Systematic research of low redshift optically selected SDSS Type-2 AGN but with apparent long-term optical variabilities from Catalina Sky Survey, I: data sample and basic results

The main objective of the paper, the first paper in a dedicated series, is to report basic results on systematic research of low-redshift optically selected SDSS Type-2 AGN but with apparent optical variabilities. For all the pipeline classified Type-2 AGN in SDSS DR16 with $z<0.3$ and $SN>10$, long-term optical V-band light curves are collected from Catalina Sky Survey. Through all light curves described by Damped Random Walk process with process parameters of $\sigma/(mag/days^{0.5})$ and $\tau/days$, 156 Type-2 AGN have apparent variabilities with process parameters at least three times larger than corresponding uncertainties and with $\ln(\sigma/(mag/days^{0.5}))>-4$, indicating central AGN activity regions directly in line-of-sight, leading the 156 Type-2 AGN as mis-classified Type-2 AGN. Furthermore, based on spectroscopic emission features around H$\alpha$, 31 out of the 156 AGN have broad H$\alpha$, indicating the 31 Type-2 AGN are actually Type-1.8/1.9 AGN. Meanwhile, 14 out of the 156 AGN have multi-epoch SDSS spectra. After checking multi-epoch spectra of the 14 objects, no clues for appearance/disappearance of broad lines indicate true Type-2 AGN rather than changing-look AGN are preferred in the collected Type-2 AGN with long-term variabilities. Moreover, a small sample of Type-2 AGN have long-term variabilities with features roughly described by theoretical TDEs expected $t^{-5/3}$, indicating probable central TDEs as further and strong evidence to support true Type-2 AGN.


INTRODUCTION
Different observational spectroscopic phenomena between broad emission line AGN (Active Galactic Nuclei) (Type-1 AGN) and narrow emission line AGN (Type-2 AGN) can be well explained by the well-known constantly being improved Unified Model (UM) of AGN, after considering effects of different orientation angles of central accretion disk (Antonucci 1993), combining with different central activities and different properties of inner dust torus etc. Marinucci et al. 2012;Oh et al. 2015;Mateos et al. 2016;Audibert et al. 2017;Balokovic et al. 2018;Brown et al. 2019;Kuraszkiewicz et al. 2021). More recent reviews on the UM can be found in Netzer (2015). Accepted the UM, Type-2 AGN are intrinsically like Type-1 AGN, but Type-2 AGN have their central accretion disk around black hole (BH) and broad line regions (BLRs) seriously obscured by central dust torus, leading to no optical broad line emission features in Type-2 AGN. The simple UM has been strongly supported by clearly detected polarized broad emission lines and/or clearly detected broad infrared emission lines for some Type-2 AGN (Miller & Goodrich 1990;Heisler, Lumsden & Bailey 1997;Tran 2003;Nagao et al. 2004;Zakamska et al. 2005;Onori et al. 2017;Savic et al. 2018;Moran et al. 2020), and the strong resonance of silicate dust at 10 m seen in absorption towards many Type-2 AGN but in emission in Type-1 AGN (Siebenmorgen et al. 2005).
However, even after considering necessary modifications to the UM, some challenges have been reported. Different evolutionary patterns in Type-1 and Type-2 AGN have been reported in Franceschini et al. (2002). Higher average star formation rates in Type-2 AGN than in Type-1 AGN have been reported in Hiner et al. (2009). Different neighbours around Type-1 AGN and Type-2 AGN can be found in Villarroel & Korn (2014) and then followed in Jiang et al. (2016). Lower stellar masses of host galaxies in Type-1 AGN than in Type-2 AGN have been reported in Zou et al. (2019), through 2463 X-ray selected AGN in the COSMOS field. More recently, different host galaxy properties have been discussed in Bornancini & Garcia Lambas (2020), to favour an evolutionary scenario rather than a strict unified model in obscured and unobscured AGN. Probably higher stellar velocity dispersions have been reported in our recent paper . As detailed discussions in Netzer (2015), the UM has been successfully applied to explain different features between Type-1 and Type-2 AGN in many different ways, however, there are many other features of structures/environments proved to be far from homogeneous among the AGN family.
In order to provide further clues to support and/or to modify the current UM of AGN, better classifying Type-1 AGN and Type-2 AGN is the first thing which should be well done in optically selected AGN, in order to ignore effects of misclassified AGN on discussions on UM of AGN. Barth et al. (2014) have reported g-band variabilities in 17 out of 173 Type-2 quasars covered in the Stripe 82 region, indicating part of Type-2 objects with their central AGN activity regions are directly being observed, and the part of Type-2 quasars are not the UM expected Type-2 quasars obscured by central dust torus. In other words, based on only optical spectroscopic broad emission line features, it is not efficient enough to classify optically selected Type-1 AGN and Type-2 AGN.
