Hα Time Delays of Active Galactic Nuclei from the Zwicky Transient Facility Broadband Photometry

In our previous work on broadband photometric reverberation mapping (PRM), we proposed the interpolated cross-correlation function (ICCF)-Cut process to obtain the time lags of the Hα emission line from two broadband lightcurves via subtracting the continuum emission from the line band. Extending the work, we enlarge our sample to the Zwicky Transient Facility (ZTF) database. We adopt two criteria to select 123 type 1 active galactic nuclei (AGNs) with sufficient variability and smooth light curves from 3537 AGNs at z < 0.09 with more than 100 epoch observations in the g and r bands from the ZTF database. We calculate the Hα time lags for 23 of them that have previous spectroscopic reverberation mapping (SRM) results using the ICCF-Cut, Just Another Vehicle for Estimating Lags In Nuclei (JAVELIN), and χ 2 methods. Our obtained Hα time lags are slightly larger than the Hβ time lags, which is consistent with the previous SRM results and the theoretical model of the AGN broad-line region. The comparisons between the SRM and PRM lag distributions and between the subtracted emission line light curves indicate that after selecting AGNs with the two criteria, combining the ICCF-Cut, JAVELIN, and χ 2 methods provides an efficient way to get the reliable Hα lags from the broadband PRM. Such techniques can be used to estimate the black hole masses of a large sample of AGNs in large multiepoch photometric sky surveys such as the Legacy Survey of Space and Time and the survey from the Wide Field Survey Telescope in the near future.


