Reverberation Mapping Data Research Articles

Empirical Models of the Hβ Broad Emission Line Gas Density Field

Abstract We present the second iteration of the caramel-gas code, an empirical model of the broad-line region (BLR) gas density field. Building on the initial development and testing of caramel-gas, we expand the meaning of the model parameter α, which initially represented only the power-law index of the dependency of emissivity on radial distance. In this work, we test a more generalized radial power-law index, α, that also includes a description of the effective emitting size(s) of the BLR structure as a function of radial distance. We select a sample of 10 active galactic nuclei (AGN) from three different Lick AGN Monitoring Project campaigns to further validate the caramel-gas code and test the generalized radial power-law index, α. Our results confirm that the caramel-gas results are in general agreement with the published results determined using the original caramel code, further demonstrating that our forward modeling method is robust. We find that a positive radial power-law index is generally favored and propose three possible scenarios: (i) the BLR structure has increasing effective emitting size(s) at larger radial distances from the central source, (ii) emission is concentrated at the outer edges of the BLR, and (iii) stronger theoretical assumptions are needed to break the degeneracies inherent to the interpretation of reverberation mapping data in terms of underlying gas properties.

Broad-line region geometry from multiple emission lines in a single-epoch spectrum

The broad-line region (BLR) of active galactic nuclei (AGNs) traces gas close to the central supermassive black hole (BH). Recent reverberation mapping (RM) and interferometric spectro-astrometry data have enabled detailed investigations of the BLR structure and dynamics as well as estimates of the BH mass. These exciting developments have motivated comparative investigations of BLR structures using different broad emission lines. In this work, we have developed a method to simultaneously model multiple broad lines of the BLR from a single-epoch spectrum. We applied this method to the five strongest broad emission lines (Hα, Hβ, Hγ, Paβ, and He Iλ5876) in the UV-to-near-IR spectrum of NGC 3783, a nearby Type I AGN that has been well studied by RM and interferometric observations. Fixing the BH mass to the published value, we fit these line profiles simultaneously to constrain the BLR structure. We find that the differences between line profiles can be explained almost entirely as being due to different radial distributions of the line emission. We find that using multiple lines in this way also enables one to measure some important physical parameters, such as the inclination angle and virial factor of the BLR. The ratios of the derived BLR time lags are consistent with the expectation of theoretical model calculations and RM measurements.

Correcting the Contamination of Second-order Spectra: Improving Hα Measurements in Reverberation Mapping Campaigns

Long-term spectroscopic monitoring campaigns on active galactic nuclei (AGNs) provide a wealth of information about its interior structure and kinematics. However, a number of the observations suffer from the contamination of second-order spectra (SOS) which will introduce some undesirable uncertainties at the red side of the spectra. In this paper, we test the effect of SOS and propose a method to correct it in the time domain spectroscopic data using the simultaneously observed comparison stars. Based on the reverberation mapping (RM) data of NGC 5548 in 2019, one of the most intensively monitored AGNs by the Lijiang 2.4 m telescope, we find that the scientific object, comparison star, and spectrophotometric standard star can jointly introduce up to ∼30% SOS for Grism 14. This irregular but smooth SOS significantly affects the flux density and profile of the emission line, while having little effect on the light curve. After applying our method to each spectrum, we find that the SOS can be corrected effectively. The deviation between corrected and intrinsic spectra is ∼2%, and the impact of SOS on time lag is very minor. This method makes it possible to obtain the Hα RM measurements from archival data provided that the spectral shape of the AGN under investigation does not have a large change.

Modelling photometric reverberation mapping data for the next generation of big data surveys. Quasar accretion discs sizes with the LSST

ABSTRACT Photometric reverberation mapping can detect the radial extent of the accretion disc (AD) in Active Galactic Nuclei by measuring the time delays between light curves observed in different continuum bands. Quantifying the constraints on the efficiency and accuracy of the delay measurements is important for recovering the AD size-luminosity relation, and potentially using quasars as standard candles. We have explored the possibility of determining the AD size of quasars using next-generation Big Data surveys. We focus on the Legacy Survey of Space and Time (LSST) at the Vera C. Rubin Observatory, which will observe several thousand quasars with the Deep Drilling Fields and up to 10 million quasars for the main survey in six broadband filter during its 10-yr operational lifetime. We have developed extensive simulations that take into account the characteristics of the LSST survey and the intrinsic properties of the quasars. The simulations are used to characterize the light curves from which AD sizes are determined using various algorithms. We find that the time delays can be recovered with an accuracy of 5 and 15 per cent for light curves with a time sampling of 2 and 5 d, respectively. The results depend strongly on the redshift of the source and the relative contribution of the emission lines to the bandpasses. Assuming an optically thick and geometrically thin AD, the recovered time-delay spectrum is consistent with black hole masses derived with 30 per cent uncertainty.

