Size Of Broad-line Region Research Articles

Revisiting the Hβ Size–Luminosity Relation Using a Uniform Reverberation-mapping Analysis

We revisit the relation between active galactic nucleus (AGN) broad-line region (BLR) size and luminosity by conducting a uniform Hβ reverberation-mapping analysis for 212 AGNs with archival light curves. Our analysis incorporates three different lag measurement methods, including the interpolated cross-correlation function (ICCF), JAVELIN, and PyROA, alongside a consistently defined lag-searching window and an alias removal procedure. We find that ICCF, albeit with larger uncertainties compared to other methods, is the most reliable method based on our visual inspection of the matches between Hβ and the shifted continuum light curves. Combining this sample with the 32 AGNs from Seoul National University AGN Monitoring Project, we obtain the best-fit relation between the BLR size (R BLR) and the continuum luminosity at 5100 Å (L 5100) with a slope significantly flatter than 0.5. By selecting a subsample of 157 AGNs with the best-quality lag measurements using a set of quantitative criteria and visual inspection, we find a consistent slope and a slightly decreased intrinsic scatter. We further investigate the effect of luminosity tracers, including L 5100, Hβ luminosity (L Hβ ), [O iii] luminosity (L [O III]), and 2–10 keV hard X-ray luminosity L 2–10keV. We find that sub-Eddington and super-Eddington AGNs exhibit systematic offsets in both R BLR–L 5100 and R BLR–L Hβ relations, while they show comparable R BLR–L [O III] and R BLR–L 2–10keV relations. We discuss the potential causes for these different deviations when employing different luminosity tracers.

Broad-line Region of the Quasar PG 2130+099. II. Doubling the Size Over Four Years?

Over the past three decades, multiple reverberation mapping (RM) campaigns conducted for the quasar PG 2130+099 have exhibited inconsistent findings with time delays ranging from ∼10 to ∼200 days. To achieve a comprehensive understanding of the geometry and dynamics of the broad-line region (BLR) in PG 2130+099, we continued an ongoing high-cadence RM monitoring campaign using the Calar Alto Observatory 2.2 m optical telescope for an extra four years from 2019 to 2022. We measured the time lags of several broad emission lines (including He ii, He i, Hβ, and Fe ii) with respect to the 5100 Å continuum, and their time lags continuously vary through the years. Especially, the Hβ time lags exhibited approximately a factor of 2 increase in the last two years. Additionally, the velocity-resolved time delays of the broad Hβ emission line reveal a back-and-forth change between signs of virial motion and inflow in the BLR. The combination of negligible (∼10%) continuum change and substantial time-lag variation (over 2 times) results in a significant scatter in the intrinsic R Hβ –L 5100 relationship for PG 2130+099. Taking the consistent changes in the continuum variability time scale and the size of the BLR into account, we tentatively propose that the changes in the measurement of the BLR size may be affected by “geometric dilution”

Size and kinematics of the low-ionization broad emission line region from microlensing-induced line profile distortions in gravitationally lensed quasars