Introduction
Reverberation mapping (RM; Blandford & McKee 1982;Peterson 1993) is an efficient and widely used method to determine the masses of the supermassive black holes (SMBHs) in active galactic nuclei (AGNs).The principle of RM is that the photons from the accretion disk travel across the broad-line region (BLR) and generate broad emission lines by the photoionization process, so that the time lag τ between the optical continuum and broad emission-line light curves reflects the size of the BLR, i.e., R BLR = cτ.By monitoring the continuum and the broad emission lines, we can obtain their light curves and calculate the time lag.By combining the velocity dispersion of the broad emission line in the spectra, we can calculate the virial mass of the SMBH at the center of the AGN.
Spectroscopic RM (SRM) uses medium-to large-sized telescopes to monitor the variability of the continuum and line emissions.It is usually very expensive and time-consuming.Although multifiber spectroscopic telescopes can obtain thousands of spectra in a single exposure, it is hard to achieve the high accuracy in the flux calibration required by the RM.Accurate fluxes are essential for extracting the light curves of the continuum and emission lines and calculating the time lag between them.Only several campaigns such as the Sloan Digital Sky Survey (SDSS) RM project (RM; Grier et al. 2017b) and the Australian Dark Energy Survey RM program (Yu et al. 2021) use the fiber spectra, while most SRM campaigns use the slit spectra to monitor the AGN continuum and broad emission lines (e.g., Bentz et al. 2009;Du et al. 2018;Bao et al. 2022).In the past decades, only about 200 AGNs have the BLR sizes measured with SRM.To obtain the BLR sizes of a large sample of AGNs, a more efficient method is needed.
Photometric reverberation mapping (PRM) employs multiband photometric observations to trace the AGN continuum and broad emission lines.The narrow and intermediate-band PRMs use specially designed filters with a narrow bandwidth (FWHM around 30 Å) or intermediate bandwidth (FWHM around 200 Å) to collect photons mainly from the broad emission lines while blocking most of the continuum emissions.For sufficiently strong emission lines, such as Hα, light curves obtained from an appropriate narrow band can be directly considered as the emission-line light curves, because the line component is dominant in this case (e.g., Haas et al. 2011;Ramolla et al. 2018).For other cases, including the narrowband PRM for slightly weaker emission lines (such as Hβ) and the intermediate-band PRM, previous works (e.g., Pozo Nuñez et al. 2012;Jiang et al. 2016) used a broad band that contains the narrow/intermediate band to determine the continuum component in the narrow/intermediate band.These methods have been proven effective in many campaigns.Nevertheless, special narrow/intermediate-band filters are only equipped on certain telescopes, and they also limit the redshift range and the sample size of AGNs.
Another PRM technique, the broadband PRM, can be applied to a large sample of AGNs across a wide redshift range with the multiepoch data from large photometric sky surveys.Compared to the narrow/intermediate-band PRM, broadband PRM is more difficult to measure the lags of broad emission lines since the broadband photometric data contains mostly the continuum flux from the accretion disk rather than the emission lines from BLR.It is critical to remove the contribution of the continuum and extract the broad emission line from the broad band (this band is named as line band hereafter).Unlike the narrow/intermediate-band cases, the continuum contribution is hard to determine in the line band of broadband PRM because we need to use an adjacent broad band (hereafter the continuum band) rather than the line band to trace the continuum.The different wavelength ranges and the small ratio of the emission line in the line band require that the continuum component should be carefully considered.
For broadband PRM, Chelouche & Daniel (2012) proposed the cross-correlation function minus auto-correlation function (CCF-ACF) method to subtract the continuum in the correlation domain, which assumes that the continuum component in the line band is identical to that in the continuum band.This method was adopted in some later works (e.g., Edri et al. 2012;Rafter et al. 2013). Pozo Nuñez et al. (2013) presented the results of both narrowband PRM and broadband PRM (using the CCF-ACF method), which showed consistency of both techniques.However, the simple assumption of the continuum components in two bands being the same has large errors due to the AGN spectral slope and the varying flux ratio of the two continuum components in different AGNs.To improve this, further works (e.g., Chelouche & Zucker 2013) considered the flux ratio of the emission line in the line band as an additional free parameter.This parameter adds to the degrees of freedom and is independent of the spectrum, so it may not match the real spectrum of the AGN.
In our previous work (Ma et al. 2023; hereafter Paper I), we proposed the cross-correlation function (ICCF)-Cut process to remove the continuum emission and isolate the emission-line from the broadband light curves.This procedure essentially follows the continuum removal proposed by Haas et al. (2011) andPozo Nuñez et al. (2012) with some modifications.We also note that other techniques where the continuum is removed in the correlation domain have been proposed by Chelouche & Daniel (2012).Compared with the CCF-ACF method, ICCF-Cut directly uses a single-epoch spectrum to determine the ratio and extract the emission-line light curves.In Paper I, we selected 4 Seyfert 1 galaxies with simultaneous broadband and Hβ light curves.We calculated their Hα time lags using two broadband light curves and further compared our extracted Hα light curves with the simultaneous Hβ light curves to examine our results.This method, along with the Just Another Vehicle for Estimating Lags In Nuclei (JAVELIN) and χ 2 methods, proves to be an efficient way to measure reliable Hα lags from broadband photometry.In this paper, we extend the range of AGN target selection for broadband PRM and apply these methods to the multiepoch data from Zwicky Transient Facility (ZTF; Masci et al. 2019).
ZTF is a time-domain survey that had its first light at Palomar Observatory in 2017.By scanning more than 3750 square degrees of the sky per hour to a depth of 20.5 mag, ZTF can produce a photometric variability catalog with nearly 300 observational epochs each year, which is ideal for the studies of the variabilities of AGN.These data can be used to improve the quality of the continuum light curves in SRM (Hu et al. 2021) and to calculate the time lags between two broad bands for continuum RM (Jha et al. 2022;Guo et al. 2022).In spite of these advantages, we find that only the sources with large variabilities and high continuities in the light curves can serve as good candidates for the broadband PRM.Therefore, in this work, we use the data of ZTF DR16 between 2018 March and 2023 January and adopt two criteria to select AGNs that are good candidates for the broadband PRM.Same as Paper I, we use three methods, namely, the ICCF-Cut, JAVELIN, and χ 2 methods, to calculate the time lags to ensure the reliabilities of the time lags.To check our results further, we also compare the ZTF broadband PRM lags with the time lags obtained by SRM.
This paper is arranged as follows.We describe the target selections in Section 2. The time lags obtained using three methods are presented in Section 3. The discussion and the comparisons between PRM and SRM are presented in Section 4. A summary is given in Section 5.