CARAMEL-gas: A Step toward Fast Empirical Models of the Broad-line-emitting Gas

Fast empirical models of the broad emission line region (BLR) are a powerful tool to interpret velocity-resolved reverberation mapping (RM) data, estimate the mass of the supermassive black holes, and gain insight into its geometry and kinematics. Much of the effort so far has been devoted to describing the emissivity of one emission line at a time. We present here an alternative approach aimed at describing the underlying BLR gas distribution, by exploiting simple numerical recipes to connect it with emissivity. This approach is a step toward describing multiple emission lines originating from the same gas and allows us to clarify some issues related to the interpretation of RM data. We illustrate this approach—implemented in the code CARAMEL-gas—using three data sets covering the Hβ emission line (Mrk 50, Mrk 1511, Arp 151) that have been modeled using the emissivity-based version of the code. As expected, we find differences in the parameters describing the BLR gas and emissivity distribution, but the emissivity-weighted lag measurements and all other model parameters including black hole mass and overall BLR morphology and kinematics are consistent with the previous measurements. We also model the Hα emission line for Arp 151 using both the gas- and emissivity-based BLR models. We find ionization stratification in the BLR with Hα arising at larger radii than Hβ, while all other model parameters are consistent within the uncertainties.

The Broad Line Region and Black Hole Mass of NGC 4151

We present a reanalysis of reverberation mapping data from 2005 for the Seyfert galaxy NGC 4151, supplemented with additional data from the literature to constrain the continuum variations over a significantly longer baseline than the original monitoring program. Modeling of the continuum light curve and the velocity-resolved variations across the Hβ emission line constrains the geometry and kinematics of the broad line region (BLR). The BLR is well described by a very thick disk with similar opening angle (θ o ≈ 57°) and inclination angle (θ i ≈ 58°), suggesting that our sight line toward the innermost central engine skims just above the surface of the BLR. The inclination is consistent with constraints from geometric modeling of the narrow-line region, and the similarity between the inclination and opening angles is intriguing given previous studies of NGC 4151 that suggest BLR gas has been observed temporarily eclipsing the X-ray source. The BLR kinematics are dominated by eccentric bound orbits, with ∼10% of the orbits preferring near-circular motions. With the BLR geometry and kinematics constrained, the models provide an independent and direct black hole mass measurement of or M ⊙, which is in good agreement with mass measurements from stellar dynamical modeling and gas dynamical modeling. NGC 4151 is one of the few nearby broad-lined Seyferts where the black hole mass may be measured via multiple independent techniques, and it provides an important test case for investigating potential systematics that could affect the black hole mass scales used in the local universe and for high-redshift quasars.

A geometric distance to the supermassive black Hole of NGC 3783

The angular size of the broad line region (BLR) of the nearby active galactic nucleus NGC 3783 has been spatially resolved by recent observations with VLTI/GRAVITY. A reverberation mapping (RM) campaign has also recently obtained high quality light curves and measured the linear size of the BLR in a way that is complementary to the GRAVITY measurement. The size and kinematics of the BLR can be better constrained by a joint analysis that combines both GRAVITY and RM data. This, in turn, allows us to obtain the mass of the supermassive black hole in NGC 3783 with an accuracy that is about a factor of two better than that inferred from GRAVITY data alone. We deriveMBH= 2.54−0.72+0.90× 107M⊙. Finally, and perhaps most notably, we are able to measure a geometric distance to NGC 3783 of 39.9−11.9+14.5Mpc. We are able to test the robustness of the BLR-based geometric distance with measurements based on the Tully–Fisher relation and other indirect methods. We find the geometric distance is consistent with other methods within their scatter. We explore the potential of BLR-based geometric distances to directly constrain the Hubble constant,H0, and identify differential phase uncertainties as the current dominant limitation to theH0measurement precision for individual sources.

