in unit of day.
We also performed further analysis on FSRQs grouped by their γ-ray photon index, as mentioned in Section 3.1; see Figure 10.In this comparative analysis, the amplitude of the structure function for high γ-ray photon index FSRQs stands out for its significantly lower value when compared with both BL Lacs and the low γ-ray photon index FSRQs.Notably, the structure function of high γ-ray photon index FSRQs shows substantial variability only beyond a 200-day timescale.This observation aligns with the hypothesis that the variability in these FSRQs resembles that of accretion disks, which are characterized by timescales over 100 days (Burke et al. 2021).In contrast, for low γ-ray photon index FSRQs, optical variability within a shorter span, particularly under 10 days, is likely attributed to jet components ( (Penston & Cannon 1970); (Fan 2005)).Furthermore, figure 10 reveals that low γ-ray photon index FSRQs (sometimes thought to be dominated by an accretion disk) exhibit more significant variability than the jet-dominated BL Lacs, particularly within the 10-to 100-day range (KS-test p<1E-16).This finding suggests a complex role of accretion disks and jets in these sources, pointing towards the necessity of further spectroscopic observations to determine the dominant factor driving these changes.

DISCUSSION
Based on our analysis, we infer that the optical component of FSRQs with high γ-ray photon index is dominated by the accretion disk.This hypothesis is based on several observational results: their low optical variability, their lower L γ compared with other FSRQs in the same cosmic period, and their accretion-disk-like characteristic timescale.These findings are consistent with the results of (Shaw et al. 2012), who reported a weak correlation between non-thermal dominance of FSRQs and low photon indices in Fermi observations.Unfortunately, due to the limited sample size, our study only separated FSRQs by γ-ray photon index into two groups.Our result is different from the result of previous studies (Ghisellini et al. 2017) which only detected accretion disc components in spectra (from ASI Astrophysical Data Center) of FSRQs at high redshift, while FSRQs at low redshift rarely showed accretion disc components in the optical band.Their result may be attributed to the accretion disc component becoming more prominent at larger redshifts, thus at higher luminosities.However our study provides the first confirmation of accretion disk-dominated FSRQs at low redshifts through their low optical variability and long characteristic timescale.It remains unclear whether there is a continuous relationship between the γ-ray photon index and the dominance of the accretion disk, or if the high accretion-disk dominance ratio only appears in the high γ-ray photon index region.(Ghisellini 2016) argued that the IR-optical band SED of FSRQs with low L γ contains smaller accretion-disk components than other FSRQs, and the flux at optical wavelengths is dominated by non-thermal radiation of the jet, which differs from the results of this study.The main reason for this difference may be our different blazar selection and grouping approach.(Ghisellini 2016) grouped the FSRQs only according to their L γ , while in this study, we considered both the L γ and redshift of the blazar simultaneously.The reason for this approach is that we believe the nature of blazars with the same L γ is not precisely identical but closely linked to their cosmic epoch.
It is important to acknowledge that the γ-ray photon index utilized in our study are based on the Fermi/LAT eight-year integration, which represents an average of the blazar γ-ray spectrum over an eight-year period.Conversely, the optical spectrum index utilized in our study is based on the result of short-term observations by Pan-STARRS1, indicating that our two photon indices are not synchronized.Consequently, caution must be exercised in interpreting the results of our study, particularly with regards to the correlation between the γ-ray and optical photon index properties.
Also, according to the blazar sequence given by (Ghisellini et al. 2017), for FSRQs and BL Lacs at high redshift, the frequency observed by Tomo-e Gozen (about 10 14 Hz) is higher than their synchrotron radiation peak ν s (about 10 12 Hz), while for BL Lacs at low redshift, the frequency observed by Tomo-e Gozen is higher than their synchrotron radiation peak ν s (about 10 16 Hz).This redshift dependence may lead to differences in observed optical variability.However, considering that the BL Lacs in the sample have roughly the same redshift distribution as the FSRQs, and the standard deviation of repeated photometry of both FSRQs and BL Lacs did not appear to be redshift-dependent, we conclude that this phenomenon does not significantly affect our results.

