# Velocity-Resolved Reverberation Mapping of NGC 3227

Misty C. Bentz Department of Physics and Astronomy, Georgia State University,
Atlanta, GA 30303, USA<EMAIL_ADDRESS>Madison Markham Department of
Physics and Astronomy, Colgate University, 13 Oak Drive, Hamilton, NY 13346,
USA  Sara Rosborough School of Physics and Astronomy, and Laboratory for
Multiwavelength Astrophysics, Rochester Institute of Technology, Rochester, NY
14623, USA  Christopher A. Onken Research School of Astronomy and
Astrophysics, Australian National University, Canberra, ACT 2611, Australia
Rachel Street LCOGT, 6740 Cortona Drive, Suite 102, Goleta, CA 93117, USA
Monica Valluri Department of Astronomy, University of Michigan, Ann Arbor, MI,
48109, USA  Tommaso Treu Packard Fellow  Department of Physics and Astronomy,
University of California, Los Angeles, CA 90095, USA

###### Abstract

We describe the results of a new reverberation mapping program focused on the
nearby Seyfert galaxy NGC 3227. Photometric and spectroscopic monitoring were
carried out from 2022 December to 2023 June with the Las Cumbres Observatory
network of telescopes. We detected time delays in several optical broad
emission lines, with H$\beta$ having the longest delay at $\tau_{\rm
cent}=4.0^{+0.9}_{-0.9}$ days and He II having the shortest delay with
$\tau_{\rm cent}=0.9^{+1.1}_{-0.8}$ days. We also detect velocity-resolved
behavior of the H$\beta$ emission line, with different line-of-sight
velocities corresponding to different observed time delays. Combining the
integrated H$\beta$ time delay with the width of the variable component of the
emission line and a standard scale factor suggests a black hole mass of
$M_{\rm BH}=1.1^{+0.2}_{-0.3}\times 10^{7}$ $M_{\odot}$. Modeling of the full
velocity-resolved response of the H$\beta$ emission line with the
phenomenological code CARAMEL finds a similar mass of $M_{\rm
BH}=1.2^{+1.5}_{-0.7}\times 10^{7}$ $M_{\odot}$, and suggests that the
H$\beta$-emitting broad line region (BLR) may be represented by a biconical or
flared disk structure that we are viewing at an inclination angle of
$\theta_{i}\approx 33\arcdeg$ and with gas motions that are dominated by
rotation. The new photoionization-based BLR modeling tool BELMAC finds general
agreement with the observations when assuming the best-fit CARAMEL results,
however BELMAC prefers a thick disk geometry and kinematics that are equally
comprised of rotation and inflow. Both codes infer a radially extended and
flattened BLR that is not outflowing.

Seyfert galaxies (1447) — Supermassive black holes (1663) — Reverberation
mapping(2019)

††software: LCO BANZAI Reduction Pipeline (McCully et al., 2018), Galfit (Peng
et al., 2002, 2010), JAVELIN (Zu et al., 2011), ULySS (Koleva et al., 2011),
CARAMEL (Pancoast et al., 2014), BELMAC (Rosborough et al., 2023), CLOUDY v17
(Ferland et al., 2017)

##  1 Introduction

The prevalence of supermassive black holes with masses of $10^{6}\lesssim
M_{\rm BH}/M_{\odot}\lesssim 10^{10}$ in the centers of massive galaxies was
one of the surprise discoveries enabled by the Hubble Space Telescope (e.g.,
Ford et al. 1994; Harms et al. 1994; Kormendy & Richstone 1995; van der Marel
et al. 1997). More surprising still was the finding that the masses of these
black holes scale with observable properties of their host galaxies (e.g.,
Ferrarese & Merritt 2000; Gebhardt et al. 2000). After three decades of study,
we now understand that these black holes generally go through at least one
period of active accretion during their lifetimes, and that the accretion
process releases huge amounts of energy across the electromagnetic spectrum,
energy that is deposited into the gas within the host galaxy and
circumgalactic environment and thus seems to play a role in modulating the
growth of the galaxy and of the black hole itself (see the reviews by, e.g.,
Fabian 2012; Heckman & Best 2014; Fan et al. 2023).

The mass of a black hole is one of its fundamental properties, and it sets the
limit for the amount of feedback power that may be released during an
accretion event. Thus it is an important measurement to constrain as we
attempt to further understand the detailed physics involved in black hole
feeding and feedback. Sagittarius A∗ is the nearest supermassive black hole,
and its mass has been precisely determined through monitoring the orbits of
individual stars via their proper motions over decade timescales (Ghez et al.,
2000; Genzel et al., 2000; Ghez et al., 2008). Unfortunately, all other
galaxies are so distant that we cannot achieve the necessary spatial
resolution in their nuclei to apply the same technique.

A variety of techniques have been developed to determine black hole masses in
other galaxies. These include dynamical modeling of the bulk motions of stars
or gas (see the review by Kormendy & Ho 2013) and kinematic studies of masing
gas clouds (e.g., Miyoshi et al. 1995). High spatial resolution is a critical
component of these techniques, which generally limits their application to
galaxies with $D\lesssim 100$ Mpc.

Black hole masses at cosmological distances are most often determined through
reverberation mapping (RM; see the recent review by Cackett et al. 2021), a
technique that makes use of the photoionized gas deep in the potential well of
an actively accreting black hole. RM utilizes spectrophotometric monitoring
with high temporal sampling to track changes in the continuum emission
(expected to arise from the accretion disk) and the “echoes” of those changes
in the broad emission-line fluxes. The time delay between the two gives the
typical light travel time across the broad line region, and thus a physical
size. With reverberation mapping, spatial resolution is replaced by temporal
resolution, and black holes at significant distances become available for
study.

One effect of having these varied techniques and their disparate limitations
is that we have two black hole mass scales currently in use: one determined
from nearby, mostly early-type inactive galaxies based on stellar and gas
dynamical modeling, and another based on reverberation mapping of more distant
active galaxies that tend to be mostly later morphological types. Because
broad-lined active galaxies with $D\lesssim 100$ Mpc are rare, there are very
few galaxies that meet the requirements for multiple techniques that would
allow us to check that these two mass scales are in agreement.

NGC 3227 is a nearby ($z=0.00377$) spiral galaxy that is interacting with its
elliptical companion, NGC 3226. Both galaxies in the pair show evidence for
nuclear activity, a fact that was first remarked upon by Curtis (1918) who
noted that the pair of galaxies contained “stellar nuclei”. NGC 3226 is
classified as a LINER (Véron-Cetty & Véron, 2006), while NGC 3227 was one of
the original sample of 12 Seyfert (1943) galaxies. The broad hydrogen lines in
the nucleus of NGC 3227, compared to the widths of the nebular lines, was
noted by Dibai & Pronik (1968) and Rubin & Ford (1968), though other early
studies have sometimes classified it as a Type II Seyfert (e.g., Khachikian &
Weedman 1974).

