Interesting Clues to Detect Hidden Tidal Disruption Events in Active Galactic Nuclei

In the manuscript, effects of Tidal Disruption Events (TDEs) are estimated on long-term AGN variability, to provide interesting clues to detect probable hidden TDEs in normal broad line AGN with apparent intrinsic variability which overwhelm the TDEs expected variability features, after considering the unique TDEs expected variability patterns. Based on theoretical TDEs expected variability plus AGN intrinsic variability randomly simulated by Continuous AutoRegressive process, long-term variability properties with and without TDEs contributions are well analyzed in AGN. Then, interesting effects of TDEs can be determined on long-term observed variability of AGN. First, more massive BHs, especially masses larger than $10^7{\rm M_\odot}$, can lead to more sensitive and positive dependence of $\tau_{TN}$ on $R_{TN}$, with $\tau_{TN}$ as variability timescale ratio of light curves with TDEs contributions to intrinsic light curves without TDEs contributions, and $R_{TN}$ as ratio of peak intensity of TDEs expected variability to the mean intensity of intrinsic AGN variability without TDEs contributions. Second, stronger TDEs contributions $R_{TN}$ can lead to $\tau_{TN}$ quite larger than 5. Third, for intrinsic AGN variability having longer variability timescales, TDEs contributions will lead $\tau_{TN}$ to be increased more slowly. The results actually provide an interesting forward-looking method to detect probable hidden TDEs in normal broad line AGN, due to quite different variability properties, especially different DRW/CAR process expected variability timescales, in different epochs, especially in normal broad line AGN with shorter intrinsic variability timescales and with BH masses larger than $10^7{\rm M_\odot}$.

There are many reported studies on the AGN variability through the DRW process.MacLeod et al. (2010) have modeled the variability of about 9000 spectroscopically confirmed quasars covered in the ★ Corresponding author Email: xgzhang@gxu.edu.cnSDSS Stripe82 region, and found correlations between the AGN parameters and the DRW process determined parameters.Bailer-Jones (2012) proposed an another fully probabilistic method for modeling AGN variability by the DRW process.Andrae, Kim & Bailer-Jones (2013) have shown that the DRW process is preferred to model AGN variability, rather than several other stochastic and deterministic models, by fitted results of long-term variabilityof 6304 quasars.Zu et al. (2013) have checked that the DRW process provided an adequate description of AGN optical variability across all timescales.Zhang & Feng (2017) have checked long-term variability properties of AGN with double-peaked broad emission lines, and found the difference in intrinsic variability timescales between normal broad line AGN and the AGN with double-peaked broad emission lines.Sanchez-Saez et al. (2018) have modeled variability by DRW process and reported statistical analysis of the connection between AGN variability and physical properties of the central AGN activities, through the 2345 sources detected in both SDSS (Sloan Digital Sky Survey) and QUEST-La Silla.Burke et al. (2020) have modeled the month-long, 30 minute-cadence, high-precision TESS (Transiting Exoplanet Survey Satellite) light curve by the DRW process in the well-known archetypical dwarf AGN NGC 4395.More recently, Suberlak, Ivezic & MacLeod (2021) have modeled 15yearslong variability of 9248 quasars covered in SDSS stripe 82 region by combining the Pan-STARRS1 PS1 (Panoramic Survey Telescope and Rapid Response System 1 Survey) and SDSS light curves.Zhang et al. (2021a) have modeled long-term variability of a composite galaxy to provide flues to support a true Type-2 AGN.There-fore, the long-term AGN variability have been well accepted to be mathematically modeled by the DRW/CAR process.
Meanwhile, as discussed in Mushotzky et al. (2011); Kasliwal et al. (2015); Guo et al. (2017); Tachibana et al. (2020); Stone et al. (2022), intrinsic AGN variability deviations from the simple DRW description on short timescales, and also the estimated intrinsic variability timescale in the DRW process probably rises with increased baseline.However, in the manuscript, long-term variability not on short timescales but with the same length of time durations are mainly considered, therefore, neither variability on short timescales nor effects of different lengths of baseline are discussed in the manuscript.Besides the long-term intrinsic AGN variability well described by the CAR/DRW process, there is an unique kind of variability related to tidal disruption events (TDEs), which cannot intrinsically follow the CAR process expected variability properties, due to unique TDEs variability patterns.The well-known pioneer work on TDEs can be found in Rees (1988) and then followed in Loeb & Ulmer (1997); Komossa et al. (2004) Mockler, Guillochon & Ramirez-Ruiz (2019); Stone et al. (2019); Parkinson et al. (2020); Lynch & Ogilvie (2021); Zhou et al. (2021); Zhang (2022), etc.The basic picture of a TDE is as follows.A star can be tidally disrupted by gravitational tidal force of a central massive black hole (BH), when it passing close to the central BH with a distance larger than event horizon of the BH but smaller than tidal disruption radius T = ★ × ( BH ★ ) 1/3 with ★ , ★ and BH as radius and mass of the being disrupted star and mass of central BH, respectively.The fallback materials can be accreted by the central massive BH, leading to time dependent TDEs variability roughly proportional to ∼ −5/3 at late times.
More recent reviews on theoretical simulations and/or observational results on TDEs can be found in Komossa (2015); Lodato et al. (2015); Stone et al. (2019).There are more than 100 TDE candidates reported in literature, see detail in https://tde.space/.Meanwhile, the well-known public sky survey projects have lead to more and more TDEs candidates detected, such as the TDEs candidates discovered through the known SDSS Stripe82 database in van Velzen et al. (2011), through the known Catalina Sky Survey (CSS, Drake et al. (2009)) in Drake et al. (2011), through the PanSTARRS (panoramic survey telescope and rapid response system) in Gezari et al. (2012); Chornock et al. (2014) Sazonov et al. (2021) from the SRG all-sky survey observations and then confirmed by optical follow-up observations.More recent review on observational properties of reported TDEs can be found in Gezari (2021).However, among the reported TDEs candidates, there are few TDEs detected in normal broad line AGN with both apparent and strong intrinsic AGN variability.
Among the reported TDE candidates, especially optical TDE can-didates, strong broad Balmer and Helium emission lines are fundamental spectroscopic characteristics, however, the detected broad emission lines are not expected to be tightly related to normal broad line regions in normal broad line AGN, but to be related to disk-like structures from TDE debris.The known cases with broad emission lines in TDEs candidates can be found in SDSS J0159 as discussed in Merloni et al. (2015); Zhang (2021b), ASASSN-14li as discussed in Holoien et al. (2016) Certainly, not similar as in quiescent galaxies, a moving star can be tidally disrupted by the central supermassive BH without a preexisting accretion disk.However, there is also an existed accretion disk around the central supermassive BH in AGN, therefore, effects of the existed accretion disk should be considered on accreting fallback TDEs debris in normal broad line AGN.Kathirgamaraju et al. (2017) have discussed effects of a pre-existing accretion disc on TDEs expected variability, leading to still TDE expected variability patterns but with a probable cut-off.Chan et al. (2019); Chan, Piran & Krolik (2020) have modeled TDEs variability in AGN with a pre-existing accretion disc, and discussed evolutions of the fallback bound debris being modified by collisions with the pre-existing disk, indicating the expected variability should be not totally similar as the TDEs expected variability patterns.However, there are so-far several TDEs candidates detected and reported in AGN.Blanchard et al. (2017) have reported a TDE candidate in a narrow line Seyfert 1 galaxy of which light curves can be roughly described by theoretical TDE model, and discussed that out-of-plane TDEs have quite weak interactions between the TDE debris and the pre-existing disk because the debris only intersect a small region of the disk.Yan & Xie (2018) have shown the TDE expected variability pattern in the lowluminosity AGN NGC 7213.Liu et al. (2020) have reported a TDE candidate in AGN SDSS J0227 with probable broad Balmer emission lines, and shown the sudden rise followed by a smooth decline trend in long-term variability in SDSS J0227.Zhang et al. (2022) have shown the TDE expected variability patterns in a narrow line Seyfert 1 galaxy.More recently, Zhang (2022b) have shown TDE expected long-term variability in the high redshift quasar SDSS J014124+010306, and Zhang (2022c) have discussed and shown TDE expected long-term variability of broad H line luminosity in low luminosity broad line AGN NGC 1097.Therefore, totally similar TDE simulating variability can be expected in normal AGN with pre-existing accretion disks.
Rare TDEs reported in normal AGN are mainly due to stronger intrinsic AGN variability than TDEs variability.However, there are enough probabilities and feasibilities to expect TDEs in normal AGN with supermassive BHs, even there are no detected TDEs expected variability features which are probably overwhelmed by strong intrinsic AGN variability in observed light curves.For intrinsic long-term AGN variability, the expected timescales are simply consistent with accretion disk orbital timescales or thermal timescales of about hundreds of days as the shown results in Kelly, Bechtold & Siemiginowska (2009) for normal AGN (including 55 AGN from the MACHO survey, 37 Palomar Green quasars, and eight Seyfert galaxies from the AGN Watch project), in Kozlowski et al. (2010) for about 2700OGLE quasars, in MacLeod et al. (2010) for about 9000 quasars covered in the SDSS Stripe82 region, and in Rumbaugh et al. (2018) for extreme variability quasars.Meanwhile, for variability from probable TDEs around supermassive BHs with masses around 10 7−8 M ⊙ in AGN, the expected years-long timescales can be compared to the timescales of intrinsic long-term AGN variability.Therefore, it is interesting to check effects of TDEs on long-term AGN variability, which could provide interesting clues to expect probable hidden TDEs in normal broad line AGN with CAR process described intrinsic variability, through the long-term light curves from the public sky survey projects.Section 2 and Section 3 present our main hypotheses and main results.Section 4 gives the discussions and further applications.Section 5 gives our final conclusions.And in the manuscript, the cosmological parameters of 0 = 70km • s −1 Mpc −1 , Ω Λ = 0.7 and Ω m = 0.3 have been adopted.2019) is mainly considered and accepted, combining with the mass-radius relation in Tout (1996) accepted for main-sequence stars.The time dependent bolometric luminosities from TDEs are simulated by the following four steps, similar as what we have done in Zhang (2022) to model X-ray variability of the relativistic TDE candidate Swift J2058.4+0516 and in Zhang (2022b,c)