Microlensing-induced distortions of broad emission line profiles observed in the spectra of gravitationally lensed quasars can be used to probe the size, geometry, and kinematics of the broad-line region (BLR). To this end, single-epoch Mg ii or Halpha line profile distortions observed in five gravitationally lensed quasars, J1131-1231, J1226-0006, J1355-2257, J1339+1310, and HE0435-1223, have been compared with simulated ones. The simulations are based on three BLR models, a Keplerian disk (KD), an equatorial wind (EW), and a polar wind (PW), with different sizes, inclinations, and emissivities. The models that best reproduce the observed line profile distortions were identified using a Bayesian probabilistic approach. We find that the wide variety of observed line profile distortions can be reproduced with microlensing-induced distortions of line profiles generated by our BLR models. For J1131, J1226, and HE0435, the most likely model for the Mg ii and Halpha BLRs is either KD or EW, depending on the orientation of the magnification map with respect to the BLR axis. This shows that the line profile distortions depend on the position and orientation of the isovelocity parts of the BLR with respect to the caustic network, and not only on their different effective sizes. For the Mg ii BLRs in J1355 and J1339, the EW model is preferred. For all objects, the PW model has a lower probability. As for the high-ionization C iv BLR, we conclude that disk geometries with kinematics dominated by either Keplerian rotation or equatorial outflow best reproduce the microlensing effects on the low-ionization Mg ii and Halpha emission line profiles. The half-light radii of the Mg ii and Halpha BLRs are measured in the range of 3 to 25 light-days. We also confirm that the size of the region emitting the low-ionization lines is larger than the region emitting the high-ionization lines, with a factor of four measured between the sizes of the Mg ii and C iv emitting regions in J1339. Unexpectedly, the microlensing BLR radii of the Mg ii and Halpha BLRs are found to be systematically below the radius-luminosity ($R -L$) relations derived from reverberation mapping, confirming that the intrinsic dispersion of the BLR radii with respect to the $R-L$ relations is large, but also revealing a selection bias that affects microlensing-based BLR size measurements. This bias arises from the fact that, if microlensing-induced line profile distortions are observed in a lensed quasar, the BLR radius should be comparable to the microlensing Einstein radius, which varies only weakly with typical lens and source redshifts.

Spectroastrometry and Reverberation Mapping of Active Galactic Nuclei. I. The Hβ Broad-line Region Structure and Black Hole Masses of Five Quasars

We conduct a reverberation mapping (RM) campaign to spectroscopically monitor a sample of selected bright active galactic nuclei with large anticipated broad-line region (BLR) sizes adequate for spectroastrometric (SA) observations by the GRAVITY instrument on the Very Large Telescope Interferometer. We report the first results for five objects, IC 4329A, Mrk 335, Mrk 509, Mrk 1239, and PDS 456, among which Mrk 1239 and PDS 456 are for the first time spectroscopically monitored. We obtain multiyear monitoring data and perform multicomponent spectral decomposition to extract the broad Hβ profiles. We detect significant time lags between the Hβ and continuum variations, generally obeying the previously established BLR size–luminosity relation. Velocity-resolved Hβ time lags illustrate diverse, possibly evolving, BLR kinematics. We further measure the Hβ line widths from mean and rms spectra and the resulting virial products show good consistency among different observing seasons. Adopting a unity virial factor and the FWHM of the broad Hβ line from the mean spectra as a measure of velocity, the obtained black hole masses averaged over seasons are logM•/M⊙=8.02−0.14+0.09 , 6.92−0.12+0.12 , 8.01−0.25+0.16 , 7.44−0.14+0.13 , and 8.59−0.11+0.07 for the five objects, respectively. Black hole mass estimations using other line width measures are also reported. For objects with previous RM campaigns, our mass estimates are in agreement with earlier results. In a companion paper, we will employ BLR dynamical modeling to directly infer the black hole mass and thereby determine the virial factors.

AGN STORM 2. VII. A Frequency-resolved Map of the Accretion Disk in Mrk 817: Simultaneous X-Ray Reverberation and UVOIR Disk Reprocessing Time Lags

X-ray reverberation mapping is a powerful technique for probing the innermost accretion disk, whereas continuum reverberation mapping in the UV, optical, and infrared (UVOIR) reveals reprocessing by the rest of the accretion disk and broad-line region (BLR). We present the time lags of Mrk 817 as a function of temporal frequency measured from 14 months of high-cadence monitoring from Swift and ground-based telescopes, in addition to an XMM-Newton observation, as part of the AGN STORM 2 campaign. The XMM-Newton lags reveal the first detection of a soft lag in this source, consistent with reverberation from the innermost accretion flow. These results mark the first simultaneous measurement of X-ray reverberation and UVOIR disk reprocessing lags—effectively allowing us to map the entire accretion disk surrounding the black hole. Similar to previous continuum reverberation mapping campaigns, the UVOIR time lags arising at low temporal frequencies are longer than those expected from standard disk reprocessing by a factor of 2–3. The lags agree with the anticipated disk reverberation lags when isolating short-timescale variability, namely timescales shorter than the Hβ lag. Modeling the lags requires additional reprocessing constrained at a radius consistent with the BLR size scale inferred from contemporaneous Hβ-lag measurements. When we divide the campaign light curves, the UVOIR lags show substantial variations, with longer lags measured when obscuration from an ionized outflow is greatest. We suggest that, when the obscurer is strongest, reprocessing by the BLR elongates the lags most significantly. As the wind weakens, the lags are dominated by shorter accretion disk lags.