Estimation of the size and structure of the broad line region using Bayesian approach

ABSTRACT Understanding the geometry and kinematics of the broad line region (BLR) of active galactic nuclei (AGN) is important to estimate black hole masses in AGN and study the accretion process. The technique of reverberation mapping (RM) has provided estimates of BLR size for more than 100 AGN now; however, the structure of the BLR has been studied for only a handful number of objects. Towards this, we investigated the geometry of the BLR for a large sample of 57 AGN using archival RM data. We performed systematic modelling of the continuum and emission line light curves using a Markov chain Monte Carlo method based on Bayesian statistics implemented in PBMAP (Parallel Bayesian code for reverberation−MAPping data) code to constrain BLR geometrical parameters and recover velocity integrated transfer function. We found that the recovered transfer functions have various shapes such as single-peaked, double-peaked, and top-hat suggesting that AGN have very different BLR geometries. Our model lags are in general consistent with that estimated using the conventional cross-correlation methods. The BLR sizes obtained from our modelling approach is related to the luminosity with a slope of 0.583 ± 0.026 and 0.471 ± 0.084 based on H β and H α lines, respectively. We found a non-linear response of emission line fluxes to the ionizing optical continuum for 93 ${{\ \rm per\ cent}}$ objects. The estimated virial factors for the AGN studied in this work range from 0.79 to 4.94 having a mean at 1.78 ± 1.77 consistent with the values found in the literature.

Untangling Optical Emissions of the Jet and Accretion Disk in the Flat-spectrum Radio Quasar 3C 273 with Reverberation Mapping Data

Abstract 3C 273 is an intensively monitored flat-spectrum radio quasar with both a beamed jet and blue bump together with broad emission lines. The coexistence of the comparably prominent jet and accretion disk leads to complicated variability properties. Recent reverberation mapping monitoring for 3C 273 revealed that the optical continuum shows a distinct long-term trend that does not have a corresponding echo in the Hβ fluxes. We compile multiwavelength monitoring data from the Swift archive and other ground-based programs and clearly find two components of emissions at optical wavelength. One component stems from the accretion disk itself, and the other component can be ascribed to the jet contribution, which also naturally accounts for the nonechoed trend in reverberation mapping data. We develop an approach to decouple the optical emissions from the jet and accretion disk in 3C 273 with the aid of multiwavelength monitoring data. By assuming that the disk emission has a negligible polarization in consideration of the low inclination of the jet, the results show that the jet contributes a fraction of ∼10% at the minimum and up to ∼40% at the maximum to the total optical emissions. This is the first time to provide a physical interpretation of the “detrending” manipulation conventionally adopted in reverberation mapping analysis. Our work also illustrates the importance of appropriately analyzing variability properties in cases of coexisting jets and accretion disks.

Kinematic Signatures of Reverberation Mapping of Close Binaries of Supermassive Black Holes in Active Galactic Nuclei. II. Atlas of Two-dimensional Transfer Functions

Abstract Most large galaxies harbor supermassive black holes (SMBHs) in their centers, and galaxies merge. Consequently, binary SMBHs should be common in galactic nuclei. However, close binaries of SMBH (CB-SMBHs) with subparsec separation cannot be imaged directly using current facilities. Some indirect signatures, such as periodic signals in light curves and double peaks in the emission-line profile, have been used to find CB-SMBH candidates, but ambiguities still exist and no definitive conclusions can be made. We have recently proposed a new method focusing on kinematic signatures that can be derived from reverberation mapping of CB-SMBHs, one that offers a promising avenue to address this important problem. In this paper, we calculated models for a wide range of parameters, but broad-line regions of two BHs are close but still not merged. The purpose of this supplementary paper is to provide an atlas of two-dimensional transfer functions of CB-SMBHs with a wide range of orbital and geometrical parameters to aid more efficient identification of CB-SMBH candidates in reverberation mapping data.