Similarly, early studies were divided regarding the potential detection of
nuclear variability in NGC 3227 (e.g., Netzer 1974; Liutyi 1977). While
Tennant & Mushotzky (1983) detected X-ray variability on timescales of $\sim
1$ day in NGC 3227, Salamanca et al. (1994) were the first to systematically
monitor the AGN with optical spectroscopy on short timescales and demonstrate
clear variability in the continuum and broad emission lines. With only 26
measurements over the course of 6 months, however, their light curves were
severely undersampled when it came to trying to constrain any time delays
between them. A similar campaign with comparable time sampling described by
Winge et al. (1995) was also plagued by the same difficulties. A re-analysis
of both datasets by Peterson et al. (2004) using a set of best practices that
had been developed for reverberation mapping studies concluded that any
potential time delays were formally consistent with zero because of the coarse
temporal sampling.

Denney et al. (2010) thus undertook a new monitoring program with the intent
of determining the first accurate and precise BLR time delay measurement for
NGC 3227, finding that the H$\beta$ broad line emission lagged the continuum
variations by $3.8\pm 0.8$ days and showed evidence for different time delays
as a function of velocity across the emission line profile. Further campaigns
by De Rosa et al. (2018) and Brotherton et al. (2020) sought to improve on
these results by more fully exploring the velocity-resolved time delays to
determine the BLR geometry and kinematics, in the hopes of deriving a more
direct constraint on the black hole mass. Preliminary modeling of the De Rosa
et al. (2018) data sets suggest that the low amplitude of variability in the
light curves may hinder any firm conclusions from being drawn (Robinson,
2022), and while Brotherton et al. (2020) provide a velocity-delay map for
H$\beta$ based on their monitoring data, the lack of details in the map
limited any potential for interpretation.

We thus undertook a new monitoring program focused on NGC 3227, which we
present in this work. Strong variability coupled with high temporal sampling
allowed us to measure broad emission-line time delays and to further explore
the velocity-resolved response of H$\beta$. These promising characteristics
also enabled a more thorough exploration of the constraints that may be placed
on the structure and kinematics of the BLR in this nearby AGN, based on two
independent modeling codes that have been developed specifically for use with
reverberation mapping data.

##  2 Observations

NGC 3227 is located in the direction of the constellation Leo at
$\alpha=10$h23m30.6s and $\delta=+19\arcdeg 51\arcmin 54\arcsec$ with a
redshift of $z=0.00377$. A surface brightness fluctuations (SBF) distance to
the companion galaxy NGC 3226 puts the pair at a distance of $D=23.7\pm 2.6$
Mpc (Tonry et al. 2001 with the adjustments of Blakeslee et al. 2001).

###  2.1 Imaging

Broad-band photometric monitoring of NGC 3227 began on 2022 December 01 and
continued through 2023 June 04 (UT dates here and throughout) under programs
LCO-2022B-003 and LCO-2023A-004. Observations were collected on the 1m
telescope network of Las Cumbres Observatory (LCO; Brown et al. 2013) using
the Sinistro imagers equipped with Johnson $V$ filters. Exposures were
scheduled to occur every $\sim 8$ hr with a typical exposure time of 60 s.
Each image covers a field of view of $26\farcm 5\times 26\farcm 5$ with a
pixel scale of 0$\farcs$389.

A total of 376 images were collected from 5 different observatory sites over
the course of the monitoring program: 93 at Siding Spring Observatory (SSO),
85 at South African Astronomical Observatory (SAAO), 84 at McDonald
Observatory, 65 at Cerro Tololo Interamerican Observatory (CTIO), and 49 at
Teide Observatory. Observations were automatically reduced by the LCO pipeline
(McCully et al., 2018), with typical CCD reductions using biases, darks, and
flats, before being downloaded from the LCO
archive111https://archive.lco.global.

Rather than rely on aperture photometry, which may include large amounts of
host-galaxy starlight that varies with the seeing and also dampens the true
brightness variations of the central AGN, we instead used the image
subtraction algorithms of Alard & Lupton (1998); Alard (2000). In general,
image subtraction works by scaling individual images to match a reference
image and then subtracting the two, removing all sources of constant flux and
leaving behind only the variable flux. Image subtraction methods are commonly
applied in studies of extragalactic transients and other time domain
phenomena, including microlensing (Udalski et al., 2008, 2015), supernovae
(Riess et al., 2001; Miknaitis et al., 2007; Melinder et al., 2008), tidal
disruption events (Holoien et al., 2016; Brown et al., 2018), as well as AGN
variability (Fausnaugh et al., 2016; Grier et al., 2017; Bentz et al., 2021a).

We began by registering all of the images to a common grid using the algorithm
of Siverd et al. (2012). We then selected the highest quality images (lowest
background and best seeing) from the subset that were obtained at SSO, and
stacked them to build a reference image (see 1). The reference image was
convolved to match, and then subtracted from, each of the 376 individual
images. Finally, aperture photometry with a radius of 9 pixels was performed
at the location of the AGN in all of the subtracted images, giving us a light
curve of the variable AGN counts.

Figure 1:  The inner $10\arcmin\times 10\arcmin$ region of the reference
image, centered on the nucleus of NGC 3227 and oriented with North up and East
to the left.

While the LCO network employs identical telescopes and detectors across sites,
we have previously found slight offsets between the measurements obtained at
different LCO locations (Bentz et al., 2021a, 2023). Accordingly, we compared
the light curves obtained at each location to the light curve obtained at SSO
and again found that, when working in counts, small adjustments were necessary
to bring them all into agreement. For a pair of light curves, we identified
the set of measurements that were taken close together in time (usually within
$0.5-1$ days) and determined the slope and intercept of the relationship
between the measurements from one observatory versus the other, taking into
account the errors in both measurements. Good agreement would be indicated by
a slope of 1.0 and intercept of 0.0, with some scatter given the small and
random variations of the AGN on very short timescales. In all comparisons, the
slope and intercept were found to deviate somewhat from these expected values,
demonstrating a difference in the counts that are registered on the detectors
at different observatory locations, likely due to factors like slight
variations in the overall sensitivities of the CCDs or differences in
atmospheric transparency. We applied a small additive and multiplicative
correction factor to each light curve to bring them into agreement with the
SSO light curve, which was the basis for the reference image.