Probing the broad line region geometry and size of the gravitationally lensed quasar Q2237+0305 with microlensing time series

Lensed quasars are powerful cosmic laboratories; they are used to simultaneously probe various astrophysical phenomena. Microlensing by stars within distant galaxies acts as strong gravitational lenses of multiply imaged quasars, and provides a unique and direct measurement of the lensed quasar internal structure. Microlensing of the continuum emitting region as well as the broad-line region (BLR) is well characterized by four observable indices, μcont, μBLR, WCI (wing-core), and RBI (red-blue), measured directly from the spectra. During the 2004−2007 monitoring period, image A of the quadruply lensed system Q2237+0305 underwent a strong microlensing amplification, while image D remained unaffected. We used 35 epochs of archival spectrophotometric data of Q2237+0305 obtained with the Very Large Telescope of the European Southern Observatory to develop an independent microlensing method for estimating the geometry and size of the BLR. We measured the index time series for the C IV line and the continuum emission at 1450 Å. We built a library of the simulated microlensing index time series that reproduce the observed times series based on three representative BLR models: Keplerian disk (KD), polar wind (PW), and equatorial wind (EW). After sampling the model parameter space, we find that KD is the predominant model, while PW and EW are less likely. We infer that the system is viewed at an intermediate viewing angle i ∼ 35°, and we estimate the most likely C IV BLR half-light radius r1/2 = 51 ± 23 light days. Our results are in good agreement with previous findings in the literature and extend the validity of the index-based approach to a temporal domain.

Probing the C iv Continuum Size–Luminosity Relation in Active Galactic Nuclei with Photometric Reverberation Mapping

Reverberation mapping accurately determines virial black hole masses only for redshifts z < 0.2 by utilizing the relationship between the Hβ broad-line region (BLR) size and the 5100 Å continuum luminosity established with ∼200 active galactic nuclei. For quasars at z ∼ 2–3 determining the BLR size is time-consuming and limited by seasonal gaps, requiring, e.g., ∼20 yr of monitoring of the C iv emission lines. In this work, we demonstrate that an efficient alternative is to use a continuum size–luminosity relation, which can be obtained up to 150 times faster than BLR sizes using photometric reverberation mapping (PRM). We outline the method and its feasibility based on simulations and propose an observational strategy that can be carried out with meter-class telescopes. In particular, we focus on the ESO La Silla 2.2 m telescope as it is suitable for an efficient PRM campaign. These observations will provide the scaling factor between the accretion disk and the BLR size (for C iv-1350 Å), which is crucial for estimating the masses of black holes at higher redshifts (z ≳ 2–3).

Hα reverberation mapping from broad-band photometry of dwarf seyfert 1 galaxy NGC 4395

Abstract NGC 4395 is a dwarf Seyfert 1 galaxy with a possible intermediate-mass black hole of several $\rm {10^4}$ solar masses in its center. As a well-studied object, its broad line region size has been measured via H$\rm {\alpha }$ time lag in numerous spectroscopic reverberation mapping (SRM) and narrow-band photometric reverberation mapping (PRM) campaigns. Here we present its H$\rm {\alpha }$ time lag measurement using broad-band photometric data, with the application of our newly-developed ICCF-Cut method as well as the JAVELIN and χ2 methods. utilizing the minute-cadence multi-band light curves obtained from the $\rm {2}$m FTN and $\rm {10.4}$m GTC telescopes in recent works, we measured its H$\rm {\alpha }$ lag as approximately 40 ∼ 90 minutes from broad-band PRM. With the H$\rm {\alpha }$ emission line velocity dispersion, we calculated its central black hole mass as $\rm M_{\rm BH} = (8\pm 4) \times 10^3\, M_{\rm \odot }$. These results are comparable with previous results obtained by narrow-band PRM and SRM, providing further support to an intermediate-mass black hole in NGC 4395. In addition, our study also validates the ICCF-Cut as an effective method for broad-band PRM, which holds the potential for widespread application in the era of large multi-epoch, high-cadence photometric surveys.

