arXiv subjects

A. M. Nierenberg

Publications and source records attributed to A. M. Nierenberg.

At least 19 recordsLinked to original sources

arXiv2026

JWST lensed quasar dark matter survey V: Hints of self-interacting dark matter from 29 quadruply imaged quasars

Theories of self-interacting dark matter (SIDM) predict the eventual core collapse of dark matter halos, a process that transforms these structures into extremely efficient gravitational lenses. We present a population-level inference on the abundance of core collapsed halos and subhalos in the mass range $10^6 - 10^{10.7} M_{\odot}$ using 29 quadruply imaged quasars, drawing on the collective lensing signal of many low-mass perturbers. Our structure formation model predicts the abundance of collapsed (sub)halos as a function of halo mass and redshift. We quantify how our results are affected by systematic uncertainties, including the abundance of globular clusters (GCs) and subhalos, and the internal structure of deeply collapsed halos. Our data exhibits a strong preference for core collapsed halos in the lens model, with Bayes factors disfavoring CDM relative to SIDM ranging from 6:1 to 24:1, depending on the assumed properties of the SIDM subhalo and GC populations. Explaining our data without core collapse requires both a GC abundance well above expectations and more subhalos than predicted by $N$-body simulations. These results pose a challenge to the CDM paradigm. We present a particle physics interpretation of these results in a companion paper.

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arXiv2026

Measurement of the minimum cold dark matter halo mass with strong gravitational lensing

We explore the lowest mass limit that can be placed on the halo mass function in CDM using 28 strong gravitational lenses. For this purpose, we study an extreme model in which the halo mass function and mass-concentration relation follow CDM, with a sharp cutoff at some mass scale, $m_{\rm{low}}$. Lensing provides a unique window into this quantity as it does not depend on the presence of baryons in dark matter halos and also allows the detection of low mass halos at cosmological distances, both in the lens galaxies and along the line-of-sight. Our model incorporates the effects of tidal stripping of subhalos, leading to the presence of many subhalos below a given model cutoff scale. We place an upper limit on the low-mass cutoff of the halo mass function of $m_{\rm{low}}<10^{8.3}$ M$_\odot$ at 10:1 odds using a prior for the normalization of the subhalo mass function from the semi-analytic model {\tt galacticus} and $m_{\rm{low}}<10^{8.2}$ M$_\odot$ at 10:1 odds using a prior from $N$-body simulations. These limits are comparable to, or stronger than, existing constraints based on Milky Way satellite galaxies. Based on these results, we forecast more than an order of magnitude improvement with a sample of 200 quadruply imaged quasar lenses. This number represents a small subset of the thousands that are anticipated to be discovered by Rubin, Euclid, and Roman. Furthermore, with this larger sample of lenses we expect to directly constrain the normalization of the subhalo mass function, thereby eliminating a major source of uncertainty in our current measurements.

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arXiv2026

JWST lensed quasar dark matter survey IV: Stringent warm dark matter constraints from the joint reconstruction of extended lensed arcs and quasar flux ratios

We present a measurement of the free-streaming length of dark matter (DM) and subhalo abundance around 28 quadruple image strong lenses using observations from JWST MIRI presented in Paper III of this series. We improve on previous inferences on DM properties from lensed quasars by simultaneously reconstructing extended lensed arcs with image positions and relative magnifications (flux ratios). Our forward modeling framework generates full populations of subhalos, line-of-sight halos, and globular clusters, uses an accurate model for subhalo tidal evolution, and accounts for free-streaming effects on halo abundance and concentration. Modeling lensed arcs leads to more-precise model-predicted flux ratios, breaking covariance between subhalo abundance and the free-streaming scale parameterized by the half-mode mass $m_{\rm{hm}}$. Assuming subhalo abundance predicted by the semi-analytic model {\tt{galacticus}} ($N$-body simulations), we infer (Bayes factor of 10:1) $m_{\rm{hm}} < 10^{7.4} \mathrm{M}_{\odot}$ ($m_{\rm{hm}} < 10^{7.2} \mathrm{M}_{\odot}$), a 0.4 dex improvement relative to omitting lensed arcs. These bounds correspond to lower limits on thermal relic DM particle masses of $6.5$ and $7.4$ keV, respectively. Conversely, assuming DM is cold, we infer a projected mass in subhalos ($10^6 < m/M_{\odot}<10^{10.7}$) of $1.7_{-1.2}^{+2.6} \times 10^7 \ \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$ at $95 \%$ confidence. This is consistent with {\tt{galacticus}} predictions ($0.9 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$), but in mild tension with recent $N$-body simulations ($0.6 \times 10^7 \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$). Our results are among the strongest bounds on WDM, and the most precise measurement of subhalo abundance around strong lenses. Further improvements will follow from the large sample of lenses to be discovered by Euclid, Rubin, and Roman.