CONCLUSION
We conducted a study of the optical variability of blazars selected from the 4LAC catalog, using observations from the Tomo-e Gozen Northern Sky Transient Survey, covering the period from MJD 58726 to 59887.Our high-speed sky survey allowed us to observe 324 blazars, with an average of 50 epochs per blazar, representing a significant increase compared to the previous study by (Bauer et al. 2009a), which had an average of only six epochs per blazar.Furthermore, the catalog used in our study was updated, which provided additional information not present in the previous study.
We focused exclusively on blazars with an optical luminosity L O higher than that of hypothetical galaxies with absolute magnitudes of M B =-23 (AB magnitude).This criterion was applied in order to enhance the probability of the correct spectroscopic classification of low-luminosity blazars and accurately calculate their optical variability.
Our study shows that there is no significant difference in the optical variability of blazars at different cosmological epochs, despite the orders of magnitude difference in their luminosity.This finding indicates that the optical variability of blazars is not directly dependent on their luminosity, nor on their redshift.As we considered the redshift dependence and L γ dependence simultaneously in our analysis, we found that blazars with low L γ at a given cosmic epoch tended to have lower optical variability.
The γ-ray photon index of FSRQs is typically higher than that of BL Lacs.We found that the photon index of BL Lacs is positively correlated at γ-ray and optical wavelengths, while the that of FSRQs is anti-correlated.Also, FSRQs with high γ-ray photon index tend to have lower optical variability, especially those with γ-ray photon index exceeding 2.6.Moreover, the distribution of standard deviation in repeated photometry of FSRQs with γ-ray photon index greater than 2.6 is significantly different from that of FSRQs with γ-ray photon index less than 2.6.The difference between these two distributions is statistically significant with a KS test P-value equal to 2.6e-6.
FSRQs with high γ-ray photon index (greater than 2.6) typically exhibit low optical variability.From an evolutionary perspective, these FSRQs are often found in regions of low L γ at a cosmic epoch, a pattern that aligns with what is observed in disk-dominated blazars.While their characteristic timescales are not immediately apparent from our observation alone, further observations and analysis will, we hope provide more insight.
When examining the structure functions of these FSRQs in comparison to those of BL Lacs, a clear distinction emerges: FSRQs generally show higher amplitudes in their structure functions.Specifically, FSRQs with high γ-ray photon index have significantly lower amplitudes compared to their low-index counterparts.This finding is intriguing as these high-index FSRQs also display noticeable variability, predominantly on timescales extending beyond 100 days.This pattern of variability, emerging from the analysis of structure functions, suggests a resemblance to the longer timescales typically associated with accretion disks.In contrast, FSRQs with low γ-ray photon index exhibit variability on much shorter timescales, often less than ten days, likely indicative of jet activity.Moreover, these low γ-ray photon index FSRQs demonstrate even greater variability than jet-dominated BL Lacs, not only on timescales less than ten days but also particularly within the 10 to 100-day range (KS-test p<1E-16), pointing towards an area worth further exploration to determine the underlying causes.Despite these differences, it's important to note that the structure functions of both BL Lac and FSRQs consistently exhibit smooth characteristics at the intraday scale.
We are initiating spectral studies of FSRQs, particularly focusing on emission line equivalent widths, to decipher the roles of accretion disks and jets.In parallel, we will continue our engagement with the Tomo-e Gozen Northern Sky Transient Survey to enrich our dataset.This sustained effort is expected to enhance our understanding of blazar luminosity variability and further illuminate the complex mechanisms driving these FSRQs.The limitations imposed by the systematic error in standard deviation subtraction are acknowledged, particularly in the context of darker objects where this method may lead to an underestimation of standard deviation.Despite this potential bias, our analysis indicates that this selection error remains consistent across various FSRQs with different γ-ray photon indices.This uniformity is evidenced by the similarity in the rank distribution of FSRQs with high γ-ray photon indices compared to those with standard γ-ray photon indices, as demonstrated by a KS-test yielding a p-value of 0.21.Consequently, we infer that the observed low variability in FSRQs with high γ-ray photon indices is not a result of the standard deviation subtraction process.
Also in our analysis, we have specifically plotted the structure function for blazars exhibiting an average Tomo-e Gozen magnitude brighter than 17.5, as depicted in Figure 13.The observed behavior of the structure function in this figure closely mirrors that presented in Figure 10.Notably, the similarity in the patterns between these two figures substantiates the assertion that the biases potentially introduced by the standard deviation subtraction do not significantly impact our results.

