\label{sec:h2o_mm}
Multiple H\(_2\)O transitions have been observed producing maser emission in galactic source \citep{Elitzur_1992}, however the dominant transition detected as stimulated emission is at 22 GHz (see Table \ref{tab:maser_props}). This transition is relatively easy to cause stimulated emission in since it corresponds at a ‘backbone’ transition (lowest levels at each rotational \(J\)-value). These transitions have large Einstein \(A\)-values, leading to trapping of the emitted photons \citep{stahler_palla_2004}, making collisional excitement and de-excitement more effective than radiation in producing these transitions. The environment needed to produce the 22 GHz H\(_2\)O emission must pump molecules to fairly high energy levels (640 K, Table \ref{tab:maser_props}). As shown by \citet{stahler_palla_2004}, shocked regions are capable of providing collisional excitement to these levels, and indeed this is where H\(_2\)O maser emission is observed in galactic, and possibly extragalactic, sources \citep{Elitzur_1992,lo2005}.
Approximately 3000 galaxies have been searched for H\(_2\)O mega-masers, resulting in about 150 detections1 \citep{tarchi2012}. Nearly all of the detections come from active galaxies, specifically radio-quiet AGN classified as Seyfert 2 (Sy2) or low-ionization nuclear emission-line regions (LINERs) with redshifts up to 0.05 (§\ref{sub:h20_agn}). These galaxies tend to all host the ‘circumnuclear’ H\(_2\)O mega-masers associated with compact disks within parsec scales of the AGN \citep{lo2005}. This makes H\(_2\)O mega-masers a unique tool to study the properties of the AGN on small scales that are otherwise heavily obscured. Two other types of H\(_2\)O mega-masers are observed corresponding to interactions with a nuclear jet and molecular outflows \citep{lo2005, tarchi2012}. There are fewer detections of masers from these mechanisms, and so I focus on circumnuclear masers in this section. In galactic sources, 22 GHz H\(_2\)O masers are associated with circumstellar material around late-type stars, and with molecular outflows due to young, embedded stars. These environments, and the reasons stated above, highly suggest a collisional pumping mechanism \citep{Elitzur_1992}. Circumnuclear H\(_2\)O mega-masers appear to arise from a related mechanism to the circumstellar sources, except that the ultimate energy source of the pump is the AGN itself \citep{lo2005}. The energy output of the AGN is significantly greater than that from late-type stars, which possibly explains why these maser sources are much brighter.
Numerous surveys have been undertaken to find H\(_2\)O mega-maser detections, notably by \citet{Braatz_1996}, who surveyed all nearby galaxies with AGN characteristics (see also \citet{Braatz_1997}). The Megamaser Cosmology Project is an on-going H\(_2\)O mega-maser survey of known sources that combines high- and low-resolution observations over long time periods to obtain geometric distances to galaxies beyond \(\gt 100\) Mpc, and infer H\(_0\) to a high precision, independent of other methods (§\ref{sub:h2o_cosmo}) \citep{reid2009_mmproject_I}. Given the applications discussed in the preceding sections, many more H\(_2\)O mega-maser will be conducted as more sensitive instrumentation becomes available.
\label{sub:h2o_hosts}
The detection rate for nearby Sy2 and LINER galaxies is about \(1/4\), while the overall detection rate for all AGN observed is just \(5\%\) \citep{tarchi2012}. What is the cause of this significant difference between different classes of AGN?
The Unified Model of AGN predicts the presence of the parsec-scale accretion disks about the SMBH surrounded by a torus or thick disk of atomic or molecular gas extending out to \(\sim 100\) pc \citep[e.g.,]{Urry_1995}. The model broadly classifies AGN based on whether the observer accretion disk and SMBH are unobscured (Type I) or obscured by the torus (Type II). The differences in the specific radio classes of AGN are more relatable to the properties of the galaxy and AGN \citep{tarchi2012}. Sy2 galaxies are predicted to have an edge-on disk or torus from the observer’s perspective. It then makes sense that most H\(_2\)O mega-maser detections come from this class since this geometric configuration maximizes the path length for the maser emission to arise from \citep{tarchi2012}. Sy2 galaxies with very-high column densities (\(\gt10^{24}\) cm\(^{-3}\), inferred in the X-ray) seem to preferentially be hosts to H\(_2\)O mega-masers \citep{Braatz_1997,Greenhill_2003}. \citet{Kondratko_2006} also find a rough correlation between H\(_2\)O mega-maser luminosities and the 2-10 keV X-ray luminosity, though the X-ray data is poor for nearly half their survey objects \citet{tarchi2012}. Other indicators include the maser emission residing within X-ray absorbed sources \citep[e.g.,]{Zhang_2010}, and higher radio luminosities with respect to non-maser galaxies \citep{Zhang_2012}.