We then calibrated the light curves using the AGN flux in the reference image.
To separate the AGN from its bright and spatially extended host galaxy, we
employed the two-dimensional surface brightness modeling package Galfit (Peng
et al., 2002, 2010). We first constructed a PSF model for the reference image
by fitting multiple Gaussians to a small cutout centered on an isolated field
star, with the background sky brightness modeled as a gradient in $x$ and $y$.
Four Gaussians were found to be sufficient to capture the detailed shape of
the PSF. We then modeled the reference image using this PSF to simulate the
AGN and several field stars, a gradient in $x$ and $y$ for the background sky
component, and multiple Sérsic profiles for the galaxies NGC 3227 and NGC
3226. Our choice of starting parameters for the Sérsic profiles was guided by
previous surface brightness models of NGC 3227 using high-resolution Hubble
Space Telescope images (Bentz et al., 2009; Bentz & Manne-Nicholas, 2018).
Once we had a good model that allowed us to cleanly separate the AGN flux from
the surrounding host galaxy, we determined the final calibration of the
reference frame by setting the zeropoint such that the recovered $V-$band
magnitudes for several field stars matched the values tabulated by the AAVSO
Photometric All Sky Survey catalog (Henden & Munari, 2014) DR10. The
calibrated $V-$band magnitude for the AGN in the reference image was then
combined with the variable flux measured from image subtraction to determine
the calibrated $V-$band light curve.

We next examined the residual counts around several non-varying field stars in
the subtracted images and compared these measurements to the uncertainties
reported on the aperture photometry at the location of the AGN. Previous work
by Zebrun et al. (2001); Hartman et al. (2005) and others has demonstrated
that the uncertainties in image subtraction measurements are often
underestimated, and we found that to hold true in the case of our analysis of
NGC 3227. We followed the basic procedure outlined by Hartman et al. (2004) to
determine that a multiplicative factor of $\sim 9$ needed to be applied to
provide more realistic uncertainties.

Finally, we examined the effectiveness of binning the light curve for
decreasing some of the noise that may result from images that were obtained
under marginal observing conditions. We found that a bin size of 0.5 days was
a good compromise between retaining much of the temporal sampling while also
decreasing some of the noise. In Figure 2, we show the final calibrated and
binned $V-$band light curve for the central AGN in NGC 3227 during this
monitoring campaign. The bottom panel shows the scatter in the residuals for a
non-varying field star of similar magnitude for comparison with the AGN
variability. The light curve is tabulated in Table 2, with flux densities
based on the absolute spectrophotometric calibration of Vega provided by
Colina et al. (1996).

Figure 2:  The final calibrated and binned $V-$band light curve for NGC 3227.
For comparison with the AGN variations and uncertainties, the bottom panel
shows the scatter in residuals for a non-varying field star of similar
brightness.

###  2.2 Spectroscopy

Spectroscopic monitoring was carried out on the LCO 2m telescope network
between UT dates 2023 February 02 and 2023 June 01 under programs
LCO-2023A-004 and ANU-2023A-002. The FLOYDS cross-dispersed spectrographs
provided wavelength coverage of $5400$ Å$-1.0\,\mu$m with a dispersion of 3.51
Å/pix in the first order, and wavelength coverage of $3200-5700$ Å in the
second order with a dispersion of 1.74 Å/pix. Spectra were obtained through a
6″ slit oriented N-S along a position angle of 0°. Observations were scheduled
every $\sim 24$ hr, and a typical visit consisted of a 900 s science exposure
together with an arc lamp and a flat field taken through the same slit.

A total of 51 spectra were acquired over the course of the program, with 42
acquired by Faulkes Telescope South and 9 by Faulkes Telescope North.
Observations were downloaded from the LCO archive after being processed by the
LCO pipeline, which splits the 2D spectra into separate orders, rectifies each
order, and applies typical CCD reductions including biases, darks, and flats.
The pipeline also provides initial wavelength and flux calibrations based on
stored wavelength and sensitivity functions. Focusing on the 2nd order
spectra, which have a higher spectral resolution and also include the [O III]
$\lambda\lambda 4959,5007$ Å doublet (see discussion below), we began with the
wavelength- and flux-calibrated 2D spectra and carried out cosmic ray
cleaning, spectral extraction through a 10 pix extraction width, and improved
wavelength calibration using the arcs taken at the same pointing as each
spectrum. We then adopted a common dispersion of 1.6 Å for all spectra and
cropped them to have the same starting and ending wavelengths.

Next, we applied the spectral scaling method of van Groningen & Wanders (1992)
to account for slight variations in the spectra caused by imprecise flux
calibration, varying weather and seeing conditions, and slight differences in
telescope pointing. The algorithm applies small shifts in wavelength and flux
and a small amount of smoothing to minimize the differences in each spectrum
relative to a reference spectrum, where the reference spectrum is generally
created from a subset of the best-quality spectra. We applied the algorithm
focusing on the spectral region around the [O III] $\lambda\lambda 4959,5007$
Å emission lines, as they are known to not vary on the short timescales that
are covered by a single observing season (Peterson et al., 2013). This allows
the [O III] doublet to be used as a set of internal comparison sources and
also explains why most reverberation mapping experiments have focused on the
H$\beta$ emission line: even though H$\alpha$ is brighter, there are no
similar strong and relatively unblended narrow lines nearby to use for
correction of the slight differences in the spectra from night to night. We
adopted an absolute flux calibration of $F(5007)=7.8\times 10^{-13}$ erg s-1
cm-2, which is based on the values determined for NGC 3227 over the last
decade through a wide slit on photometric nights, as reported by De Rosa et
al. (2018) and Brotherton et al. (2020).

Figure 3 displays the mean and root-mean-square (rms) of all the final
calibrated and scaled spectra. The rms spectrum highlights the variable
spectral components, which include the AGN continuum and broad emission lines,
while non-varying components like the narrow lines are eliminated.

Figure 3:  Mean (top) and rms (bottom) spectra of NGC 3227 based on the
observed-frame spectra obtained throughout the monitoring program. The strong
broad emission lines are labeled for ease of identification.  Table 1:
Emission-Line Time Lags and Widths

|  |  |  | mean | rms
---|---|---|---|---|---
Line | $\tau_{\rm cent}$ | $\tau_{\rm peak}$ | $\tau_{\rm jav}$ | FWHM | $\sigma_{\rm line}$ | FWHM | $\sigma_{\rm line}$
| (days) | (days) | (days) | (km s-1) | (km s-1) | (km s-1) | (km s-1)
H$\beta$ | $4.03^{+0.85}_{-0.94}$ | $2.50^{+2.25}_{-1.25}$ | $2.671^{+0.126}_{-1.795}$ | $5070.3\pm 69.1$ | $1943.1\pm 12.5$ | $3710.0\pm 186.4$ | $1682.3\pm 39.2$
H$\gamma$ | $2.73^{+0.61}_{-0.72}$ | $1.50^{+1.00}_{-0.25}$ | $1.156^{+0.237}_{-0.087}$ | $3860.7\pm 62.5$ | $1548.2\pm 21.5$ | $4313.3\pm 179.0$ | $1566.0\pm 60.5$
H$\delta$ | $3.16^{+0.93}_{-1.00}$ | $1.50^{+1.50}_{-0.75}$ | $1.336^{+2.387}_{-0.165}$ | $4254.5\pm 743.2$ | $1763.4\pm 33.7$ | $4612.8\pm 405.0$ | $1869.0\pm 77.9$
He II | $0.94^{+1.07}_{-0.81}$ | $0.25^{+0.50}_{-0.25}$ | $0.003^{+0.685}_{-0.062}$ |  $\cdots$ |  $\cdots$ | $6586.2\pm 414.0$ | $2615.6\pm 72.7$

Note. — Reported time lags are in the observer’s frame, while, per convention,
line widths are measured in the rest frame.