Target Selections
The main science goal of ZTF is to discover young supernovae nightly and search for rare and exotic transients (Masci et al. 2019).ZTF has g, r, and i filters; however, for most targets, only the g and r bands have adequate data for the broadband PRM.Therefore, in this work, the redshift of AGNs is limited to be lower than 0.09 so that the Hα emission line can fall into the r band.Figure 1 shows the spectrum of one AGN and the transmission functions of the ZTF broad bands.We use the r band to trace the Hα line and the g band to trace the continuum. 5To combine the ZTF public and private data (ZTF Image Service; IRSA 2022).which have different cadences, the light curves are resampled into the mean values of one-day bins.At z < 0.09, most AGNs are extended sources in morphology, the seeing and airmass have significant impacts on the accuracy of the photometry.Only part of AGNs in ZTF have sufficiently accurate data for broadband PRM.So in this work, we use two criteria to select the targets for PRM from ZTF.To select AGNs with sufficient variability, we use the Welch-Stetson J Variability Index (Welch & Stetson 1993) to examine the variability of AGNs.The J index is composed of the relative error (δ) and a weighting factor (w i ).The relative error is defined by Stetson (1996) as Here, n is the number of observations, σ f,i is the measurement error, and f is the mean flux of the light curve.To reduce the influence of a very large flux change within a few data points, which is unphysical, the weighting factor is defined as The J index is defined as Here sgn simply returns the sign of the value.J < 0 means that the variability is dominated by the uncertainties of the observation.Because ZTF data have different numbers of observations for different targets, and the J index is only related to the flux while not related to the observation epoch, some AGNs with a lot of observations and sufficient variability may have a small J index.However, some AGNs with very unsmooth light curves may still have a large J index (see the middle panel of Figure 2 as an example).Therefore, only using the J index to select targets is not sufficient for the ZTF data.
In addition to evaluating the variability with the J index, it is also necessary to select AGNs with smooth light curves to reduce the uncertainties in both the observations and photometric data processing as much as possible.After excluding the data points that deviate from the mean flux by 3σ, we use the second derivative to evaluate the smoothness of light curves.The first-order variation is Here, t i is the epoch of the observation.To avoid the influence of highly unevenly sampled data due to the lack of observations such as seasonal gaps, the intervals of the points to calculate the second derivative are limited to t i+2 − t i < 20 days.The smoothness index s is defined as We exclude AGNs with large s values, which have very large irregular variabilities during very short times.The AGN light curves are usually well modeled by the damped random walk (DRW; Kelly et al. 2009;Kozłowski et al. 2010;MacLeod et al. 2010;Zu et al. 2013).However, the rapid, large, and irregular variabilities of AGNs are often not consistent with the DRW model (Kelly et al. 2009) and are probably caused by errors in the observations for these ZTF targets.Considering the variabilities (J index) as well as the smoothness (s) of the light curves, we select AGNs with J > 1 and J/s > 4000.From 3537 AGNs that have more than 100 observational epochs in both the g and r bands, 123 AGNs are selected by these criteria.Figure 2 shows the example light curves of one selected AGN and two excluded AGNs.
One of the purposes of this work is to verify the ICCF-Cut approach we recently proposed in Paper I; therefore, we select 23 AGNs that have previous SRM results (Stalin et al. 2011;Du et al. 2018;Du & Wang 2019;Hu et al. 2021;Lu et al. 2021;Bao et al. 2022;Lu et al. 2022;U et al. 2022) for further Hα time-lag calculation.Figure 3 presents our final targets.The parameters of the selected 23 AGNs are shown in Table 1.
In addition, our Hα time-lag measurement requires a singleepoch spectrum.Some of these AGNs have the spectra from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Luo et al. 2015), the SDSS (York et al. 2000), and the Burst Alert Telescope AGN Spectroscopic Survey (BASS; Koss et al. 2017).For those AGNs without publicly available spectra, we obtain their single-epoch spectra using the Beijing Faint Object Spectrograph and Camera (BFOSC; Fan et al. 2016) of the Xinglong 2.16 m telescope, where we use the Grism 4 with a dispersion of 198 Å mm −1 and the slit width of 1″8.We also use the Yunnan Faint Object Spectrograph and Camera (YFOSC; Wang et al. 2019) of the Lijiang 2.4 m telescope in China, where we use the Grism 3 with a dispersion of 215 Å mm −1 and the slit width of 2″5.The spectra are reduced by the standard IRAF (Tody 1986(Tody , 1993) ) routine.In particular, the data are reduced with PyFOSC (Fu 2020), a pipeline toolbox based on PyRAF (Science Software Branch at STScI 2012) for the long-slit spectroscopy. 6The host galaxy contribution is about 30%-40% but with large uncertainties.For some AGNs, we fail to decompose the host galaxy components due to the low spectral resolution of the spectra.All the spectra are presented in the Appendix (Figure A1) and the epochs of spectroscopic data for each source are listed in Tables 2-4.

