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

Abstract

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.

Full text

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A Scaling Relation Between Megamaser Disk Radius and Black
Hole Mass in Active Galactic Nuclei
Mark Wardle
Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109,
Australia; mark.wardle@mq.edu.au
Farhad Yusef-Zadeh
Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208;
zadeh@northwestern.edu
ABSTRACT
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 22GHz H2O masers. For initial cloud column densities ? 1023.5cm−2the 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.
Subject headings: galaxies: accretion, accretion disks — Seyfert — Galaxy: cen-
ter — ISM: clouds — masers — stars: formation
arXiv:1108.2175v1 [astro-ph.CO] 10 Aug 2011

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1.Introduction
The nuclei of some Seyfert 2 galaxies are home to powerful 22GHz water masers located
in a circumnuclear disk within a parsec of the central massive black hole. In almost edge-on
systems, VLBI observations of the maser kinematics enable an accurate determination of
the black hole mass. The archetypal system is NGC 4258, for which the black hole mass has
been measured to 1% accuracy (e.g., Herrnstein et al. 2005; Humphreys et al. 2008). Recent
VLBA observations of Seyfert 2 galaxies have discovered a limited number of additional
examples with high inclination angles, allowing precise determinations of the mass of their
host black holes as well as the physical size of the maser disks, which range from 0.1–1pc
(Herrnstein et al. 2008; Kuo et al. 2010).
The physical parameters of the disks can be inferred from the conditions necessary to
generate the masers. Collisional inversion of the 22GHz H2O transition requires densities of
107–1011cm−3, temperatures in the range 300–1000K, and a sufficient column of water to
ensure maser amplification (e.g. Neufeld & Melnick 1991). These conditions are plausibly
produced by irradiation of a molecular disk by the central X-ray source as long as the surface
density exceeds ∼ 1gcm−2and warping exposes the disk surface to the center (Neufeld et
al. 1994; Maloney 2002). Parsec-scale maser disks must therefore have masses of at least
104M?. In the case of NGC 4258 the required conditions can be achieved in a standard
steady-state alpha accretion disk. This can explain the required disk mass and also explain
the outer edge as where the column density becomes too low to shield molecular gas from
the X-ray flux from the center. However, this picture fails in other systems which have lower
central luminosities and therefore lower accretion rates and low-surface density alpha disks
(Maloney 2002).
Further insight is provided by examining the center of the Milky Way Galaxy, where
there is strong evidence of star formation occurring in a sub-parsec scale disk within ∼
5 × 106years. Approximately 100 massive stars orbit within a few tenths of a parsec of
the ∼ 4 × 106M?black hole Sgr A* (Bartko et al. 2010; Lu et al. 2010; Do et al. 2009;
see also the recent review by Genzel et al. 2010 and references cited therein). About 2/3
of these are localized in a clockwise rotating stellar disk with a wide range of eccentricities
(Levin & Beloborodov 2003), with the remainder loosely distributed, possibly in a larger
counter-rotating disk (Paumard et al. 2006; but see Lu et al. 2009). Stellar disks could be
created by the tidal disruption of an inspiralling stellar cluster (Gerhard 2001; McMillan
& Portegies Zwart 2003; Portegies Zwart et al. 2003; Kim et al. 2004; G¨ urkan & Rasio
2005), but this mechanism produces a far more disordered stellar system than observed, and
a non-existent population of massive stars shed from the cluster extending beyond 0.3 pc
from Sgr A*; furthermore the inspiralling time scale is longer than the stellar ages (Paumard