Table 2: Continuum and Emission-Line Light Curves

Continuum |  | Emission Lines
---|---|---
HJD | $V$ |  | HJD | H$\beta$ | H$\gamma$ | H$\delta$ | He II
59914.6126 | $7.566\pm 0.111$ |  | 59978.1643 | $5.747\pm 0.105$ | $2.408\pm 0.093$ | $0.725\pm 0.101$ | $2.474\pm 0.120$
59915.2338 | $7.415\pm 0.164$ |  | 59980.2065 | $5.488\pm 0.068$ | $2.335\pm 0.061$ | $0.783\pm 0.066$ | $2.345\pm 0.078$
59916.2424 | $6.597\pm 0.149$ |  | 59981.2027 | $5.752\pm 0.063$ | $2.464\pm 0.056$ | $0.676\pm 0.062$ | $2.771\pm 0.073$
59917.0131 | $7.005\pm 0.143$ |  | 59984.1662 | $5.639\pm 0.078$ | $2.365\pm 0.070$ | $0.730\pm 0.077$ | $2.508\pm 0.090$
59918.0019 | $7.340\pm 0.148$ |  | 59985.1536 | $5.766\pm 0.058$ | $2.380\pm 0.051$ | $0.752\pm 0.056$ | $2.441\pm 0.066$

Note. — Heliocentric Julian dates are provided as HJD$-2400000$ (days).
$V-$band flux densities have units of $10^{-15}$ erg s-1 cm-2 Å-1 while
emission-line fluxes have units of $10^{-13}$ erg s-1 cm-2. Table 2 is
published in its entirety in the machine-readable format. A portion is shown
here for guidance regarding its form and content.

Table 3: Light Curve Statistics

Time Series | $N$ |  $\langle\Delta T\rangle$ (days) |  $\Delta T_{\rm med}$ (days) | $\langle F\rangle$ | $\langle\sigma_{F}/F\rangle$ | $F_{\rm var}$ | $R_{\rm max}$
---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
V | 203 | $0.9\pm 0.5$ | 0.75 | $6.24\pm 0.61$ | 0.018 | 0.096 | $1.570\pm 0.031$
H$\beta$ | 51 | $2.4\pm 2.8$ | 1.25 | $5.05\pm 0.79$ | 0.013 | 0.157 | $1.735\pm 0.033$
H$\gamma$ | 51 | $2.4\pm 2.8$ | 1.25 | $1.97\pm 0.49$ | 0.030 | 0.249 | $2.173\pm 0.086$
H$\delta$ | 51 | $2.4\pm 2.8$ | 1.25 | $0.57\pm 0.30$ | 0.137 | 0.513 | $9.315\pm 3.895$
He II | 51 | $2.4\pm 2.8$ | 1.25 | $2.02\pm 0.67$ | 0.040 | 0.334 | $4.294\pm 0.301$

Note. — $V-$band flux densities have units of $10^{-15}$ erg s-1 cm-2 Å-1
while emission-line fluxes have units of $10^{-13}$ erg s-1 cm-2.

##  3 Analysis

###  3.1 Line Width Measurements

For each of the broad emission lines visible in the spectra of NGC 3227, we
report the line widths in both the mean spectrum and the rms spectrum. Line
widths were determined by setting a local linear continuum under each line and
then measuring the distribution of flux directly from the data above the
continuum within a specified wavelength window. Line widths were quantified in
two ways: the full width at half-maximum flux (FWHM) and the velocity
dispersion of the line profile ($\sigma_{\rm line}$). The uncertainties in the
line widths were determined by selecting a random subset of spectra, building
a new mean and rms spectrum from this subset, recording the FWHM and
$\sigma_{\rm line}$, and repeating the process 1000 times to build up
distributions of the measurements. In Table 1, we report the median and inner
68% confidence interval as the line width and its associated uncertainties,
for both FWHM and $\sigma_{\rm line}$ as measured in the mean spectrum and the
rms spectrum.

We note that all reported line widths have been corrected for instrumental
resolution by assuming that $\Delta\lambda_{\rm
obs}^{2}\approx\Delta\lambda_{\rm true}^{2}+\Delta\lambda_{\rm disp}^{2}$
(Peterson et al., 2004). The width of the [O III] $\lambda 5007$ Å emission
line was reported to be ${\rm FWHM}=485$ km s-1 when measured through a narrow
slit at high spectral resolution by Whittle (1992), and we take this
measurement to represent $\Delta\lambda_{\rm true}$. The measured width of [O
III] $\lambda 5007$ Å in our spectra ($\Delta\lambda_{\rm obs}$) is ${\rm
FWHM}=16.58$ Å. We thus adopted a resolution correction of $\Delta\lambda_{\rm
disp}=14.47$ Å or 866 km s-1.

Figure 4:  Light curves (left) for the continuum and broad emission lines
throughout the course of the monitoring program. Cross-correlation functions
(right) are for each light curve relative to the continuum, and in the case of
the continuum is the auto-correlation function.

###  3.2 Emission-Line Light Curves and Time Delays

Light curves of the broad emission lines H$\beta$, He II, H$\gamma$, and
H$\delta$ were generated by fitting a local linear continuum under each line
and integrating the flux above this continuum for each calibrated and scaled
spectrum. While simplistic, this method accounts for all of the flux in a line
without having to rely on the discretion of the user in choosing an
appropriate set of model parameters to properly fit asymmetric or complicated
line shapes. The non-varying narrow component of each line is included as a
simple flux offset. Table 2 tabulates the light curves. Table 3 lists basic
information and variability statistics about each light curve; for each
spectral feature listed in column (1), we give the number of measurements in
column (2), and the average and median temporal sampling, respectively, in
columns (3) and (4). Column (5) lists the mean flux and standard deviation,
while column (6) lists the mean fractional error. Column (7) gives the noise-
corrected fractional variation, which is computed as

$F_{\rm var}=\frac{\sqrt{\sigma^{2}-\delta^{2}}}{\langle F\rangle}$ (1)

where $\sigma^{2}$ is the variance of the fluxes, $\delta^{2}$ is their mean-
square uncertainty, and $\langle F\rangle$ is the mean flux. Column (8) lists
the ratio of the maximum to the minimum flux.

The typical time delay between each emission-line light curve and the
continuum light curve was then assessed. Throughout this work, we adopt the
final $V-$band light curve from photometry as the continuum light curve
because it has several advantages over the continuum as measured from the
spectra. In particular, the use of broad-band photometry, even on a small
telescope, allows a high S/N to be reached in a short amount of observing
time. The wide field of view of the detectors available on small telescopes
provide ample field stars that are observed simultaneously with the science
target, providing a more accurate calibration than can generally be achieved
for ground-based long-slit spectroscopy. The abundance of small optical
telescopes around the globe allows a significantly higher temporal sampling to
be achieved, and the image subtraction methods employed in our analysis
produce a high-fidelity light curve without the damping effect of nonvariable
flux components. Finally, the $V$ band was chosen because of its widespread
availability and because it includes a mostly line-free portion of the
spectrum for local AGNs like NGC 3227.

