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We report the discovery of the ‘mm fundamental plane of black hole accretion’, which is a tight correlation between the nuclear 1 mm luminosity (Lν, mm), the intrinsic 2–10 keV X-ray luminosity (LX, 2–10) and the supermassive black hole (SMBH) mass (MBH) with an intrinsic scatter (σint) of 0.40 dex. The plane is found for a sample of 48 nearby galaxies, most of which are low-luminosity active galactic nuclei. Combining these sources with a sample of high-luminosity (quasar-like) nearby AGN, we show that the plane still holds. We also find that MBH correlates with Lν, mm at a highly significant level, although such correlation is less tight than the mm fundamental plane (σint = 0.51 dex). Crucially, we show that spectral energy distribution (SED) models for both advection-dominated accretion flows (ADAFs) and compact jets can explain the existence of these relations, which are not reproduced by the standard torus-thin accretion disc models usually associated to quasar-like AGN. The ADAF models reproduces the observed relations somewhat better than those for compact jets, although neither provides a perfect fit. Our findings thus suggest that radiatively inefficient accretion processes such as those in ADAFs or compact (and thus possibly young) jets may play a key role in both low- and high-luminosity AGN. This mm fundamental plane also offers a new, rapid method to (indirectly) estimate SMBH masses.

 

The co-evolution of galaxies and supermassive black holes (SMBHs) underpins our understanding of galaxy evolution, but different methods to measure SMBH masses have only infrequently been cross-checked. We attempt to identify targets to cross-check two of the most accurate methods, megamaser, and cold molecular gas dynamics. Three promising galaxies are selected from all those with existing megamaser SMBH mass measurements. We present Atacama Large Millimeter/sub-millimeter Array (ALMA) 12CO (2–1) and 230-GHz continuum observations with angular resolutions of ≈0${_{.}^{\prime\prime}}$5. Every galaxy has an extended rotating molecular gas disc and 230-GHz continuum source(s), but all also have irregularities and/or non-axisymmetric features: NGC 1194 is highly inclined and has disturbed and lopsided central 12CO (2–1) emission; NGC 3393 has a nuclear disc with fairly regular but patchy 12CO (2–1) emission with little gas near the kinematic major axis, faint emission in the very centre, and two brighter structures reminiscent of a nuclear ring and/or spiral; NGC 5765B has a strong bar and very bright 12CO (2–1) emission concentrated along two bisymmetric offset dust lanes and two bisymmetric nuclear spiral arms. 12CO (2–1) and 12CO (3–2) observations with the James Clerk Maxwell Telescope are compared with the ALMA observations. Because of the disturbed gas kinematics and the impractically long integration times required for higher angular resolution observations, none of the three galaxies is suitable for a future SMBH mass measurement. None the less, increasing the number of molecular gas observations of megamaser galaxies is valuable, and the ubiquitous disturbances suggest a link between large-scale gas properties and the existence of megamasers.

 

With two central galaxies engaged in a major merger and a remarkable chain of 19 young stellar superclusters wound around them in projection, the galaxy cluster SDSS J1531+3414 (z= 0.335) offers an excellent laboratory to study the interplay between mergers, active galactic nucleus (AGN) feedback, and star formation. New Chandra X-ray imaging reveals rapidly cooling hot (T∼ 10⁶K) intracluster gas, with two “wings” forming a concave density discontinuity near the edge of the cool core. LOFAR 144 MHz observations uncover diffuse radio emission strikingly aligned with the “wings,” suggesting that the “wings” are actually the opening to a giant X-ray supercavity. The steep radio emission is likely an ancient relic of one of the most energetic AGN outbursts observed, with 4pV> 10⁶¹erg. To the north of the supercavity, GMOS detects warm (T∼ 10⁴K) ionized gas that enshrouds the stellar superclusters but is redshifted up to +800 km s⁻¹with respect to the southern central galaxy. The Atacama Large Millimeter/submillimeter Array detects a similarly redshifted ∼10¹⁰M_⊙reservoir of cold (T∼ 10²K) molecular gas, but it is offset from the young stars by ∼1–3 kpc. We propose that the multiphase gas originated from low-entropy gas entrained by the X-ray supercavity, attribute the offset between the young stars and the molecular gas to turbulent intracluster gas motions, and suggest that tidal interactions stimulated the “beads-on-a-string” star formation morphology.

