A Reverberation Mapping Study of a Highly Variable Active Galactic Nucleus 6dFGS gJ022550.0-060145

We use LCOGT observations (MJD 59434−59600) with a total exposure time of ≃50 hr and a median cadence of 0.5 day to measure the interband time delays (with respect to u) in the g, r, and i continua of a highly variable active galactic nucleus (AGN), 6dFGS gJ022550.0-060145. We also calculate the expected time delays of the X-ray reprocessing of a static Shakura–Sunyaev disk according to the source's luminosity and virial black hole mass; the two parameters are measured from the optical spectrum of our spectroscopic observation via the Lijiang 2.4 m telescope. It is found that the ratio of the measured time delays to the predicted ones is 2.6−1.3+1.3 . With optical light curves (MJD 53650–59880) from our new LCOGT and archival Zwicky Transient Facility, Pan-STARRS, Catalina Sky Survey, and ATLAS observations, and Wide-field Infrared Survey Explorer (WISE) data (MJD 55214−59055), we also measured time delays between WISE W1/W2 and the optical emission. W1 and W2 have time delays (with respect to V), 9.6−1.6+2.9×102 days and 1.18−0.10+0.13×103 days in the rest frame, respectively; hence, the dusty torus of 6dFGS gJ022550.0-060145 should be compact. The time delays of the W1 and W2 bands are higher than the dusty torus size–luminosity relationship of Lyu et al. By comparing the infrared and optical variability amplitude, we find that the dust-covering factors of the W1 and W2 emission regions are 0.7 and 0.6, respectively. Future broad emission-line reverberation mapping of this target and the results of this work enable us to determine the sizes of the AGN main components simultaneously.