Time delays were measured using the interpolated cross-correlation function
(ICCF) method of Gaskell & Sparke (1986); Gaskell & Peterson (1987) with the
modifications of White & Peterson (1994). The cross-correlation function is
determined twice with the ICCF method, first by interpolating one light curve
and then the other. The two resultant CCFs are averaged together to provide
the final CCF, and we display these in Figure 4 along with the continuum and
emission-line light curves.

The peak of the CCF ($r_{\rm max}$) occurs at the time shift for which the two
light curves are most highly correlated. This time delay is often reported as
$\tau_{\rm peak}$. A slight variation is to report $\tau_{\rm cent}$, which is
the time delay associated with the centroid of the points around $\tau_{\rm
peak}$ above some threshold (typically $0.8r_{\rm max}$). We prefer $\tau_{\rm
cent}$ because it is less susceptible to noise than is $\tau_{\rm peak}$ (cf.
Peterson et al. 2004).

The uncertainties on $\tau_{\rm peak}$ and $\tau_{\rm cent}$ were derived
following the flux randomization and random subset sampling (FR/RSS) method of
Peterson et al. (1998, 2004). The FR/RSS method accounts for uncertainties in
the time delay arising from noise in the flux measurements as well as the
inclusion (or exclusion) of each individual data point. A large number of
FR/RSS realizations ($N=1000$) build up distributions of $\tau_{\rm peak}$ and
$\tau_{\rm cent}$ measurements. From these distributions, we report the
medians and inner 68% confidence intervals as the time delay values and their
associated uncertainties. Time delays in the observed frame are tabulated in
Table 1.

We also measured the emission-line time delays using JAVELIN (Zu et al.,
2011). JAVELIN assumes a damped random walk for the behavior of the driving
continuum light curve, and optimizes the parameters for a top-hat transfer
function to predict the responding emission-line light curve(s). Even though
JAVELIN is capable of fitting multiple emission-line light curves at the same
time, we were unsuccessful in fitting them all simultaneously, so we instead
fit each one separately. The best-fit time delays are listed in Table 1, and
while they agree well with $\tau_{\rm peak}$, they generally do not agree with
$\tau_{\rm cent}$. Differences between $\tau_{\rm peak}$ and $\tau_{\rm cent}$
are caused by the shape of the CCF, which is in turn related to the transfer
function. We speculate that in this case, JAVELIN’s assumption of a top hat
may not be a good match to the actual transfer function of NGC 3227.

Using the same methods as described above, we also divided the H$\beta$ broad
emission line into 5 separate bins, with similar flux in all bins, and
generated a light curve for each one to assess the H$\beta$ gas response as a
function of line-of-sight velocity. The time delay between the continuum and
the light curve associated with each bin was then determined through cross
correlation following the same methods outlined above. As we show in Figure 5,
there are clear differences in the time delay associated with each bin across
the broad emission-line profile, with the longest time delays near the line
center and the shortest time delay associated with the blue wing. This
velocity-resolved behavior is qualitatively similar to what has been observed
in previous velocity-resolved analyses of NGC 3227 (Denney et al., 2010; De
Rosa et al., 2018; Brotherton et al., 2020).

Figure 5:  Velocity-resolved time delays (top) across the broad H$\beta$
emission-line profile (bottom).  Table 4: Broad-line region model parameter
values

Parameter | Brief Description | H$\beta$
---|---|---
log_10 (M/M_⊙) | Black hole mass | 7.09^+0.35_-0.34
r_mean (light days) | Mean radius of line emission | 5.50^+1.64_-1.33
r_median (light days) | Median radius of line emission | 5.03^+1.79_-1.44
r_min (light days) | Minimum radius of line emission | 2.54^+3.20_-1.65
σ_r (light days) | Radial extent of line emission | 2.33^+5.23_-1.10
τ_mean (days) | Mean time delay | 4.93^+0.64_-0.67
τ_median (days) | Median time delay | 3.81^+0.56_-0.52
θ_o (degrees) | Opening angle | 64.7^+18.3_-11.8
θ_i (degrees) | Inclination angle | 33.2^+13.5_-9.1
β | Shape parameter of radial distribution | 0.84^+0.64_-1.14
γ | Disk face concentration parameter | 3.95^+0.75_-1.14
ξ | Transparency of the mid-plane | 0.49^+0.38_-0.30
κ | Cosine illumination function parameter | -0.28^+0.19_-0.15
f_ellip | Fraction of elliptical orbits | 0.71^+0.14_-0.37
f_flow | Inflow vs. outflow | 0.45^+0.38_-0.30
θ_e (degrees) | Ellipse angle | 57.5^+12.1_-26.8
σ_turb | Turbulence | 0.006^+0.018_-0.004
r_out (light days) | Outer radius of line emission (fixed parameter) | 78
T | Temperature or likelihood softening | 65

Note. — Tabulated values are the median and 68% confidence intervals.

Figure 6:  Histograms displaying the posterior distributions of the BLR model
parameters for H$\beta$.

###  3.3 CARAMEL Modeling

Using the full velocity-resolved response of an emission line to constrain the
geometry and kinematics of the BLR is usually approached in two ways: through
the inverse approach, in which deconvolution of the emission-line response
produces a velocity-delay map (e.g., Horne et al. 2004; Skielboe et al. 2015;
Anderson et al. 2021), or through forward modeling, in which a self-consistent
set of models are used to predict the emission-line response and then compared
to the observations (e.g., Pancoast et al. 2014; Rosborough et al. 2023). The
first approach has the advantage of relying on a relatively small set of
assumptions and has the ability to make use of all the details in the data,
but short baselines, irregular sampling, and noisy data complicate the
deconvolution process, and the results are difficult to interpret without
extensive modeling. The second approach is relatively easy to interpret, but
is fundamentally limited by a larger set of core assumptions and the level of
flexibility and completeness in the models.

CARAMEL is a phenomenological modeling code that was developed to explore the
BLR using reverberation data sets. It is described in detail by Pancoast et
al. (2014) and we have previously used it in the study of other nearby AGNs
(Bentz et al., 2021b, 2022, 2023). By exploring the parameter space of
geometric and kinematic models that may represent the BLR, CARAMEL is able to
provide a direct and primary constraint on the black hole mass (without
resorting to the use of a scale factor) and can also provide insight into
various characteristics of interest, such as the inclination of the BLR to our
line of sight. In the few cases where independent measurements are available,
they have been to found to be in general agreement with CARAMEL results, such
as the mass of the black hole and the BLR inclination in NGC 4151 (Bentz et
al., 2022), and the general structural parameters of the BLR in NGC 3783
(Gravity Collaboration et al., 2021; Bentz et al., 2021b).