Seyfret 1 galaxies are predicted to be observed face-on; one H\(_2\)O mega-maser has been observed from this class in NGC 2782 and it remains unclear on how this arises \citep{Tarchi_2011}. However, \citet{Tarchi_2011} also find a high occurence rate (corrected for the volume-limited sample) for H\(_2\)O mega-masers in narrow-line Sy1 galaxies, a subset of Sy1 galaxies that exhibit narrow Balmer lines and strong Fe II emission \citep{tarchi2012}. This certainly complicates being able to predict the AGN properties mostly likely to result in H\(_2\)O mega-maser emission. Proposed explanations for this occurence include intermediate viewing angle between Sy1 and Sy2, accretion rates within the circumnuclear disk near the Eddington limit, small SMBH masses, and strong molecular outflows fueled by extreme radiation pressure \citep{tarchi2012}. Despite searches in \(\sim 400\) galaxies, no H\(_2\)O mega-masers have been detected in radio-loud or elliptical galaxies, regardless of AGN type \citep{tarchi2012}.
\label{sub:h20_agn}
Circumnuclear H\(_2\)O mega-masers exhibit emission at three peaks in the velocity dimension: one centered at the systematic velocity of the AGN, and two red- and blue-shifted from the center by hundreds of km/s. Through high-resolution observations with the VLBI, the maser sources are resolved out to show that these components are distributed in a near planar distribution, where each velocity component arises from different regions in a parsec-scale disk around the nucleus. Assuming the disk is seen edge-on (as expected for Sy2 galaxies), the shifted velocity components correspond to components tangent to the line-of-sight on either side. This is direct proof of the expected circumnuclear disks predicted by the Unified Model \citep{lo2005}. An example observation is shown in Figure \ref{fig:h2o_ngc4258} for NGC 4258 \citep{Bragg_2000}, the most studied object in this class (see also \citet{Miyoshi_1994} & \citet{Herrnstein_1999}). Other H\(_2\)O mega-maser spectra show similar properties, along with the further evidence for a rotating disk from the observed linear increase in the systematic velocity component \citep{lo2005}.
Modelling these disk based on the maser components reveals Keplerian or sub-Keplerian motion, and the planar geometry of the resolved maser spots suggest a thin disk \citep{lo2005}. In the rotating disk model, the aforementioned constant rate of increase of the systematic velocity results from the centripetal acceleration \(dv/dt = v_r^2/r\), where the radial velocities correspond to the high-velocity components. Then the constant velocity gradient can be written as \[\label{eq:disk_rot} \frac{dV}{d\theta} = D \frac{dV}{db} = D \frac{v_r}{R}\] where the impact parameter \(b= \theta D\), with \(\theta\) being the angular offset from the center of the disk \citep{lo2005}. Since \(dV/dt\), \(dV/d\theta\) can be measured, one can solve for the distance to the source. This was accomplished for the first time by \citet{Miyoshi_1994}, and is now being used in other systems as a means of measuring the Hubble Constant (§\ref{sub:h2o_cosmo}). For NGC 4258, \citet{Herrnstein_1999} find a distance of \(7.2\pm0.5\) Mpc, which remains one of the most accurate measurements for a galaxy.
The modeled rotation curves allow for the masses of the nuclei to be measured. While it is generally assumed that galactic nuclei host SMBHs, direct evidence is difficult to establish \citep{lo2005}. The proximity of H\(_2\)O mega-masers to the nuclei make them excellent tools to test for the existence of SMBHs. The mass to radius ratio should be \(6.7\times10^{27}\) g/cm, using the Schwarzchild radius \citep{lo2005}. For NGC 4258, the Keplerian rotation curve yields a ratio of \(2\times10^{25}\) g/cm from VLBI observations. Such a high-ratio is difficult to explain in terms of a supremely dense cluster of compact objects. Using the Keplerian rotation curves observed from seven other systems (NGC 6264, NGC 1194, NGC 2273, NGC 2960, NGC 4388, NGC 6323), \citet{kuo2011_mmproject_III} rules out a cluster of compact objects as potential explanation for galactic nuclei through explicit modeling based on Plummer profiles. This evidence is highly-compelling for the existence of SMBHs. \citet{kuo2011_mmproject_III} then assume that the nuclei are SMBHs, and combine previously published values for distance with the results of the Keplerian rotation curve model to infer black hole masses ranging between \(0.76-6.5\times10^7\) M\(_{\odot}\). The error on these measurements is about 11%, with the dominant error source coming from uncertainties in the Hubble Constant2.
\citet{wardle2012_bhmass} have derived a model for the formation of these circumnuclear disks around AGN. They argue that impacts of molecular clouds, within some impact parameter, can cause the formation of a thin Keplerian disk. By equating the specific angular momentum at the edge of the disk to that of the material that can just barely be captured by the interaction, they find a relation between the radius of the circumnuclear disk and the mass of the SMBH: \(R=4G\lambda^2M/v^2\), where \(\lambda\) is the fraction of angular momentum maintained in the interaction, \(M\) is the SMBH mass, and \(v\) is the initial velocity of the cloud. They find that the relation holds for eight disks with H\(_2\)O mega-maser emission, largely within observational error. They suggest that the impact of a cloud on one of these disks could create gravitationally unstable episodes, which may potentially give rise to mega-maser emission \citep{Milosavljevi_2004} such that only a fraction host Keplerian circumnuclear disks.
