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Lijie Liu

Publications and source records attributed to Lijie Liu.

At least 37 records · Page 2Linked to original sources

WISDOM Project -- XV. Giant Molecular Clouds in the Central Region of the Barred Spiral Galaxy NGC 5806

We present high spatial resolution ($\approx24$ pc) Atacama Large Millimeter/sub-millimeter Array $^{12}$CO(2-1) observations of the central region of the nearby barred spiral galaxy NGC 5806. NGC 5806 has a highly structured molecular gas distribution with a clear nucleus, a nuclear ring and offset dust lanes. We identify $170$ spatially- and spectrally-resolved giant molecular clouds (GMCs). These clouds have comparable sizes ($R_{\mathrm{c}}$) and larger gas masses, observed linewidths ($σ_{\mathrm{obs,los}}$) and gas mass surface densities than those of clouds in the Milky Way disc. The size -- linewidth relation of the clouds is one of the steepest reported so far ($σ_{\mathrm{obs,los}}\propto R_{\mathrm{c}}^{1.20}$), the clouds are on average only marginally bound (with a mean virial parameter $\langleα_{\mathrm{vir}}\rangle\approx2$), and high velocity dispersions are observed in the nuclear ring. These behaviours are likely due to bar-driven gas shocks and inflows along the offset dust lanes, and we infer an inflow velocity of $\approx120$ kms$^{-1}$ and a total molecular gas mass inflow rate of $\approx5$ M$_\odot$ yr$^{-1}$ into the nuclear ring. The observed internal velocity gradients of the clouds are consistent with internal turbulence. The number of clouds in the nuclear ring decreases with azimuthal angle downstream from the dust lanes without clear variation of cloud properties. This is likely due to the estimated short lifetime of the clouds ($\approx6$ Myr), which appears to be mainly regulated by cloud-cloud collision and/or shear processes. Overall, it thus seems that the presence of the large-scale bar and gas inflows to the centre of NGC 5806 affect cloud properties.

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WISDOM Project -- XIII. Feeding molecular gas to the supermassive black hole in the starburst AGN-host galaxy Fairall 49

The mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) is probing supermassive black holes (SMBHs) in galaxies across the Hubble sequence via molecular gas dynamics. We present the first WISDOM study of a luminous infrared galaxy with an active galactic nuclei (AGN): Fairall 49. We use new ALMA observations of the CO(2-1) line with a spatial resolution of about 80 pc together with ancillary HST imaging. We reach the following results: (1) The CO kinematics are well described by a regularly rotating gas disk with a radial inflow motion, suggesting weak feedback on the cold gas from both AGN and starburst activity; (2) The dynamically inferred SMBH mass is 1.6 +/- 0.4 (rnd) +/- 0.8 (sys) x 10^8 Msun, assuming that we have accurately subtracted the AGN and starburst light contributions, which have a luminosity of about 10^9 Lsun; (3) The SMBH mass agrees with the SMBH-stellar mass relation but is about 50 times higher than previous estimates from X-ray variability; (4) The dynamically inferred molecular gas mass is 30 times smaller than that inferred from adopting the Galactic CO-to-H_2 conversion factor (X_CO) for thermalised gas, suggesting low values of X_CO; (5) the molecular gas inflow rate increases steadily with radius and may be as high as 5 Msun/yr. This work highlights the potential of using high-resolution CO data to estimate, in addition to SMBH masses, the X_CO factor and gas inflow rates in nearby galaxies.

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WISDOM Project XII. Clump properties and turbulence regulated by clump-clump collisions in the dwarf galaxy NGC404

We present a study of molecular structures (clumps and clouds) in the dwarf galaxy NGC 404 using high-resolution (0.86x0.51 pc^2) Atacama Large Millimeter/sub-millimeter Array ^{12}CO(2-1) observations. We find two distinct regions in NGC 404: a gravitationally-stable central region (Toomre parameter Q=3-30) and a gravitationally-unstable molecular ring (Q<=1). The molecular structures in the central region have a steeper size -- linewidth relation and larger virial parameters than those in the molecular ring, suggesting gas is more turbulent in the former. In the molecular ring, clumps exhibit a shallower mass -- size relation and larger virial parameters than clouds, implying density structures and dynamics are regulated by different physical mechanisms at different spatial scales. We construct an analytical model of clump-clump collisions to explain the results in the molecular ring. We propose that clump-clump collisions are driven by gravitational instabilities coupled with galactic shear, that lead to a population of clumps whose accumulation lengths (i.e. average separations) are approximately equal to their tidal radii. Our model-predicted clump masses and sizes (and mass -- size relation) and turbulence energy injection rates (and size -- linewidth relation) match the observations in the molecular ring very well, suggesting clump-clump collisions is the main mechanism regulating clump properties and gas turbulence in that region. As expected, our collision model does not apply to the central region, where turbulence is likely driven by clump migration.