Introduction
Active galactic nuclei (AGNs) are powered by the accretion of gas to their central supermassive black holes (SMBHs; e.g., Page & Thorne 1974) and emit a continuous spectrum of radiation from extreme ultraviolet to infrared (IR) wavelengths (e.g., Burbidge 1967;Shields 1978).Measuring the size and structure of the accretion disk is essential for understanding the SMBH accretion physics and probing the cosmology via gravitationally lensed quasars (Tie & Kochanek 2018).
In theory, researchers developed several accretion disk models.For instance, the standard geometrically thin but optically thick disk model (Shakura-Sunyaev disk (SSD); Shakura & Sunyaev 1973) with a moderate dimensionless accretion rate (i.e., the ratio of the mass accretion rate to the Eddington accretion rate), the optically and geometrically thick disk (SLIM; Abramowicz et al. 1988) with a high dimensionless accretion rate, the advection-dominated accretion flow (ADAF) model (Narayan & Yi 1995) with a low accretion rate, and the luminous hot accretion flow (LHAF) model (Yuan et al. 2007).It is generally believed that the accretion mode of a luminous AGN is an SSD.
Due to the small angular size of an AGN central engine, it is challenging to spatially resolve its structure using current facilities.To overcome this limitation, researchers adopt the reverberation-mapping (RM) technique to resolve the central engine by measuring time delays between light curves at different wavelengths (e.g., Clavel et al. 1991;Cackett et al. 2021).For an SSD, the temperature distribution follows the relation T(R) ∝ R −4/3 , where T and R are the effective temperatures and the disk radius, respectively.Hence, one would expect that the light travel time delay across the SSD obeys the lag-wavelength relation of τ(λ) ∝ λ 4/3 .However, measuring the time delay of the continuum emission is challenging because of small sizes (∼1 lt-day) and weak variations (∼10%).Hence, high-cadence observations with high signal-to-noise ratios (S/Ns) are required.
Recent observations (e.g., Fausnaugh et al. 2016;McHardy et al. 2018;Guo et al. 2022b;Cackett et al. 2023;Fian et al. 2023) reveal that the measured AGN continuum time delays are 2 or 3 times larger than the SSD prediction.The discrepancy between the predicted and measured AGN continuum time delays challenges the black hole accretion theory and is commonly referred to as the "accretion disk oversize" problem.
Several explanations are proposed for the "accretion disk oversize" problem.For instance, the disk luminosity is underestimated by up to an order of magnitude (Gaskell 2017); the X-ray corona height can be large (Kammoun et al. 2021); the SSD can have strong winds and can produce a flat disk temperature profile (Sun et al. 2019); the SSD might emit non-blackbody radiation (Hall et al. 2018); the time-dependent SSD and corona are magnetically coupled (Sun et al. 2020); diffuse emission from the inner parts of the broad-line regions contributes significantly to the observed continua (e.g., Cackett et al. 2018Cackett et al. , 2022;;Sun et al. 2018b); the disk has axisymmetric temperature perturbations (Neustadt & Kochanek 2022); and the accretion disk may have a steep rim or rippled structures (Starkey et al. 2023).The universal validity of these explanations has yet to be proven.
Recent observations of high-luminosity AGNs suggest that the measured time delays are roughly consistent with theoretical expectations (Homayouni et al. 2019;Yu et al. 2020).Moreover, Li et al. (2021) found an inverse correlation between the ratio of the measured time delay to the SSD prediction and AGN luminosity (also see Guo et al. 2022a).This correlation is a promising avenue for understanding the physical nature of the "accretion disk oversize" problem.The anticorrelation should be verified with more disk RM observations.
The AGN unification model suggests that the central region of an AGN is surrounded by a geometrically and optically thick dusty structure known as the "dusty torus" (for a recent review, see, e.g., Netzer 2015).The structure of the dusty torus is unknown, but it is thought to be approximately annular.The continuum emission reaching the dust regions is scattered and absorbed by dust particles and then re-emitted in the IR.The ratio of the AGN's IR luminosity to its optical luminosity (L IR /L optical ) probes the fraction of the solid angle covered by dust, which is the dust-covering factor.IR RM allows us to resolve the geometric structure of the dusty torus (Barvainis 1992).
In this work, we use the disk and IR RM to probe the disk and torus sizes of a highly variable AGN, 6dFGS gJ022550.0-060145.The paper is organized as follows.Section 2 describes the observations and data.Section 3 presents the analysis of the time series.Our results are discussed in Section 4. We summarize our conclusions in Section 5.
Throughout this paper, we adopt the cosmology with Ω m = 0.3, Ω Λ = 0.7, and H 0 = 70 km s −1 Mpc −1 .The reported time delays are in the rest frame unless otherwise specified.

Target and Observations
Our target is 6dFGS gJ022550.0-060145,which is located at (J2000) R.A. = 02:25:50.04,decl.= −06:01:45.1,and with a redshift of z = 0.318 (Monroe et al. 2016).This source is highly variable according to the Catalina Sky Survey (CSS; 1 Drake et al. 2009) and Zwicky Transient Facility (ZTF; 2 Masci  et al. 2018) observations (Section 2.1).We use the Las Cumbres Observatory Global Telescope (LCOGT3 ) in four optical bands (u, g, r, and i) from 2021 August 3 to 2022 January 16 to intensively monitor this source.The median cadence of our LCOGT observations is 0.5 day.To probe the intrinsic AGN variability, we require that the S/Ns for our observations are higher than 50 for the g (∼4700 Å), r (∼6215 Å), and i (∼7545 Å) bands; for the u band (∼3540 Å), the S/N is larger than 40 since its variability amplitude is expected to be higher than other bands.Hence, for the air mass 1.4, the required exposure time durations for the u, g, r, and i bands are 650, 90, 60, and 60 s, respectively.The total LCOGT exposure time is ∼50 hr.