Among optically selected Type-2 AGN with none detected broad emission lines, there are at least two interesting kinds of mis-classified AGN (AGN have their central AGN activity regions been directly observed, but been classified as Type-2 AGN through single-epoch spectroscopic results): the called True Type-2 AGN (TT2 AGN) without hidden central BLRs (broad emission line regions), the called changing-look AGN (CLAGN) with transitioned types between Type-1 with broad emission lines and Type-2 without apparent broad emission lines.
The first kind of mis-classified AGN, the True Type-2 AGN (TT2 AGN) without hidden central BLRs, have been firstly reported in Tran (2003) that there are no hidden central BLRs in some Type-2 AGN through studying polarized broad emission lines. And then, Shi et al. (2010); Barth et al. (2014); Zhang (2014); Li et al. (2015); Pons & Watson (2016) have confirmed the existence of the rare kind of TT2 AGN. More recently, We Zhang et al. (2021d) have reported the composite galaxy SDSS J1039 to be classified as a TT2 AGN, due to its apparent long-term optical variabilities and none existence of broad emission lines. Moreover, considering study of TT2 AGN should provide further clues on formation and/or suppression of central BLRs in AGN, Elitzur & Ho (2009); Cao (2010); Nicastro et al. (2013); Ichikawa et al. (2015); Elitzur & Netzer (2016) have discussed and proposed theoretical models and/or explanations on probable disappearance of BLRs in TT2 AGN, either depending on physical proper-ties of central AGN activities and/or depending on properties of central dust obscurations. Although the very existence of TT2 AGN is still an open question, as the well known case of NGC 3147 previously classified as a TT2 AGN but now discussed in Bianchi et al. (2019) reported with detected broad H in high quality HST spectrum. Probably, either the very existence of TT2 AGN with none hidden central BLRs or the quite weak broad emission lines in TT2 AGN can lead some Type-1 AGN (central regions directly observed) to be mis-classified as Type-2 AGN, indicating that there are some mis-classified Type-1 AGN in the optically selected Type-2 AGN, if only single-epoch spectroscopic emission line features are considered.
The second kind of mis-classified AGN, the changing-look AGN (CLAGN), have been firstly reported in NGC 7603 in Tohline & Osterbrock (1976) with its broad H becoming much weaker in one year. After studying on CLAGN for more than four decades, there are more than 40 CLAGN reported in the literature, according to the basic properties that spectral types of AGN are transitioned between Type-1 AGN (apparent broad Balmer emission lines and/or Balmer decrements near to the theoretical values) and Type-2 AGN (no apparent broad Balmer emission lines and/or Balmer decrements much different from the theoretical values).
There are several well known individual CLAGN, such as the CLAGN Mrk1086 which has firstly reported in Cohen et al. (1986) with its type changed from Type-1.9 to Type-1 in 4 years, and then followed in McElroy et al. (2016), and as the CLAGN in NGC 1097 reported in Storchi-Bergmann et al. (1993) with the detected Seyfert 1 nucleus which has previously shown only LINER characteristics, and as the CLAGN NGC 7582 reported in Aretxaga et al. (1999) with the transition toward a Type-1 Seyfert experienced by the classical Type-2 Seyfert nucleus, and as the CLAGN NGC 3065 reported in Eracleous & Halpern (2001) with the new detected broad Balmer emission lines, and as the CLAGN Mrk 590 reported in Denney et al. (2014) with its type changed from Seyfert 1 in 1970s to Seyfert 1.9 in 2010s, and as the CLAGN NGC 2617 reported in Shappee et al. (2014) classified as a Seyfert 1.8 galaxy in 2003 but as a Seyfert 1 galaxy in 2013, and as the CLAGN SDSS J0159 reported in LaMassa et al. (2015) with its type transitioned from Type-1 in 2000 to Type-1.9 in 2010, and as the CLAGN SDSS J1554 reported in Gezari et al. (2017) with its type changed from Type-2 to Type-1 in 12 years.
More recently, we Zhang (2021b) have reported the bluest CLAGN SDSS J2241 with its flux ratio of broad H to broad H changed from 7 in 2011 to 2.7 in 2017. Moreover, besides the individual CLAGN, MacLeod et al. (2016) have reported ten CLAGN with variable and/or changing-look broad emission line features, and Yang et al. (2018) have reported a sample of 21 CLAGN with the appearance or the disappear-ance of broad Balmer emission lines within a few years, and Potts & Villforth (2021) have reported six CLAGN within the redshift range 0.1 < < 0.3 using SDSS difference spectra, and Green et al. (2022) have reported 61 newly discovered CLAGN candidates through multi-epoch spectroscopic properties in the known Time Domain Spectroscopic Survey in SDSS-IV. Different models have been proposed to explain the nature of CLAGN, such as the dynamical movement of dust clouds well discussed in Elitzur (2012), the common variations in accretion rates well discussed in Elitzur et al. (2014), the variations in accretion rates due to transient events as discussed in Eracleous et al. (1995);Blanchard et al. (2017). Although theoretical explanations to CLAGN are still unclear, spectroscopic properties in quiet state of CLAGN could lead to CLAGN with central activity regions directly observed but mis-classified as Type-2 AGN.