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WISDOM project -- XI. Star Formation Efficiency in the Bulge of the AGN-host Galaxy NGC 3169 with SITELLE and ALMA

The star formation efficiency (SFE) has been shown to vary across different environments, particularly within galactic starbursts and deep within the bulges of galaxies. Various quenching mechanisms may be responsible, ranging from galactic dynamics to feedback from active galactic nuclei (AGN). Here, we use spatially-resolved observations of warm ionised gas emission lines from the imaging Fourier transform spectrograph SITELLE at the Canada-France-Hawaii Telescope (CFHT) and cold molecular gas (CO(2-1)) from the Atacama Large Millimeter/sub-millimeter Array (ALMA) to study the SFE in the bulge of the AGN-host galaxy NGC 3169. After distinguishing star-forming regions from AGN-ionised regions using emission-line ratio diagnostics, we measure spatially-resolved molecular gas depletion times (τ_dep = 1/SFE) with a spatial resolution of \approx 100 pc within a galactocentric radius of 1.8 kpc. We identify a star-forming ring located at radii 1.25 \pm 0.6 kpc with an average τ_dep of 0.3 Gyr. At radii < 0.9 kpc, however, the molecular gas surface densities and depletion times increase with decreasing radius, the latter reaching approximately 2.3 Gyr at a radius \approx 500 pc. Based on analyses of the gas kinematics and comparisons with simulations, we identify AGN feedback, bulge morphology and dynamics as the possible causes of the radial profile of SFE observed in the central region of NGC 3169.

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WISDOM Project -- X. The morphology of the molecular ISM in galaxy centres and its dependence on galaxy structure

We use high-resolution maps of the molecular interstellar medium (ISM) in the centres of eighty-six nearby galaxies from the millimetre-Wave Interferometric Survey of Dark Object Masses (WISDOM) and Physics at High Angular Resolution in Nearby GalaxieS (PHANGS) surveys to investigate the physical mechanisms setting the morphology of the ISM at molecular cloud scales. We show that early-type galaxies tend to have smooth, regular molecular gas morphologies, while the ISM in spiral galaxy bulges is much more asymmetric and clumpy when observed at the same spatial scales. We quantify these differences using non-parametric morphology measures (Asymmetry, Smoothness and Gini), and compare these measurements with those extracted from idealised galaxy simulations. We show that the morphology of the molecular ISM changes systematically as a function of various large-scale galaxy parameters, including galaxy morphological type, stellar mass, stellar velocity dispersion, effective stellar mass surface density, molecular gas surface density, star formation efficiency and the presence of a bar. We perform a statistical analysis to determine which of these correlated parameters best predicts the morphology of the ISM. We find the effective stellar mass surface (or volume) density to be the strongest predictor of the morphology of the molecular gas, while star formation and bars maybe be important secondary drivers. We find that gas self-gravity is not the dominant process shaping the morphology of the molecular gas in galaxy centres. Instead effects caused by the depth of the potential well such as shear, suppression of stellar spiral density waves and/or inflow affect the ability of the gas to fragment.

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FaceEraser: Removing Facial Parts for Augmented Reality

Our task is to remove all facial parts (e.g., eyebrows, eyes, mouth and nose), and then impose visual elements onto the ``blank'' face for augmented reality. Conventional object removal methods rely on image inpainting techniques (e.g., EdgeConnect, HiFill) that are trained in a self-supervised manner with randomly manipulated image pairs. Specifically, given a set of natural images, randomly masked images are used as inputs and the raw images are treated as ground truths. Whereas, this technique does not satisfy the requirements of facial parts removal, as it is hard to obtain ``ground-truth'' images with real ``blank'' faces. To address this issue, we propose a novel data generation technique to produce paired training data that well mimic the ``blank'' faces. In the mean time, we propose a novel network architecture for improved inpainting quality for our task. Finally, we demonstrate various face-oriented augmented reality applications on top of our facial parts removal model. The source codes are released at \href{https://github.com/duxingren14/FaceEraser}{duxingren14/FaceEraser} on github for research purposes.