Time-lag Calculations
For the broadband PRM, the continuum is dominant, and the broad emission line only contributes a small fraction of the total flux in the broad band.We need to remove the contribution of the continuum and extract the broad emission line from the broad band.In Paper I, we proposed the ICCF-Cut approach,7 which is a combination of a cut procedure and the ICCF method (Gaskell & Peterson 1987;White & Peterson 1994;Peterson et al. 1998).We extract the light curve of the broad emission line in the broad band via the cut procedure, and then we use the ICCF method to compute the time lag of the broad emission line corresponding to the continuum.The whole process described above is named as the ICCF-Cut process in this paper.We assume that the continuum flux in the line band (in this work, the ZTF r band) equals a fixed fraction α of the flux in the continuum band (the ZTF g band) for each AGN.The extracted Hα light curve can be expressed as Here, L line (t), L cont (t), and L Hα (t) are the light curves of the line band, continuum band, and Hα emission line, respectively.In this equation, we ignored the contribution of other emission lines such as Hβ and [OIII] in the g band, since they are much weaker than the continuum and the broad Hα line.In Paper I we also conducted the simulations and found that the effect of other emission lines can be neglected.The fraction α value can be obtained from the single-epoch spectrum and the broadband light curves: Here F cont , F line , and F Hα are the fluxes of the continuum band, line band, and Hα line obtained from the integral of the singleepoch spectrum, and L line,t and L cont,t are the fluxes of the line band and continuum band at each data point obtained from the linearly interpolated photometric light curves.For the 23 ZTF AGNs, some of their spectra and photometry are not synchronous.Besides, observation strategies such as the slit width and aperture size may cause the differences between the spectroscopy and photometry.So the latter term of Equation ( 7) is added to adjust the ratio calculated from the spectra (i.e., 1 − F Hα /F line ) to the photometry data, and the minimum function is used to make sure that the extracted Hα light curve contains all the contributions of the Hα emission line (see detailed discussion in Paper I). Same as in Paper I, we also consider the influence of the host galaxy and season gaps.We use the flux variation gradient (Choloniewski 1981;Winkler et al. 1992;Pozo Nuñez et al. 2012) to determine the contribution of the host galaxy.Because the observational duration of ZTF is as long as several years, there are large season gaps without observations.The spectral index of the continuum and the value of α may change during the long observation durations.We divide the light curve into several parts according to the season gaps.For each part, the  value of α is adjusted according to the ratio between line-band and continuum-band fluxes.
Besides the ICCF-Cut process, we also used the JAVELIN (Zu et al. 2011(Zu et al. , 2013(Zu et al. , 2016) ) and χ 2 methods to calculate the Hα time lags of the AGNs.JAVELIN uses the DRW process to model the AGN light curves and uses the Markov Chain Monte Carlo DRW processes to reproduce the light curves and obtain the distributions of the parameters, including the time lag.We use the JAVELIN Pmap Model (Zu et al. 2016), which can separate the continuum component and the strong emission-line component blended in the line band via thousands of fittings.Since there are a lot of fitting parameters, the results of JAVELIN are more dependent on the quality of light curves and may have large scatters for light curves with short durations and/or large errors.Because the ZTF is the photometric sky survey with a 48 inch telescope, the photometric accuracy should be considered carefully.The χ 2 method (Czerny et al. 2013;Bao et al. 2022) calculates the correlation between two light curves by weighting the observational uncertainties.It can be Note.The meaning of the superscripts in the Hβ lag column and the Spec Epoch column is the same as in Table 2. Note.The meaning of the superscripts in the Hβ lag column and the Spec Epoch column is the same as in Table 2.
used to evaluate the influence of errors and the feasibility of the broadband PRM with large errors.More details on the ICCF-Cut, JAVELIN, and χ 2 methods can be found in Paper I.
Combining the ICCF-Cut, JAVELIN, and χ 2 methods, we obtain the Hα time lags of 23 AGNs that all have SRM results.If the three methods can give consistent results of Hα lags, we consider the PRM results to be more reliable.However, since the ICCF-Cut process and the χ 2 method share a similar principle and use the same pair of light curves (i.e., continuumband light curve and the extracted Hα light curve) to calculate the time lags, it is expected that the two methods can give consistent results in most cases.However, there are also some cases when the results given by the two methods are not consistent, which is mainly due to the large errors of ZTF light curves.In such cases, the χ 2 method may not be as suitable as the ICCF-Cut process.
With these considerations, we divide these AGNs into three lists.List I has five AGNs that all have simultaneous SRM observation data.For these AGNs, we can compare their simultaneous Balmer line lags and the shape of emission-line light curves with SRM.It can increase the reliabilities of our Hα lag results further.For AGNs in List II, the lag distributions of the ICCF-Cut, JAVELIN, and χ 2 methods, or at least those of the ICCF-Cut and JAVELIN methods are consistent, and the extracted Hα light curves are similar to the lagged g-band continuum light curves (here, the lagged light curve refers to the light curve that is lagged as well as scaled).Meanwhile, the obtained broadband PRM Hα lags are the same as or slightly larger than the SRM Hβ lags, which is consistent with the structure of BLR (Korista & Goad 2004) and the results of previous works (Kaspi et al. 2000;Bentz et al. 2010;Grier et al. 2012).For AGNs in List III, the JAVELIN results for some AGNs are not consistent with those from any of the other two methods.Some AGNs have three consistent lag distributions, but the obtained Hα lags are much larger than SRM Hβ lags.These deviations mean that the results of AGNs in List III are not very convincing.