Besides the spectroscopic features well applied to classify Type-1 AGN and Type-2 AGN, long-term variabilities, one of fundamental intrinsic characteristics of AGN (Rees 1984;Ulrich et al. 1997;Madejski & Sikora 2016;Baldassare et al. 2020) tightly related to central BH accreting processes, can also be well applied to classify AGN: Type-1 AGN with apparent long-term optical variabilities, but Type-2 AGN with no apparent long-term optical variabilities because of serious obscurations of central AGN activities. And the longterm optical variabilities of AGN can be be well modeled by the well-applied Continuous AutoRegressive process (CAR process) firstly proposed by Kelly et al. (2009) and then the improved damped random walk process (DRW process) in Kozlowski et al. (2010); Zu et al. (2013); Kelly et al. (2014); Starkey et al. (2016); Zu et al. (2016). Therefore, combining variability properties and spectroscopic properties can lead to more confident classifications of AGN, which is the main objective of the paper, in order to check how many Type-1 AGN (central activity regions directly observed) mis-classified as Type-2 AGN through optical spectroscopic emission features.
The manuscript is organized as follows. Section 2 presents the data sample of the pipeline classified Type-2 AGN in SDSS DR16 (Sloan Digital Sky Survey, Data Release 16, Ahumada et al. (2020)). Section 3 shows the method to describe the long-term variabilities from CSS (Catalina Sky Survey) (Drake et al. 2009(Drake et al. , 2014Graham et al. 2017;Singhal et al. 2021) for the collected SDSS pipeline classified Type-2 AGN and the basic results on a small sample of optically selected SDSS Type-2 AGN with apparent longterm variabilities. Section 4 shows the main spectroscopic results for the collected Type-2 AGN but with apparent longterm optical variabilities. Section 5 shows the necessary discussions. Section 6 gives the final summaries and conclusions. And in the manuscript, the cosmological parameters of 0 = 70km · s −1 Mpc −1 , Ω Λ = 0.7 and Ω = 0.3 have been adopted.
2. PARENT SAMPLES OF SDSS PIPELINE CLASSIFIED TYPE-2 AGN As well described in https://www.sdss.org/dr16/spectro/catalogs/, each spectroscopic object has a main classification in SDSS: GALAXY, QSO or STAR. And, for objects classified as GALAXY, there are at least three subclasses , STARBURST, STARFORMING, AGN. Here, the main classification of GALAXY (class='galaxy') and subclass of AGN (subclass = 'AGN') are mainly considered to collect the SDSS pipeline classified low redshift Type-2 AGN. Here, only one main criterion of redshift smaller than 0.3 ( < 0.3) is applied to collect all the low redshift Type-2 AGN from SDSS pipeline classified main galaxies in DR16, through the SDSS provided SQL (Structured Query Language) Search tool (http://skyserver.sdss.org/dr16/en/tools/search/sql.aspx) by the following query SELECT p l a t e , f i b e r i d , mjd , r a , d e c FROM S p e c O b j a l l WHERE c l a s s = ' g a l a x y ' and s u b c l a s s = 'AGN' and ( z b e t w e e n 0 and 0 . 3 0 ) and z w a r n i n g =0 and s n m e d i a n > 10 In the query above, 'SpecObjall' is the SDSS pipeline provided database including basic properties of spectroscopic emission features of emission line galaxies in SDSS DR16, 'snmedian' means the median signal-to-noise (SN) of SDSS spectra, class='galaxy' and subclass='AGN' mean the SDSS spectrum can be well identified with a galaxy template and the galaxy has detectable emission lines that are consistent with being a Seyfert or LINER by the dividing line applied in the known BPT diagram (Baldwin et al. 1981;Kewley et al. 2001;Kauffmann et al. 2003a;Kewley et al. 2006Kewley et al. , 2019Zhang et al. 2020) Tremonti et al. (2004). Certainly, when the sample is created for the SDSS Type-2 AGN but with apparent optical variabilities, there are detailed discussions in the following sections in the manuscript on procedure to determine host galaxy contributions in SDSS spectra and procedure to describe emission lines after subtractions of starlight. Based on the collected line parameters and the other necessary information of the Type-2 AGN from the SDSS databases, Fig. 1  Lemmon, along-side the 1.0-meter telescope (field of view about 0.3 deg 2 ). The 0.7-meter Schmidt telescope (field of view about 19.4 deg 2 ) is located on Mt. Bigelow, just east of Mt. Lemmon. The CSS telescopes operate 24 nights per lunation with a 4-5 day break surrounding the full moon. The CSS database encompasses about 10-years long photometry for more than 500 million objects with V magnitudes between 11.5 and 21.5 from an area of 33,000 square degrees.