Multiband Light Curves
We use the Python 3-based Automated Photometry Of Transients (AutoPhOT; 4 Brennan & Fraser 2022) package to perform point-spread function (PSF) photometry on the LCOGT images of 6dFGS gJ022550.0-060145.AutoPhOT is a convenient automated pipeline to estimate the image PSF and perform the PSF fitting and zero-point calibration.We calibrate the g, r, i, and u magnitudes against the custom catalog from the 16th Data Release of the Sloan Digital Sky Surveys5 (Ahumada et al. 2020).Full details of all optical photometric measurements determined with AutoPhOT are given in the Appendix.The light curves are shown in Figure 1 and given in Table 1.
We have g-and r-band light curves from LCOGT and ZTF.To merge them into new g-and r-band light curves and improve the cadences, we performed intercalibrations to ensure light curves from different telescopes were on the same flux scale.Our intercalibration process was as follows.First, we calculated the difference between the mean LCOGT and ZTF g (r) magnitudes, i.e., mag mag lco ztf .Note that we only considered ZTF observations with MJD > 59400 and MJD < 59650 for the intercalibration.Second, the difference was added to the ZTF g (r) light curves, and the results were "appended" to the LCOGT g (r) observations.
Our target was also observed by the Wide-field IR Survey Explorer (WISE; 8 Wright et al. 2010) and the Near-Earth Object WISE Reactivation mission (NEOWISE; 9 Mainzer et al. 2011)  in the W1 and W2 bands.WISE scanned the sky every 6 months except in the hibernation phase (from 2011 February 1 to 2013 October 3).We reject low-quality WISE observations with the flags "qi_fact" < 1, "SSA" < 5, and "moon_mask" = 1.The remaining data points are rebinned by every 180 days; in the rebin, we use the median value whose uncertainty is estimated via the average absolute deviation.The rebinned light curves are shown in Figure 2. Like optical observations, WISE W1 and W2 light curves show evident mid-IR variations.
To compare the optical long-term light curves with the extensive yet sporadic WISE data, we construct a long synthetic V-band light curve from the LCOGT, ZTF, CSS, PS1, and ATLAS data.First, we convert the ATLAS o and c magnitudes into g and r magnitudes following Equation (1) (Tonry et al. 2018): Second, we convert all g and r magnitudes into the synthetic V-band magnitudes by using Equation (2) (Jester et al. 2005): Third, we rebin the synthetic V-band magnitudes every 50 days (the bottom panel of Figure 2).The rebinned V-band light curve was used to determine the correlation coefficients and time delays between the V and WISE bands.Both the WISE and V-band light curves are irregularly sampled and interpolations are required in the cross-correlation analysis (see Section 3.1).We use the rebinned light curves rather than the raw data to ensure that the interpolation is robust and not sensitive to possible outliers in the raw data.