Modelling the AGN broad-line region using single-epoch spectra − II. Nearby AGNs

ABSTRACTThe structure of the broad-line region (BLR) is an essential ingredient in the determination of active galactic nucleus (AGN) virial black hole masses, which in turn are important to study the role of black holes in galaxy evolution. Constraints on the BLR geometry and dynamics can be obtained from velocity-resolved studies using reverberation mapping data (i.e. monitoring data). However, monitoring data are observationally expensive and only available for a limited sample of AGNs, mostly confined to the local Universe. Here, we explore a new version of a Bayesian inference, physical model of the BLR that uses an individual spectrum and prior information on the BLR size from the radius–luminosity relation, to model the AGN BLR geometry and dynamics. We apply our model to a sample of 11 AGNs, which have been previously modelled using monitoring data. Our single-epoch BLR model is able to constrain some of the BLR parameters with inferred parameter values that agree within the uncertainties with those determined from the modelling of monitoring data. We find that our model is able to derive stronger constraints on the BLR for AGNs with broad emission lines that qualitatively have more substructure and more asymmetry, presumably as they contain more information to constrain the physical model. The performance of this model makes it a practical and cost-effective tool to determine some of the BLR properties of a large sample of low- and high-redshift AGNs, for which monitoring data are not available.

The Sloan Digital Sky Survey Reverberation Mapping Project: Comparison of Lag Measurement Methods with Simulated Observations

Abstract We investigate the performance of different methodologies that measure the time lag between broad-line and continuum variations in reverberation mapping data using simulated light curves that probe a range of cadence, time baseline, and signal-to-noise ratio in the flux measurements. We compare three widely adopted lag-measuring methods: the interpolated cross-correlation function (ICCF), the z-transformed discrete correlation function (ZDCF), and the Markov chain Monte Carlo code JAVELIN, for mock data with qualities typical of multiobject spectroscopic reverberation mapping (MOS-RM) surveys that simultaneously monitor hundreds of quasars. We quantify the overall lag-detection efficiency, the rate of false detections, and the quality of lag measurements for each of these methods and under different survey designs (e.g., observing cadence and depth) using mock quasar light curves. Overall JAVELIN and ICCF outperform ZDCF in essentially all tests performed. Compared with ICCF, JAVELIN produces higher quality lag measurements, is capable of measuring more lags with timescales shorter than the observing cadence, is less susceptible to seasonal gaps and signal-to-noise ratio degradation in the light curves, and produces more accurate lag uncertainties. We measure the Hβ broad-line region size–luminosity (R–L) relation with each method using the simulated light curves to assess the impact of selection effects of the design of MOS-RM surveys. The slope of the R–L relation measured by JAVELIN is the least biased among the three methods and is consistent across different survey designs. These results demonstrate a clear preference for JAVELIN over the other two nonparametric methods for MOS-RM programs, particularly in the regime of limited light-curve quality as expected from most MOS-RM programs.

Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. VIII. Structure of the Broad-line Region and Mass of the Central Black Hole in Mrk 142

Abstract This is the eighth in a series of papers reporting on a large reverberation mapping (RM) campaign to measure black hole (BH) mass in active galactic nuclei with high accretion rates. We employ the recently developed dynamical modeling approach for broad-line regions (BLRs) based on the method of Pancoast et al. to analyze the RM data set of Mrk 142 observed in the first monitoring season. In this approach, continuum variations are reconstructed using a damped random walk process, and BLR structure is delineated using a flexible disk-like geometry, in which BLR clouds move around the central BH with Keplerian orbits or inflow/outflow motion. The approach also includes the possibilities of anisotropic emission from BLR clouds, nonlinear response of the line emission to the continuum, and different long-term trends in the continuum and emission-line variations. We implement the approach in a Bayesian framework that is apt for parallel computation and use a Markov chain Monte Carlo technique to recover the parameters and uncertainties for the modeling, including the mass of the central BH. We apply three BLR models with different prescriptions of BLR cloud distributions and find that the best model for fitting the data of Mrk 142 is a two-zone BLR model, consistent with the theoretical BLR model surrounding slim accretion disks. The best model yields a BH mass of , resulting in a virial factor of for the full width at half maximum of the Hβ line measured from the mean spectrum. The virial factors for the other measures of the Hβ line width are also presented.