The Seoul National University AGN Monitoring Project. III. Hβ Lag Measurements of 32 Luminous Active Galactic Nuclei and the High-luminosity End of the Size–Luminosity Relation

We present the main results from a long-term reverberation mapping campaign carried out for the Seoul National University AGN Monitoring Project (SAMP). High-quality data were obtained during 2015–2021 for 32 luminous active galactic nuclei (AGNs; i.e., continuum luminosity in the range of 1044–46 erg s−1) at a regular cadence, of 20–30 days for spectroscopy and 3–5 days for photometry. We obtain time lag measurements between the variability in the Hβ emission and the continuum for 32 AGNs; 25 of those have the best lag measurements based on our quality assessment, examining correlation strength and the posterior lag distribution. Our study significantly increases the current sample of reverberation-mapped AGNs, particularly at the moderate-to-high-luminosity end. Combining our results with literature measurements, we derive an Hβ broadline region size–luminosity relation with a shallower slope than reported in the literature. For a given luminosity, most of our measured lags are shorter than the expectations, implying that single-epoch black hole mass estimators based on previous calibrations could suffer large systematic uncertainties.

The sub-parsec structure of AGN with VLTI/GRAVITY

AbstractThe central parsec of AGN is a key region for the launching of winds, and near-infrared interferometry is a unique tool for its study. With GRAVITY at the VLT interferometer, we can now spatially resolve not just the hot dust continuum on milliarcsecond ‘torus’ scales through imaging but also the broad-line region (BLR) on microarcsecond scales through spectro-astrometry. We have mapped the kinematics of the BLR in seven nearby AGN, measured sizes of the hot dust for seventeen AGN, and reconstructed dust images for two AGN. BLR kinematics has allowed us to measure the BLR size and supermassive black hole mass independent of reverberation mapping. The ongoing GRAVITY+ upgrade will greatly enhance the sensitivity and sky coverage of GRAVITY, and first results demonstrate its power for AGN science at z∼2 and beyond.

Spectral Variability Studies in Active Galactic Nuclei: Exploring Continuum and Emission Line Regions in the Age of LSST and JWST

The investigation of emission line regions within active galaxies (AGNs) has a rich and extensive history, now extending to the use of AGNs and quasars as “standardizable” cosmological indicators, shedding light on the evolution of our universe. As we enter the era of advanced observatories, such as the successful launch of the JWST and the forthcoming Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), the landscape of AGN exploration across cosmic epochs is poised for exciting advancements. In this work, we delve into recent developments in AGN variability research, anticipating the substantial influx of data facilitated by LSST. The article highlights recent strides made by the AGN Polish Consortium in their contributions to LSST. The piece emphasizes the role of quasars in cosmology, dissecting the intricacies of their calibration as standard candles. The primary focus centers on the relationship between the broad-line region size and luminosity, showcasing recent breakthroughs that enhance our comprehension of this correlation. These breakthroughs encompass a range of perspectives, including spectroscopic analyses, photoionization modeling, and collaborative investigations with other cosmological tools. The study further touches on select studies, underlining how the synergy of theoretical insights and advancements in observational capabilities has yielded deeper insights into these captivating cosmic entities.