Time
A grid of 31 evenly distributed log( , /years) range from -3 to 0 are applied to create templates for each impact parameter .Therefore, the created templates include 736 (640) timedependent viscous-delayed accretion rates for 31 different of each 23 (20) impact parameters for the main-sequence star with polytropic index of 4/3 (5/3).
Second, for TDEs with model parameters of and different from the list values in and in , , the corresponding viscousdelayed accretion rates are created by the following two line interpretations.Assuming that 1 , 2 in the are the two values nearer to the input , and that 1 , 2 in the , are the two values nearer to the input , the first linear interpretation is applied to find the viscous-delayed accretion rates with input but with = 1 and = 2 by The second linear interpretation is applied to find the viscous-delayed accretion rates with input and with input by Third, for TDEs with input parameters of BH and * different from 10 6 M ⊙ and 1M ⊙ , the viscous-delayed accretion rates and the corresponding time information in observer frame are created by the following scaling relations as shown in Guillochon, Manukian & Ramirez-Ruiz (2014); Mockler, Guillochon & Ramirez-Ruiz (2019), where BH, 6 , ★ , ★ and represent central BH mass in unit of 10 6 M ⊙ , stellar mass in unit of M ⊙ , mass-radius relation determined stellar radius in unit of R ⊙ , and redshift of host galaxy, respectively.Fourth, the time dependent bolometric luminosities bol, t, TDE from TDEs can be finally calculated by bol, t, TDE = × ( ) 2 (5) where and are the light speed and the energy transfer efficiency around central BH.The value will be further discussed in the following subsections.Therefore, for a TDE with given model parameters of central BH mass , stellar mass ★ and polytropic index of the central being disrupted main-sequence star, the impact parameter , the viscous timescale , redshift and energy transfer efficiency , time dependent bol, t, TDE can be well simulated by the theoretical TDEs model.
Based on the four steps, TDE expected time dependent bolometric luminosities can be simulated by accepted the only criterion that the TDE model parameters determined tidal radius larger than the event horizon of central BH.
Before the end of the subsection, two points are noted.First, the circularizations in TDEs as discussed in Kochanek (1994); Bonnerot et al. (2016);Hayasaki, Stone & Loeb (2016); Zanazzi & Ogilvie (2020); Lynch & Ogilvie (2021) are not considered in the manuscript.The circularization emissions in TDEs have been probably detected in the TDE candidate ASASSN-15lh in Leloudas et al. (2016) and in TDE candidate AT 2019avd in Chen, Dou & Shen (2022), due to the two clear peaks (or two clear phases) detected in the NUV and/or optical band light curves.However, among the more than 100 reported TDEs candidates, there are rare TDEs candidates of which optical light curves have re-brightened peaks, indicating the ratio of TDEs with clear circularization emissions is very low.Therefore, we mainly consider the simple case that the fallback timescales of the circularizations are significantly smaller than the viscous timescales of the accretion processes, and the fallback materials will circularize into a disk as soon as possible.Second, the expected plateau phase in TDEs expected light curves with considerations of pre-existing accretion disk of AGN are not considered in the manuscript, because the plateau phase has small time duration and/or no plateau phases in some AGN (such as the results in Yan & Xie (2018); Zhang et al. (2022); Zhang (2022b,c), etc.) due to low surface density of pre-existing accretion disk of AGN.

