AGN disks and black holes on the weighting scales

Abstract

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 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 σ 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 σ 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 NGC 3393 and UGC 3789, the masses seem well constrained through the linear approach. For IC 1481, 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.

A Precision Measurement of the Mass of the Black Hole in NGC 3258 from High-resolution ALMA Observations of Its Circumnuclear Disk

“…For megamaser galaxies with well-measured values of σ , VLBI observations typically achieve ξ ∼ 10 − 100 (Greenhill et al 1996;Lodato & Bertin 2003;Kondratko et al 2008;Greene et al 2010;Huré et al 2011;Kuo et al 2011;Yamauchi et al 2012;Greene et al 2016;Gao et al 2016Gao et al , 2017Zhao et al 2018), while for the prototypical megamaser disk in NGC 4258, ξ ∼ 1000 with high-velocity maser sources detected to within ∼0.02r g of the active nucleus (Miyoshi et al 1995;Herrnstein et al 2005;Humphreys et al 2013). For comparison, published ALMA CO imaging of ETGs has typically reached relatively low ξ values (e.g., ξ 2: Davis et al 2013;Onishi et al 2017;Paper I;Davis et al , 2018 with one exception being the high resolution observations of NGC 1332 presented by Barth et al (2016a), which achieved ξ ∼ 10 along the disk's projected major axis.…”

GG Tauri A: gas properties and dynamics from the cavity to the outer disk

“…This is ∼10% of the total mass of the stars. A 10% mass ratio should lead to a small deviation (about 5%) from the Keplerian law (Huré et al 2011) outside the ring.…”

Two mass conjectures on axially symmetric black hole-disk systems

“…The question of estimating masses or determining rotation curves in toroidal systems has been addressed, within Newtonian physics, in the astrophysical literature [5][6][7][8][9]. We would like to stress that our methods are different and we work within the general relativistic context.…”