We followed the approach described in our previous work (Bentz et al., 2021b,
2022, 2023) and first carried out a decomposition of each spectrum using the
ULySS package (Koleva et al., 2011). We modeled all of the continuum and
emission-line features in the spectra and then subtracted the continuum
components and any emission lines close in wavelength to H$\beta$, leaving an
isolated H$\beta$ feature corresponding to each observational epoch. These
isolated observed H$\beta$ profiles were then fed into CARAMEL for comparison
with the line profiles created from each model, along with the driving
continuum light curve.

In Figure 6 we display the posterior probability distribution function for the
model parameters preferred by CARAMEL, and we tabulate the median and 68%
confidence interval for each parameter in Table 4. The median values of these
parameters indicate that the H$\beta$-emitting region of the BLR may be
represented by the surface or “skin” of a biconical or flared disk structure
with its axis of symmetry inclined to our line of sight at an angle of
$\theta_{i}=33.2^{+13.5}_{-9.1}$ degrees, with preferential radiation back
towards the central source ($\kappa=-0.28^{+0.19}_{-0.15}$), and with gas
motions that are dominated by rotation ($f_{\rm ellip}=0.71^{+0.14}_{-0.37}$).
We include an illustrative example of this geometry in Figure 7, and note that
strong inward anisotropy of hydrogen emission from the BLR is expected due to
the high densities and correspondingly large line optical depths in the gas
(Ferland et al., 1992).

Figure 7:  Representative geometric model of the H$\beta$ emission in the BLR
of NGC 3227. The left panel is oriented edge on, with an Earth-based observer
at large $+x$ values, and the right panel shows the Earth-based observer’s
view. The transparency of each point is related to the strength of the
response of the gas, with more opaque points having a stronger response to
continuum fluctuations.

##  4 Discussion

###  4.1 Radius vs. Luminosity

Previous measurements of the H$\beta$ time delay in NGC 3227 range from $\sim
2$ days (De Rosa et al., 2018) to $\sim 7$ days (Brotherton et al., 2020). The
time delay of H$\beta$ is expected to change as a function of the central AGN
luminosity. The relationship for these two quantities follows a power-law
shape with a slope of $\approx 0.5$ for a sample of local Seyferts (the
$R_{\rm BLR}-L$ relationship; Bentz et al. 2006, 2009, 2013), and each
individual AGN is expected to have its own $R_{\rm BLR}-L$ relationship as its
luminosity varies (e.g., Bentz et al. 2007; Kilerci Eser et al. 2015), so we
would not expect to always measure the same time delay for a specific emission
line in a single AGN.

Nevertheless, the time delay that we find for H$\beta$ of $\tau_{\rm
cent}=4.03^{+0.85}_{-0.94}$ days is nearly the same as the time delay reported
by Denney et al. (2010), $\tau_{\rm cent}=3.76^{+0.76}_{-0.82}$ days. We find
a mean continuum flux of $f_{\rm cont}=(9.56\pm 0.04)\times 10^{-15}$ erg s-1
cm-2 Å-1 at $5100\times(1+z)$ Å. After correcting for the host-galaxy
starlight contribution to the continuum, $f_{\rm gal}=(5.1\pm 0.5)\times
10^{-15}$ erg s-1 cm-2 Å-1, derived from high-resolution Hubble Space
Telescope imaging following the methods of Bentz et al. (2009, 2013), we find
an AGN luminosity of $\log(\lambda L_{\rm 5100}/L_{\odot})=42.21\pm 0.11$.
This is very similar to the luminosity reported by Denney et al. (2010), after
correction for the distance of $D=23.7\pm 2.6$ Mpc assumed here, of
$\log(\lambda L_{\rm 5100}/L_{\odot})=42.24\pm 0.12$. Interestingly, both of
these measurements lie exactly on the best-fit $R_{\rm BLR}-L$ relationship of
Bentz et al. (2013).

On the other hand, the two H$\beta$ time delay measurements reported by De
Rosa et al. (2018) lie below the $R_{\rm BLR}-L$ relationship, while the
H$\beta$ time delay reported by Brotherton et al. (2020) lies above it, even
after ensuring uniformity in the assumed distances, Galactic extinction, and
method of starlight correction when deriving the AGN luminosity. The longer
time delay reported by Brotherton et al. (2020), when compared to the
measurements presented here and by Denney et al. (2010), seems to tentatively
agree with the expectation of a steeper slope for the $R_{\rm BLR}-L$
relationship of a single AGN when the optical luminosity is used as a proxy
for the ionizing luminosity (Kilerci Eser et al., 2015). However, the AGN
luminosity was quite similar during the monitoring program of Brotherton et
al. (2020) and the programs described by De Rosa et al. (2018), yet the time
delays that were derived are quite different. We note that the amplitude of
variability relative to the noise was significantly lower in the light curves
presented by De Rosa et al. (2018). If the measurements of $\tau_{\rm cent}$
and their larger uncertainties are preferred over those of $\tau_{\rm jav}$,
then the measurements of De Rosa et al. (2018) are within the typical scatter
around the $R_{\rm BLR}-L$ relationship, and they agree with the time delay
measurement reported by Brotherton et al. (2020) at the $3\sigma$ level.

###  4.2 Black Hole Mass

Because of its proximity, NGC 3227 is one of the few Seyfert galaxies that has
previous dynamical mass measurements. We note that dynamical masses are
linearly dependent on the adopted distance to the galaxy, so any comparison of
masses from different techniques must keep this detail in mind. NGC 3227 is
near enough that its redshift of $z=0.00377$ cannot be used to accurately
predict its distance. Instead, throughout this work we have adopted the SBF-
based distance to NGC 3226 as the distance to NGC 3227 (given their clear
ongoing interaction). The SBF distance of $D=23.7\pm 2.6$ Mpc is based on the
analysis of Tonry et al. (2001), with slight adjustments by Blakeslee et al.
(2001). In addition, a careful assessment of the predicted distance based on
the Tully & Fisher (1977) relationship by Robinson et al. (2021) finds
$D=24.3\pm 4.9$ Mpc for NGC 3227, which is in good agreement.

Previous mass constraints from stellar dynamical modeling (Davies et al.,
2006) and from gas dynamical modeling (Hicks & Malkan, 2008) used different
distances from our adopted value and from each other, both relying on various
measurements of the redshift instead. Adjusting the dynamical masses to
account for their assumed distances relative to our adopted distance gives a
stellar dynamical mass of $M_{\rm BH}=(1.9\pm 0.9)\times 10^{7}$ $M_{\odot}$
and a gas dynamical mass of $M_{\rm BH}=(3.1^{+1.5}_{-0.6})\times 10^{7}$
$M_{\odot}$. While these values agree with each other, they have generally not
agreed with reverberation-based masses, being a factor of $4-5$ larger (Denney
et al., 2010; De Rosa et al., 2018).