For Mrk 841 in List I, we first calculate the time-lag distributions with the ICCF-Cut, JAVELIN, and χ 2 methods for the whole observational duration.The obtained Hα lag distributions from the three methods are consistent.The extracted Hα light curve is similar to the lagged continuum g-band light curve, as shown in Figure 4 panel (b).Then, we calculate the time-lag distribution for part of the light curves that have simultaneous SRM Hβ observations (Bao et al. 2022).By comparing with the SRM Hβ light curve, we can find that the shape of the extracted Hα light curve is very similar to the SRM Hβ light curve, and the ICCF result between the extracted Hα and SRM Hβ light curves is close to zero (see panels (c) and (d) in Figure 5).It proves the reliability of the extracted Hα light curve.The time lags given by the three methods of this part of light curves are consistent with each other and close to the lag results of the whole light curves, which further assures the reliability of the obtained Hα time lags for Mrk 841.
For Mrk 817, the results are shown in Figures 6 and 7.The JAVELIN lag of the whole light curves is slightly larger than others and the χ 2 lag distributions have larger scatters compared to other methods.However, the similar shape of the extracted Hα, lagged g, and lagged SRM Hβ light curves (Lu et al. 2021) for both the whole and part of the light curves, as well as the consistent lag distributions from at least two methods, can indicate the reliability of the Hα time lags for Mrk 817.
For NGC 5548, there are not enough data for some observational seasons.We only use two years of data, which have enough observations.For the whole light curves (Figure 8), three methods also give consistent results, though the extracted Hα light curve does not match very well with the lagged g-band light curve.For part of the light curves (The data used to create this figure are available.)(Figure 9), which have simultaneous SRM Hα observations (Lu et al. 2022), the JAVELIN result is not consistent with the other two results, which means that the results for part of the light curves are not as reliable as those for the whole light curves.The reason may be that part of the light curves has fewer data points and a shorter duration.
For PG 0007 + 106, the qualities of light curves are not as good as the other four AGNs.From Table 1, the value of J/s for PG 0007 + 106 is the smallest among five AGNs in List I, which may account for the inconsistent JAVELIN results with the other two methods and the large scatters of JAVELIN lag distributions for both the whole light curves (Figure 10) and part of the light curves (Figure 11; the simultaneous Hβ light curve is from Bao et al. 2022).Therefore, we consider the results of PG 0007 + 106 not as reliable as other AGNs, which is also confirmed by the comparison between PRM Hα lags and SRM Hβ lags (see Table 2).
For PG 1440 + 356, three methods give consistent results despite the large scatters of lag distributions (Figures 12 and  13).However, by comparing our Hα lags with simultaneous SRM Hβ (Hu et al. 2021), the high correlation coefficient r of ICCF-Cut in Figure 13 panel (e) as well as the close-to-zero ICCF lag in panel (d) still make the results reliable.The large scatters of the JAVELIN and χ 2 methods probably mean that the ICCF-Cut process is more suitable for the broadband PRM.The obtained Hα lags of five AGNs in List I are listed in Table 2.
For AGNs in List II, the extracted Hα light curves are similar to the lagged g-band continuum and the lag distributions of the ICCF-Cut and JAVELIN are consistent.For six out of eight AGNs in List II, the results of the χ 2 method are also consistent with the results of the other two methods.For Mrk 1044 and PGC 3096594, the χ 2 results are much larger than the ICCF-Cut and JAVELIN results, which may result from the large observational uncertainties of the ZTF light curves.By comparing our broadband PRM results with nonsimultaneous SRM results, it can be found that our obtained Hα lags are the same as or slightly larger than the SRM Hβ lags, which is consistent with previous works and theoretical predictions that the BLR size of the Hα line is usually larger than that of the Hβ emission line.The obtained Hα lags of eight AGNs in List II are listed in Table 3. Their light curves and lag distributions are shown in the Appendix (Figures B1-B8).
For 8 out of 10 AGNs in List III, the results given by the three methods are not well consistent.The χ 2 results are consistent with the ICCF-Cut results, while the scatters of χ 2 lag distributions are larger.However, the JAVELIN lag distributions show different peaks from ICCF-Cut and χ 2 lag distributions.Therefore, we consider these results not as reliable as the results in List I and List II.For Mrk 335 and PGC 3095715, although the lag distributions of the three methods are consistent with each other, their Hα lags are more than 3 times the previous SRM Hβ lags, which are much larger than theoretical predictions.A reason may be that the broadband PRM results for these two targets may have large uncertainties.Another reason may be that the mean luminosities of the photometric observation periods are larger than those of the spectroscopic observation periods.According to the R − L relation, the time lags in these photometric observation periods are larger than the time lags in the SRM observation periods.Besides, we note that for PGC 3095715, the Hβ time lag from SRM is even smaller than the average cadence of ZTF light curves, so it is reasonable that we fail to obtain such small lags via ZTF light curves.The obtained Hα lags of 10 AGNs in List III are listed in Table 4. Their light curves and lag distributions are shown in the Appendix (Figures C1-C10).