Based on RA and DEC of the collected 14354 SDSS Type-2 AGN, long-term light curves can be collected and downloaded from http://nesssi.cacr.caltech.edu/DataRelease/ for 12881 out of the collected 14354 SDSS Type-2 AGN, with searching radius of 3 arcseconds. Meanwhile, as discussed in Drake et al. (2009) and descriptions in CSS homepage, there is a photometry blending flag for CSS light curves, probably causing by different photometric detections in different seeing conditions and/or by causing by two and more sources detected within the searching radius. Fortunately, among the download light curves of the 12881 Type-2 AGN, all the blending flags are zero, indicating that the light curves can be used reliably. Moreover, when cross matching database between CSS and SDSS, 3520 of the 12881 Type-2 AGN have their collected light curves with more than one CSS IDs. Therefore, two simple criteria are applied to determine the final accepted CSS light curves for the 3520 Type-2 AGN. First, if the multiple CSS light curves with different IDs for one Type-2 AGN have the same mean photometric magnitudes within the same time durations, the CSS light curve with more data points (corresponding longer time durations) is accepted as the CSS light curve of the Type-2 AGN. Second, if the multiple CSS light curves with different IDs for one Type-2 AGN have quiet different mean photometric magnitudes, the CSS light curve with mean photometric V-band magnitude nearer to SDSS photometric g-band Petrosian magnitude is accepted as the CSS light curve of the Type-2 AGN, due to the CSS V-band and the SDSS g-band covering similar wavelength ranges. Fig. 2 shows the light curves of SDSS 0271-51883-0252 (PLATE-MJD-FIBERID) and 1239-52760-0047 as examples to show applications of the two criteria above to determine the final accepted CSS light curve. For the SDSS 0271-51883-0252, there are two CSS light curves with IDs of 1001055046612 and 3001077014184. For the same time durations of the two light curves with MJD-53000 from 912 to 3365, there are similar mean photometric magnitudes about 13.9, therefore, the CSS light curve with ID:1001055046612 having more data points and also longer time duration is accepted as the final light curve of SDSS 0271-51883-0252. For the SDSS 1239-52760-0047, the collected CSS light curves with two IDs of 1107056047455 and 2108145011988 have mean magnitude difference to be about 0.5mag. Considering the SDSS photometric g-band magnitude about 18.36, therefore, the CSS light curve (ID:1107056047455) with mean V-band magnitude 17.85 is the final accepted light curve of SDSS 1239-52760-0047. Actually, the final accepted light curves of the SDSS 0271-51883-0252 and 1239-52760-0047, two candidates of Type-2 AGN with apparent variabilities in the manuscript, are also shown in the following Fig. 3.
Then, in order to check whether are there apparent variabilities, the commonly accepted DRW process (Kelly et al. 2009;Kozlowski et al. 2010;Zu et al. 2013) is applied to describe the collected light curves. There are many other reported studies on the AGN variabilities through the DRW process. MacLeod et al. (2010) have modeled the variabilities of about 9000 spectroscopically confirmed quasars covered in the SDSS 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 variabilities by the DRW process. Andrae, Kim & Bailer-Jones (2013) have shown that the DRW process is preferred to model AGN variabilities, rather than several other stochastic and deterministic models, by fitted results of long-term variabilities of 6304  quasars. Zu et al. (2013) have checked that the DRW process provided an adequate description of AGN optical variabilities across all timescales. Zhang & Feng (2017a) 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. More recently, in our previous paper, Zhang et al. (2021d) have shown apparent long-term variabilities well described by the DRW process to report a composite galaxy as a better candidate of true Type-2 AGN. Therefore, the DRW process determined parameters from the long-term variabilities can be well used to predict whether are there apparent clues to support central AGN activities.
In the manuscript, the public code of JAVELIN (Just Another Vehicle for Estimating Lags In Nuclei) described in Kozlowski et al. (2010) and provided by Zu et al. (2013) has been applied here to describe the long-term CSS variabilities of the 12881 Type-2 AGN. When the JAVELIN code is applied, through the MCMC (Markov Chain Monte Carlo) (Foreman-Mackey et al. 2013) analysis with the uniform logarithmic priors of the DRW process parameters of and covering every possible corner of the parameter space (0 < / < 1 + 5 and 0 < /( / 0.5 ) < 1 + 2), the posterior distributions of the DRW process parameters can be well determined and provide the final accepted parameters and the corresponding statistical confidence limits. Meanwhile, when the JAVELIN is applied, each long-term CSS light curve has been firstly re-sampled with one mean value for multiple observations per day. Then, the best descriptions to each re-sampled light curve can be well determined.