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et al. 2006; but see Fujii et al. 2008). A more attractive alternative is that these disks could
form “in-situ” by gravitational collapse in a disk of gas captured by the black hole (Levin
& Beloborodov 2003; Nayakshin et al. 2007), a process previously considered in the context
of AGN (Kolykhalov & Sunyaev 1980; Shlosman & Begelman 1987; Collin & Zahn 1999;
Goodman 2003).
The compactness of the stellar disks relative to molecular cloud dimensions implies that
the raw material for the disk is captured from a cloud as it temporarily engulfs Sgr A* while
passing through the central parsec of the Galaxy (c.f. Sanders 1981; Bottema & Sanders
1986); the cancellation of angular momentum of captured cloud the material that passes on
opposite sides of the black hole naturally produces a compact, gravitationally unstable disk
that is consistent with dimensions, mass and kinematic properties of the observed stellar disk
(Wardle & Yusef-Zadeh 2008, hereafter Paper I; Bonnell & Rice 2008; Mapelli et al. 2008;
Alig et al. 2011). This process may also be responsible for the parsec-scale circumnuclear
ring (Sanders 1998; Paper I).
A link between the stellar disk at the Galactic center and AGN megamaser disks was
suggested by Milosavljevi´ c & Loeb (2004) who argued that the masing disks are gravitation-
ally unstable and would eventually create stellar disks analogous to those seen around Sgr
A*. However, the maser distribution and kinematics in the edge-on systems are very thin and
close to keplerian, so that at least in these systems the megamaser disks are gravitationally
stable.
In this Letter, we show that the cloud capture scenario outlined in Paper I creates
gravitationally stable sub-parsec disks with physical conditions conducive to the formation
of megamasers. We begin by showing that systems with well-determined host black hole
masses and Keplerian rotation profiles display a strong correlation between disk size and
black hole mass (§2). In §3 we consider a simple model for the partial capture of molecular
clouds and demonstrate that this correlation is a natural outcome of the cloud-engulfment
scenario, and that, for reasonable parameters, initial cloud column densities ∼ 1023cm−2will
create a non-self-gravitating molecular disk consistent with the observed megamaser disks.
Our conclusions are summarised in §4.
2.A Correlation Between Megamaser Disk Size and Black Hole Mass
Of the dozen AGNs for which VLBI observations have determined the black hole mass
quite precisely (see discussion in Kuo et al. 2011), we discard three with rotation curves that
are flatter than Keplerian indicating that the mass of the stellar cluster or disk is affecting

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the dynamics - NGC 1068, NGC 3079, and IC 1481 (Greenhill et al. 1996; Kondratko et
al. 2005; and Mamyoda et al. 2009, respectively). The remainder are tabulated by Kuo et
al. (2011). Table 1 lists the physical properties of the remaining eight megamaser disks, and
for comparison the properties of the stellar disk of Sgr A*. Columns 1 to 3 show the name
of the Galaxy, the measured mass of the black hole, and the inner and outer radii of the
disk. The upper limits to the disk mass estimated from the errors to the Keplerian fit to the
rotation profile are a few percent of the black hole mass (Kuo et al. 2011). For comparison
we have also included the compact stellar disk around Sgr A* (Lu et al. 2010).
The remarkable similarity of size scale of the stellar disk surrounding Sgr A* and the
megamaser disks suggest that they could be formed the same way.
For each of these, we plot the range of radii over which the megamasers trace out a disk
against the host black hole mass (see Fig. 1). For comparison we have included the range of
radii of the S-stars orbiting Sgr A*. Remarkably, there is a well-defined upper envelope to
the maser disk radii which scales linearly with black hole mass, given approximately by
Rmax= 0.31 M7pc. (1)
where the central black hole mass is M = M7× 107M?. The outer edge of the maser
disks may simply reflect that the surface density of the disk falls below the ∼ 1gcm−2
needed to shield molecules from the hard X-ray flux from the central source (Maloney 2002).
However, there is no obvious reason why this radius should follow this trend. Our preferred
explanation, outlined in the following section, is that the outer radius is set by a physical
truncation of the disk because the scale determined kinematics of cloud capture depends
linearly on the black hole mass (see eq. 5).
3. Disk Formation by Cloud Capture
In Paper I we showed that partial capture of molecular clouds passing through the
central parsec of the galaxy by the 4 × 106M? black hole Sgr A* would naturally create
a disk on the 0.1 parsec scale of the stellar disk. There we focussed on the formation of
self-gravitating disks, which because of the short cooling time of the gas create stars on
a timescale comparable to a few orbital times, so that star formation would occur before
the disk settles into a thin ordered structure; the resulting stellar orbits have a range of
eccentricities and inclinations.
Here we apply this scenario to the very thin and well-ordered megamaser disks, with
two key differences from our earlier analysis. First, we explicitly follow the scaling with
black hole mass rather than fixing at the value Sgr A*; second, we focus on capture events

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Table 1.Physical Characteristics of Megamaser Disks
Source BH Mass 107M?
Disk Size (pc)
NGC 1194a
NGC 2273a
UGC 3789a
NGC 2960a
NGC 4258b
NGC 4388a
NGC 6264a
NGC 6323a
6.5±0.3
0.75±0.04
1.04±0.05
1.16±0.05
3.7±0.01
0.84±0.02
2.91±0.04
0.94±0.01
0.53-1.33
0.028-0.084
0.084-0.30
0.13-0.37
0.17-0.29
0.24-0.29
0.24-0.80
0.13-0.30
Sgr A*c
0.43±0.02 0.038-0.13
aKuo et al. 2011
bHerrnstein et al. 2008
ccompact stellar disk; Lu et al. 2008