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WISDOM Project -- IX Giant Molecular Clouds in the Lenticular Galaxy NGC4429: Effects of Shear and Tidal Forces on Clouds

We present high spatial resolution (12pc) Atacama Large Millimeter/sub-millimeter Array CO(J=3-2) observations of the nearby lenticular galaxy NGC4429. We identify 217 giant molecular clouds within the 450pc radius molecular gas disc. The clouds generally have smaller sizes and masses but higher surface densities and observed linewidths than those of Milky Way disc clouds. An unusually steep size - line width relation and large cloud internal velocity gradients (0.05 - 0.91 km s^-1 pc^-1) and observed Virial parameters (alpha_obs,vir = 4.0) are found, that appear due to internal rotation driven by the background galactic gravitational potential. Removing this rotation, an internal Virial equilibrium appears to be established between the self-gravitational (Usg) and turbulent kinetic (Eturb) energies of each cloud, i.e. alpha_sg,vir=Usg/Eturb = 1.3. However, to properly account for both self and external gravity (shear and tidal forces), we formulate a modified Virial theorem and define an effective Virial parameter alpha_eff,vir = alpha_sg,vir + Usg/Eext (and associated effective velocity dispersion). The NGC4429 clouds then appear to be in a critical state in which the self-gravitational energy and the contribution of external gravity to the cloud's energy budget (Eext) are approximately equal, i.e. Eext/Usg~1. As such, alpha_eff,vir = 2.2 and most clouds are not virialised but remain marginally gravitationally bound. We show this is consistent with the clouds having sizes similar to their tidal radii and being generally radially elongated. External gravity is thus as important as self-gravity to regulate the clouds of NGC4429.

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WISDOM Project -- VII. Molecular gas measurement of the supermassive black hole mass in NGC 7052

Supermassive black hole (SMBH) masses can be measured by resolving the dynamical influences of the SMBHs on spatially-resolved tracers of the central potentials. Modern long-baseline interferometers have enabled the use of molecular gas as such a tracer. We present here Atacama Large Millimeter/submillimeter Array observations of the elliptical galaxy NGC 7052 at 0.11 arcseconds (37 pc) resolution in the 12CO(2-1) line and 1.3mm continuum emission. This resolution is sufficient to resolve the region in which the potential is dominated by the SMBH. We forward model these observations, using a multi-Gaussian expansion of a Hubble Space Telescope F814W image and spatially-constant mass-to-light ratio to model the stellar mass distribution. We infer a SMBH mass of $2.5\pm0.3\times10^9\,\mathrm{M_\odot}$ and a stellar I-band mass-to-light ratio of $4.6\pm 0.2\,\mathrm{M_\odot/L_{\odot,I}}$ ($3σ$ confidence intervals). This SMBH mass is significantly larger than that derived using ionised gas kinematics, which however appear significantly more kinematically disturbed than the molecular gas. We also show that a central molecular gas deficit is likely to be the result of tidal disruption of molecular gas clouds due to the strong gradient in the central gravitational potential.

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WISDOM project -- VIII. Multi-scale feedback cycles in the brightest cluster galaxy NGC 0708

We present high-resolution (synthesised beam size 0."088x0."083 or 25x23 pc$^2$) Atacama Large Millimetre/submillimetre Array (ALMA) $^{12}$CO(2-1) line and 236 GHz continuum observations, as well as 5 GHz enhanced Multi-Element Radio Linked Interferometer Network (e-MERLIN) continuum observations, of NGC 0708; the brightest galaxy in the low-mass galaxy cluster Abell 262. The line observations reveal a turbulent, rotating disc of molecular gas in the core of the galaxy, and a high-velocity, blue-shifted feature ~0."4 (~113 pc) from its centre. The sub-millimetre continuum emission peaks at the nucleus, but extends towards this anomalous CO emission feature. No corresponding elongation is found on the same spatial scales at 5 GHz with e-MERLIN. We discuss potential causes for the anomalous blue-shifted emission detected in this source, and conclude that it is most likely to be a low-mass in-falling filament of material condensing from the hot intra-cluster medium via chaotic cold accretion, but it is also possible that it is a jet-driven molecular outflow. We estimate the physical properties this structure has in these two scenarios, and show that either explanation is viable. We suggest future observations with integral field spectrographs will be able to determine the true cause of this anomalous emission, and provide further evidence for interaction between quenched cooling flows and mechanical feedback on both small and large scales in this source.