Kinematic Signatures of Reverberation Mapping of Close Binaries of Supermassive Black Holes in Active Galactic Nuclei

Abstract Close binaries of supermassive black holes (CB-SMBHs) with separations of ≲0.1 pc as the final stage of galaxy mergers are sources of low-frequency gravitational waves; however, they are still elusive observationally because they are not spatially resolved. Fortunately, reverberation as echoes of broad emission lines to ionizing continuum conveys invaluable information on the dynamics of broad-line regions (BLRs) governed by SMBHs in the central regions of active galactic nuclei (AGNs). In this paper, we demonstrate how to compose the hybrid two-dimensional transfer functions (TFs) of binary BLRs around the CB-SMBHs in AGNs, providing an opportunity for identifying them from reverberation mapping (RM) data. It is found that there are variation-coupling effects in the TFs arising from the coupling of CB-SMBH light curves in the Fourier space. We provide semi-analytical formulations of the TFs for kinematic maps of the gas. For cases with the simplest variation-coupling effects, we make calculations for several BLR models and reveal significant distinctions from those of single active black holes. In principle, the difference is caused by the orbital motion of the CB-SMBH systems. In order to search for CB-SMBHs in time-domain space, selection of target candidates should focus on local AGNs with Hβ double-peaked profiles and weaker near-infrared emission. High-fidelity RM campaigns of monitoring the targets in future will provide opportunities to reveal these kinematic signatures of the CB-SMBHs and hence measurements of their orbital parameters.

Stability of the Broad-line Region Geometry and Dynamics in Arp 151 Over Seven Years

Abstract The Seyfert 1 galaxy Arp 151 was monitored as part of three reverberation mapping campaigns spanning 2008–2015. We present modeling of these velocity-resolved reverberation mapping data sets using a geometric and dynamical model for the broad-line region (BLR). By modeling each of the three data sets independently, we infer the evolution of the BLR structure in Arp 151 over a total of 7 yr and constrain the systematic uncertainties in nonvarying parameters such as the black hole mass. We find that the BLR geometry of a thick disk viewed close to face-on is stable over this time, although the size of the BLR grows by a factor of ∼2. The dynamics of the BLR are dominated by inflow, and the inferred black hole mass is consistent for the three data sets, despite the increase in BLR size. Combining the inference for the three data sets yields a black hole mass and statistical uncertainty of log10( / ) = with a standard deviation in individual measurements of 0.13 dex.

The Sloan Digital Sky Survey Reverberation Mapping Project: Composite Lags at z ≤ 1

Abstract We present composite broad-line region (BLR) reverberation mapping lag measurements for Hα, Hβ, He ii λ4686, and Mg ii for a sample of 144, z ≲ 1 quasars from the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project. Using only the 32-epoch spectroscopic light curves in the first six-month season of SDSS-RM observations, we compile correlation function measurements for individual objects and then coadd them to allow the measurement of the average lags for our sample at mean redshifts of 0.4 (for Hα) and ∼0.65 (for the other lines). At similar quasar luminosities and redshifts, the sample-averaged lag decreases in the order of Mg ii, Hα, Hβ, and He ii. This decrease in lags is accompanied by an increase in the mean line width of the four lines, and is roughly consistent with the virialized motion for BLR gas in photoionization equilibrium. These are among the first RM measurements of stratified BLR structure at z > 0.3. Dividing our sample by luminosity, Hα shows clear evidence of increasing lags with luminosity, consistent with the expectation from the measured BLR size–luminosity relation based on Hβ. The other three lines do not show a clear luminosity trend in their average lags due to the limited dynamic range of luminosity probed and the poor average correlation signals in the divided samples, a situation that will be improved with the incorporation of additional photometric and spectroscopic data from SDSS-RM. We discuss the utility and caveats of composite lag measurements for large statistical quasar samples with reverberation mapping data.

A New Approach to the Internal Calibration of Reverberation-Mapping Spectra

We present a new procedure for the internal (night-to-night) calibration of timeseries spectra, with specific applications to optical AGN reverberation mapping data. The traditional calibration technique assumes that the narrow [O iii] λ5007 emission-line profile is constant in time; given a reference [O iii] λ5007 line profile, nightly spectra are aligned by fitting for a wavelength shift, a flux rescaling factor, and a change in the spectroscopic resolution. We propose the following modifications to this procedure: (1) we stipulate a constant spectral resolution for the final calibrated spectra, (2) we employ a more flexible model for changes in the spectral resolution, and (3) we use a Bayesian modeling framework to assess uncertainties in the calibration. In a test case using data for MCG+08-11-011, these modifications result in a calibration precision of ∼1 millimagnitude, which is approximately a factor of five improvement over the traditional technique. At this level, other systematic issues (e.g., the nightly sensitivity functions and Feii contamination) limit the final precision of the observed light curves. We implement this procedure as a python package (mapspec), which we make available to the community.