Z X G
Based on the JAVELIN code determined process parameters of and at least three times larger than their corresponding uncertainties, there are 156 Type-2 AGN which have apparent long-term variabilities. The long-term light curves and corresponding best-fitting results of the 156 Type-2 AGN are shown in Fig. 3, and the corresponding two dimensional posterior distributions in contour of the parameters of and are shown in Fig. 4. And the basic information of the 156 Type-2 AGN are listed in Table 1, including information of plate-mjd-fiberid, SDSS coordinate based name (Jhhmmss.s±ddmmss.s), redshift , averge photometric CSS V-band magnitude, SDSS provided g-band Petrosian magnitude, 3 , 2 , the parameters and uncertainties of ln( ) and ln( ). Properties of 3 and 2 of the 156 Type-2 AGN are also shown as small circles in dark green in left panel of Fig Before proceeding further, one additional point is noted. As discussed in Graham et al. (2017); Laurenti et al. (2020), uncertainties of CSS photometric magnitudes are overestimated at the brighter magnitudes, but underestimated at fainter magnitudes. Therefore, it is necessary to check effects of corrections of photometric magnitude uncertainties on the variability properties. Fig. 5 shows photometric magnitude distributions of the collected 156 Type-2 AGN with apparent variabilities and the 12881 Type-2 AGN in the parent sample. The mean photometric magnitudes are 16.17 (standard deviation 1.51) and 16.58 (standard deviation 0.92) for the 156 Type-2 AGN with apparent variabilities and for the 12881 Type-2 AGN, respectively. Therefore, the collected 156 Type-2 AGN with apparent variabilities do not tend to be chosen from brighter or fainter sources. In other words, there are tiny effects of corrections of uncertainties of photometric magnitudes on the collected 156 Type-2 AGN through variability properties.
Besides properties of log( 2 ), log ( 3 ), and log( 3 /erg/s), left panel of Fig. 6 shows properties of ln( /( / 0.5 )) (mean value about -2.45 and standard deviation about 0.54) and ln( / ) (mean value about 5.06 and standard deviation about 1.09). Before proceeding further, as well discussed on variability properties of OGLE-III quasars in Kozlowski et al. (2010) (see their Figure 9) by the same method as the JAVELIN code, the DRW process parameters of /( / 0.5 ) and / have values about 0.005-0.52 and about 10-1000days, strongly indicating that the measured parameters of ln( /( / 0.5 )) and ln( / ) of the 156 Type-2 AGN are reliable enough. Moreover, right panel of Fig. 6 shows distributions of , with mean values of 81 and 84 for the 156 Type-2 AGN and the other Type-2 AGN, respectively, indicating there are no effects of different numbers of data points on the measured DRW process parameters. Besides the 156 Type-2 AGN with ln( /( / 0.5 )) larger than -4, the other Type-2 AGN have their measured ln( /( / 0.5 )) smaller than -10. Therefore, in left panel of Fig. 6, there are no plots on the other Type-2 AGN with ln( /( / 0.5 )) smaller than -10.
Finally, based on the DRW process well applied to describe intrinsic AGN activities, there are 1.2% (156/12881) optically selected Type-2 AGN which have apparent long-term optical variabilities, indicating the 156 Type-2 AGN of which central AGN activity regions directly in the line-of-sight.

SPECTROSCOPIC RESULTS OF THE 156 TYPE-2 AGN BUT WITH LONG-TERM VARIABILITIES
In order to confirm the 156 Type-2 AGN are well classified as Type-2 AGN by spectroscopic results, the spectra properties should be further discussed. Due to apparent host galaxy contributions to the SDSS spectra of the 156 Type-2 AGN, the starlight in the SDSS spectra should be firstly determined. Here, the commonly accepted SSP (simple stellar population) method has been applied. More detailed descriptions on the SSP method can be found in Bruzual & Charlot (2003); Kauffmann et al. (2003);Cid Fernandes et al. (2005); Cappellari (2017). And the SSP method has been applied in our previous papers Zhang (2014) Zhang (2021aZhang ( ,b, 2022. Here, we do not show further discussions on the SSP method any more, but simple descriptions on SSP method are described as follows. The 39 simple stellar population templates in Bruzual & Charlot (2003) have been exploited, which can be used to well-describe the characteristics of almost all the SDSS galaxies as detailed discussions in Bruzual & Charlot (2003). Meanwhile, there is an additional component, a fourth degree polynomial function describe component, which is applied to describe probable intrinsic In Kozlowski et al. (2010), the unit of is mag/years 0.5 . Here, the values 0.005-0.52 are calculated by /mag/years 0.5 larger than 0.1 and smaller than 10 as shown in Figure 9 in Kozlowski et al. (2010).  The information of plate-mjd-fiberid is marked as title of each panel. In order to show clear parameter difference between different objects, the same limit from -4.5 to 0 has been applied to x-axis, and the same limit from 3 to 8 has been applied to y-axis. Z X G AGN continuum emissions after considering the apparent variabilities or to modify continuum shapes when to describe the SDSS spectra by the templates. Meanwhile, when the SSP method is applied, the narrow emission lines listed in http://classic.sdss.org/dr1/algorithms/speclinefits.html#linelist are masked out by full width at zero intensity about 450km s −1 , And the wavelength ranges from 4450 to 5600Å and from 6250 to 6750Å are also masked out for the probably broad H and the broad H emission lines. Moreover, when the SSP method is applied, there is only one criterion that the strengthen factor of each simple stellar population template is not smaller than zero. Then, through the Levenberg-Marquardt least-squares minimization technique (the MPFIT package), SDSS spectra with emission lines being masked out can be well described by the SSP method for the 155 Type-2 AGN with apparent variabilities, besides the SDSS 1870-53383-0466 (plate-mjd-fiberid) with quite different redshifts estimated from emission lines and from absorption lines which will be individually discussed in the following section. Here, the SSP method determined host galaxy contributions are not shown in plots for all the 155 Type-2 AGN (SDSS 1870-53383-0466 not included), but left panels of Fig. 7 show an example on the SSP determined host galaxy contributions in the Type-2 AGN SDSS 2374-53765-0174 due to its stronger narrow emission lines.