 

We present a study of the molecular gas of seven early-type galaxies with high angular resolution data obtained as part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) project with the Atacama Large Millimeter/submillimeter Array. Using a fixed spatial-scale approach, we study the mass surface density (Σ) and velocity dispersion (σ) of the molecular gas on spatial scales ranging from 60 to 120 pc. Given the spatial resolution of our data (20–70 pc), we characterize these properties across many thousands of individual sightlines (≈50 000 at our highest physical resolution). The molecular gas along these sightlines has a large range (≈2 dex) of mass surface densities and velocity dispersions $\approx 40~{{\ \rm per\ cent}}$ higher than those of star-forming spiral galaxies. It has virial parameters αvir that depend weakly on the physical scale observed, likely due to beam smearing of the bulk galactic rotation, and is generally supervirial. Comparing the internal turbulent pressure (Pturb) to the pressure required for dynamic equilibrium (PDE), the ratio Pturb/PDE is significantly less than unity in all galaxies, indicating that the gas is not in dynamic equilibrium and is strongly compressed, in apparent contradiction to the virial parameters. This may be due to our neglect of shear and tidal forces, and/or the combination of three-dimensional and vertical diagnostics. Both αvir and Pturb anticorrelate with the global star-formation rate of our galaxies. We therefore conclude that the molecular gas in early-type galaxies is likely unbound, and that large-scale dynamics likely plays a critical role in its regulation. This contrasts to the giant molecular clouds in the discs of late-type galaxies, that are much closer to dynamical equilibrium.

 

We present a CO dynamical estimate of the mass of the supermassive black hole (SMBH) in three nearby early-type galaxies: NGC 0612, NGC 1574, and NGC 4261. Our analysis is based on Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 3–6 observations of the 12CO(2–1) emission line with spatial resolutions of 14–58 pc (0.01″–0.26″). We detect disc-like CO distributions on scales from ≲ 200 pc (NGC 1574 and NGC 4261) to ≈10 kpc (NGC 0612). In NGC 0612 and NGC 1574 the bulk of the gas is regularly rotating. The data also provide evidence for the presence of a massive dark object at the centre of NGC 1574, allowing us to obtain the first measure of its mass, MBH = (1.0 ± 0.2) × 108 M⊙ (1σ uncertainty). In NGC 4261, the CO kinematics is clearly dominated by the SMBH gravitational influence, allowing us to determine an accurate black hole mass of (1.62 ± 0.04) × 109 M⊙ (1σ uncertainty). This is fully consistent with a previous CO dynamical estimate obtained using a different modelling technique. Signs of non-circular gas motions (likely outflow) are also identified in the inner regions of NGC 4261. In NGC 0612, we are only able to obtain a (conservative) upper limit of MBH ≲ 3.2 × 109 M⊙. This has likely to be ascribed to the presence of a central CO hole (with a radius much larger than that of the SMBH sphere of influence), combined with the inability of obtaining a robust prediction for the CO velocity curve. The three SMBH mass estimates are overall in agreement with predictions from the MBH − σ* relation.