Time Dependent Bolometric Luminosities from the well-known AGN NGC5548
In the manuscript, the observed long-term light curve c, t, N5548 of continuum luminosity at 5100Å over 13 years of the well-known broad line AGN NGC5548 ( = 0.01717) in Peterson et al. (2002) and in the AGNWATCH project (https://www.asc.ohio-state.edu/astronomy/agnwatch/n5548/lcv/) is collected as the AGN variability template.Then, the time dependent bolometric luminosity from NGC5548 bol, t, N5548 = 10 × c, t, N5548 is calculated by the bolometric corrections.The bolometric correction factor 10 is accepted, based on the statistical properties of spectral energy distributions of broad line AGN discussed in Richards et al. (2006); Duras et al. (2020) and also on the more recent discussed results in Netzer (2020).
Moreover, based on the well discussed results in Peterson et al. (2004); Bentz et al. (2010); Pancoast et al. (2014), the central BH mass can be accepted as ∼ 6.7 × 10 7 M ⊙1 in the wellknown reverberation mapped broad line AGN NGC5548 in the AG-NWATCH project and in the LAMP (Lick AGN Monitoring Project) project (https://www.physics.uci.edu/~barth/lamp.html).And Lu et al. (2016) have reported similar BH mass of NGC5548 by the reverberation mapped results through Lĳiang 2.4m telescope at Yunnan Observatory.More recently, Williams et al. (2020); Horne et al. (2021) have reported similar BH mass of NGC5548, through the space telescope and optical reverberation mapping project.Then, based on the well discussed results in Davis & Laor (2011), the energy transfer efficiency around the central BH in NGC5548 can be well estimated as which will be applied in Equation ( 5) above.

Time Dependent Bolometric Luminosities with considerations of both AGN and TDE
There are three kinds of mock light curves bol, t created by AGN intrinsic variability plus TDEs contributions, from simplicity to complexity.The first kind is to simply add mock light curve bol, t, TDE to the light curve bol, t, N5548 .The second kind is to add mock light curve bol, t, TDE to a randomly modified light curve bol, t, AGN which is created by bol, t, N5548 plus a CAR process randomly created long-term variability.The third kind is created by CAR process randomly simulated long-term variability with different central physical properties.
The first kind of bol, t are simply created as follows.Mock light curves bol, t, TDE are created by randomly selected TDEs model parameters.The BH mass and is fixed to 6.7 × 10 7 M ⊙ and 0.072 (the values of NGC5548).The stellar mass ★ is randomly selected from −2 < log( ★ /M ⊙ ) < 1.The polytropic index is selected to be 4/3 or 5/3.The impact parameter is randomly selected from the minimum to the maximum .The viscous timescale is randomly selected from the minimum , to the maximum , .Here, there is a criterion that the expected tidal radius larger than event horizon of central BH ( s = 2 BH /2 ).Then, with = 4/3 ( = 5/3), 1200 (1200) mock light curves bol, t, TDE are randomly created.Considering TDEs with different starting times randomly from 0 to 3000days, the mock bol, t are created by bol, t = bol, t+t s , TDE + bol, t, N5548 Then, different white noises defined by signal-to-noise ratio (SNR) randomly from 30 to 80 are added to the mock light curves bol, t .
And the observational uncertainties of bol, t, N5548 are accepted as the uncertainties of bol, t .Before proceeding further, simple discussions are given to describe why values of SNRs for white noises are randomly selected from 30 to 80.As the collected information of the long-term light curve of NGC5548, the mean ratio of continuum emissions to uncertainties of continuum emissions is about 32.Meanwhile, to our knowledge, among our collected low-redshift ( < 0.35) SDSS (Sloan Digital Sky Survey) quasars, such as the sample discussed in Zhang ( 2023), the highest signal-to-noise ratio of SDSS spectra is about 74.Therefore, when adding white noises to the created mock light curves in the manuscript, corresponding SNRs are randomly selected from 30 to 80.Meanwhile, accepted SNRs from 30 to 80, corresponding photometric magnitude uncertainty can be simply estimated to be from 0.036mag to 0.013mag, which are similar as the magnitude uncertainties of light curves of quasars provided by SDSS Stripe82 database (MacLeod et al. 2010).
The second kind of bol, t are created as follows.The mock light curves bol, t+t s , TDE are similarly created, but the AGN variability template bol, t, AGN is created by bol, t, AGN = bol, t, N5548 + ( ) where ( ) is a randomly created light curve with mean of zero.And the ( ) (with expected variance around 0.012) is randomly created through the CAR process described in  , shown in the top right panel of Fig. 2. In each panel, top corner shows the results for all the 1200 mock light curves , , however the contour is plotted for the cases with > 0.5.In each panel, from top to bottom, dashed red lines show = 5, 2, 1, respectively.And in each top corner, symbols in red and in dark green show the cases with SNR larger than 55 and smaller than 55, respectively.Meanwhile, in each top corner, due to dense data points, the error bars with uncertainties about 20% are not plotted.Kelly, Bechtold & Siemiginowska (2009) where ( ) a white noise process with zero mean and variance equal to 1. Here, the parameter is randomly selected from 100days to 1000days, as the shown results in MacLeod et al. (2010)  is selected to be around 0.012 (leading to similar variance as those in NGC5548).The selected parameters of and lead the ( ) with mean of zero and variance similar as the bol, t, N5548 .The dependence of bolometric luminosity on redshift 0 ∝ 1.22 × , shown in Fig, 1, is well determined from all the 23093 SDSS quasars in Shen et al. (2011) with measured continuum luminosity at 5100Å.There is a strong positive correlation between redshift and bolometric luminosity calculated by 10 times of the continuum luminosity at 5100Å, with Spearman rank correlation coefficient 0.66 ( < 10 −15 ) and with RMS scatter about 0.29.Here, 6 different values of 0.05, 0.1, 0.2, 0.3, 0.5, 1 are accepted as input redshift, applied to determine 0 .Meanwhile, based on the three different BH masses = 10 6 , 10 7 , 5 × 10 7 M ⊙ , three different energy transfer efficiency = 0.06, 0.15, 0.3 and the six redshift, the bol, t+t s , TDE ( , , ) can be randomly created.Then, the mock light curves bol, t are similarly created by bol, t = bol, t+t s , TDE ( , , ) + bol, t, CAR And different white noises defined by SNRs randomly from 30 to 80 are added to the mock light curves bol, t .For each series [ , , , , ], 1200 mock light curves are created with contributions of TDEs.Finally, there are 2 × 3 × 3 × 6 × 2 × 1200 = 259200 mock light curves created after considering TDEs contributions to intrinsic AGN variability.And 10% are accepted as the uncertainties of bol, t .
Actually, besides the linear dependence of bolometric luminosity on redshift, dependence of BH mass on redshift is also checked through the reported parameters of the quasars in Shen et al. (2011).However, the Spearman Rank correlation coefficient for the dependence is only 0.29, quite weaker than the dependence of bolometric luminosity on redshift.Therefore, rather than dependence of BH mass on redshift, the linear dependence of bolometric luminosity on redshift is accepted in the manuscript.The application of the linear dependence of bolometric luminosity on redshift can reduce one free model parameter to create the third kind of mock light curves.Moreover, as shown in MacLeod et al. (2010); Kelly, Bechtold & Siemiginowska (2009), there is a dependence of process parameter on BH mass.However, the dependence is very loose, with Spearman Rank correlation coefficient about 0.23.Therefore, in the manuscript, the loose dependence of process parameter on BH mass is not accepted.And accepted the BH mass and and redshift are independent parameters, much wider parameter space can be occupied to create the mock light curves, and more efficient conclusions can be obtained.
Before the end of the section, three points are noted.First and foremost, in order to clearly show properties of model parameters applied to create TDEs contributions and to create ( ), Table 1 shows the accepted values and/or accepted ranges of the applied model parameters.Besides, the main objective of the manuscript is to determine effects of TDEs contributions on observed long-term AGN variability from simplicity to complexity.Therefore, when the first kind and the second kind of mock light curves are created, the oversimplified procedure is firstly applied with the fixed BH mass (the BH mass of NGC5548), the fixed energy transfer efficiency (determined by the BH mass of NGC5548) and the fixed redshift (the redshift of NGC5548).Then, effects of randomly selected values of model parameters are considered through the third kind of mock light curves.Last but not the least, for the three kinds of mock light curves bol, t , the corresponding maximum BH mass is 6.7 × 10 7 M ⊙ (the BH mass of NGC5548), which is a large (near to the Hills mass limit) but reasonable value, see the maximum BH mass about 66 × 10 6 M ⊙ determined by the MOS-FIT in TDEs candidates in Mockler, Guillochon & Ramirez-Ruiz (2019).Meanwhile, when the third kind of mock light curves are created, the Equation ( 6) is not applied to determined energy transfer efficiency, after considering the listed values of in Mockler, Guillochon & Ramirez-Ruiz (2019) that high could be expected around central BH with masses around 10 6 M ⊙ .And also as the shown results in Mockler, Guillochon & Ramirez-Ruiz (2019), the collected values from 0.06 to 0.3 are also reasonable to create time dependent TDEs expected bolometric luminosities for the third kind of mock light curves.