Discussion
After correcting the extinction of the Milky Way (Schlegel et al. 1998), we use the mean flux values of the g and r bands and the spectra to obtain the continuum luminosity L 5100 .The uncertainty in the continuum luminosity is calculated from the propagation of the flux errors, which are set as the variability in the g and r bands.We then plot the distribution of R BLR for the 23 AGNs versus their L 5100 values.The result is shown in Figure 14, where we also list some results from previous SRM works (Kaspi et al. 2000;Bentz et al. 2010;Grier et al. 2017a).Our results from the Hα PRM are mostly consistent with the commonly adopted R BLR ∝ L α relationship (Panda et al. 2019).Because only g-and r-band data of ZTF are used, the redshift is limited to be smaller than 0.09.Most of the selected 23 AGNs are located in the middle of the R-L relation, which has large dispersions.With more data released and the improved quality for ZTF i-band light curves, as well as other large multiepoch photometric sky surveys in the future, we expect to expand the ranges of redshift and luminosity of our sample.
Since the 23 AGNs have previous Hβ time-lag measurements from SRM, we can compare our obtained Hα lags with them.Some previous works have found that the Hα time lags are slightly larger than the Hβ time lags when measured at the same time (Kaspi et al. 2000;Bentz et al. 2010).As shown in Figure 15, our result is consistent with this relation, which proves that our measured Hα time lags are mostly reasonable.By comparing different points in Figure 15 for Lists I, II, and III, it can be found that the AGNs with consistent lag distributions of the three methods show small scatters.It can ensure our broadband PRM results further.By comparing the results obtained with different methods in Figure 15, the ICCF-Cut results show the smallest scatters which means that the ICCF-Cut may be more suitable and convincing than the JAVELIN and χ 2 methods for the broadband PRM.Moreover, the List I sample (except PG 0007+106) generally has fewer scatters on the Hα-Hβ lag distribution than those from List II and List III, since the photometric and spectroscopic data are synchronous.Some large scatters for List II and List III samples in Figure 15 may come from the asynchrony of the photometry and the spectra.