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arXiv2026

The free-streaming length of dark matter from JWST observations of 28 strong gravitational lenses

The formation of gravitationally bound overdensities of dark matter (DM), or \textit{halos}, is a generic prediction of theories with particle DM. We present a measurement of halo properties in 28 quadruple image strong lens systems recently observed by JWST, and use these observations to constrain the free-streaming length, $λ_{\rm{FS}}$, of DM, a quantity that depends on the DM particle mass and formation mechanism. We improve on previous lensing analyses by simultaneously reconstructing extended lensed arcs with image positions and relative magnifications, enhancing sensitivity to perturbations by halos. Our analysis rules out deviations from the predictions of cold dark matter (CDM) on scales above $10^{7.2} M_{\odot}$ and $10^{7.4} M_{\odot}$ for subhalo abundance predicted by cosmological $N$-body simulations and semi-analytic models, respectively. These bounds correspond to upper limits $λ_{\rm{FS}}<6.0 \ \rm{kpc}$ and $λ_{\rm{FS}}<7.0 \ \rm{kpc}$, and lower limits on the mass of a spin--1/2 thermal relic DM particle $m_{\rm{therm}}>7.4 \ \rm{keV}$ and $m_{\rm{therm}}>6.5 \ \rm{keV}$. Conversely, assuming a negligible free-streaming length, as predicted by CDM, we measure a projected mass in subhalos around elliptical galaxies $1.7_{-1.2}^{+2.6} \times 10^7 \ \mathrm{M}_{\odot} \ \rm{kpc^{-2}}$ at $95 \%$ confidence. These inferences confirm key predictions of the CDM paradigm.

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arXiv2025

JWST Lensed Quasar Dark Matter Survey III: Dark Matter Sensitive Flux Ratios and Warm Dark Matter Constraint from the Full Sample

We present the full sample of measurements of the warm dust emission of 31 strongly-lensed, multiply imaged quasars, observed with JWST MIRI multiband imaging, which we use to constrain the particle properties of dark matter. The strongly lensed warm dust region of quasars is compact and statistically sensitive to a population of dark matter halos down to masses of $10^6$ M$_\odot$. The high spatial resolution and infrared sensitivity of MIRI make it uniquely suited to measure multiply imaged warm dust emission from quasars and thus to infer the properties of low-mass dark halos. We use the measured flux ratios to test for a warm dark matter turnover in the halo mass function. To infer the dark matter parameters, we use a forward modeling pipeline which explores dark matter parameters while also accounting for tidal stripping effects on subhalos, globular clusters, and complex deflector macromodels with $m=1, m=3, \text{ and } m=4$ elliptical multipole moments. Adopting a comparable prior on the projected density of substructure to our previous analyses, the data presented here provide a factor of 2 improvement in sensitivity to a turnover in the halo mass function. Assuming subhalo abundance predicted by the semi-analytic model galacticus we infer with a Bayes factor of 10:1, a half-mode mass $m_{\rm{hm}} < 10^{7.8} M_{\odot}$ (m>5.6 keV for a thermally produced dark matter particle). If instead we use a prior from N-body simulations, we infer $m_{\rm{hm}} < 10^{7.6} M_{\odot}$ (m>6.4 keV). This is one of the strongest constraints to date on a turnover on the halo mass function, and the flux ratios and inference methodology presented here can be used to test a broad range of dark matter physics.