After Properties of the second component in H will provide clues to support whether are there broad components in H . Then, through the Levenberg-Marquardt least-squares minimization technique, the emission lines around H can be well described. Meanwhile, when the Gaussian functions above are applied, the following three criteria are accepted. First, each Gaussian component has line intensity not smaller than zero. Second, the first (the second) components of the each doublet have the same redshift and the same line width. Third, the first (the second) components of the [N ] doublet have the flux ratio to be fixed to the theoretical value 3. As an example, right panels of Fig. 7 show the best descriptions to the emission lines around H in SDSS 2374-53765-0174, and the corresponding residuals calculated by line spectrum minus the best fitting results and then divided by uncertainties of the spectrum.
Then, line parameters of [N ] and H of the 156 Type-2 AGN but with apparent variabilities can be well measured and listed in Table 2, after subtractions of host galaxy contributions. Then, based on the measured parameters, 31 out of the 156 Type-2 AGN have probable broad H , considering the following two criteria. On the one hand, the second moment of H has its measured line parameters at least three times larger than corresponding uncertainties. On the other hand, the second component of H has its measured second moment larger than 1000km/s, or at least three times larger than both the first moment of H and the second moment of [N ] doublet. There are 17 Type-2 AGN with measured second moment of the second component of H larger than 1000km/s, and 14 Type-2 AGN with the second component of H at least three times larger than both the first moment of H and the second moment of [N ] doublet. Therefore, among the 156 Type-2 AGN, the 31 Type-2 AGN with probable broad component in H should be preferred to be classified as Type-1.8/1.9 AGN, not as Type-2 AGN.
Before proceeding further, two points are noted. On the one hand, as the shown results in Fig. 8, due to complex broad emission lines in SDSS 2419-54139-0050, the best fitting results to the emission lines around H are not so good. However, the fitting results can be clearly applied to support a broad emission component in H . Therefore, there are no further applications of more Gaussian components to describe the broad H in SDSS 2419-54139-0050, because there are no further discussions on broad line properties in the manuscript. On the other hand, there are two Gaussian functions applied to describe each narrow emission line,in order to test whether are there broad emission line features. However, the 10 Gaussian functions should lead to larger uncertainties of each model parameters, leading the measured parameters (especially of the second component) 3 times smaller than the corresponding uncertainties. Therefore, in Table 2, there are  no listed parameters in some collected Type-2 AGN, due to measured line parameters smaller than corresponding uncertainties.
Besides the 31 AGN of which spectra shown in Fig. 8, the other Type-2 AGN have been carefully checked through the F-test technique, as what we have done in Zhang et al. (2021d) by two different model functions. Besides the model function discussed above, the other model function has been considered by 10 Gaussian functions plus an additional broad Gaussian component. Then comparing with different estimated 2 values by the two model functions, it can be con-firmed that the broad Gaussian component is not preferred with confidence level higher than 5sigma. In other words, the other optically selected 125 Type-2 AGN (156-31) have no clues on broad emission lines but have apparent long-term optical variabilities. As described above, the AGN SDSS J075736.47+532557.1 is an unique object, due to its redshift determined to be zero through emission line features. However, as shown in Fig. 9,  Figure 8. Each two columns in each row show the similar results as those shown in Fig. 7, but for the 31 Type-2 AGN with both long-term variabilities and probable broad H emission component described by dashed purple line.  Moreover, as the shown emission lines around H in right panel of Fig. 9 in SDSS J075736.47+532557.1, there are no clues on probably broad emission component in H . Therefore, besides the quite different redshifts from absorption and emission lines, SDSS J075736.47+532557.1 is an optically selected Type-2 AGN but with apparent long-term optical variabilities. Further discussions on quite different redshifts from absorption and emission lines in SDSS J075736.47+532557.1 is beyond the scope of the manuscript, but will be give in our manuscript in preparation, and there are no further discussions on SDSS J075736.47+532557.1 in the manuscript.