Optical Spectrum
We aim to use the SSD to predict the time delays of 6dFGS gJ022550.0-060145and compare the predicted time delays with the measured ones.To do so, we need to measure the black hole mass (M BH ) of our target.We use the Yunnan Faint Object Spectrograph and Camera (YFOSC) mounted on the Lijiang 2.4 m telescope at the Yunnan Observatories of the Chinese Academy of Sciences to take a high S/N optical spectrum of our source on 2022 November 20.The YFOSC has a 2k × 4k back-illuminated CCD detector (Lu et al. 2019;Wang et al. 2019).We adopt the "grism8" configuration with a 2 5 slit.The corresponding wavelength coverage and resolution are 3858-7330 Å and 4900, respectively.The exposure time is 30 minutes, and the corresponding spectral S/N is 19.We employed IRAF V2.17 software to perform the spectroscopic reduction.The reduction process includes bias correction, flat correction, spectral extraction, and wavelength calibration.By rotating the long slit, we exposed the object star with a nearby comparison star simultaneously.The comparison star is used as the standard to do the flux calibration and telluric correction (for more details, please see Lu et al. 2021).
We perform quasar spectral decomposition analyses to the Lijiang 2.4 m spectrum following our previous work (e.g., Sun et al. 2015).The adopted continuum model consists of a power law and the iron template of Vestergaard & Wilkes (2001).Three Gaussians are used to fit the continuum-subtracted broad emission lines.As for narrow emission lines, we use a single Gaussian to fit each one.The best-fitting model is obtained by minimizing the χ 2 statistic.The full width at half-maximum (FWHM) of each bestfitting broad emission-line profile (a summation of the three Gaussian components) is measured.The continuum luminosity at the rest frame 5100 Å(5100 ÅL 5100 Å ) and the Hα luminosity (L Hα ) is also calculated from the best-fitting power-law model and the Hα broad emission-line profile, respectively.Figure 3 shows our optical spectrum fitting results.Some best-fitting parameters are shown in Table 2.Then, we use the Hα and Hβ virial mass estimators to estimate M BH (i.e., Equations ( 5) and (10) in  where M e is the solar mass and the coefficients a 1 , a 2 , b 1 , b 2 , c 1 , and c 2 are 0.379, 0.91, 0.43, 0.5, 2.1, and 2, respectively.(Bentz et al. 2009).Recently, it has been found that the BLR radius depends upon both the AGN luminosity and the Eddington ratio (e.g., Du et al. 2016Du et al. , 2018;;Fonseca Alvarez et al. 2020), i.e., the BLR radius-luminosity relation of Bentz et al. (2009) can significantly overestimate the true BLR size for high Eddington ratio sources.The Eddington ratio of our target is low because L AGN /L Edd = 0.23 ± 0.01, where L AGN is the bolometric luminosity (see Equation (5)) and L Edd is the Eddington luminosity.Therefore, we use the BLR radius-luminosity relation (i.e., Equation (2) in Bentz et al. 2009) to roughly estimate R Hβ , which is -+ 83.5 0.6 0.5 lt-day.

Time Delay
To estimate time delays between each band relative to the u band for 6dFGS GJ022550.0-060145,we use PyCCF (Sun et al. 2018a), which is a Python tool to obtain the interpolated cross-correlation coefficient (r) as a function of the time lag.The lag ranges of PyCCF are from −60 to 60 days (which are significantly longer than our expected time delays, i.e., several days), with a uniform step of 0.7 day (i.e., roughly 1.5 times the median cadence).The measured lags are estimated from the centroids of the interpolated cross-correlation functions (ICCFs), i.e., the r-weighted mean lags whose > r r 0.9 max .PyCCF employs the random subset selection and flux redistribution to assess the underlying distribution of the time delay.The ICCFs and time delay distributions are shown in the upper-left and lower-left panels of Figure 4.The 50th, 84th, and 16th percentiles of the distributions are the measured time delay and the 1σ upper and lower limits.The time delay results of the g, r, and i bands (with respect to u) are 3.8 2.3 2.5 days, respectively.The dusty torus produces IR emissions.Therefore, measuring the time delays of the W1 and W2 bands (with respect to the optical emission) can probe the sizes of the dusty torus.We again use PyCCF to measure the time delay of the WISE W1 (or W2) light curve with respect to the V-band light curve.The lag ranges of PyCCF are from −200 to 3000 days, with a uniform step of 50 days.We use the asymmetric lag ranges because, physically speaking, the dust emission should respond to optical variations with significant time delays.The 3 lt-day, respectively.Hence, the BLR radius inferred from the BLR radius-luminosity relation is smaller than the dust reverberation radius by a factor of 11 ∼ 14.This factor is larger than those in Koshida et al. (2014).In addition, the emission regions of W1 and W2 are statistically identical to each other.