Results based on the Long-Term Variabilities of bol, t, N5548
As the discussed results in Kelly, Bechtold & Siemiginowska (2009) (see their Fig.4), the long-term variability bol, t, N5548 of NGC5548 has intrinsic variability timescale about 214days.The same method as shown in Equation ( 7)-( 12) in Kelly, Bechtold & Siemiginowska (2009) (the kbs09 method) is applied to analyze variability of bol, t, N5548 , in order to ensure the applied kbs09 method in the manuscript is reliable.Here, rather than the public JAVELIN (Just Another Vehicle for Estimating Lags In Nuclei) code in Zu, Kochanek & Peterson (2011); Zu et al. (2013), the kbs09 method is applied in the manuscript, due to the following main reason.For each mock light curve with about 1500 data points (time duration longer than 10 years), the kbs09 method running in Surface Stu-dio2 can give the final best-fitting results in ten minutes through the Levenberg-Marquardt least-squares minimization technique (the , , ) + bol, t, CAR .2: The second column, the third column, the fourth column, the fifth column, the sixth column, the seventh column and the eighth column show the parameters of BH mass in units of M ⊙ , logarithmic stellar mass in units of M ⊙ energy transfer efficiency , redshift , , logarithmic in units of years and shifted time in units of days, applied in theoretical TDE model.

