Computational complexity of μ calculation

The structured singular value μ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems

The Megamaser Cosmology Project: I. VLBI observations of UGC 3789

The Megamaser Cosmology Project (MCP) seeks to measure the Hubble Constant (Ho) in order to improve the extragalactic distance scale and constrain the nature of dark energy. We are searching for sources of water maser emission from AGN with sub-pc accretion disks, as in NGC 4258, and following up these discoveries with Very Long Baseline Interferometric (VLBI) imaging and spectral monitoring. Here we present a VLBI map of the water masers toward UGC 3789, a galaxy well into the Hubble Flow. We have observed masers moving at rotational speeds up to 800 km/s at radii as small as 0.08 pc. Our map reveals masers in a nearly edge-on disk in Keplerian rotation about a 10^7 Msun supermassive black hole. When combined with centripetal accelerations, obtained by observing spectral drifts of maser features (to be presented in Paper II), the UGC 3789 masers may provide an accurate determination of Ho, independent of luminosities and metallicity and extinction corrections.Comment: 18 pages, 3 figures, 4 table

The innermost region of the water megamaser radio galaxy 3C403

The standard unified scheme of active galactic nuclei requires the presence of high column densities of gas and dust potentially obscuring the central engine. So far, few direct subarcsecond resolution studies of this material have been performed toward radio galaxies. The goal of this paper is to elucidate the nuclear environment of the prototypical X-shaped Fanaroff-Riley type II radio galaxy 3C403, the only powerful radio galaxy known to host a water megamaser. Very Large Array A-array and single-dish Green Bank and Effelsberg 1.3 cm measurements were performed to locate and monitor the water maser emission. Very Long Baseline Interferometry 6 cm continuum observations were taken to analyze the spatial structure of the nuclear environment at even smaller scales, while the CO J=1-0 and 2-1 transitions were observed with the IRAM 30-m telescope to search for thermal emission from a spatially extended, moderately dense gas component.[abridged]Comment: 11 pages, 12 figures, accepted by A&A. For a version with high quality figures, see http://erg.ca.astro.it/~atarchi/3C403

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.Comment: 29 pages, 8 figures, Accepted by Ap

Infrared Spectra of Meteoritic SiC Grains

We present here the first infrared spectra of meteoritic SiC grains. The mid-infrared transmission spectra of meteoritic SiC grains isolated from the Murchison meteorite were measured in the wavelength range 2.5--16.5 micron, in order to make available the optical properties of presolar SiC grains. These grains are most likely stellar condensates with an origin predominately in carbon stars. Measurements were performed on two different extractions of presolar SiC from the Murchison meteorite. The two samples show very different spectral appearance due to different grain size distributions. The spectral feature of the smaller meteoritic SiC grains is a relatively broad absorption band found between the longitudinal and transverse lattice vibration modes around 11.3 micron, supporting the current interpretation about the presence of SiC grains in carbon stars. In contrast to this, the spectral feature of the large (> 5 micron) grains has an extinction minimum around 10 micron. The obtained spectra are compared with commercially available SiC grains and the differences are discussed. This comparison shows that the crystal structure (e.g., beta-SiC versus alpha-SiC) of SiC grains plays a minor role on the optical signature of SiC grains compared to e.g. grain size.Comment: 7 pages, 6 figures. To appear in A&

The Megamaser Cosmology Project: IV. A Direct Measurement of the Hubble Constant from UGC 3789

In Papers I and II from the Megamaser Cosmology Project (MCP), we reported initial observations of water 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 Ho with 16% uncertainty. We have since conducted more VLBI observations of the spatial-velocity structure of these water 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 signifcantly improved accuracy. We find Ho = 68.9 +/- 7.1 km/s/Mpc; this estimate of Ho is independent of other methods and is accurate to +/-10%, including sources of systematic error. This places UGC 3789 at a distance of 49.6 +/- 5.1 Mpc, with a central supermassive black hole of (1.16 +/- 0.12) x 10^7 Msun.Comment: to appear in Ap