The Seoul National University AGN Monitoring Project. IV. Hα Reverberation Mapping of Six AGNs and the Hα Size–Luminosity Relation

The broad-line region (BLR) size–luminosity relation has paramount importance for estimating the mass of black holes in active galactic nuclei (AGNs). Traditionally, the size of the Hβ BLR is often estimated from the optical continuum luminosity at 5100 Å, while the size of the Hα BLR and its correlation with the luminosity is much less constrained. As a part of the Seoul National University AGN Monitoring Project, which provides 6 yr photometric and spectroscopic monitoring data, we present our measurements of the Hα lags of high-luminosity AGNs. Combined with the measurements for 42 AGNs from the literature, we derive the size–luminosity relations of the Hα BLR against the broad Hα and 5100 Å continuum luminosities. We find the slope of the relations to be 0.61 ± 0.04 and 0.59 ± 0.04, respectively, which are consistent with the Hβ size–luminosity relation. Moreover, we find a linear relation between the 5100 Å continuum luminosity and the broad Hα luminosity across 7 orders of magnitude. Using these results, we propose a new virial mass estimator based on the Hα broad emission line, finding that the previous mass estimates based on scaling relations in the literature are overestimated by up to 0.7 dex at masses lower than 107 M ⊙.

The variability of the broad-line Balmer decrement for quasars from the Sloan Digital Sky Survey reverberation mapping

ABSTRACT Based on the spectral decomposition through a code of PrepSpec, the light curves (spanning 6.5 yr in the observed frame) of the broad-line Balmer decrement, i.e. the flux ratio of the broad Hα to the broad Hβ line, are calculated for a sample of 44 Sloan Digital Sky Survey reverberation-mapped quasars (z &amp;lt; 0.53). It is found that the logarithm of the mean broad-line Balmer decrement is 0.62 with a standard deviation of 0.15 dex. The relations between the mean Balmer decrement and the supermassive black hole accretion properties (the luminosity, black hole mass, Eddington ratio, and accretion rate) are investigated and no obvious correlations are found. It is found that there are 27 quasars ($61{{\ \rm per\ cent}}$ ) showing strong negative correlations between the Balmer decrement variance and the continuum variance, i.e. the Balmer decrement would be smaller with larger continuum flux. Assuming that the dust obscuration leads to the variance in the Balmer decrement and the continuum, an expected slope is −1/3, which is not consistent with most of measured slopes. Using the interpolated cross-correlation function, the time delays between the inverse Balmer decrement and the continuum are measured for 14 quasars with the maximum correlation coefficient larger than 0.6. It suggests that the size corresponding to the Balmer decrement lag extends from the broad-line region size to the torus size.

Estimating AGN Black Hole Masses via Continuum Reverberation Mapping in the Era of LSST

Spectroscopic reverberation mapping (RM) is a direct approach widely used to determine the mass of black holes (BHs) in active galactic nuclei (AGNs). However, it is very time consuming and difficult to apply to a large AGN sample. The empirical relation between the broad-line region size and luminosity (Hβ R BLR–L) provides a practical alternative yet is subject to large scatter and systematic bias. Based on the relation between the continuum emitting region size and luminosity (R CER–L) reported by Netzer (2022), we present a new BH mass estimator via continuum RM (CRM) by comparing R CER and R BLR, assuming that the continuum lags are dominated by the diffuse continuum emission. Using a sample of 21 AGNs, we find a tight R BLR–R CER relation (scatter∼0.28 dex) and that R BLR is larger than R CER at 5100 Å by an average factor of 8.1. This tight relation enables the BH mass estimation based on the CRM combined with the velocity information. Applying the relation to rest objects in our CRM sample, we demonstrate that the predicted R BLR,CRM follows the existing Hβ R BLR–L relation well and the estimated CRM BH masses are consistent with the RM/single-epoch BH masses using Hβ. This method will provide significant applications for BH mass estimation thanks to the short continuum lags and the easily accessible high-cadence, large-area photometric data, especially in the era of Legacy Survey of Space and Time.