3:
The last two panels show the CAR process parameters of in units of days and 2 2 (expected variance of the CAR created light curve) applied to created light curves ( ). 4: In each cell for the parameters, if there is only one value, meaning that the parameter is fixed to the listed value.
5: In each cell for the parameters, if the mathematical symbol ∈ is used, meaning that the parameter is randomly selected from the minimum value to the maximum value listed in the square brackets following the mathematical symbol ∈. 6: In each cell for the parameters, if the mathematical symbol ⊂ is used, meaning that value of the parameter is chosen from the values listed in the square brackets following the mathematical symbol ⊂.
7: In the last column, the parameter 2 2 shows the expected variance of the CAR process created light curve.Based on the variance 0.012 of the light curve of NGC5548, the 2 2 is accepted to be larger than 0.25 × 0.012 and smaller than 4 × 0.012 for the created ( ) in the second kind and the third kind of mock light curves.8: In the fifth column, the is randomly selected from 0.6 to 4 if = 4/3, and randomly selected from 0.5 to 2.5 if = 5/3.known MPFIT package, Markwardt 2009), however, the JAVELIN code will give the final results in more than one hour.
The bol, t, N5548 is shown in top left panel of Fig. 2, with the kbs09 method determined best descriptions through the Maximum Likelihood method combining with the Markov Chain Monte Carlo (MCMC) technique (Foreman-Mackey et al. 2013), with the kbs09 method determined process parameters through the MPFIT package accepted as starting values of the process parameters in the MCMC technique.The determined posterior distributions of the parameters of and are shown in the bottom left panel of Fig. 2, with accepted log( / ) ∼ 2.34 +0.107 −0.076 ( ∼ 219 +60 −36 days) which is well consistent with the reported 214days in Kelly, Bechtold & Siemiginowska (2009).Therefore, the applied kbs09 method is reliable enough.
Through the kbs09 method applied through the Levenberg-Marquardt least-squares minimization technique, variability properties, especially the CAR process parameters of and , can be well determined for the total 2400 mock light curves bol, t created by bol, t, N5548 plus bol, t, TDE .Top middle panel and top right panel of Fig. 2 show an example of bol, t, TDE and an example of bol, t .For the shown example in top right panel of Fig. 2 without clear TDEs expected variability features, the determined variability timescale is about 520days, as the shown posterior distributions in bottom right panel of Fig. 2 determined by MCMC technique applied in the kbs09 method, significantly longer than the intrinsic 219days of NGC5548, indicating TDEs contributions can lead to larger variability timescales.
In order to show clearer effects of TDEs contributions, two parameters and are defined, as ratio of the peak intensity of bol, t, TDE to the mean intensity of bol, t, N5548 , and as ratio of the variability timescale of bol, t to the intrinsic variability timescale 219days of bol, t, N5548 .Then, Fig. 3 shows the dependence of on of the 2400 mock light curves bol, t , 1200 light curves based on the bol, t, TDE created with = 4/3 and 1200 light curves based on the bol, t, TDE created with = 5/3.For > 0.5 (stronger TDEs contributions), there are positive correlations between on , with the Spearman rank correlation coefficient is about 0.71 (0.79) with < 10 −15 for the cases with = 4/3 ( = 5/3).Here, the critical value > 0.5 is simply determined that the variance of of the data points with > 0.5 is at least 2000 times larger than the variance of of the data points with < 0.5.Actually, small different critical values from 0.5 have few effects on the discussed results.After considering the uncertainties in both coordinates, the positive dependence with > 0.5 can be simply described by log( )( = 4/3) = 0.20 + 0.58 log( ) log( )( = 5/3) = 0.21 + 0.89 log( ) , the scatters of can be well expected, and provide robust clues in the manuscript to detect hidden TDEs in broad line AGN with apparent intrinsic variability.Similar scatters of can also be expected in the following subsections.

Results based on the Long-Term Variabilities of bol, t, AGN
Similar as the results on bol, t, N5548 , top panels of Fig. 4 show an example of mock light curve bol, t, TDE (in middle panel) and an example of mock light curve , (in right panel) created by bol, t, AGN shown in the left panel plus the bol, t, TDE shown in the middle panel.And the kbs09 method is applied to determine the intrinsic variability timescale of bol, t, AGN as ∼ 620days through the Levenberg-Marquardt least-squares minimization technique.Bottom panels of Fig. 4 shows the dependence of on of the 2400 mock light curves bol, t based on the bol, t, AGN .For > 0.5, the Spearman rank correlation coefficient is about 0.63 (0.68) with < 10 −15 for the cases with = 4/3 ( = 5/3).The positive dependence with > 0.5 can be simply described by log( )( = 4/3) = 0.03 + 0.30 log( ) log( )( = 5/3) = 0.15 + 0.40 log( ) through the same FITEXY code.Similar results can be found that longer variability timescales can be confirmed with larger TDEs contributions, and SNRs have few effects on the results.However, the intrinsic AGN variability have longer variability timescales, the will increase more slowly, based on the smaller slopes shown in the equations above.