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arXiv2023

JWST lensed quasar dark matter survey I: Description and First Results

The flux ratios of gravitationally lensed quasars provide a powerful probe of the nature of dark matter. Importantly, these ratios are sensitive to small-scale structure, irrespective of the presence of baryons. This sensitivity may allow us to study the halo mass function even below the scales where galaxies form observable stars. For accurate measurements, it is essential that the quasar's light is emitted from a physical region of the quasar with an angular scale of milli-arcseconds or larger; this minimizes microlensing effects by stars within the deflector. The warm dust region of quasars fits this criterion, as it has parsec-size physical scales and dominates the spectral energy distribution of quasars at wavelengths greater than 10$μ$m. The JWST Mid-Infrared Instrument (MIRI) is adept at detecting redshifted light in this wavelength range, offering both the spatial resolution and sensitivity required for accurate gravitational lensing flux ratio measurements. Here, we introduce our survey designed to measure the warm dust flux ratios of 31 lensed quasars. We discuss the flux-ratio measurement technique and present results for the first target, DES J0405-3308. We find that we can measure the quasar warm dust flux ratios with 3% precision. Our simulations suggest that this precision makes it feasible to detect the presence of 10$^7$ M$_\odot$ dark matter halos at cosmological distances. Such halos are expected to be completely dark in Cold Dark Matter models.

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arXiv2019

Gaia GraL: Gaia DR2 Gravitational Lens Systems. V. Doubly-imaged QSOs discovered from entropy and wavelets

The discovery of multiply-imaged gravitationally lensed QSOs is fundamental to many astronomical and cosmological studies. However, these objects are rare and challenging to discover due to requirements of high-angular resolution astrometric, multiwavelength photometric and spectroscopic data. This has limited the number of known systems to a few hundred objects. We aim to reduce the constraints on angular resolution and discover multiply-imaged QSO candidates by using new candidate selection principles based on unresolved photometric time-series and ground-based images from public surveys. We selected candidates for multiply-imaged QSOs based on low levels of entropy computed from Catalina unresolved photometric time-series or Euclidean similarity to known lenses in a space defined by the wavelet power spectra of Pan-STARSS DR2 or DECaLS DR7 images, combined with multiple {\it Gaia} DR2 sources or large astrometric errors and supervised and unsupervised learning methods. We then confirmed spectroscopically some candidates with the Palomar Hale, Keck-I, and ESO/NTT telescopes. Here we report the discovery and confirmation of seven doubly-imaged QSOs and one likely double quasar. This demonstrates the potential of combining space-astrometry, even if unresolved, with low spatial-resolution photometric time-series and/or low-spatial resolution multi-band imaging to discover multiply-imaged lensed QSOs.

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arXiv2019

Double dark matter vision: twice the number of compact-source lenses with narrow-line lensing and the WFC3 grism

The magnifications of compact-source lenses are extremely sensitive to the presence of low mass dark matter halos along the entire sight line from the source to the observer. Traditionally, the study of dark matter structure in compact-source strong gravitational lenses has been limited to radio-loud systems, as the radio emission is extended and thus unaffected by microlensing which can mimic the signal of dark matter structure. An alternate approach is to measure quasar nuclear-narrow line emission, which is free from microlensing and present in virtually all quasar lenses. In this paper, we double the number of systems which can be used for gravitational lensing analyses by presenting measurements of narrow-line emission from a sample of 8 quadruply imaged quasar lens systems, WGD J0405-3308, HS 0810+2554, RX J0911+0551, SDSS J1330+1810, PS J1606-2333, WFI 2026-4536, WFI 2033-4723 and WGD J2038-4008. We describe our updated grism spectral modelling pipeline, which we use to measure narrow-line fluxes with uncertainties of 2-10\%, presented here. We fit the lensed image positions with smooth mass models and demonstrate that these models fail to produce the observed distribution of image fluxes over the entire sample of lenses. Furthermore, typical deviations are larger than those expected from macromodel uncertainties. This discrepancy indicates the presence of perturbations caused by small-scale dark matter structure. The interpretation of this result in terms of dark matter models is presented in a companion paper.