The Damping Timescale
Quasar UV/optical light curves are often fitted by the damped random walk (DRW) model (e.g., Kelly et al. 2009;Sun et al. 2018b;Burke et al. 2021).The covariance matrix of the DRW model is s t t exp 2 damping , where Δt, σ, and t damping are the time interval between two observations, the short-term variability amplitude, and the damping timescale.It is often speculated that the damping timescale is closely related to quasar properties (e.g., Kelly et al. 2009;Sun et al. 2018b).For instance, Burke et al. (2021) obtain the relationship between the DRW damping timescale and SMBH mass: Meanwhile, it is stressed that the damping timescale can easily be biased unless the intrinsic t damping is less than 10% of the light-curve duration (e.g., Kozłowski 2017;Hu et al. 2024).The synthetic V-band light curve of our target has a long duration of ∼6230 days (observed frame), enabling us to robustly measure the damping timescale since the expected damping timescale in the observed frame is only 109 (1 + z) = 143.7 days (Equation (4); Burke et al. 2021).We fit the synthetic V-band light curve with the DRW model via JAVELIN 10 (Zu et al. 2011, 2013).We search the best-fitting DRW parameters by Markov Chain Monte Carlo (MCMC) sampling and obtain the amplitude s = -+ 0.19 0.04 0.06 mag and the rest-frame damping timescale = -+ t 7.5 10 damping,obs 2.9 7.1 2 days.Our measured damping timescale is about 7 times larger than the expected value.Hence, it might be that the damping timescale predicted by Equation (4) (Burke et al. 2021) is underestimated (Zhou et al. 2024).

Discussion
In this section, we discuss the accretion disk and dusty torus sizes of 6dFGS GJ022550.0-060145according to the measured time delays.