Results based on the Long-Term Variabilities of bol, t, CAR
In the subsection, it is interesting to check effects of different model parameters on the dependence of on which are determined through the MPFIT package applied in the kbs09 method.Fig. 6 shows the dependence of on for the cases (cases-6-2-4, the first number '6' means BH mass as 10 6 M ⊙ , the second number '2' means 0 /100days = 2, and the third number '4' means × 3 = 4) with = 10 6 M ⊙ , 0 = 200days, and = 4/3.It is clear that TDEs contributions around BHs with masses around 10 6 M ⊙ have few effects on the dependence of on , all results shown in Fig. 6 with Spearman rank correlation coefficients smaller than 0.3 for the data points with > 1, even considering different redshift and different .The results can be well expected due to smaller variability timescales of TDEs around BHs with masses around 10 6 M ⊙ , relative to the long time durations of  , , ) shown in the middle panels and the mock light curves bol, t shown as dots plus error bars in dark green in the right panels.In each left panel, the input model parameters of BH mass 6 (in unit of 10 6 M ⊙ ), redshift, 0 are listed in blue characters.In each middle panel, the input TDEs model parameters of , , stellar mass ★ , , , and are listed in blue characters.In each right panel, solid red line shows the kbs09 method determined best descriptions to the bol, t , and the corresponding determined timescale is listed in blue characters.similar results, no apparent positive dependence of on , for the cases (cases-6-6-4) with = 10 6 M ⊙ , 0 = 600days, and = 4/3, and for the cases (cases-6-2-5) with = 10 6 M ⊙ , 0 = 200days, and = 5/3, and for the cases (cases-6-6-5) with = 10 6 M ⊙ , 0 = 600days, and = 5/3.Therefore, we do not show the results on cases-6-6-4, cases-6-2-5, and cases-6-6-5 in plots.And there are no further discussions on the results with = 10 6 M ⊙ , but the determined Spearman rank correlation coefficients are listed in Table 2 for all the cases with BH mass 10 6 M ⊙ .In one word, contributions of TDEs around BHs with masses 10 6 M ⊙ cannot provide clear clues on central TDEs, through longterm variability.
Then, similar as the discussed results on dependence of on for the cases with = 10 6 M ⊙ , the results on the dependence of on are also discussed with BH masses as 10 7 M ⊙ and 5 × 10 7 M ⊙ .Based on two different values of , two different values of 0 and two different values of , there are 8 cases named as cases-7-2-4 (the first number '7' means BH mass as log( /M ⊙ ) = 7, the second number '2' means 0 /100days = 2, and the third number '4' means × 3 = 4), cases-7-6-4, cases-7-2-5, cases-7-6-5, cases-7.7-2-4(the first number '7.7' means BH mass as log( /M ⊙ ) = log(5× 10 7 ) ∼ 7.7), cases-7.7-6-4,cases-7.7-2-5,cases-7.7-6-5.Then, similar as the discussed results for the 18 × 4 dependences for the four cases with = 10 6 M ⊙ , all the 144 (18×8) dependences of on for > are carefully checked in all the cases with = 10 7 M ⊙ , 5 × 10 7 M ⊙ .Here, the critical values = 0.3 and = 0.15 are simply determined and accepted for the cases with = 10 7 M ⊙ and with = 5 × 10 7 M ⊙ , respectively, after simply considering the variance of of the data points with > at least 2000 times larger than the variance of of the data points with < .The determined Spearman Rank Correlation coefficients are listed in Table 2.Meanwhile, for the correlations with correlation coefficients larger than 0.3, through the same FITEXY code, the strong positive correlations between and for > 0.3 can be well described by log( with determined also listed in Table 2. Here, not all the 144 (18×8) dependences of on are shown in plots, but the dependence with maximum Spearman Rank correlation coefficient is shown in Fig. 7 among the 18 dependences in each case with = 10 7 M ⊙ , = 5 × 10 7 M ⊙ .Meanwhile, based on the determined Coefficients and the slope (if there was) listed in Table 2 for the 216 dependences in the 12 cases with = 10 6 M ⊙ , = 10 7 M ⊙ , = 5 × 10 7 M ⊙ , properties of Coefficients and slope are shown in Fig. 8.
Based on the determined Coefficients listed in Table 2 and the shown results in Fig. 8, the following seven points can be found.First, comparing with the cases with = 10 6 M ⊙ , there are more sensitive and clearer positive dependence of on ( > 0.3), due to the results with Spearman rank correlation coefficients larger than 0.3: almost all the cases with input 0 = 200 and = 10 7 M ⊙ have coefficients larger than 0.3 for the correlations with > 0.3.Second, for the cases with = 10 7 M ⊙ , intrinsic variability timescales long as 600days should lead to no clear positive dependence of on , but intrinsic variability timescales long as 200days can lead to clear positive dependence of on .Third, for the cases with = 10 7 M ⊙ , the positive dependence of on are steeper (larger ) in the cases with = 5/3 than with = 4/3.Fourth, comparing with cases with = 10 6 M ⊙ and = 10 7 M ⊙ , there are more sensitive and clearer positive dependence of on for the cases with = 5 × 10 7 M ⊙ , due to the results with Spearman rank correlation coefficients larger than 0.3: all the cases with input 0 = 200 and half of the cases with 0 = 600 have Figure 6.On the dependence of on for the mock light curves based on the long-term variability bol, t, CAR created with = 10 6 M ⊙ , 0 = 200days plus the bol, t, TDE created with = 4/3.For the panels from top to bottom, the results are based on the redshift of 0.05, 0.1, 0.2, 0.3, 0.5, and 1.0, respectively.For the panels from left to right, the results are based on the of 0.06, 0.15 and 0.3, respectively.In each panel, the Spearman rank correlation coefficient for the correlation between and ( > 1) is listed in blue characters.In each panel, pluses in red and in dark green show the results with SNR larger than 55 and smaller than 55, respectively.In each panel, due to large number of dense data points, the error bars with uncertainties about 20% -25% are not plotted.
coefficients larger than 0.3 for the correlation with > 0.15.Fifth, for the cases with BH masses about 5 × 10 7 M ⊙ , intrinsic variability timescales long as 600days but only with = 5/3 should lead to clear positive dependence of on , but intrinsic variability timescales long as 200days almost can lead to clear positive dependence of on .Sixth, the positive dependence of on are steeper (larger ) in the cases with = 5/3 than with = 4/3.Seventh, there are few effects of SNR on dependences of on , such as the shown results in Fig. 7. Based on the results above, we can find that • BH mass has apparent effects on the dependence of on .Larger BH masses can lead to more apparent and steeper dependence of on .
• Polytropic index has apparent effects on the dependence of on .= 5/3 can lead to more apparent and steeper dependence of on .
• Energy transfer efficiency has tiny effects on the dependence of on .At least, energy transfer efficiency changing from 0.06 to 0.3 cannot lead to clear changes in the dependence of on .