Modelling reverberation mapping data – II. Dynamical modelling of the Lick AGN Monitoring Project 2008 data set

We present dynamical modeling of the broad line region (BLR) for a sample of five Seyfert 1 galaxies using reverberation mapping data taken by the Lick AGN Monitoring Project in 2008. By modeling the AGN continuum light curve and H$\beta$ line profiles directly we are able to constrain the geometry and kinematics of the BLR and make a measurement of the black hole mass that does not depend upon the virial factor, $f$, needed in traditional reverberation mapping analysis. We find that the geometry of the BLR is generally a thick disk viewed close to face-on. While the H$\beta$ emission is found to come preferentially from the far side of the BLR, the mean size of the BLR is consistent with the lags measured with cross-correlation analysis. The BLR kinematics are found to be consistent with either inflowing motions or elliptical orbits, often with some combination of the two. We measure black hole masses of $\log_{10}(M_{\rm\,BH}/M_\odot)=6.62^{+0.10}_{-0.13}$ for Arp 151, $7.42^{+0.26}_{-0.27}$ for Mrk 1310, $7.51^{+0.23}_{-0.14}$ for NGC 5548, $6.42^{+0.24}_{-0.18}$ for NGC 6814, and $6.99^{+0.32}_{-0.25}$ for SBS 1116+583A. The $f$ factors measured individually for each AGN are found to correlate with inclination angle, although not with $M_{\rm\,BH}$, $L_{5100}$, or FWHM/$\sigma$ of the emission line profile.

Modelling reverberation mapping data – I. Improved geometric and dynamical models and comparison with cross-correlation results

We present an improved and expanded simply parameterized phenomenological model of the broad line region (BLR) in active galactic nuclei (AGN) for modeling reverberation mapping data. By modeling reverberation mapping data directly, we can constrain the geometry and dynamics of the BLR and measure the black hole mass without relying on the normalization factor needed in the traditional analysis. For realistic simulated reverberation mapping datasets of high-quality, we can recover the black hole mass to $0.05-0.25$ dex uncertainty and distinguish between dynamics dominated by elliptical orbits and inflowing gas. While direct modeling of the integrated emission line light curve allows for measurement of the mean time lag, other details of the geometry of the BLR are better constrained by the full spectroscopic dataset of emission line profiles. We use this improved model of the BLR to explore possible sources of uncertainty in measurements of the time lag using cross-correlation function (CCF) analysis and in measurements of the black hole mass using the virial product. Sampling the range of geometries and dynamics in our model of the BLR suggests that the theoretical uncertainty in black hole masses measured using the virial product is on the order of 0.25 dex. These results support the use of the CCF to measure time lags and the virial product to measure black hole masses when direct modeling techniques cannot be applied, provided the uncertainties associated with the interpretation of the results are taken into account.

A BAYESIAN METHOD FOR THE INTERCALIBRATION OF SPECTRA IN REVERBERATION MAPPING

Flux calibration of spectra in reverberation mapping (RM) is most often performed by assuming the flux constancy of some specified narrow emission lines, which stem from an extended region that is sometimes partially spatially resolved, in contrast to the point-like broad-line region and the central continuum source. The inhomogeneous aperture geometries used among different observation sets in a joint monitoring campaign introduce systematic deviations to the fluxes of broad lines and central continuum, and intercalibration over these data sets is required. As an improvement to the previous empirical correction performed by comparing the (nearly) contemporaneous observation points, we describe a feasible Bayesian method that obviates the need for (nearly) contemporaneous observations, naturally incorporates physical models of flux variations, and fully takes into account the measurement errors. In particular, it fits all the data sets simultaneously regardless of samplings and makes use of all of the information in the data sets. A Markov Chain Monte Carlo implementation is employed to recover the parameters and uncertainties for intercalibration. Application to the RM data sets of NGC 5548 with joint monitoring shows the high fidelity of our method.