For most reverberation analyses, black hole mass is calculated from the time
delay ($\tau$) and line width ($V$) as:

$M_{\rm BH}=f\frac{c\tau V^{2}}{G}$ (2)

where $c$ is the speed of light, and $G$ is the gravitational constant. An
extensive analysis of reverberation datasets and analysis procedures by
Peterson et al. (2004) provided a list of best practices, particularly
recommending the use of $\tau_{\rm cent}$ for the time delay and $\sigma_{\rm
line}(rms)$ for the line width. The scale factor $f$ encodes all the geometric
and kinematic details of the BLR, including the inclination angle to our line
of sight. Since these details are generally unknown for individual AGNs, a
population-average scale factor, $\langle f\rangle$, is usually adopted so
that the $M_{\rm BH}-\sigma_{\star}$ relationship for AGNs with masses from
reverberation is brought into general agreement with the relationship for
mostly quiescent galaxies with black hole masses from dynamical modeling
(e.g., Onken et al. 2004). For the combination of $\tau_{\rm cent}$ and
$\sigma_{\rm line}(rms)$, the value of $\langle f\rangle$ has been found to
range from 2.8 (Graham et al., 2011) to 5.5 (Onken et al., 2004), depending on
the exact details and the sample that is included. We generally prefer to
adopt $\langle f\rangle=4.8$ from Batiste et al. (2017) because of their
careful treatment of the effects of galaxy morphology, including bars, on the
determination of $\sigma_{\star}$.

While in practice, the adoption of $\langle f\rangle$ minimizes any bias in
the full sample of reverberation masses, it also means that the reverberation
mass for any particular AGN may be over/underestimated by a factor of a few.
If we assume that the variance in $f$ values between different AGNs is mainly
due to their random inclinations to our line of sight (as suggested by the
analysis of Williams et al. 2018), then $\langle f\rangle\approx 5$ implies a
typical inclination of 27°. For an AGN that is observed at a lower (more face-
on) inclination, $\langle f\rangle\approx 5$ would significantly underestimate
the correction needed to convert the line-of-sight velocity component to the
true velocity when determining $M_{\rm BH}$. And in the case of NGC 3227, a
factor of $\sim 4$ discrepancy between the reverberation mass and the
dynamical masses could be resolved if the AGN were found to be viewed at an
angle of $\sim 15$°.

Using the measurements for H$\beta$ listed in Table 1 indicates $M_{\rm
BH}=1.07^{+0.23}_{-0.25}\times 10^{7}$ $M_{\odot}$. This is somewhat larger
than the masses that were determined by Denney et al. (2010) and De Rosa et
al. (2018), but the 1$\sigma$ range formally agrees with the low end of the
uncertainties on the much higher mass reported by Brotherton et al. 2020. The
time delay for H$\beta$ found in this work and the analysis of Denney et al.
(2010) are nearly identical, however, somewhat perplexingly, while the FWHM
measurements of H$\beta$ agree within the uncertainties, $\sigma_{\rm line}$
is $\sim 300$ km s-1 (22%) larger in our measurements leading to a larger
derived mass. The rms line profile presented by Denney et al. (2010) shows a
clear double-peaked shape without strong wings, while the rms line profile in
our observations has strong wings and the same blue peak but without the
corresponding red peak, potentially indicating a significant change in the
properties of the reverberating gas.

The H$\beta$ mass from our time delay and line width measurements is in good
agreement with the mass from CARAMEL modeling of $\log
M/M_{\odot}=7.09^{+0.35}_{-0.34}$ or $M_{\rm BH}=1.23^{+1.52}_{-0.67}\times
10^{7}$ $M_{\odot}$, and in this case, the good agreement is likely because
the inclination angles preferred by CARAMEL ($\theta_{i}=33.2^{+13.5}_{-9.1}$)
are similar to the population average value implied by $\langle
f\rangle\approx 5$. Interestingly, this inclination angle agrees with the
results of a reanalysis of the geometry of the spatially resolved narrow line
region (Falcone et al., 2023), while an earlier analysis suggested a much
smaller value of $\theta_{i}\approx 15\arcdeg$ (Fischer et al., 2013).

Additionally, while the black hole mass from this reverberation program agrees
with the dynamical masses, there are still good reasons to revisit the
dynamical constraints. Gas dynamical modeling is known to be susceptible to
biases when the gas exhibits noncircular motions, and this worry should be
taken seriously in the presence of an AGN (e.g., Verdoes Kleijn et al. 2006;
Jeter et al. 2019). While stellar dynamical modeling is usually held to be
more accurate, the stellar dynamical modeling analysis of Davies et al. (2006)
relied on fairly shallow but high spatial resolution observations of the
nucleus of NGC 3227, and the $S/N$ of the observations only allowed $V$ and
$\sigma$ to be constrained for the stellar kinematics. Best practices in
stellar dynamical modeling require that the kinematic constraints include not
only $V$ and $\sigma$, but also additional higher order terms to reduce the
degeneracy between velocity anisotropy of the stellar distribution and $M_{\rm
BH}$ (Binney & Mamon, 1982). Because of this potential degeneracy, deeper
observations that provide more detailed information regarding the nuclear
stellar kinematics are needed to accurately assess the dynamical constraints
on the black hole mass in NGC 3227.

###  4.3 BLR Structure and Kinematics

Modeling of the velocity-resolved H$\beta$ response in NGC 3227 with CARAMEL
suggests that the BLR may be represented by the surface of a biconical
structure or flared disk, oriented at $\sim 33\arcdeg$ to our line of sight
and with gas motions that are dominated by rotation around a black hole with
$M_{\rm BH}\approx 1.2\times 10^{7}$ $M_{\odot}$. While there are independent
measurements of the inclination and black hole mass with which we can compare
the CARAMEL constraints, as we have described above, there are few options for
independent tests of the other BLR properties determined by CARAMEL.

One promising new tool that is currently being developed is BELMAC (Broad
Emission-Line Mapping Code; Rosborough et al. 2023), an extension of TORMAC
(Almeyda et al., 2017, 2020) that has been adapted for application to the BLR.
BELMAC simulates the velocity-resolved response of an emission line to an
input driving light curve. Using photoionization grids and a 3D ensemble of
gas clouds, BELMAC simulates the observed response of the gas clouds to
continuum variations for various user-specified geometries, velocity fields,
and cloud properties.

While BELMAC is not yet able to independently explore and optimize the models
to determine a best fit to the observed behavior of an emission line (though
that capability is currently under development), we were able to use it in its
current form to carry out two important tests: (1) when given the results of
the CARAMEL models, could BELMAC confirm that the models provided a good fit
to the data?, and (2) what types of geometric and kinematic parameters allow
BELMAC to most closely replicate the observed integrated H$\beta$ light curve
and mean and rms line profiles?