Summary
From AGNs at redshift z < 0.09 in the ZTF DR16 catalog, we use the variability J index and the smoothness s index to select AGNs with significant variabilities and high-quality light curves.From 3537 AGNs, we select 123 AGNs and obtain the Hα time lags of 23 AGNs, which all have the SRM lag results.
By assuming that the continuum flux in the r band is equal to a fraction of the continuum flux in the g band, we use the ICCF-Cut, JAVELIN, and χ 2 methods to calculate the Hα emission line time lags from the light curves in the g and r bands.For four out of five AGNs with simultaneous SRM observations in List I, we obtain consistent results with the SRM results.For eight AGNs in List II, the extracted Hα light curves are similar to the lagged g-band light curves.For six out of the eight AGNs, the lag distributions of the three methods are consistent.For the other two AGNs in List II, the lag distributions of ICCF-Cut and JAVELIN methods are consistent, while the χ 2 lags are much larger.For 10 AGNs in List III, the inconsistency between the results obtained from three methods makes the results not as convincing as in List I and II.We still need more observational data or to improve the methods to determine reliable Hα lags.
We compare our derived Hα time lags with the Hβ R − L relationship obtained from the SRM and find that our results are consistent with previous works.By comparing the obtained Hα lags with the SRM Hβ lags, we can check the reliability of our Hα lags further.We noticed that the scatters of the ICCF-Cut results are smaller than those of the JAVELIN and χ 2 methods, which means that the ICCF-Cut may be more suitable than the JAVELIN and χ 2 methods for the broadband PRM.In general, the Hα lags obtained from the broadband PRM are slightly larger than or consistent with the Hβ lags obtained from SRM, which is consistent with previous works and theoretical predictions (e.g., Collin-Souffrin & Lasota 1988;Baldwin et al. 1995;Korista & Goad 2004).
All the results above indicate that after selecting AGNs with J index and s index, combining the ICCF-Cut, JAVELIN, and χ 2 methods is an efficient way to obtain the reliable Hα line lags with the broadband PRM.These PRM methods can be used to study the BLR sizes and BH masses of a large sample of AGNs in the era of large multiepoch photometric sky surveys (e.g., Czerny et al. 2023)