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arXiv2019

Astrophysical Tests of Dark Matter with Maunakea Spectroscopic Explorer

We discuss how astrophysical observations with the Maunakea Spectroscopic Explorer (MSE), a high-multiplexity (about 4300 fibers), wide field-of-view (1.5 square degree), large telescope aperture (11.25 m) facility, can probe the particle nature of dark matter. MSE will conduct a suite of surveys that will provide critical input for determinations of the mass function, phase-space distribution, and internal density profiles of dark matter halos across all mass scales. N-body and hydrodynamical simulations of cold, warm, fuzzy and self-interacting dark matter suggest that non-trivial dynamics in the dark sector could have left an imprint on structure formation. Analysed within these frameworks, the extensive and unprecedented datasets produced by MSE will be used to search for deviations away from cold and collisionless dark matter model. MSE will provide an improved estimate of the local density of dark matter, critical for direct detection experiments, and will improve estimates of the J-factor for indirect searches through self-annihilation or decay into Standard Model particles. MSE will determine the impact of low mass substructures on the dynamics of Milky Way stellar streams in velocity space, and will allow for estimates of the density profiles of the dark matter halos of Milky Way dwarf galaxies using more than an order of magnitude more tracers. In the low redshift Universe, MSE will provide critical redshifts to pin down the luminosity functions of vast numbers of satellite systems, and MSE will be an essential component of future strong lensing measurements to constrain the halo mass function. Across nearly all mass scales, the improvements offered by MSE, in comparison to other facilities, are such that the relevant analyses are limited by systematics rather than statistics.

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arXiv2018

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

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 datasets using a geometric and dynamical model for the broad line region (BLR). By modeling each of the three datasets independently, we infer the evolution of the BLR structure in Arp 151 over a total of seven years and constrain the systematic uncertainties in non-varying 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 $\sim 2$. The dynamics of the BLR are dominated by inflow and the inferred black hole mass is consistent for the three datasets, despite the increase in BLR size. Combining the inference for the three datasets yields a black hole mass and statistical uncertainty of $\log_{10}($M$_{\rm BH}/\rm{M}_{\odot})=6.82^{+0.09}_{-0.09}$ with a standard deviation in individual measurements of 0.13 dex.

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arXiv2017

Probing dark matter substructure in the gravitational lens HE0435-1223 with the WFC3 grism

Strong gravitational lensing provides a powerful test of Cold Dark Matter (CDM) as it enables the detection and mass measurement of low mass haloes even if they do not contain baryons. Compact lensed sources such as Active Galactic Nuclei (AGN) are particularly sensitive to perturbing subhalos, but their use as a test of CDM has been limited by the small number of systems which have significant radio emission which is extended enough avoid significant lensing by stars in the plane of the lens galaxy, and red enough to be minimally affected by differential dust extinction. Narrow-line emission is a promising alternative as it is also extended and, unlike radio, detectable in virtually all optically selected AGN lenses. We present first results from a WFC3 grism narrow-line survey of lensed quasars, for the quadruply lensed AGN HE0435-1223. Using a forward modelling pipeline which enables us to robustly account for spatial blending, we measure the [OIII] 5007 Å~ flux ratios of the four images. We find that the [OIII] fluxes and positions are well fit by a simple smooth mass model for the main lens. Our data rule out a $M_{600}>10^{8} (10^{7.2}) M_\odot$ NFW perturber projected within $\sim$1\farcs0 (0\farcs1) arcseconds of each of the lensed images, where $M_{600}$ is the perturber mass within its central 600 pc. The non-detection is broadly consistent with the expectations of $Λ$CDM for a single system. The sensitivity achieved demonstrates that powerful limits on the nature of dark matter can be obtained with the analysis of $\sim20$ narrow-line lenses.

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arXiv2016

The Missing Satellite Problem in 3D

It is widely believed that the large discrepancy between the observed number of satellite galaxies and the predicted number of dark subhalos can be resolved via a variety of baryonic effects which suppress star formation in low mass halos.Supporting this hypothesis, numerous high resolution simulations with star formation, and associated feedback have been shown to reproduce the satellite luminosity function around Milky Way-mass simulated galaxies at redshift zero. However, a more stringent test of these models is their ability to simultaneously match the satellite luminosity functions of a range of host halo masses and redshifts. In this work we measure the luminosity function of faint (sub-Small Magellanic Cloud luminosity) satellites around hosts with stellar masses 10.5$<\log_{10}$M$_*$/M$_\odot<11.5$ to an unprecedented redshift of 1.5. This new measurement of the satellite luminosity function provides powerful new constraining power; we compare these results with predictions from four different simulations and show that although the models perform similarly over-all, no one model reproduces the satellite luminosity function reliably at all redshifts and host stellar masses. This result highlights the continued need for improvement in understanding the fundamental physics that governs satellite galaxy evolution.