DISCUSSIONS AND FURTHER APPLICATIONS
It is necessary to check whether intrinsic AGN variability can provide quite different variability timescales in different epochs.Here, based on the 13years-long light curve bol, t, N5548 , 100 different 2000dayslong (about 10times of the intrinsic variability timescale 200days) light curves can be randomly collected from bol, t, N5548 with time duration from a randomly given starting time 0 < 0 /days < 3600 to 0 + 2000.The kbs09 method is applied to determine the variability timescales of the 100 different 2000days-long light curves.Then, we can find that the ratios of to the variability timescale 219days of bol, t, N5548 have mean value 1.02 with standard deviation 0.11.It is clear that light curves in different epochs cannot lead variability timescale varying so large as the results shown in Fig. 3 with large TDEs contributions.Similar results can be found from the mock light curves of bol, t, AGN and bol, t, CAR .
Furthermore, there are seven more points we should note.First, in order to find more clearer effects of TDEs contributions on long-term AGN variability, the time duration is longer as 13years in the bol, t .Once there were shorter time durations applied, the dependence of on would have larger scatters, due to probably only part of TDEs contributions covered in bol, t .Moreover, the simulating light curves are based on BH masses smaller than 10 8 M ⊙ .When BH mass is larger than 10 8 M ⊙ , more massive but shorter-lived mainsequence stars are necessary to simulate suitable TDEs, otherwise tidal disruption radius should be smaller than event horizon of central BH.Therefore, the large BH mass is selected to be 5 × 10 7 M ⊙ in the manuscript.
Second, as the discussed and shown results in MacLeod et al. (2010); Kelly, Bechtold & Siemiginowska (2009), the parameter and are probably connected.However, the connection between and is quite loose.Therefore, in the manuscript, there are no considerations of the connection and , when the third kind of mock light curves bol, t are simulated.With the similar considerations, due to the loose dependence of energy transfer efficiency and BH mass discussed in Davis & Laor (2011), the energy transfer efficiency is randomly selected to be 0.06, 0.15 and 0.3.Otherwise, the expected energy transfer efficiency around = 10 6 M ⊙ should be small to be 0.008, an extremely smaller value.
Third, besides BH masses and intrinsic variability timescales, there are no further considerations on the other parameters related to TDEs model.Actually, the parameters, such as the stellar mass ★ and impact parameter , should have effects on the , because commonly larger ★ and can commonly lead to stronger TDEs expected bolometric luminosities.As examples, Fig. 9 shows the dependence of on the stellar mass ★ and on the impact parameter for the simulated light curves bol, t by bol, t, N5548 plus TDEs contributions.For the shown dependence of on the stellar mass ★ , there are positive correlations with Spearman rank correlation coefficients about 0.35 and 0.61 ( < 10 −15 ) for the results with = 4/3 and with = 5/3, respectively.And, for the shown dependence of on the , there are positive correlations with Spearman rank correlation coefficients about 0.76 and about 0.54 ( < 10 −15 ) for the results with = 4/3 and with = 5/3, respectively.Even for ★ around one solar mass or gently larger than 1, can be well larger than 2. Certainly, for the cases with smaller BH masses, the positive correlations on ★ and on should be not so strong.However, not similar as the central BH masses and redshift of normal AGN which can be well estimated through spectroscopic features, the ★ and can not be previously measured.And the main objective is to provide clues to detect probable hidden TDEs in normal AGN.Probability of more massive main-sequence stars being tidally disrupted with larger in TDEs in normal AGN is not the objective of the manuscript.If there was a more massive main-sequence star was tidally disrupted with larger in a normal broad line AGN, it would be more preferred to detect the expected hidden TDEs.Therefore, in the manuscript, effects of the model parameters related to the theoretical TDEs model are not discussed.
Fourth, as discussed in Kozlowski (2017), shorter time baseline should lead to underestimated process parameter in DRW/CAR process.Considering the expected longer due to larger contributions from TDEs, intrinsic values of process parameter should be larger than the currently determined values for the created mock light curves.Therefore, combining with the input value of process parameter for bol, t, CAR , larger values of could be expected, leading to more apparent dependence of on to support our final conclusions.Meanwhile, accepted the criterion reported in Kozlowski (2017) that there are good estimations of process parameters for light curves with / < 0.1 (similar to process parameter divided by time baseline), the determined parameters are not biased for the mock light curves created with 0 = 200days ( / ∼ 200days/13years ∼ 0.04 < 0.1).Therefore, even only considering the results based on 0 = 200days, similar conclusions on effects of TDEs contributions can be given.
Fifth  2019) is applied in the manuscript, leading to expected time-dependent decline −5/3 at late times.However, besides standard TDE model expected variability pattern, there are slow TDEs, such as the discussed results in Graham et al. (2017), probably leading to shallower decline closer to −1 .The slow TDEs could lead to much longer time durations than standard TDEs.However, based on the discussed results ) for all the dependences.Bottom panel shows the legends used in top panels.The four numbers included in 'cases-n0-n1-n2-n3' shown in legends have the following meanings, 'n0' means logarithmic BH mass, 'n1' means the value of 0 /100, 'n2' means the values of 3 × and 'n2' means the value of , for example, 'cases-7.7-2-4-0.30'means the 6 dependences (relative to six different values of redshift) of on for the case with = 5 × 10 7 M ⊙ , 0 = 200days, 3 × = 4/3 and = 0.30.In top right panel, due to many dependences with coefficients smaller than 0.3, there are some dependences with their over-plotted with = 0.In top left panel, horizontal red line marks the position of Spearman Rank correlation coefficient of 0.3.above, more apparent difference between characteristic timescales of TDEs variability and characteristic timescales of intrinsic AGN variability should lead to more apparent dependence of on .Therefore, even without considering rare numbers of slow TDEs, considerations of slow TDEs could lead to more apparent clues to support our final conclusions.
Sixth, as more recent discussions in Burke et al. (2022), host galaxy dilution could have strong effects on determined process parameter.However, accepted host galaxy contribution as an constant component with none variability (almost inevitable), the host galaxy dilution should have few effects on process parameter of , because the host galaxy contribution can be included in the parameter 0 in Equation ( 12) above.In the manuscript, the ratio of from the light curves with and without TDEs contributions are mainly considered, therefore, the host galaxy dilution has few effects on our final conclusions.
Seventh, although all the quasars with measurements of continuum luminosities are collected from Shen et al. (2011) to determine the dependence of bolometric luminosity on redshift shown in Fig. 1, some weak quasars are actually not included in the collected quasars, due to their lower continuum emissions.However, considering the very loose (or very weakly positive) dependence of DRW process parameter on luminosity as simply discussed in Kelly, Bechtold & Siemiginowska (2009);MacLeod et al. (2010), lower bolometric luminosities should lead to no variations of (or lower) DRW process parameter of intrinsic AGN variability.There- fore, even considering contributions of the lost weak quasars, there should be not different conclusions if accepted no dependence of DRW process parameter on luminosity, or lead to more apparent clues to support our final conclusions if accepted weakly positive dependence of DRW process parameter on luminosity.
Based on the expected effects of TDEs contributions on long-term AGN variability, to check variability properties in different epochs of normal AGN could provide clues on probable central hidden TDEs in normal AGN with apparently intrinsic variability.In one word, the results in the manuscript provide an interesting and practical method to detect probable hidden TDEs in normal AGN with apparent intrinsic variability, especially for AGN with smaller intrinsic variability timescales but BH masses larger than 10 7 M ⊙ .To report detected hidden TDEs in normal AGN through quite different in different epochs can provide robust evidence to support the results in the manuscript.Considering TDEs expected time durations about several years for ∼ 10 7 M ⊙ , baseline about (more than) 10years-long should be necessary for light curves to detected clues for hidden TDEs in broad line AGN.Therefore, combining light curves from different sky survey projects should be the efficient way to build light curves with baseline longer than 10 years.Unfortunately, there are quite different qualities, such as different baseline, different time steps, different SNRs, different covered wavelength ranges, different transmission curves for different filters, etc., for light curves from different sky survey projects.Before checking probably different intrinsic variability properties in different epochs from different sky survey projects, effects of the quite different qualities should be firstly and clearly determined.In current stage, long-term light curves from CSS and from ZTF for a large sample of SDSS quasars have been collected, and basic results are currently in writing.In the near future, effects of different qualities on variability properties for light curves from CSS and ZTF and a small sample of quasars with quite different in light curves from CSS and from ZTF will be discussed and reported as soon as possible.It is a great pity that we can not currently give a clear estimation on detection rates of hidden TDEs through combinations of light curves from different sky survey projects, especially because we do not know what key parameters related to AGN dominate probable TDEs contributions.However, the results in the manuscript are showing a practicable way to detect hidden AGN in normal broad line AGN with apparent variability.To detect hidden TDEs in broad line AGN through different variability properties in different epochs is our main objective in the near future.

