The Megamaser Cosmology Project. III. Accurate Masses of Seven Supermassive Black Holes in Active Galaxies with Circumnuclear Megamaser Disks

Observations of H$_2$O masers from circumnuclear disks in active galaxies for the Megamaser Cosmology Project allow accurate measurement of the mass of supermassive black holes (BH) in these galaxies. We present the Very Long Baseline Interferometry (VLBI) images and kinematics of water maser emission in six active galaxies: NGC~1194, NGC~2273, NGC~2960 (Mrk~1419), NGC~4388, NGC~6264 and NGC~6323. We use the Keplerian rotation curves of these six megamaser galaxies, plus a seventh previously published, to determine accurate enclosed masses within the central $\sim0.3$ pc of these galaxies, smaller than the radius of the sphere of influence of the central mass in all cases. We also set lower limits to the central mass densities of between 0.12 and 60 $\times 10^{10} M_{\odot}$~pc$^{-3}$. For six of the seven disks, the high central densities rule out clusters of stars or stellar remnants as the central objects, and this result further supports our assumption that the enclosed mass can be attributed predominantly to a supermassive black hole. The seven BHs have masses ranging between 0.76 and 6.5$\times$10$^7 M_{\odot}$. The BH mass errors are $\approx11$\%, dominated by the uncertainty of the Hubble constant. We compare the megamaser BH mass determination with other BH mass measurement techniques. The BH mass based on virial estimation in four galaxies is consistent with the megamaser BH mass given the latest empirical value of $\langle f \rangle$, but the virial mass uncertainty is much greater. MCP observations continue and we expect to obtain more maser BH masses in the future.Comment: 18 pages, 4 figures. This paper has been submitted to ApJ. An updated version of this paper will be posted when it gets accepte

Cosmology and the Hubble Constant: On the Megamaser Cosmology Project (MCP)

The Hubble constant Ho describes not only the expansion of local space at redshift z ~ 0, but is also a fundamental parameter determining the evolution of the universe. Recent measurements of Ho anchored on Cepheid observations have reached a precision of several percent. However, this problem is so important that confirmation from several methods is needed to better constrain Ho and, with it, dark energy and the curvature of space. A particularly direct method involves the determination of distances to local galaxies far enough to be part of the Hubble flow through water vapor (H2O) masers orbiting nuclear supermassive black holes. The goal of this article is to describe the relevance of Ho with respect to fundamental cosmological questions and to summarize recent progress of the the `Megamaser Cosmology Project' (MCP) related to the Hubble constant.Comment: 10 pages, 7 postscript figures (8 ps files), IAU Symposium 287, uses iaus.cl

Kerncraft: A Tool for Analytic Performance Modeling of Loop Kernels

Achieving optimal program performance requires deep insight into the interaction between hardware and software. For software developers without an in-depth background in computer architecture, understanding and fully utilizing modern architectures is close to impossible. Analytic loop performance modeling is a useful way to understand the relevant bottlenecks of code execution based on simple machine models. The Roofline Model and the Execution-Cache-Memory (ECM) model are proven approaches to performance modeling of loop nests. In comparison to the Roofline model, the ECM model can also describes the single-core performance and saturation behavior on a multicore chip. We give an introduction to the Roofline and ECM models, and to stencil performance modeling using layer conditions (LC). We then present Kerncraft, a tool that can automatically construct Roofline and ECM models for loop nests by performing the required code, data transfer, and LC analysis. The layer condition analysis allows to predict optimal spatial blocking factors for loop nests. Together with the models it enables an ab-initio estimate of the potential benefits of loop blocking optimizations and of useful block sizes. In cases where LC analysis is not easily possible, Kerncraft supports a cache simulator as a fallback option. Using a 25-point long-range stencil we demonstrate the usefulness and predictive power of the Kerncraft tool.Comment: 22 pages, 5 figure

The Megamaser Cosmology Project. X. High Resolution Maps and Mass Constraint for SMBHs