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arXiv2015

The Lick AGN Monitoring Project 2011: Spectroscopic Campaign and Emission-Line Light Curves

In the Spring of 2011 we carried out a 2.5 month reverberation mapping campaign using the 3 m Shane telescope at Lick Observatory, monitoring 15 low-redshift Seyfert 1 galaxies. This paper describes the observations, reductions and measurements, and data products from the spectroscopic campaign. The reduced spectra were fitted with a multicomponent model in order to isolate the contributions of various continuum and emission-line components. We present light curves of broad emission lines and the AGN continuum, and measurements of the broad H-beta line widths in mean and root-mean square (rms) spectra. For the most highly variable AGNs we also measured broad H-beta line widths and velocity centroids from the nightly spectra. In four AGNs exhibiting the highest variability amplitudes, we detect anticorrelations between broad H-beta width and luminosity, demonstrating that the broad-line region "breathes" on short timescales of days to weeks in response to continuum variations. We also find that broad H-beta velocity centroids can undergo substantial changes in response to continuum variations; in NGC 4593 the broad H-beta velocity shifted by ~250 km/s over a one-month duration. This reverberation-induced velocity shift effect is likely to contribute a significant source of confusion noise to binary black hole searches that use multi-epoch quasar spectroscopy to detect binary orbital motion. We also present results from simulations that examine biases that can occur in measurement of broad-line widths from rms spectra due to the contributions of continuum variations and photon-counting noise.

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arXiv2014

Detection of substructure with adaptive optics integral field spectroscopy of the gravitational lens B1422+231

Strong gravitational lenses can be used to detect low mass subhalos, based on deviations in image fluxes and positions from what can be achieved with a smooth mass distribution. So far, this method has been limited by the small number of (radio-loud, microlensing free) systems which can be analysed for the presence of substructure. Using the gravitational lens B1422+231, we demonstrate that adaptive optics integral field spectroscopy can also be used to detect dark substructures. We analyse data obtained with OSIRIS on the Keck I Telescope, using a Bayesian method that accounts for uncertainties relating to the point spread function and image positions in the separate exposures. The narrow-line [OIII] fluxes measured for the lensed images are consistent with those measured in the radio, and show a significant deviation from what would be expected in a smooth mass distribution, consistent with the presence of a perturbing low mass halo. Detailed lens modelling shows that image fluxes and positions are fit significantly better when the lens is modelled as a system containing a single perturbing subhalo in addition to the main halo, rather than by the main halo on its own, indicating the significant detection of substructure.The inferred mass of the subhalo depends on the subhalo mass density profile: the 68% confidence interval for the perturber mass within 600 pc are: 8.2$^{+0.6}_{-0.8}$, 8.2$^{+0.6}_{-1}$ and 7.6$\pm0.3$ $\log_{10}$[M$_{\rm{sub}}$/M$_\odot$] respectively for a singular isothermal sphere, a pseudo-Jaffe, and an NFW mass profile. This method can extend the study of flux ratio anomalies to virtually all quadruply imaged quasars, and therefore offers great potential to improve the determination of the subhalo mass function in the near future.

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arXiv2013

Do gravitational lens galaxies have an excess of luminous substructure?

Strong gravitational lensing can be used to directly measure the mass function of their satellites, thus testing one of the fundamental predictions of cold dark matter cosmological models. Given the importance of this test it is essential to ensure that galaxies acting as strong lenses have dark and luminous satellites which are representative of the overall galaxy population. We address this issue by measuring the number and spatial distribution of luminous satellites in ACS imaging around lens galaxies from the Sloan Lens Advanced Camera for Surveys (SLACS) lenses, and comparing them with the satellite population in ACS imaging of non lens galaxies selected from COSMOS, which has similar depth and resolution to the ACS images of SLACS lenses. In order to compare the samples of lens and non lens galaxies, which have intrinsically different stellar mass distributions, we measure, for the first time, the number of satellites per host as a continuous function of host stellar mass for both populations. We find that the number of satellites as a function of host stellar mass, as well as the spatial distribution are consistent between the samples. Using these results, we predict the number of satellites we would expect to find around a subset of the Cosmic Lens All Sky Survey (CLASS) lenses, and find a result consistent with the the number observed by Jackson et al. 2010. Thus we conclude that within our measurement uncertainties there is no significant difference in the satellite populations of lens and non lens galaxies.