Accretion Disk Size
We estimate the bolometric luminosity (L AGN ) from 5100 Å L 5100 Å with the quasar bolometric correction of Runnoe et al. (2012): and the result is . According to the SSD, the expected time delay (τ SSD ; with respect to the u band) of 6dFGS gJ022550.0-060145as a function of the rest-frame wavelength is (e.g., Fausnaugh et al. 2016;Li et al. 2021) where 0.23 0.01 0.01 is the ratio of L AGN to the Eddington luminosity, and λ u is the rest-frame u-band wavelength.Note that this formula is valid if the radiative efficiency is η = 0.1.We compare the measured time delays (red stars) against the SSD predictions (the black curve) in Figure 5.We use emcee11 (Foreman-Mackey et al. 2013) to fit Equation (7) to the restframe time delay measurements of the g (∼3566 Å in the rest frame), r (∼4715 Åin the rest frame), and i (∼5725 Å in the rest frame) bands relative to the u band (∼2686 Å in the rest frame), which are 2.3 2.2 3.0 , and 3.8 2.3 2.5 days (Section 3.1), respectively.
where τ 0 is a free parameter, λ is the rest-frame wavelength, and λ u is the rest-frame wavelength of the u band.The fitting method is via the maximum likelihood method, and the likelihood is , where τ obs is the measured rest-frame time lag, σ τ is the 1σ uncertainty of τ obs , and τ th is given by Equation (7).The best-fit value of τ 0 is - + 2.5 1.1 1.2 , and the best-fitting relation is shown as the red curve in Figure 5. Comparing τ 0 with τ 0,SSD , we find that the ratio of the former to the latter is 1.3 (the uncertainties are estimated via MCMC).This ratio seems larger than unity, albeit with substantial uncertainties.Many previous works also suggest the "accretion disk oversize" problem (e.g., Fausnaugh et al. 2016;McHardy et al. 2018;Guo et al. 2022b;Fian et al. 2023;Sharp et al. 2024), i.e., the observed time lags are about 3 times larger than the SSD prediction.Moreover, Li et al. (2021) propose that this ratio of the observed to SSD time lag inversely correlates with the AGN luminosity (see also Guo et al. 2022a).Given its larger uncertainties, 6dFGS gJ022550.0-060145fits the anticorrelation found by Li et al. (2021) and Guo et al. (2022a).Future better time-lag measurements of this source can test the anticorrelation and provide additional clues to the "accretion disk oversize" problem.
Another notable feature is that the time lag of g (with respect to u) seems to be larger than the time lags of r and i (with respect to u).Suppose this feature is real rather than due to statistical uncertainties.In that case, the feature might be related to the lag excess in the Balmer jump (whose rest-frame wavelength is ∼3600 Å), as seen in some local AGNs (e.g., Cackett et al. 2018, 2023, andreferences therein).
Interband time lags are often interpreted as the X-ray light travel time differences across different disk emission regions.In this idea, the variable X-ray emission can illuminate the accretion-disk surface and is reprocessed as variable UV/optical emission (e.g., Krolik et al. 1991;Cackett et al. 2007).If so, the X-ray luminosity should be comparable to the disk power for our highly variable target (a similar argument is made by Dexter et al. 2019 for a changing-look quasar).We estimate the rest-frame monochromatic luminosity of the u band using the average magnitude (∼17.315) of our LCOGT observations, which is L u = 10 30.03 erg s −1 Hz −1 ; at the redshift of 0.318, the rest-frame effective wavelength for the u band is 2686 Å.Hence, we expect the rest-frame monochromatic luminosity at 2500 Å, L 2500 Å ; L u .Then, we estimate the rest-frame monochromatic luminosity at 2 keV, L 2 keV , via the well-known empirical relation between L 2 keV and L 2500 Å (e.g., Steffen et al. 2006): i.e., L 2 keV = 10 26.15 erg s −1 Hz −1 .For the power-law spectrum with a photon index of −2, the total X-ray luminosity L X ; 2 keVL 2 keV = 7 × 10 43 erg s −1 .The ratio of L X to L AGN (the bolometric luminosity) is only 2.3%.Hence, the observed X-ray emission is not powerful enough to drive the observed optical variations unless the corona's X-ray emission is extremely anisotropic.The same conclusion is obtained by Dexter et al. (2019) and Marculewicz et al. (2023), who obtain interband time lags for an X-ray weak quasar.The recent threedimensional magnetohydrodynamic simulations of an AGN accretion disk also suggest that X-ray is unlikely to be the main driver of UV/optical variations (Secunda et al. 2023).The UV reprocessing (Gardner & Done 2017) or magnetic coupling between the corona and disk (Sun et al. 2020) may play an important role in driving UV/optical coordinated variations with interband lags.0.8 0.5 0.7 , indicating that the torus structure is compact.
We can use the V-band light curve and the time delaycorrected WISE light curves to infer the torus covering factor, which is defined as where ΔL IR and ΔL V are the luminosity variability amplitudes of the IR and optical flares, respectively.The corresponding covering factors for WISE W1 and W2 are 0.7 and 0.6, respectively.These covering factors are similar to the results obtained by Stalevski et al. (2016) via the IR-to-bolometric luminosity ratio.We can compare the disk sizes with BLR and torus sizes.According to Equation (7), the size of the i band is ;6.8 lt-day, which is smaller than the expected self-gravity radius (12 ltday; Lobban & King 2022) by a factor of ∼2.The BLR size is expected to be -+ 83.5 0.6 0.5 lt-day according to the BLR sizeluminosity relation (Section 2.2), which is ∼7 times larger than the self-gravity radius.Following Lyu et al. (2019; see their Equation (9)), we can estimate the dust sublimation radius from the luminosity (also see Barvainis 1987), which is R sub ; 800 lt-day.According to the WISE and optical light curves, the torus size in W1/W2 is ∼1000 lt-day (Section 3.1); the WISE W1/W2 torus size is close to R sub and is ∼10 times larger than the BLR size, which is qualitatively consistent with the AGN unification model.The measured torus size can be reasonably treated as the outer boundary of the BLR.Hence, the BLR should be a very extended structure, roughly consistent with the dust-inflated accretion disk producing the BLR (e.g., Baskin & Laor 2018).