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WISDOM project -- VI. Exploring the relation between supermassive black hole mass and galaxy rotation with molecular gas

Empirical correlations between the masses of supermassive black holes (SMBHs) and properties of their host galaxies are well-established. Among these is the correlation with the flat rotation velocity of each galaxy measured either at a large radius in its rotation curve or via a spatially-integrated emission line width. We propose here the use of the de-projected integrated CO emission line width as an alternative tracer of this rotation velocity, that has already been shown useful for the Tully-Fisher (luminosity-rotation velocity) relation. We investigate the correlation between CO line widths and SMBH masses for two samples of galaxies with dynamical SMBH mass measurements, with respectively spatially-resolved and unresolved CO observations. The tightest correlation is found using the resolved sample of 24 galaxies as $\log (M_\mathrm{BH}/\mathrm{M_\odot})=(7.5\pm0.1)+(8.5\pm0.9)[\log(W_\mathrm{50}/\sin i \,\mathrm{km\,s}^{-1})-2.7]$, where $M_\mathrm{BH}$ is the central SMBH mass, $W_{50}$ the full-width at half-maximum of a double-horned emission line profile, and $i$ the inclination of the CO disc. This relation has a total scatter of $0.6\,$dex, comparable to those of other SMBH mass correlations, and dominated by the intrinsic scatter of $0.5\,$dex. A tight correlation is also found between the de-projected CO line widths and the stellar velocity dispersions averaged within one effective radius. We apply our correlation to the COLD GASS sample to estimate the local SMBH mass function.

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Reinforced Axial Refinement Network for Monocular 3D Object Detection

Monocular 3D object detection aims to extract the 3D position and properties of objects from a 2D input image. This is an ill-posed problem with a major difficulty lying in the information loss by depth-agnostic cameras. Conventional approaches sample 3D bounding boxes from the space and infer the relationship between the target object and each of them, however, the probability of effective samples is relatively small in the 3D space. To improve the efficiency of sampling, we propose to start with an initial prediction and refine it gradually towards the ground truth, with only one 3d parameter changed in each step. This requires designing a policy which gets a reward after several steps, and thus we adopt reinforcement learning to optimize it. The proposed framework, Reinforced Axial Refinement Network (RAR-Net), serves as a post-processing stage which can be freely integrated into existing monocular 3D detection methods, and improve the performance on the KITTI dataset with small extra computational costs.

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Revealing the intermediate-mass black hole at the heart of the dwarf galaxy NGC 404 with sub-parsec resolution ALMA observations

We estimate the mass of the intermediate-mass black hole at the heart of the dwarf elliptical galaxy NGC 404 using Atacama Large Millimeter/submillimeter Array (ALMA) observations of the molecular interstellar medium at an unprecedented linear resolution of ~0.5 pc, in combination with existing stellar kinematic information. These ALMA observations reveal a central disc/torus of molecular gas clearly rotating around the black hole. This disc is surrounded by a morphologically and kinematically complex flocculent distribution of molecular clouds, that we resolve in detail. Continuum emission is detected from the central parts of NGC 404, likely arising from the Rayleigh-Jeans tail of emission from dust around the nucleus, and potentially from dusty massive star-forming clumps at discrete locations in the disc. Several dynamical measurements of the black hole mass in this system have been made in the past, but they do not agree. We show here that both the observed molecular gas and stellar kinematics independently require a ~5x10$^5$ Msun black hole once we include the contribution of the molecular gas to the potential. Our best estimate comes from the high-resolution molecular gas kinematics, suggesting the black hole mass of this system is 5.5$^{+4.1}_{-3.8}\times$10$^5$ Msun (at the 99% confidence level), in good agreement with our revised stellar kinematic measurement and broadly consistent with extrapolations from the black hole mass - velocity dispersion and black hole mass - bulge mass relations. This highlights the need to accurately determine the mass and distribution of each dynamically important component around intermediate-mass black holes when attempting to estimate their masses.