Are the optically selected Type-2 AGN with apparent
variabilities Changing-Look AGN? As described in the Introduction, the optically selected Type-2 AGN but with apparent long-term variabilities could be candidates of changing-look AGN at quiet state. However, multi-epoch spectra are necessary to check whether an AGN was a changing-look AGN. Among the collected Type-2 AGN with apparent variabilities, there are 14 objects which have multi-epoch spectra, collected based on the SDSS pipeline provided parameter 'Nspecobs' which can be found in the second extension of Fits file of each SDSS spectrum. Then, the collected multi-epoch spectra of each Type-2 AGN are well checked and shown in Fig. 10, and no signs can be found on appearance or disappearance of broad emission lines in different epochs. As the shown information of plate-mjd-fiberid in top-left corner in each panel of Fig. 10, time differences among the epochs of the multiple spectra can be well determined as 375days, 281days, 281days, 277days, 5days, 5days, 84days, 97days, 20days, 3days, 18days, 20days, 239days and 17days for the Type-2 AGN listed from left to right and from Z X G top to bottom. Therefore, at current stage, there are not enough evidence to support that the collected Type-2 AGN but with apparent long-term variabilities are changing-look AGN (probably due to smaller time differences among the multi-epochs?).

Are the optically selected Type-2 AGN with apparent variabilities True Type-2 AGN?
As described in the Introduction, the optically selected Type-2 AGN but with apparent long-term optical variabilities could be candidates of true Type-2 AGN. The long-term optical variabilities can be well applied to confirm that the central regions have been directly observed, along with the loss of broad emission lines, the optically selected Type-2 AGN, especially the 125 objects with apparent variabilities Figure 11. TDE roughly expected variabilities described by −5/3 shown in solid red line in the long-term CSS light curve of SDSS 0747-52234-0400. but without broad emission lines, can be accepted as the good candidates of true Type-2 AGN.
Actually, among the Type-2 AGN with apparent long-term optical variabilities, there is an unique TDE (Tidal disruption event) expected variabilities in the SDSS 0747-52234-0400. TDEs have been well studied in detail for more than four decades (Rees 1988 Here, systematic studying on TDE expected variabilities in SDSS 0747-52234-0400 with apparent long-term variabilities is beyond the scope of the manuscript. Therefore, there are no further discussions on SDSS 0747-52234-0400 with apparent long-term variabilities related to TDEs which will be discussed in detail in our manuscript in preparation, but Fig. 11 shows the TDE expected variabilities roughly described by −5/3 in SDSS 0747-52234-0400. Besides SDSS 0747-52234-0400, there are several other Type-2 AGN with their long-term light curves having variability features including a smooth declining trend but with small decrease followed by none-variability component, such as in SDSS 0284-51662-0558, SDSS 0284-51943-0551, SDSS 0538-52029-0359, SDSS 0914-52721-0233, SDSS 1052-52466-0280, SDSS 2789-54555-0281, SDSS 2572-54056-0139, etc., of which light curves roughly described by −5/3 are shown in Fig. 12. The probable TDEs provide strong and further evidence to support the objects as true Type-2 AGN, due to tidal disruption radii about tens of Schwarzschild radii quite close to central black hole. In our manuscript in preparation, detailed discussions on variabilities related to probable TDEs should be given for the small sample of optically selected Type-2 AGN but with apparent variabilities.
Besides the long-term variabilities related to central AGN activities or to probable TDEs, another evidence should be reported to support the loss of broad emission lines. However, based on the collected SDSS spectra of the Type-2 AGN, there are only 31 AGN with probably broad emission lines, leading the 31 AGN to be classified as Type-1.8/1.9 AGN. For the other 125 Type-2 AGN with no broad emission lines in current collected SDSS spectra, it is confident to be accept as true Type-2 AGN. Certainly, high quality spectra should be necessary in the near future to confirm them as true Type-2 AGN without no broad emission lines.

Comparing with previous work
As described in Introduction, Barth et al. (2014) have reported g-band variabilities in 17 out of 173 Type-2 quasars covered in the Stripe 82 region, indicating about 5.8% ((17-7)/173, with 7 objects having detected broad emission lines) of optical selected Type-2 AGN have apparent variabilities. However, in the manuscript, among the 12881 SDSS pipeline classified Type-2 AGN with CSS light curves, there are 156 objects with apparent long-term variabilities, indicating about 0.97% ((156-31)/12881, with 31 objects having detected broad emission lines) optical selected low redshift Type-2 AGN have apparent variabilities, about six times smaller than the reported results in Barth et al. (2014). Therefore, in the subsection, it is interesting to explain the different number ratios in Barth et al. (2014) and in the manuscript, for Type-2 AGN with and without long-term variabilities. The following two reasons are mainly considered.
On the one hand, as well discussed in Barth et al. (2014), the selected 7 of the 17 Type-2 quasars have detected broad emission lines in their re-observed Keck high quality spectra. Probably the other 10 Type-2 quasars could have detected broad emission lines in high quality spectra, leading a number ratio quite smaller than 5.8%.
On the other hand, if Type-2 AGN with apparent long-term variabilities were evenly distributed in space, the quite different number ratios should give interesting clues on properties of central dust torus in AGN. As one of fundamental structures in Unified model of AGN, properties of dust torus have been well studied for more than four decades, especially on properties of opening angles (covering factor) of dust torus. Arshakian (2005) have proposed the receding torus model, based on the statistically significant correlation between the half opening angle of the torus and [O ] emission-line luminosity. Zhuang et al. (2018) have reported that the halfopening angle of the torus declines with increasing accretion rate until the Eddington ratio reaches 0.5, above which the trend reverses. However, Netzer et al. (2016); Stalevski et al. (2016) have found no evidence for a luminosity dependence Z X G of the torus covering factor in AGN. More recent review on dust torus can be found in Almeida & Ricci (2017).