Figure 1 .
Figure 1.Spectrum of Mrk 110 and transmission functions of the ZTF broad bands.

Figure 3 .
Figure 3. Distributions of the J and s parameters of 3537 ZTF AGNs.The orange triangles represent 23 selected AGNs for which we obtain the Hα lags.

Figure 4 .
Figure 4. Light curves and lag distributions for Mrk 841.The upper left panel shows the light curves of the continuum band (g) and line band (r).The bottom left panel shows the extracted Hα light curve compared with the lagged continuum-band light curve.The three right panels show the lag distributions between the continuum band and extracted Hα light curves with the ICCF-Cut, JAVELIN, and χ 2 methods, respectively.The red line represents the median value of the lag distribution.(The data used to create this figure are available.)

Figure 5 .Figure 6 .
Figure 5.Light curves and lag distributions for Mrk 841 in the period with simultaneous SRM observation.The upper left panel shows the light curves of the continuum band (g) and line band (r).The middle and bottom left panels show the extracted Hα light curves compared with the lagged continuum band and SRM Hβ broad-line light curves.The upper right panel shows the lag distribution between the SRM Hβ and extracted Hα light curves given by ICCF.The other three panels show the lag distributions between the continuum-band and extracted Hα light curves with the ICCF-Cut, JAVELIN, and χ 2 methods, respectively.The red line represents the median value of the lag distribution.(The data used to create this figure are available.)

Figure 7 .Figure 8 .
Figure 7. Same as Figure 5 but for Mrk 817.(The data used to create this figure are available.)

Figure 9 .
Figure 9. Same as Figure 5 but for NGC 5548, except that the SRM light curve for comparison here is Hα broad-line light curve.(The data used to create this figure are available.)

Figure 11 .Figure 12 .
Figure 11.Same as Figure 5 but for PG 0007 + 106.(The data used to create this figure are available.) , such as the Legacy Survey of Space and Time (Vera C. Rubin Observatory; LSST Science Collaboration et al. 2017) and the multiband photometric survey from the Wide Field Survey Telescope (Wang et al. 2023), in the near future.These surveys will improve the observation cadence (1-3 days), enabling the application of the PRM methods along with the modifications we have proposed.

Figure 13 .
Figure 13.Same as Figure 5 but for PG 1440 + 356.(The data used to create this figure are available.)

Figure A1 .
Figure A1.Spectra of 23 AGNs used in this paper.The flux is normalized to the peak value of Hα emission line.The wavelength range shown here refers to that of ZTF r band, which is used to calculate the Hα ratio in r band (i.e., F Hα /F line in Equation (7)).

Figure B1 .
Figure B1.Same as Figure 4 but for MCG +08-11-011.(The data used to create this figure are available.)

Figure C3 .
Figure C3.Same as Figure 4 but for Mrk 290.(The data used to create this figure are available.)

Figure C9 .
Figure C9.Same as Figure 4 but for PG 2130 + 099.(The data used to create this figure are available.)

Table 1
List of 23 Selected AGNs

Table 4
Hα Lag Results (in Days) of 10 AGNs in List III