The Hα Broadband Photometric Reverberation Mapping of Four Seyfert 1 Galaxies

Broadband photometric reverberation mapping (PRM) has been investigated for active galactic nuclei (AGNs) in recent years, but mostly on accretion disk continuum RM. Due to the small fraction of broad emission lines in the broad band, PRM for emission lines is very challenging. Here, we present an ICCF-Cut method for broadband PRM to obtain the Hα broad-line lag and apply it to four Seyfert 1 galaxies: MCG+08-11-011, NGC 2617, 3C 120, and NGC 5548. All of them have high-quality broadband lightcurves with daily/subdaily cadences, which enable us to extract Hα lightcurves from the line band by subtracting the contributions from the continuum and host galaxy. Their extracted Hα lightcurves are compared with the lagged continuum-band lightcurves, as well as the lagged Hβ lightcurves obtained by spectroscopic RM (SRM) at the same epochs. The consistency of these lightcurves and the comparison with the SRM Hβ lags provide support for the Hα lags of these AGNs, in a range from 9 to 19 days, obtained by the ICCF-Cut, JAVELIN, and χ 2 methods. The simulations for evaluating the reliability of the Hα lags and the comparisons between the SRM Hβ and PRM Hα lags indicate that the consistency of the ICCF-Cut, JAVELIN, and χ 2 results can ensure the reliability of the derived Hα lags. These methods may be used to estimate the broad-line region sizes and black hole masses of a large sample of AGNs in large multi-epoch, high-cadence photometric surveys such as LSST in the future.

Mid-infrared dusty torus sizes in active galactic nuclei with Hβ reverberation mapping

ABSTRACT We compile optical and mid-infrared light curves from the time-domain surveys (i.e. CRTS, PTF, ZTF, and ASAS-SN) and Wide-field Infrared Survey Explorer (WISE) archive for a selected sample of active galactic nuclei (AGNs) with Hβ reverberation mapping (RM) measurements. We measure the time lags (and thus torus sizes) of W1 (∼3.4 $\mu$ m) and W2 (∼4.6 $\mu$ m) band light curves relative to the optical one using the MICA method. Through Hβ RM, the sample has well-measured AGN properties, therefore allowing us to reliably constrain the relations between torus sizes and AGN properties. We perform linear regressions for the relations between torus sizes and 5100 Å luminosities ($R\propto L_{5100}^{\beta }$ ) in two cases: β = 0.5 and β set free. The latter case yields β ≈ 0.37 ± 0.028 for both W1 and W2 bands, shallower than the expected value of 0.5, possibly due to the dependence of torus size on accretion rate. For β = 0.5, by combining with the previous K band RM measurements, we obtain the characteristic broad-line region (BLR) and tours sizes following RBLR:RK :RW1:RW2 = 1.0:6.2:9.2:11.2. We investigate the deviations of the W1 and W2 band observed torus sizes from the corresponding best-fitting relations (with β = 0.5) and find that they both are correlated with accretion rate. As the accretion rate increases, the torus sizes tend to be shortened compared to the anticipated sizes from the best-fitting relations, similar to the behaviour found in BLRs. Such behaviours can be explained by the self-shadowing effect of slim discs. This is further supported by ratios of the W1 and W2 band torus sizes to BLR sizes, which do not show significant correlations with AGN properties.

In Situ Star Formation in Accretion Disks and Explanation of Correlation between the Black Hole Mass and Metallicity in Active Galactic Nuclei

Recent observations show that the metallicity Z BLR of the broad-line region (BLR) in active galactic nuclei (AGNs) is solar to supersolar, which is positively correlated with the mass of supermassive black holes (M BH) and does not evolve with the redshift up to z ∼ 7. We revisit the M BH−Z BLR correlation with more AGNs with M BH ∼ 106–8 M ⊙ and find that the positive correlation becomes flat in the low-mass range. It is known that the outer part of accretion disks is gravitationally unstable and can fragment into stars. Considering the star formation and supernovae in the outer AGN disk, we calculate the metal enrichment and find that the positive M BH−Z BLR correlation can be roughly reproduced if the stellar mass distribution is “top heavy.” We find that the observed BLR size is more or less similar to the self-gravity radius of the AGN disk, which suggests that the BLR may be closely correlated with the underlying accretion process.

