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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. 

Strong-lensing time delays enable the measurement of the Hubble constant ( H 0 ) independently of other traditional methods. The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD). Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses. However, this approach could potentially bias the H 0 measurement or underestimate the errors. For this work, we broke the MSD for the first time using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging. This approach allowed us to robustly estimate H 0 , effectively implementing a maximally flexible mass model. Following a blind analysis, we estimated the angular diameter distance to the lens galaxy D d  = 865 −81 +85 Mpc and the time-delay distance D Δt  = 2180 −271 +472 Mpc, giving H 0  = 77.1 −7.1 +7.3 km s −1 Mpc −1 – for a flat Λ cold dark matter cosmology. The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and line-of-sight effects, and those related to the mass–anisotropy degeneracy and projection effects. Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system ( H 0  = 78.3 −3.3 +3.4 km s −1 Mpc −1 ) and for seven lenses ( H 0  = 74.2 −1.6 +1.6 km s −1 Mpc −1 ), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us ( H 0  = 73.3 −5.8 +5.8 km s −1 Mpc −1 ). This agreement corroborates the methodology of time-delay cosmography. 

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 betweenfand other AGN/BLR parameters. We find (i) evidence for a correlation between the virial coefficient ${\log }_{10}\left(f_{\mathrm{mean},\sigma }\right)$and black-hole mass, (ii) marginal evidence for a similar correlation between ${\log }_{10}\left(f_{\mathrm{rms},\sigma }\right)$and black-hole mass, (iii) marginal evidence for an anticorrelation of BLR disk thickness with ${\log }_{10}\left(f_{\mathrm{mean},\mathrm{FWHM}}\right)$and ${\log }_{10}\left(f_{\mathrm{rms},\mathrm{FWHM}}\right)$, and (iv) marginal evidence for an anticorrelation of inclination angle with ${\log }_{10}\left(f_{\mathrm{mean},\mathrm{FWHM}}\right)$, ${\log }_{10}\left(f_{\mathrm{rms},\sigma }\right)$, and ${\log }_{10}\left(f_{\mathrm{mean},\sigma }\right)$. Last, we find marginal evidence for a correlation between line-profile shape, when using the root-mean-square spectrum, ${\log }_{10}{\left(\mathrm{FWHM}/\sigma \right)}_{\mathrm{rms}}$, and the virial coefficient, ${\log }_{10}\left(f_{\mathrm{rms},\sigma }\right)$, and investigate how BLR properties might be related to line-profile shape usingcaramelmodels. 

Abstract We have modeled the velocity-resolved reverberation response of the Hβbroad 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 HβBLR 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 ${\log }_{10}\left(\mathrm{FWHM}/\sigma \right)$, 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 Hβemission 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.