Figure 8: H$\beta$ and model light curves (left) as black points and blue
curve, respectively. Mean and rms line profile in black and grey,
respectively, and the model mean and rms line profiles in blue and light blue,
respectively, for broad H$\beta$. The narrow H$\beta$ line profile is in
yellow and the overall fit is in red (right). The light curve and line profile
models were created using BELMAC with parameters interpreted from Table 4.
Figure 9: The same as Figure 8, but with model parameters adjusted to best
match the H$\beta$ light curve, line profile, and rms profile.

We began by calculating the photoionization grids using CLOUDY v17.03 (Ferland
et al., 2017) assuming a bolometric luminosity for NGC 3227 of $\log L_{\rm
bol}=43.16$ erg s-1 (where $L_{\rm bol}=9\lambda L_{\rm 5100}$; Kaspi et al.
2000; Merritt 2022) and an SED based on the average of 17 local, unobscured
AGNs with Eddington ratios $<0.1$ from Jin et al. (2012). The BELMAC model
results shown in Figure 8 were then created using the median values of
$r_{min}$, $r_{mean}$, $\theta_{i}$, and $M_{\rm BH}$ listed in Table 4.
Although $\gamma$ and $\xi$ are not BELMAC parameters, they imply a biconical
geometry, as shown in Figure 7, which is a BELMAC geometry configuration. To
obtain a better match to the H$\beta$ data, $\theta_{o}$ was used as a guide
rather than a fixed parameter. Assuming a bicone, $\theta_{o}$ is
approximately the separation angle between each cone and the midplane.
Therefore, the angular distribution of clouds ranged from $5-55\arcdeg$, where
$0\arcdeg$ is the midplane, for each cone. Similarly, the emission
distribution described by CARAMEL’s $\beta$ and $\sigma_{r}$ parameters
provide estimates for the cloud distribution, gas density distribution, and
covering fraction. In BELMAC, the number density of clouds with radius and gas
density of the clouds with radius are, respectively, $N(r)\propto r^{p}$ and
$n_{H}(r)\propto r^{-s}$, where $p$ and $s$ are the free parameters. The
cross-sectional area of the clouds is primarily determined from the covering
fraction. To approximately match CARAMEL’s emission distribution, we adopted
$p=-2$, $s=-1.45$, with a gas density at the outer radius of $\log n_{H}=9.3$
cm-3, and a covering fraction of 0.4. Lastly, rotational and radial motions
were included in the BELMAC model, where the radial cloud motion is influenced
by radiation pressure and gravity. Therefore, using the CARAMEL parameters
listed in Table 4 to guide the above described BELMAC parameters, the radial
motion is entirely an inflow. In general, the model is able to reproduce the
integrated light curve fairly well, and does a reasonable job matching the
mean and rms line profiles, though there is some mismatch in the wings of the
mean line profile and the blue peak of the rms profile.

In comparison, Figure 9 shows the best BELMAC model results to the data. Since
there is currently no parameter optimization capability, the parameters were
manually adjusted until a reasonable match to the data was found. However, the
same $r_{min}$, $r_{mean}$, and $M_{\rm BH}$ determined by CARAMEL were used,
as well as the same photoionization grids. The best model found is a disk with
a half-angular width $30\arcdeg$ (analogous to $\theta_{o}$) and inclined to
our line of sight at $35\arcdeg$. About $53\%$ of the clouds in the model have
bound elliptical orbits and $47\%$ are unbound hyperbolic orbits, of which
$98\%$ are inflowing. The geometry is described by $p=-1.7$, $s=-1.3$, where
the gas density at the outer radius is $\log n_{H}=9.2$ cm-3, and the covering
fraction is 0.33. Other than the overall shape of this BELMAC BLR model, which
is a thick disk rather than a bicone, and a preference for a stronger inflow
component, the parameters are in general agreement with those inferred by
CARAMEL, lending additional credence to the derived inclination angle and
black hole mass. Furthermore, while some of the details appear to be slightly
different between the preferred models from the two codes, we note that it is
not straightforward to directly compare them since CARAMEL models the emission
itself while BELMAC includes a full distribution of gas clouds, including
those that may be shielded or only weakly emitting. Nevertheless, both agree
that the H$\beta$-emitting BLR is extended in radius and of similar predicted
size, that the geometry is flattened rather than spherical, and that the
kinematics are not dominated by outflows (as might be expected for a disk
wind) but instead are dominated by rotation and/or inflow.

##  5 Summary

We have carried out a new optical reverberation mapping campaign focused on
the nearby broad-lined Seyfert NGC 3227. Using the LCO global network of
telescopes, we employed broad-band photometry to track the continuum
variations coupled with spectroscopy to track the responses of the broad
emission lines. Time delays relative to the continuum variations were found
for the H$\beta$, He II, H$\gamma$, and H$\delta$ broad emission lines. We
also detected velocity-resolved time delays across the broad H$\beta$
emission-line profile.

Modeling of the velocity-resolved H$\beta$ response with CARAMEL finds a black
hole mass of $\log M/M_{\odot}=7.09^{+0.35}_{-0.34}$ or $M_{\rm
BH}=1.2^{+1.5}_{-0.7}\times 10^{7}$ $M_{\odot}$, which agrees well with the
mass determined from the H$\beta$ time delay and line width when atypical
scaling factor is assumed, $M_{\rm BH}=1.1^{+0.2}_{-0.3}\times 10^{7}$
$M_{\odot}$. This good agreement is likely due to the intermediate inclination
that is preferred by the models, $\theta_{i}\approx 33\arcdeg$, which is
similar to the population-average inclination angle that is implied by typical
RM scale factors of $\langle f\rangle=4-5$. The models also suggest that the
H$\beta$-emitting BLR may be represented by the inner surface of a biconical
or flared disk structure, and that the gas motions are dominated by rotation.

Finally, using the photoionization-based modeling code BELMAC, we confirmed
that the CARAMEL results provide a reasonable fit to the H$\beta$ light curve
and mean and rms line profiles, though there is some mismatch in the line
wings. To correct for this mismatch, BELMAC prefers a thick disk geometry,
rather than a bicone, and roughly equal weight between rotation and inflow.
While they disagree about these details, both codes agree on several general
properties, including that the H$\beta$-emitting BLR is extended in radius,
flattened rather than spherical, and that the kinematics are dominated by
rotation and/or inflow rather than outflow. Future improvements to the BELMAC
code will allow a more thorough exploration of reasonable BLR parameter
combinations for this AGN and others, and a more detailed comparison with the
modeling results from CARAMEL.

MCB gratefully acknowledges support from the NSF through grant AST-2009230. MM
was supported by National Science Foundation grant No. 2050829 to Georgia
State University under the Research Experiences for Undergraduates program. SR
was supported by NSF grant AST-2009508. CAO was supported by the Australian
Research Council (ARC) through Discovery Project DP190100252. MV was supported
by the NSF through AST-2009122. TT gratefully acknowledges supprt by NSF
through grant AST-1907208. LCOGT

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