There are no definite conclusions on the receding torus model, however, the receding torus model can be well applied to explain the quite different number ratios on the Type-2 AGN with apparent variabilities. For our sample in lower redshift and in lower line luminosity than the Type-2 quasars in Barth et al. (2014), smaller opening angles expected by the receding torus model are expected for the low redshift objects in our sample, leading to fewer Type-2 AGN with apparent variabilities which can be detected in our sample.

SUMMARIES AND CONCLUSIONS
The main summaries and conclusions are as follows.
• Through the SDSS provided SQL search tool in DR16, 14354 SDSS pipeline classified low redshift ( < 0.3) Type-2 AGN can be collected from SDSS main galaxies with spectral signal-to-noise larger than 10, and located into the AGN region in the BPT diagram of O3HB versus N2HA.
• Among the collected 14354 Type-2 AGN, long-term CSS V-band light curves of 12881 Type-2 AGN can be collected from the CSS.
• The well-known DRW process is applied to describe the CSS light curves of the 12881 Type-2 AGN, leading to the well determined process parameters of and . And based on the measured ln( /( / 0.5 )) larger than -4 and 3 times larger than corresponding uncertainties, 156 Type-2 AGN are collected with apparent long-term variabilities.
• For the 156 Type-2 AGN with apparent variabilities, the well-applied SSP method is accepted to determine host galaxy contributions in SDSS spectra. After subtractions of starlight, emission lines around H can be well measured by multiple Gaussian functions, leading to 31 objects with detected broad H . There are no signs (confidence level higher than 5sigma by the F-test technique) for broad emission lines in the other 125 Type-2 AGN with long-term variabilities.
• For the 156 optically selected Type-2 AGN with apparent variabilities, there are 14 objects having multi-epoch SDSS spectra. After checking the multi-epoch SDSS spectra, there are no clues to appearance or disappearance of broad lines. The results indicate that the collected Type-2 AGN classified as the changing-look AGN should be not preferred at current stage.
• For the 125 (156-31) optically selected Type-2 AGN without broad lines but with apparent variabilities, they could be well accepted as candidates of True Type-2 AGN (AGN without hidden central broad emission line regions).
• For the 156 optically selected Type-2 AGN with apparent variabilities, there are a small sample of objects with their long-term variabilities having features roughly described by TDE expected −5/3 , indicating probable central TDEs which can be applied as further evidence to support true Type-2 AGN.
• The smaller number ratio of Type-2 AGN with variabilities to normal Type-2 AGN than in high redshift and high luminosity Type-2 quasars reported in Barth et al. (2014) could be applied to probably support the receding torus model in AGN, if the reported Type-2 quasars with variabilities in Barth et al. (2014) were true Type-2 quasar without central hidden BLRs.

ACKNOWLEDGEMENTS
Zhang gratefully acknowledges the anonymous referee for giving us constructive comments and suggestions to greatly improve the paper. Zhang gratefully thanks the scientific research funds provided by GuangXi University and the kind grant support from NSFC-12173020. This manuscript has made use of the data from the SDSS projects, http://www.sdss3.org/, managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaborations. The manuscript has made use of the data from the Catalina Sky Survey (CSS) http://nesssi.cacr.caltech.edu/DataRelease/, funded by the National Aeronautics and Space Administration under Grant No. NNG05GF22G issued through the Science Mission Directorate Near-Earth Objects Observations Program. The paper has made use of the public JAVELIN code http://www.astronomy.ohio-state.edu/~yingzu/codes.html#javelin as an approach to reverberation mapping that computes the lags between the AGN continuum and emission line light curves and their statistical confidence limits, and the MPFIT package https://pages.physics.wisc.edu/~craigm/idl/cmpfit.html to solve the least-squares problem through the Levenberg-Marquardt technique, and the MCMC code https://emcee.readthedocs.io/en/stable/index.html.  (  N -The first column shows the pmf information of plate-mjd-fiberid of each Type-2 AGN, the second column shows the redshift information of each Type-2 AGN, the third column shows the SDSS coordinate based name (Jhhmmss.s±ddmmss.s) of each Type-2 AGN, the fourth column shows the mean photometric magnitude of the CSS light curve of each Type-2 AGN, the fifth column shows the SDSS provided photometric g-band Petrosian magnitude of each Type-2 AGN, the sixth column shows the [O ] line luminosity log( 3 /( / )) of each Type-2 AGN, the seventh column and the eighth column show the log( 3 ) and log( 2 ) of each Type-2 AGN, the last two columns show the determined ln( /( / 0.5 )) and ln( / ) of each Type-2 AGN.