The Megamaser Cosmology Project. V. An Angular Diameter Distance to NGC 6264 at 140 Mpc

We present the direct measurement of the Hubble constant, yielding the direct measurement of the angular-diameter distance to NGC 6264 using the H$_{2}$O megamaser technique. Our measurement is based on sensitive observations of the circumnuclear megamaser disk from four observations with the Very Long Baseline Array, the Green Bank Telescope and the Effelsberg Telescope. We also monitored the maser spectral profile for 2.3 years using the Green Bank Telescope to measure accelerations of maser lines by tracking their line-of-sight velocities as they change with time. The measured accelerations suggest that the systemic maser spots have a significantly wider radial distribution than in the archetypal megamaser in NGC 4258. We model the maser emission as arising from a circumnuclear disk with orbits dominated by the central black hole. The best fit of the data gives a Hubble constant of $H_{0} =$ 68$pm$9 km s$^{-1}$ Mpc$^{-1}$, which corresponds to an angular-diameter distance of 144$pm$19 Mpc. In addition, the fit also gives a mass of the central black hole of (3.09$pm$0.42)$times10^{7}$ $M_{odot}$. The result demonstrates the feasibility of measuring distances to galaxies located well into the Hubble flow by using circumnuclear megamaser disks.

The Extreme Spin of the Black Hole in Cygnus X-1

The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black holes accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular momentum vector, we have determined that Cygnus X-1 contains a near-extreme Kerr black hole with a spin parameter a/M>0.95 (3sigma). For a less probable (synchronous) dynamical model, we find a/M>0.92 (3sigma). In our analysis, we include the uncertainties in black hole mass, orbital inclination angle and distance, and we also include the uncertainty in the calibration of the absolute flux via the Crab. These four sources of uncertainty totally dominate the error budget. The uncertainties introduced by the thin-disk model we employ are particularly small in this case given the extreme spin of the black hole and the disks low luminosity.