The precision of these SMBH mass measurements enable their use for constraining the low end of the \(M_{\mathrm{BH}}-\sigma_{\star}\) relation, where \(\sigma_{\star}\) is the velocity dispersion of stars in the bulge \citep{greene2010_bhmass}. The high-end of this relation is well-constrained based on mass measurements in massive elliptical galaxies. These galaxies harbour SMBHs with masses \(\gt 10^8\) M\(_{\odot}\), allowing their masses to be measured from stellar and gas kinematic distributions at measurable distances from the nuclei \citep{greene2010_bhmass}. These kinematic distributions become difficult to measure below black holes masses of \(10^8\) M\(_{\odot}\). Since circumnuclear H\(_2\)O masers are located at parsec-scales from the nucleus, they can be used to measure SMBH mass at lower masses. \citet{greene2010_bhmass} add SMBH masses derived from the circumnuclear H\(_2\)O masers and find evidence that these lower mass SMBHs do not follow the same powerlaw relation as more massive SMBH hosting galaxies. Previous to these results, the \(M_{\mathrm{BH}}-\sigma_{\star}\) relation exhibited low-scatter about the power-law relation.
\label{sub:h2o_cosmo}
The Megamaser Cosmology Project (MCP) is an on-going ambituous project to provide a high-precision measurement of Hubble’s Constant (\(H_0\)), independent of previous estimates \citep{reid2009_mmproject_I}. The project relies on the ability to measure the distances to known H\(_2\)O mega-maser hosts with Keplerian circumnuclear disks to high precision (§\ref{sub:h20_agn}). To reach uncertainties in \(H_0\) less than 10% for each maser hosting galaxy, a significant observational time investment is require from multiple facilities. Multy-epoch observations are conducted with single dish facilities (GBT & Arecibo) on a near monthly basis to constrain the centripetal acceleration, \(dV/dt\). These are then combined with a VLBI observation (sometimes multiple), which constrains the angular acceleration of the maser spots, \(dV/d\theta\).
The MCP has now applied their technique for measuring the distance and \(H_0\) for four galaxies: UGC 3789 \citep{Braatz_2010,reid2013_mmproject_IV}, NGC 6264 \citep{Kuo_2013}, NGC 6323 \citep{kuo2015_mmproject_VI}, and NGC 5765b \citep{gao2015}. All of these measurements required multi-epoch observations, along with modeling several aspects of the disks themselves in order to measure the desired parameter \(H_0\). In total, 10 parameters need to be constrained: \(H_0\), black hole mass, black hole line-of-sight velocity, the peculiar velocity and 6 parameters constraining the disk. \citet{reid2013_mmproject_IV} used Metropolis-Hastings sampling (MCMC) to simultaneously fit the entire model with all of the available observational data. For all four galaxies, this technique provided well-constrained posterior distributions and excellent Markov Chain diagnostics (low autocorrelation, \(\sim 30\%\) acceptance rate of samples, etc...). They find values of \(H_0=68.9\pm7.1\) km/s/Mpc for UGC 3789, \(H_0=68\pm9\) km/s/Mpc for NGC 6264, \(H_0=73^{+26}_{-22}\) km/s/Mpc for NGC 6323, and \(H_0=66.0\pm6.0\) km/s/Mpc for NGC 5765b, which all agree within the quoted 1\(\sigma\) errors from the posterior distributions. The expected uncertainties are near the target 10% expected for the survey \citep{reid2013_mmproject_IV}, except for NGC 6323 which has a significantly lower surface brightness and is near the sensitivity limits of current instrumentation \citep{kuo2015_mmproject_VI}. To reach the 3% uncertainty limit of other experimentally derived values of \(H_0\), the MCP project estimated they would need to perform this analysis for 10 galaxies, each with an individual uncertainty limit of \(\sim 10\%\) \citep{reid2013_mmproject_IV}.
Constraining \(H_0\) is important for constraining the \(w\) parameter for the equation of state for dark energy \citep{reid2013_mmproject_IV}. The constraints derived by \citet{reid2013_mmproject_IV} are combined with the WMAP7 results in Figure \ref{fig:h20_H0_w} (red contours). Shaded regions in the figure are from the WMAP results alone, and the blue contours show the expected constraints available upon completion of the MCP. The combined WMAP7 and \citet{reid2013_mmproject_IV} results give \(w=-0.98\pm0.20\). The constraints from the completed MCP are expected to reduce the uncertainty to \(\pm0.10\). By utilizing the newest Planck results, it may possible to further constrain \(w\) beyond these expectations.