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arXiv2013

The Cosmic Evolution of Faint Satellite Galaxies as a Test of Galaxy Formation and the Nature of Dark Matter

The standard cosmological model based on cold dark matter (CDM) predicts a large number of subhalos for each galaxy-size halo. It is well known that matching the subhalos to the observed properties of luminous satellites of galaxies in the local universe poses a significant challenge to our understanding of the astrophysics of galaxy formation. We show that the cosmic evolution and host mass dependence of the luminosity function of satellites provides a powerful new diagnostic to disentangle astrophysical effects from variations in the underlying dark matter mass function. We illustrate this by comparing the results of recent observations of satellites out to $z=0.8$ based on Hubble Space Telescope images with the predictions of three different sets of state-of-the art semi-analytic models with underlying CDM power spectra and one semi-analytic model with an underlying Warm Dark Matter (WDM) power spectrum. We find that even though CDM models provide a reasonable fit to the local luminosity function of satellites around galaxies comparable or slightly larger than the Milky Way, they do not reproduce the data as well for different redshift and host galaxy stellar mass. This tension indicates that further improvements are likely to be needed in the description of star formation if the models are to be reconciled with the data. The WDM model matches the observed mass dependence and redshift evolution of satellite galaxies more closely than any of the CDM models, indicating that a modification of the underlying power spectrum may offer an alternative solution to this tension. We conclude by presenting predictions for the color magnitude relation of satellite galaxies to demonstrate how future observations will be able to further distinguish between these models and help constrain baryonic and non-baryonic physics.

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arXiv2013

The Lick AGN Monitoring Project 2011: Fe II Reverberation from the Outer Broad-Line Region

The prominent broad Fe II emission blends in the spectra of active galactic nuclei have been shown to vary in response to continuum variations, but past attempts to measure the reverberation lag time of the optical Fe II lines have met with only limited success. Here we report the detection of Fe II reverberation in two Seyfert 1 galaxies, NGC 4593 and Mrk 1511, based on data from a program carried out at Lick Observatory in Spring 2011. Light curves for emission lines including H-beta and Fe II were measured by applying a fitting routine to decompose the spectra into several continuum and emission-line components, and we use cross-correlation techniques to determine the reverberation lags of the emission lines relative to V-band light curves. In both cases the measured lag (t_cen) of Fe II is longer than that of H-beta, although the inferred lags are somewhat sensitive to the choice of Fe II template used in the fit. For spectral decompositions done using the Fe II template of Veron-Cetty et al. (2004), we find t_cen(Fe II)/t_cen(H-beta) = 1.9+-0.6 in NGC 4593 and 1.5+-0.3 in Mrk 1511. The detection of highly correlated variations between Fe II and continuum emission demonstrates that the Fe II emission in these galaxies originates in photoionized gas, located predominantly in the outer portion of the broad-line region.

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arXiv2012

The Lick AGN Monitoring Project 2011: Dynamical Modeling of the Broad Line Region in Mrk 50

We present dynamical modeling of the broad line region (BLR) in the Seyfert 1 galaxy Mrk 50 using reverberation mapping data taken as part of the Lick AGN Monitoring Project (LAMP) 2011. We model the reverberation mapping data directly, constraining the geometry and kinematics of the BLR, as well as deriving a black hole mass estimate that does not depend on a normalizing factor or virial coefficient. We find that the geometry of the BLR in Mrk 50 is a nearly face-on thick disk, with a mean radius of 9.6(+1.2,-0.9) light days, a width of the BLR of 6.9(+1.2,-1.1) light days, and a disk opening angle of 25\pm10 degrees above the plane. We also constrain the inclination angle to be 9(+7,-5) degrees, close to face-on. Finally, the black hole mass of Mrk 50 is inferred to be log10(M(BH)/Msun) = 7.57(+0.44,-0.27). By comparison to the virial black hole mass estimate from traditional reverberation mapping analysis, we find the normalizing constant (virial coefficient) to be log10(f) = 0.78(+0.44,-0.27), consistent with the commonly adopted mean value of 0.74 based on aligning the M(BH)-σ* relation for AGN and quiescent galaxies. While our dynamical model includes the possibility of a net inflow or outflow in the BLR, we cannot distinguish between these two scenarios.

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