Spectroastrometric Reverberation Mapping of Broad-line Regions

Spectroastrometry measures source astrometry as a function of wavelength/velocity. Reverberations of spectroastrometric signals naturally arise in broad-line regions (BLRs) of active galactic nuclei (AGNs) as a result of the continuum variations that drive responses of the broad emission lines with time delays. Such signals provide a new diagnostic for mapping BLR kinematics and geometry, complementary to the traditional intensity reverberation mapping (RM) technique. We present a generic mathematical formalism for spectroastrometric RM and show that under realistic parameters of a phenomenological BLR model, the spectroastrometric reverberation signals vary on a level of several to tens of microarcseconds, depending on the BLR size, continuum variability, and angular-size distance. We also derive the analytical expressions of spectroastrometric RM for an inclined ring-like BLR. We develop a Bayesian framework with a sophisticated Monte Carlo sampling technique to analyze spectroastrometric data and infer the BLR properties, including the central black hole mass and angular-size distance. We demonstrate the potential of spectroastrometric RM in spatially resolving BLR kinematics and geometry through a suite of simulation tests. The application to realistic observation data of 3C 273 obtains tentative, but enlightening results, reinforcing the practical feasibility of conducting spectroastrometric RM experiments on bright AGNs with the operating Very Large Telescope Interferometer as well as possibly with the planned next-generation 30 m class telescopes.

Toward measuring supermassive black hole masses with interferometric observations of the dust continuum

This work focuses on active galactic nuclei (AGNs) and on the relation between the sizes of the hot dust continuum and the broad-line region (BLR). We find that the continuum size measured using optical/near-infrared interferometry (OI) is roughly twice that measured by reverberation mapping (RM). Both OI and RM continuum sizes show a tight relation with the Hβ BLR size, with only an intrinsic scatter of 0.25 dex. The masses of supermassive black holes (BHs) can hence simply be derived from a dust size in combination with a broad line width and virial factor. Since the primary uncertainty of these BH masses comes from the virial factor, the accuracy of the continuum-based BH masses is close to those based on the RM measurement of the broad emission line. Moreover, the necessary continuum measurements can be obtained on a much shorter timescale than those required monitoring for RM, and they are also more time efficient than those needed to resolve the BLR with OI. The primary goal of this work is to demonstrate a measuring of the BH mass based on the dust-continuum size with our first calibration of the RBLR–Rd relation. The current limitation and caveats are discussed in detail. Future GRAVITY observations are expected to improve the continuum-based method and have the potential of measuring BH masses for a large sample of AGNs in the low-redshift Universe.

Supermassive Black Hole and Broad-line Region in NGC 5548: Results from Five-season Reverberation Mapping

NGC 5548 is one of the active galactic nuclei (AGNs) selected for our long-term spectroscopic monitoring with the Lijiang 2.4 m telescope, aiming at investigating the origin and evolution of broad-line regions (BLRs), accurately measuring the mass of supermassive black holes (SMBHs), and understanding the structure and evolution of the AGN. We have performed five-season observations for NGC 5548 with the median sampling interval ranging from 1.25 to 3 days. The light curves of the 5100 Å continuum and broad emission lines are measured after subtracting contamination of the host galaxy starlight. The time lags of the broad He ii, He i, Hγ, and Hβ lines with respect to the 5100 Å continuum are obtained for each season and their mean time lags over the five seasons are 0.69, 4.66, 4.60, and 8.43 days, respectively. The Hγ and Hβ velocity-resolved lag profiles in the seasons of 2015, 2018, 2019, and 2021 are constructed, from which an “M-shaped” structure is found in 2015 but disappears after 2018. Our five-season reverberation mapping (RM) yields an average virial SMBH mass of M •/107 M ⊙ = 14.22, with a small standard deviation of 1.89. By combining the previous 18 RM campaigns and our five-season campaign for NGC 5548, we find that there exists a time lag of 3.5 yr between the changes in the BLR size and optical luminosity. In addition, we construct the BLR radius−luminosity relation and the virial relation for NGC 5548.