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Abstract The virial coefficient (f), which is meant to encapsulate broad-line region (BLR) geometry and kinematics, remains one of the largest sources of systematic uncertainty in black hole mass estimates for active galactic nuclei (AGNs). While the use of a sample average 〈f〉 enables black hole mass estimates across large samples and cosmological distances, individual AGNs may deviate from this average due to differences in BLR structure and viewing angle. In previous work, we reported marginal evidence for a correlation betweenfand the shape of the broad Hβemission line, ${\log }_{10}(\mathrm{FWHM}/\sigma )$ . In this work, we update our sample to include 10 new sources withCARAMELBLR dynamical modeling, increasing both the black hole mass range and statistical power of our analysis. We find marginal evidence for a correlation betweenfand ${\log }_{10}(\mathrm{FWHM}/\sigma )$ , with a slope and intrinsic scatter consistent with previous results. The confirmation of this trend across a larger sample further supports the idea that line profile shape may reflect BLR properties in a way that directly impactsf. If confirmed with future BLR dynamical modeling of sources within a wider range of ${\log }_{10}(\mathrm{FWHM}/\sigma )$ , this relationship could enable empirical estimates of the virial coefficient and improve single-epoch black hole mass estimates across cosmic time. 

Abstract We present the second iteration of thecaramel-gascode, an empirical model of the broad-line region (BLR) gas density field. Building on the initial development and testing ofcaramel-gas, we expand the meaning of the model parameterα, 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 thecaramel-gascode and test the generalized radial power-law index,α. Our results confirm that thecaramel-gasresults are in general agreement with the published results determined using the originalcaramelcode, 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. 

Abstract We combine our dynamical modeling black-hole mass measurements from the Lick AGN Monitoring Project 2016 sample with measured cross-correlation time lags and line widths to recover individual scale factors, f , used in traditional reverberation-mapping analyses. We extend our sample by including prior results from Code for AGN Reverberation and Modeling of Emission Lines ( caramel ) studies that have utilized our methods. Aiming to improve the precision of black-hole mass estimates, as well as uncover any regularities in the behavior of the broad-line region (BLR), we search for correlations between f and other AGN/BLR parameters. We find (i) evidence for a correlation between the virial coefficient log 10 ( f mean , σ ) and black-hole mass, (ii) marginal evidence for a similar correlation between log 10 ( f rms , σ ) and black-hole mass, (iii) marginal evidence for an anticorrelation of BLR disk thickness with log 10 ( f mean , FWHM ) and log 10 ( f rms , FWHM ) , and (iv) marginal evidence for an anticorrelation of inclination angle with log 10 ( f mean , FWHM ) , log 10 ( f rms , σ ) , and log 10 ( f mean , σ ) . Last, we find marginal evidence for a correlation between line-profile shape, when using the root-mean-square spectrum, log 10 ( FWHM / σ ) rms , and the virial coefficient, log 10 ( f rms , σ ) , and investigate how BLR properties might be related to line-profile shape using caramel models. 

Abstract We have modeled the velocity-resolved reverberation response of the H β broad emission line in nine Seyfert 1 galaxies from the Lick Active Galactic Nucleus (AGN) Monitoring Project 2016 sample, drawing inferences on the geometry and structure of the low-ionization broad-line region (BLR) and the mass of the central supermassive black hole. Overall, we find that the H β BLR is generally a thick disk viewed at low to moderate inclination angles. We combine our sample with prior studies and investigate line-profile shape dependence, such as log 10 ( FWHM / σ ) , on BLR structure and kinematics and search for any BLR luminosity-dependent trends. We find marginal evidence for an anticorrelation between the profile shape of the broad H β emission line and the Eddington ratio, when using the rms spectrum. However, we do not find any luminosity-dependent trends, and conclude that AGNs have diverse BLR structure and kinematics, consistent with the hypothesis of transient AGN/BLR conditions rather than systematic trends.