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Estimating the molecular gas mass of low-redshift galaxies from a combination of mid-infrared luminosity and optical properties

We present CO(J=1-0) and/or CO(J=2-1) spectroscopy for 31 galaxies selected from the ongoing MaNGA survey, obtained with multiple telescopes. This sample is combined with CO observations from the literature to study the correlation of the CO luminosities ($L_{\rm CO(1-0)}$) with the mid-infrared luminosities at 12 ($L_{12 μm}$) and 22 $μ$m ($L_{\rm 22 μm}$), as well as the dependence of the residuals on a variety of galaxy properties. The correlation with $L_{\rm 12 μm}$ is tighter and more linear, but galaxies with relatively low stellar masses and blue colors fall significantly below the mean $L_{\rm CO(1-0)}-L_{\rm 12μm}$ relation. We propose a new estimator of the CO(1-0) luminosity (and thus the total molecular gas mass) that is a linear combination of three parameters: $L_{\rm 12 μm}$, $M_\ast$ and $g-r$. We show that, with a scatter of only 0.18 dex in log $(L_{\rm CO(1-0)})$, this estimator provides unbiased estimates for galaxies of different properties and types. An immediate application of this estimator to a compiled sample of galaxies with only CO(J=2-1) observations yields a distribution of the CO(J=2-1) to CO(J=1-0) luminosity ratios ($R21$) that agrees well with the distribution of real observations, in terms of both the median and the shape. Application of our estimator to the current MaNGA sample reveals a gas-poor population of galaxies that are predominantly early-type and show no correlation between molecular gas-to-stellar mass ratio and star formation rate, in contrast to gas-rich galaxies. We also provide alternative estimators with similar scatters, based on $r$ and/or $z$ band luminosities instead of $M_\ast$. These estimators serve as cheap and convenient $M_{\rm mol}$ proxies to be potentially applied to large samples of galaxies, thus allowing statistical studies of gas-related processes of galaxies.

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WISDOM project -- V. Resolving molecular gas in Keplerian rotation around the supermassive black hole in NGC 0383

As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM), we present a measurement of the mass of the supermassive black hole (SMBH) in the nearby early-type galaxy NGC 0383 (radio source 3C 031). This measurement is based on Atacama Large Millimeter/sub-milimeter Array (ALMA) cycle 4 and 5 observations of the 12CO(2-1) emission line with a spatial resolution of 58x32pc2 (0."18x0."1). This resolution, combined with a channel width of 10 km/s, allows us to well resolve the radius of the black hole sphere of influence (measured as R_SOI = 316pc = 0."98), where we detect a clear Keplerian increase of the rotation velocities. NGC 0383 has a kinematically-relaxed, smooth nuclear molecular gas disc with weak ring/spiral features. We forward-model the ALMA data cube with the Kinematic Molecular Simulation (KinMS) tool and a Bayesian Markov Chain Monte Carlo method to measure a SMBH mass of (4.2+/-0.7)x10^9 Msun, a F160W-band stellar mass-to-light ratio that varies from 2.8+/-0.6 Msun/Lsun in the centre to 2.4+/-0.3 Msun/Lsun at the outer edge of the disc and a molecular gas velocity dispersion of 8.3+/-2.1 km/s (all 3-sigma uncertainties). We also detect unresolved continuum emission across the full bandwidth, consistent with synchrotron emission from an active galactic nucleus. This work demonstrates that low-J CO emission can resolve gas very close to the SMBH (~140,000 Schwarzschild radii) and hence that the molecular gas method is highly complimentary to megamaser observations as it can probe the same emitting material.

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Deep Fitting Degree Scoring Network for Monocular 3D Object Detection

In this paper, we propose to learn a deep fitting degree scoring network for monocular 3D object detection, which aims to score fitting degree between proposals and object conclusively. Different from most existing monocular frameworks which use tight constraint to get 3D location, our approach achieves high-precision localization through measuring the visual fitting degree between the projected 3D proposals and the object. We first regress the dimension and orientation of the object using an anchor-based method so that a suitable 3D proposal can be constructed. We propose FQNet, which can infer the 3D IoU between the 3D proposals and the object solely based on 2D cues. Therefore, during the detection process, we sample a large number of candidates in the 3D space and project these 3D bounding boxes on 2D image individually. The best candidate can be picked out by simply exploring the spatial overlap between proposals and the object, in the form of the output 3D IoU score of FQNet. Experiments on the KITTI dataset demonstrate the effectiveness of our framework.