 

SPEX Left LU is a software package for exactly solving unsymmetric sparse linear systems. As a component of the sparse exact (SPEX) software package, SPEX Left LU can be applied to any input matrix, A , whose entries are integral, rational, or decimal, and provides a solution to the system \( Ax = b \) , which is either exact or accurate to user-specified precision. SPEX Left LU preorders the matrix A with a user-specified fill-reducing ordering and computes a left-looking LU factorization with the special property that each operation used to compute the L and U matrices is integral. Notable additional applications of this package include benchmarking the stability and accuracy of state-of-the-art linear solvers and determining whether singular-to-double-precision matrices are indeed singular. Computationally, this article evaluates the impact of several novel pivoting schemes in exact arithmetic, benchmarks the exact iterative solvers within Linbox, and benchmarks the accuracy of MATLAB sparse backslash. Most importantly, it is shown that SPEX Left LU outperforms the exact iterative solvers in run time on easy instances and in stability as the iterative solver fails on a sizeable subset of the tested (both easy and hard) instances. The SPEX Left LU package is written in ANSI C, comes with a MATLAB interface, and is distributed via GitHub, as a component of the SPEX software package, and as a component of SuiteSparse. 

The content and distribution of cool interstellar medium (<30 K) can indicate the evolutionary mechanisms that transform late-type to early-type galaxies (ETGs). To investigate this, ALMA observations of 12CO[2-1] line emission were obtained for five dusty ETGs from a complete sample in low-density environments. Four of the ETGs have massive (∼109 M⊙), extended molecular gas reservoirs with effective radii ∼3–5 kpc. This work provides a kinematic and structural analysis of these observations, to explore possible evolutionary mechanisms. Axisymmetric or bisymmetric kinematic models were fitted to observations of molecular gas discs, to quantify the dominant structures present and highlight additional structures or asymmetries. Integral field unit observations of these ETGs were also examined where available. Two of the ETGs, GAMA64646 and 622305, appear to have undergone tidal disturbance leading to molecular gas discs and/or star-forming inner rings. GAMA272990 may have undergone a merger, leading to an elliptical galaxy with an embedded star-forming molecular gas disc. GAMA622429 has probably undergone a minor merger, indicated by asymmetry in molecular gas distribution and disturbance in optical images. The remaining ETG, GAMA177186, was affected by source confusion from an offset source which could be a high-mass dust- and gas-rich object at high redshift. Overall, it appears that a high proportion of dusty ETGs in low-density environments have massive, extended molecular gas reservoirs, and have undergone some kind of interaction as part of their recent evolution. Secular evolution can then (re-)transform the ETGs from star-forming to passive galaxies.

 

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 (AGNs): Fairall 49. We use new ALMA observations of the CO(2 − 1) line with a spatial resolution of ∼80 pc together with ancillary HST imaging. We reach the following results: (1) The CO kinematics are well described by a regularly rotating gas disc 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) × 108 M⊙ assuming that we have accurately subtracted the AGN and starburst light contributions, which have a luminosity of ∼109 L⊙; (3) The SMBH mass agrees with the SMBH−stellar mass relation but is ∼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-H2 conversion factor (XCO) for thermalized gas, suggesting low values of XCO; (5) the molecular gas inflow rate increases steadily with radius and may be as high as ∼5 M⊙ yr−1. This work highlights the potential of using high-resolution CO data to estimate, in addition to SMBH masses, the XCO factor, and gas inflow rates in nearby galaxies.

 

We present a study of molecular structures (clumps and clouds) in the dwarf galaxy NGC 404 using high-resolution (≈0.86 × 0.51 pc2) Atacama Large Millimeter/sub-millimeter Array 12CO(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, which 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 are 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.

 

To meet the growing need for extended or exact precision solvers, an efficient framework based on Integer-Preserving Gaussian Elimination (IPGE) has been recently developed, which includes dense/sparse LU/Cholesky factorizations and dense LU/Cholesky factorization updates for column and/or row replacement. This paper discusses our ongoing work developing the sparse LU/Cholesky column/row-replacement update and the sparse rank-l update/downdate. We first present some basic background for the exact factorization framework based on IPGE. Then we give our proposed algorithms along with some implementation and data-structure details. Finally, we provide some experimental results showcasing the performance of our update algorithms. Specifically, we show that updating these exact factorizations can typically be 10x to 100x faster than (re-)factorizing the matrices from scratch.