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High precision mapping of H |$_{2}$| O megamaser emission from active galaxies has revealed more than a dozen Keplerian H |$_{2}$| O maser discs, which enable a |$\sim$| 4 per cent uncertainty estimate of the Hubble constant as well as providing accurate masses for the central black holes. These discs often have well-defined inner and outer boundaries of maser emission on sub-parsec scales. In order to better understand the physical conditions that determine the inner and outer radii of a maser disc, we examine the distributions of gas density and X-ray heating rate in a warped molecular disc described by a power-law surface density profile. For a suitable choice of the disc mass, we find that the outer radius |$R_{\rm out}$| of the maser disc predicted from our model can match the observed value, with |$R_{\rm out}$| mainly determined by the maximum heating rate or the minimum density for efficient maser action, depending on the combination of the Eddington ratio, black hole mass, and disc mass. Our analysis also indicates that the inner radius for maser action is comparable to the dust sublimation radius, suggesting that dust may play a role in determining the inner radius of a maser disc. Finally, our model predicts that H |$_{2}$| O gigamaser discs could exist at the centres of high-z quasars, with disc sizes of |$\gtrsim 10-30$| pc. [ABSTRACT FROM AUTHOR]

In Papers I and II from the Megamaser Cosmology Project, we reported initial observations of H2O masers in an accretion disk of a supermassive black hole at the center of the galaxy UGC 3789, which gave an angular-diameter distance to the galaxy and an estimate of H0 with 16% uncertainty.We have since conducted more very long baseline interferometric observations of the spatial-velocity structure of these H2O masers, as well as continued monitoring of its spectrum to better measure maser accelerations. These more extensive observations, combined with improved modeling of the masers in the accretion disk of the central supermassive black hole, confirm our previous results, but with significantly improved accuracy. We find H0 = 68.9 ± 7.1 km s-1 Mpc-1 this estimate of H0 is independent of other methods and is accurate to ±10%, including sources of systematic error. This places UGC 3789 at an angular-diameter distance of 49.6 ± 5.1 Mpc, with a central supermassive black hole of (1.16 ± 0.12) ×107 M☉. [ABSTRACT FROM AUTHOR]