We present high resolution (sub-mas) VLBI maps of nuclear H2O megamasers for seven galaxies. In UGC6093, the well-aligned systemic masers and high-velocity masers originate in an edge-on, flat disk and we determine the mass of the central SMBH to be M_SMBH = 2.58*10^7Msun(+-7%). For J1346+5228, the distribution of masers is consistent with a disk, but the faint high-velocity masers are only marginally detected, and we constrain the mass of the SMBH to be in the range 1.5-2.0*10^7Msun. The origin of the masers in Mrk1210 is less clear, as the systemic and high-velocity masers are misaligned and show a disorganized velocity structure. We present one possible model in which the masers originate in a tilted, warped disk, but we do not rule out the possibility of other explanations including outflow masers. In NGC6926, we detect a set of redshifted masers, clustered within a pc of each other, and a single blueshifted maser about 4.4pc away, an offset that would be unusually large for a maser disk system. Nevertheless, if it is a disk system, we estimate the enclosed mass to be M_SMBH<4.8*10^7 Msun . For NGC5793, we detect redshifted masers spaced about 1.4pc from a clustered set of blueshifted features. The orientation of the structure supports a disk scenario as suggested by Hagiwara et al.(2001). We estimate the enclosed mass to be M SMBH<1.3*10^7 Msun. For NGC2824 and J0350-0127, the masers may be associated with pc or sub-pc scale jets or outflows.Comment: Accepted by Ap

Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator

In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to several interesting cases.Comment: 15 pages, two eps files, to appear in Phys. Rev. A 53 (6) (1996

A size of ~1 AU for the radio source Sgr A* at the centre of the Milky Way

Although it is widely accepted that most galaxies have supermassive black holes (SMBHs) at their centers^{1-3}, concrete proof has proved elusive. Sagittarius A* (Sgr A*)^4, an extremely compact radio source at the center of our Galaxy, is the best candidate for proof^{5-7}, because it is the closest. Previous Very Long Baseline Interferometry (VLBI) observations (at 7mm) have detected that Sgr A* is ~2 astronomical unit (AU) in size^8, but this is still larger than the "shadow" (a remarkably dim inner region encircled by a bright ring) arising from general relativistic effects near the event horizon^9. Moreover, the measured size is wavelength dependent^{10}. Here we report a radio image of Sgr A* at a wavelength of 3.5mm, demonstrating that its size is \~1 AU. When combined with the lower limit on its mass^{11}, the lower limit on the mass density is 6.5x10^{21} Msun pc^{-3}, which provides the most stringent evidence to date that Sgr A* is an SMBH. The power-law relationship between wavelength and intrinsic size (The size is proportional to wavelength^{1.09}), explicitly rules out explanations other than those emission models with stratified structure, which predict a smaller emitting region observed at a shorter radio wavelength.Comment: 18 pages, 4 figure

Radio continuum of galaxies with H2_{2}O megamaser disks: 33 GHz VLA data

We investigate the nuclear environment of galaxies with observed 22 GHz water megamaser in their subparsec edge-on accretion disks, using 33 GHz (9mm) radio continuum data from VLA, with a resolution of ~ 0.2-0.5 arcsecs, and relate the maser and host galaxy properties to those of its radio continuum emission. Eighty-seven percent (21 out of 24) galaxies in our sample show 33 GHz radio continuum emission at levels of 4.5-240 $\sigma$. Five sources show extended emission, including one source with two main components and one with three main components. The remaining detected 16 sources exhibit compact cores within the sensitivity limits. Little evidence is found for extended jets (>300 pc) in most sources. Either they do not exist, or our chosen frequency of 33 GHz is too high for a detection of these supposedly steep spectrum features. In only one source among those with known maser disk orientation, NGC4388, we found an extended jet-like feature that appears to be oriented perpendicular to the water megamaser disk. Smaller 100-300 pc sized jets might also be present, as is suggested by the beam-deconvolved morphology of our sources. Whenever possible, central positions with accuracies of 20-280 mas are provided. A correlation analysis shows that the 33 GHz luminosity weakly correlates with the infrared luminosity. The 33 GHz luminosity is anticorrelated with the circular velocity of the galaxy. The black hole masses show stronger correlations with water maser luminosity than with 1.4 GHz, 33 GHz, or hard X-ray luminosities. Furthermore, the inner radii of the disks show stronger correlations with 1.4 GHz, 33 GHz, and hard X-ray luminosities than their outer radii, suggesting that the outer radii may be affected by disk warping, star formation, or peculiar density distributions.Comment: 18 pages, 10 figures, Accepted for publication in A&