Figure 1 .
Figure 1.(a): Photometric uncertainties of Tomo-e Gozen's photometry for SDSS standard stars.We obtained a total of 8,057,340 epochs of 283,605 SDSS standard stars between MJD 58726 and 59869.To determine the photometric uncertainty of Tomo-e Gozen at a given magnitude, we calculated the median of the standard deviation of repeated photometry for each star with the same r-band bin (0.01 mag) in the SDSS catalog; (b): The relationship between number of measurements and number of objects.In this study we only used blazars with more than 5 epochs; (c): Number of measurements pairs with time lag τ (day) of FSRQs and BL Lacs.(Due to the difference in redshift between BL Lacs and FSRQs, their τ distributions in the rest frame are different.);(d): Mean Tomo-e Gozen magnitude histogram of FSRQs and BL Lacs.(e): Bandpass of Tomo-e Gozen transparent window and Gaia G-band (Gaia et al. 2018).

Figure 3 .
Figure 3.The distribution of K-corrected optical luminosity LO, plotted against redshift for FSRQs and BL Lacs.The color of each symbol corresponds to the standard deviation of the repeated photometry (light curve).We have excluded blazars with LO below any of the Lg lines, which represent the K-corrected optical luminosity of differents types of hypothetical galaxies with absolute magnitude of MB =-23 AB mag.The symbols of the excluded blazers were blurred.

Figure 4 .
Figure 4.The relationship between the γ-ray photon indices (x-axis) and the optical photon indices (y-axis) is depicted for FSRQs (left panel) and BL Lacs (right panel).The top inset shows the histogram of the γ-ray photon indices, and the right inset displays the optical photon indices, with FSRQs indicated in blue and BL Lacs in red.The color intensity of each symbol reflects the standard deviation of the optical repeated photometry (light curve) for the respective sources.

Figure 5 .
Figure 5. Distribution of standard deviation of repeated photometry of blazars which were observed more than 5 times.The blue line represents the overall FSRQs, the red line represents the FSRQs with high γ-ray photon indices (greater than > 2.6), and the green line represents BL Lacs.

Figure 6 .
Figure 6.The distribution of K-corrected Lγ versus redshift of FSRQs and BL Lacs.The color of the symbol stands for the standard deviation of the repeated photometry (light curve).

Figure 7 .
Figure 7.The distribution of relative luminosity index (RL) versus the optical variability of FSRQs and BL Lacs.The red solid line in the figure indicates the linear regression fit to the data.The color of the symbol stands for the γ-ray photon indices.

Figure 8 .
Figure 8.The distribution of the γ-ray photon index and the optical photon index of FSRQs (left) and BL Lacs (right) for each zone.(The kernel density estimate plot was generated using the sns.kdeplot function from the Seaborn data visualization library (version 0.12) in Python.)

Figure 9 .
Figure 9. Structure function of FSRQs (brown; 10966 data pairs for each point) and BL Lacs (green; 34015 data pairs for each point), and previous results from(Bauer et al. 2009a) and(Bauer et al. 2009b).The rest frame interval τ is in unit of day.

Figure 10 .
Figure 10.Structure function of low γ-ray photon index FSRQs (blue; 7689 data pairs for each point), BL Lacs (green; 34015 data pairs for each point) and high γ-ray photon index FSRQs (red; 3278 data pairs for each point).
Figure 12. a: Correlation between the mean mag and standard deviation for FSRQs and BL Lacs.b: Histogram of the mean mag of FSRQs with different γ-ray photon indices.

Figure 13 .
Figure 13.Structure function of low γ-ray photon indices FSRQs with average Tomo-e Gozen magnitude brighter than 17.5 (blue; 7504 data pairs for each point), BL Lacs with average Tomo-e Gozen magnitude brighter than 17.5 (green; 32442 data pairs for each point) and high γ-ray photon indices FSRQs with average Tomo-e Gozen magnitude brighter than 17.5 (red; 2953 data pairs for each point).