CONCLUSIONS
Finally, we give our main conclusions as follows.Based on the AGN variability templates simulated by the CAR process and the variability from theoretical TDEs model, effects of TDEs contributions can be well estimated on the long-term variability properties of normal AGN with apparent intrinsic variability.Stronger TDEs contributions can lead to longer variability timescale of observational long-term AGN variability, especially for AGN with smaller intrinsic variability timescales and with BH masses larger than 10 7 M ⊙ .Therefore, the re- 1: From column 4 to column 6 and from column 10 to column 12, there are two numbers ' ( )' in each cell, where is the slope of the formula log( ) = + × log( ), and is the determined Spearman rank correlation coefficient for the data points with larger than the critical values shown in textbody.If is smaller than 0.3, then is set to be zero.

2:
6 means the BH mass in unit of 10 6 M ⊙ .3: 0 means the input variability timescale in unit of days, when the third kind of bol, t are simulated.
sults provide an interesting forward-looking and practicable method to detect central hidden TDEs in normal broad line AGN based on quite different variability properties in different epochs, especially in broad line AGN with shorter intrinsic variability timescales and with BH masses larger than 10 7 M ⊙ .

Figure 1 .
Figure 1.Dependence of bolometric luminosity (10 times of the continuum luminosity at 5100Å) on redshift for all the collected SDSS quasars with reliable measurements of continuum luminosity from Shen et al. (2011).Solid red line shows the best description 0 = 44.96+ 1.22 × .

Figure 2 .
Figure 2. Top left panel shows bol, t, N5548 of NGC5548 (in dark green) and the kbs09 method determined best descriptions (solid red line).Bottom left panel shows the MCMC technique determined two-dimensional posterior distributions in contour of and of bol, t, N5548 .Top middle panel shows an example of mock TDEs light curve bol, t, TDE with model parameters marked in the panel.And due to small SNR, the light curve bol, t, TDE is not smooth.Top right panel shows an example of mock light curve bol, t (solid circles plus error bars in dark green) by bol, t, N5548 shown in the top left panel plus the bol, t, TDE shown in the top middle panel, and the kbs09 method determined best descriptions (solid red line).Bottom right panel shows the MCMC technique determined two-dimensional posterior distributions in contour of and of bol, t shown in the top-right panel.

Figure 3 .
Figure 3. Dependence of on and simple linear description in solid red line, based on the mock light curves , created by bol, t, N5548 plus contributions of TDEs with = 4/3 (in the left panel), and with = 5/3 (in the right panel).In left panel, solid red circle shows the results for the mock light curve , shown in the top right panel of Fig. 2. In each panel, top corner shows the results for all the 1200 mock light curves , , however the contour is plotted for the cases with > 0.5.In each panel, from top to bottom, dashed red lines show = 5, 2, 1, respectively.And in each top corner, symbols in red and in dark green show the cases with SNR larger than 55 and smaller than 55, respectively.Meanwhile, in each top corner, due to dense data points, the error bars with uncertainties about 20% are not plotted.

Figure 4 .
Figure 4. Top panels show the results similar as those shown in top panels of Fig. 2, but based on the light curve bol, t, AGN shown in the top left panel.Bottom panels show the results similar as those in Fig. 3, but based on the light curve bol, t, AGN with intrinsic variability timescale about 620days.In the bottom right panel, the solid red circle shows the results for the mock light curve , shown in the top right panel.In top corners of bottom panels, due to large number of dense data points, the error bars with uncertainties about 20% are not plotted.

Figure 5 .
Figure5.Two examples on the mock light curves bol, t, CAR shown as dots plus error bars in dark green in left panels, the mock light curves bol, t, TDE ( , , ) shown in the middle panels and the mock light curves bol, t shown as dots plus error bars in dark green in the right panels.In each left panel, the input model parameters of BH mass 6 (in unit of 10 6 M ⊙ ), redshift, 0 are listed in blue characters.In each middle panel, the input TDEs model parameters of , , stellar mass ★ , , , and are listed in blue characters.In each right panel, solid red line shows the kbs09 method determined best descriptions to the bol, t , and the corresponding determined timescale is listed in blue characters.

Figure 9 .
Figure 9. Dependence of on the stellar mass ★ (top panels) and on the impact parameter (bottom panels) for the simulated light curves bol, t by bol, t, N5548 plus TDEs contributions with = 4/3 (left panels) and with = 5/3 (right panels).In each panel, horizontal dashed red lines show = 2 and = 5, respectively.
Hung et al. (2020))9)ed inLiu et al. (2017), PS18kh as discussed inHoloien et al. (2019), AT2018hyz as discussed inShort et al. (2020);Hung et al. (2020), etc., indicating the reported broad emission lines in the TDE candidates are not related to normal BLRs in normal broad line AGN, but are tightly related to TDE debris.Moreover, there are several TDE candidates, their UVband spectra have been well checked, such as the PS18kh, ASASSN-15lh, ASASSN-14li, etc., there are no broad Mg 2800Å emission lines.And moreover, in the TDEs candidates with detected optical broad emission lines, there are no clues on DRW process expected variability, except the TDEs expected variability patterns.In other words, there are no confirmed evidence to support central TDEs in normal broad line AGN with apparent intrinsic AGN variability.

Dependent Bolometric Luminosities from TDEs
for normal quasars.Then, the mock bol, t are similarly created by bol, t = bol, t+t s , TDE + bol, t, AGN(11)And different white noises defined by SNRs randomly from 30 to 80 are added to the mock light curves bol, t .Here, the light curve bol, t, AGN has different intrinsic variability timescale and amplitude from those of bol, t, N5548 , which will provide further considerations of effects of TDEs on long-term variability of AGN.And the observational uncertainties of bol, t, N5548 are accepted as the uncertainties of bol, t .The third kind of bol, t is mainly created as follows after considering different parameters of BH mass, redshift, energy transfer efficiency, etc.The AGN variability template bol, t, CAR is created by the CAR process determined ( 0 = 44.96+ 1.22 × (12) where 0 is selected to be 200days or 600days (a common value and a large value of intrinsic variability timescale in quasars, see results in MacLeod et al. (2010); Kelly, Bechtold & Siemiginowska (2009); Kozlowski et al. (2010); Rumbaugh et al. (2018)), and 2 2

Table 1 .
Model Parameters applied to create the three kinds of mock light curves The first column shows which kind of mock light curves, '1st' means the first kind of mock light curve bol, t = bol, t+ts , TDE + bol, t, N5548 , '2nd' means the second kind of mock light curve bol, t = bol, t+ts , TDE + bol, t, N5548 + ( ) (with ( ) as CAR process created variability), '3rd' means the third kind of mock light curve bol, t = bol, t+ts , TDE (

Table 2 .
Parameters and Spearman rank correlation coefficients for the dependence of on