AGN disks and black holes on the weighting scales

We exploit our formula for the gravitational potential of finite size, power-law disks to derive a general expression linking the mass of the black hole in active galactic nuclei (AGN), the mass of the surrounding disk, its surface density profile (through the power index s), and the differential rotation law. We find that the global rotation curve v(R) of the disk in centrifugal balance does not obey a power law of the cylindrical radius R (except in the confusing case s = -2 that mimics a Keplerian motion), and discuss the local velocity index. This formula can help to understand how, from position-velocity diagrams, mass is shared between the disk and the black hole. To this purpose, we have checked the idea by generating a sample of synthetic data with different levels of Gaussian noise, added in radius. It turns out that, when observations are spread over a large radial domain and exhibit low dispersion (standard deviation less than 10% typically), the disk properties (mass and s-parameter) and black hole mass can be deduced from a non linear fit of kinematic data plotted on a (R, Rv 2)-diagram. For a deviation higher than 10%, masses are estimated fairly well from a linear regression (corresponding to the zeroth-order treatment of the formula), but the power index s is no longer accessible. We have applied the model to 7 AGN disks whose rotation has already been probed through water maser emission. For NGC3393 and UGC3789, the masses seem well constrained through the linear approach. For IC1481, the power-law exponent s can even be deduced. Because the model is scale-free, it applies to any kind of star/disk system. Extension to disks around young stars showing deviation from Keplerian motion is thus straightforward.Comment: accepted for publication in A&

Near-Infrared Reverberation by Dusty Clumpy Tori in Active Galactic Nuclei

According to recent models, the accretion disk and black hole in active galactic nuclei are surrounded by a clumpy torus. We investigate the NIR flux variation of the torus in response to a UV flash for various geometries. Anisotropic illumination by the disk and the torus self-occultation contrast our study with earlier works. Both the waning effect of each clump and the torus self-occultation selectively reduce the emission from the region with a short delay. Therefore, the NIR delay depends on the viewing angle (where a more inclined angle leads to a longer delay) and the time response shows an asymmetric profile with a negative skewness, opposing to the results for optically thin tori. The range of the computed delay coincides with the observed one, suggesting that the viewing angle is primarily responsible for the scatter of the observed delay. We also propose that the red NIR-to-optical color of type-1.8/1.9 objects is caused by not only the dust extinction but also the intrinsically red color. Compared with the modest torus thickness, both a thick and a thin tori display the weaker NIR emission. A selection bias is thus expected such that NIR-selected AGNs tend to possess moderately thick tori. A thicker torus shows a narrower and more heavily skewed time profile, while a thin torus produces a rapid response. A super-Eddington accretion rate leads to a much weaker NIR emission due to the disk self-occultation and the disk truncation by the self-gravity. A long delay is expected from an optically thin and/or a largely misaligned torus. A very weak NIR emission, such as in hot-dust-poor active nuclei, can arise from a geometrically thin torus, a super-Eddington accretion rate or a slightly misaligned torus.Comment: 15 pages, 15 figures, Accepted for publication in Ap

A Scaling Relation Between Megamaser Disk Radius and Black Hole Mass in Active Galactic Nuclei

Several thin, Keplerian, sub-parsec megamaser disks have been discovered in the nuclei of active galaxies and used to precisely determine the mass of their host black holes. We show that there is an empirical linear correlation between the disk radius and the black hole mass. We demonstrate that such disks are naturally formed by the partial capture of molecular clouds passing through the galactic nucleus and temporarily engulfing the central supermassive black hole. Imperfect cancellation of the angular momenta of the cloud material colliding after passing on opposite sides of the hole leads to the formation of a compact disk. The radial extent of the disk is determined by the efficiency of this process and the Bondi-Hoyle capture radius of the black hole, and naturally produces the empirical linear correlation of the radial extent of the maser distribution with black hole mass. The disk has sufficient column density to allow X-ray irradiation from the central source to generate physical and chemical conditions conducive to the formation of 22 GHz H2O masers. For initial cloud column densities less than ~10^{23.5} cm^-2 the disk is non-self gravitating, consistent with the ordered kinematics of the edge-on megamaser disks; for higher cloud columns the disk would fragment and produce a compact stellar disk similar to that observed around Sgr A* at the galactic centre.Comment: Minor revisions. Fig 1. corrected. ApJ Letters, in pres

The Megamaser Cosmology Project. III. Accurate Masses of Seven Supermassive Black Holes in Active Galaxies with Circumnuclear Megamaser Disks

Observations of H$_2$O masers from circumnuclear disks in active galaxies for the Megamaser Cosmology Project allow accurate measurement of the mass of supermassive black holes (BH) in these galaxies. We present the Very Long Baseline Interferometry (VLBI) images and kinematics of water maser emission in six active galaxies: NGC~1194, NGC~2273, NGC~2960 (Mrk~1419), NGC~4388, NGC~6264 and NGC~6323. We use the Keplerian rotation curves of these six megamaser galaxies, plus a seventh previously published, to determine accurate enclosed masses within the central $\sim0.3$ pc of these galaxies, smaller than the radius of the sphere of influence of the central mass in all cases. We also set lower limits to the central mass densities of between 0.12 and 60 $\times 10^{10} M_{\odot}$~pc$^{-3}$. For six of the seven disks, the high central densities rule out clusters of stars or stellar remnants as the central objects, and this result further supports our assumption that the enclosed mass can be attributed predominantly to a supermassive black hole. The seven BHs have masses ranging between 0.76 and 6.5$\times$10$^7 M_{\odot}$. The BH mass errors are $\approx11$\%, dominated by the uncertainty of the Hubble constant. We compare the megamaser BH mass determination with other BH mass measurement techniques. The BH mass based on virial estimation in four galaxies is consistent with the megamaser BH mass given the latest empirical value of $\langle f \rangle$, but the virial mass uncertainty is much greater. MCP observations continue and we expect to obtain more maser BH masses in the future.Comment: 18 pages, 4 figures. This paper has been submitted to ApJ. An updated version of this paper will be posted when it gets accepte