Summary
We used LCOGT to monitor a highly variable AGN, 6dFGS gJ022550.0-060145.Continuum lags between the u, g, r, and i bands have been detected in our target.Here are our main conclusions: 1.The rest-frame time delays of the g, r, and i bands with respect to the u band are 3 days, respectively.The two time delays are close, which means that the dusty torus of 6dFGS gJ022550.0-060145 is relatively dense.5.The measured W1 and W2 time delays (with respect to the optical emission; Figure 6) are larger than the IR lag-luminosity relation of Lyu et al. (2019).The dustcovering factors of the W1 and W2 emission regions are 0.7 and 0.6, respectively.
Future continuum RM of AGNs with various M BH , L AGN , and other properties (e.g., the X-ray intensity; e.g., Marculewicz et al. 2023) can resolve the accretion disk oversize problem and critically test the SMBH accretion physics.target by 1 ∼ 3 mag; and (3) the stars' variability amplitudes at the g, r, and i bands are smaller than 3% according to their Pan-STARRS light curves (Flewelling et al. 2020).A total number of 11 standard stars are selected, and the resulting standard star catalog is used by AutoPhOT.

Figure 1 .
Figure 1.The light curves of 6dFGS gJ022550.0-060145,observed by LCOGT for the u, g, r, and i bands.

Figure 2 .
Figure 2. The multiband light curves of 6dFGS GJ022550.0-060145.Light curves in the top panel are from PS1, ATLAS, CSS, ZTF, and LCOGT.The second and third panels show the WISE W1 and W2 light curves.The bottom panel presents the rebinned synthetic V-band light curve.

Figure 3 .
Figure3.Spectroscopic decomposition results for 6dFGS gJ022550.0-060145.The left and right panels are for Hα and Hβ, respectively.The dark-blue dashed curves and red solid curves represent the data and best-fitting models, respectively.The purple and green curves are for the power-law continua and the best-fitting iron templates.The light-blue dashed and yellow curves correspond to the narrow and broad emission lines, respectively.
CCFs and time delay distributions are shown in the upper-right and lower-right panels of Figure 4.The results are -W2).That is, the distances of W1 and W2 to the V band are -

Figure 4 .
Figure 4.The PyCCF time delay measurements.The upper-left and upper-right panels are the optical and IR CCFs.The lower-left panel shows the rest-frame time delays of g, r, and i (with respect to u).The upper-right panel demonstrates the time delays of WISE W1 and W2 (with respect to V ).

4. 2 .
The Dusty Torus of 6dFGS gJ022550.0-060145We present our target on the IR time delay-L AGN plane (see Figure 6) of Lyu et al. (2019).Comparing with the IR time delay-L AGN of Lyu et al. (2019), 6dFGS gJ022550.0-060145has larger time delays in the W1 (by a factor of - bands.Similar to Lyu et al. (2019), we also find the time delay ratio between W1 and W2 is -+

Figure 5 .
Figure5.Time delays (with respect to the u band) as a function of wavelengths in the rest frame.The black curve shows the SSD predictions for 6dFGS gJ022550.0-060145.The red solid curve is the best-fitting relationship; the red dashed curves correspond to the 1σ confidence intervals.

Figure 6 .
Figure6.The rest-frame time delay between W1 (W2) and the optical emission.The left and right panels are for W1 and W2, respectively.In each panel, the gray dots are the Palomar-Green quasars ofLyu et al. (2019), and the blue lines are their best-fitting relations and 1σ confidence ranges.The red star represents 6dFGS GJ022550.0-060145.
We cannot use the RM to obtain the size of the broad-line region (BLR) because of the lack of broad emission-line light curves.Early RM studies suggest that the Hβ BLR size (R Hβ ) correlates tightly with 5100 ÅL 5100 Å Burke et al. (2021)g timescale is larger than the t damping -M BH relation ofBurke et al. (2021)by a factor of 7. 4. Using optical data from ZTF, PS1, CSS, and ATLAS, and the WISE IR light curves, we have measured time delays of IR W1 and W2 bands with optical emission, and the results are -