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JINGLE, a JCMT legacy survey of dust and gas for galaxy evolution studies: II. SCUBA-2 850 μm data reduction and dust flux density catalogues

We present the SCUBA-2 850 $μm$ component of JINGLE, the new JCMT large survey for dust and gas in nearby galaxies, which with 193 galaxies is the largest targeted survey of nearby galaxies at 850 $μm$. We provide details of our SCUBA-2 data reduction pipeline, optimised for slightly extended sources, and including a calibration model adjusted to match conventions used in other far-infrared data. We measure total integrated fluxes for the entire JINGLE sample in 10 infrared/submillimetre bands, including all WISE, Herschel-PACS, Herschel-SPIRE and SCUBA-2 850 $μm$ maps, statistically accounting for the contamination by CO(J=3-2) in the 850 $μm$ band. Of our initial sample of 193 galaxies, 191 are detected at 250 $μm$ with a $\geq$ 5$σ$ significance. In the SCUBA-2 850 $μm$ band we detect 126 galaxies with $\geq$ 3$σ$ significance. The distribution of the JINGLE galaxies in far-infrared/sub-millimetre colour-colour plots reveals that the sample is not well fit by single modified-blackbody models that assume a single dust-emissivity index $(β)$. Instead, our new 850 $μm$ data suggest either that a large fraction of our objects require $β< 1.5$, or that a model allowing for an excess of sub-mm emission (e.g., a broken dust emissivity law, or a very cold dust component 10 K) is required. We provide relations to convert far-infrared colours to dust temperature and $β$ for JINGLE-like galaxies. For JINGLE the FIR colours correlate more strongly with star-formation rate surface-density rather than the stellar surface-density, suggesting heating of dust is greater due to younger rather than older stellar-populations, consistent with the low proportion of early-type galaxies in the sample.

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WISDOM project - IV. A molecular gas dynamical measurement of the supermassive black hole mass in NGC 524

We present high angular resolution (0.3" or 37 pc) Atacama Large Millimeter/sub-millimeter Array (ALMA) observations of the CO(2-1) line emission from a central disc in the early-type galaxy NGC 524. This disc is shown to be dynamically relaxed, exhibiting ordered rotation about a compact 1.3mm continuum source, which we identify as emission from an active supermassive black hole (SMBH). There is a hole at the centre of the disc slightly larger than the SMBH sphere of influence. An azimuthal distortion of the observed velocity field is found to be due to either a position angle warp or radial gas flow over the inner 2.5". By forward-modelling the observations, we obtain an estimate of the SMBH mass of $4.0^{+3.5}_{-2.0}\times10^8\,\mathrm{M_\odot}$, where the uncertainties are at the $3σ$ level. The uncertainties are dominated by the poorly constrained inclination and the stellar mass-to-light ratio of this galaxy, and our measurement is consistent with the established correlation between SMBH mass and stellar velocity dispersion. Our result is roughly half that of the previous stellar dynamical measurement, but is consistent within the uncertainties of both. We also present and apply a new tool for modelling complex molecular gas distributions.

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WISDOM Project - III: Molecular gas measurement of the supermassive black hole mass in the barred lenticular galaxy NGC4429

As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) project we present an estimate of the mass of the supermassive black hole (SMBH) in the nearby fast-rotating early-type galaxy NGC4429, that is barred and has a boxy/peanut-shaped bulge. This estimate is based on Atacama Large Millimeter/submillimeter Array (ALMA) cycle-2 observations of the 12CO(3-2) emission line with a linear resolution of ~13 pc (0"18x0"14). NGC4429 has a relaxed, flocculent nuclear disc of molecular gas that is truncated at small radii, likely due to the combined effects of gas stability and tidal shear. The warm/dense 12CO(3-2) emitting gas is confined to the inner parts of this disc, likely again because the gas becomes more stable at larger radii, preventing star formation. The gas disc has a low velocity dispersion of 2.2$^{+0.68}_{-0.65}$ km/s. Despite the inner truncation of the gas disc, we are able to model the kinematics of the gas and estimate a mass of (1.5$\pm0.1^{+0.15}_{-0.35}$)$\times$10$^8$ Msun for the SMBH in NGC4429 (where the quoted uncertainties reflect the random and systematic uncertainties, respectively), consistent with a previous upper limit set using ionised gas kinematics. We confirm that the V-band mass-to-light ratio changes by ~30% within the inner 400 pc of NGC4429, as suggested by other authors. This SMBH mass measurement based on molecular gas kinematics, the sixth presented in the literature, once again demonstrates the power of ALMA to constrain SMBH masses.

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