Essential closures and AC spectra for reflectionless CMV, Jacobi, and Schrödinger operators revisited

We provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of absolutely continuous measures. As an elementary application of the notion of the essential closure of subsets of R we revisit the fact that CMV, Jacobi, and Schrödinger operators, reflectionless on a set ∈ of positive Lebesgue measure, have absolutely continuous spectrum on the essential closure ⋶^e of the set ∈ (with uniform multiplicity two on ∈). Though this result in the case of Schrödinger and Jacobi operators is known to experts, we feel it nicely illustrates the concept and usefulness of essential closures in the spectral theory of classes of reflectionless differential and difference operators

Characterizing the radial oxygen abundance distribution in disk galaxies

We examine the possible dependence of the radial oxygen abundance distribution on non-axisymmetrical structures (bar/spirals) and other macroscopic parameters such as the mass, the optical radius R25, the color g-r, and the surface brightness of the galaxy. A sample of disk galaxies from the CALIFA DR3 is considered. We adopted the Fourier amplitude A2 of the surface brightness as a quantitative characteristic of the strength of non-axisymmetric structures in a galactic disk, in addition to the commonly used morphologic division for A, AB, and B types based on the Hubble classification. To distinguish changes in local oxygen abundance caused by the non-axisymmetrical structures, the multiparametric mass--metallicity relation was constructed as a function of parameters such as the bar/spiral pattern strength, the disk size, color index g-r in the SDSS bands, and central surface brightness of the disk. The gas-phase oxygen abundance gradient is determined by using the R calibration. We find that there is no significant impact of the non-axisymmetric structures such as a bar and/or spiral patterns on the local oxygen abundance and radial oxygen abundance gradient of disk galaxies. Galaxies with higher mass, however, exhibit flatter oxygen abundance gradients in units of dex/kpc, but this effect is significantly less prominent for the oxygen abundance gradients in units of dex/R25 and almost disappears when the inner parts are avoided. We show that the oxygen abundance in the central part of the galaxy depends neither on the optical radius R25 nor on the color g-r or the surface brightness of the galaxy. Instead, outside the central part of the galaxy, the oxygen abundance increases with g-r value and central surface brightness of the disk.Comment: 11 pages, 6 figures; accepted for publication in A&

Oxygen abundance distributions in six late-type galaxies based on SALT spectra of HII regions

Spectra of 34 H II regions in the late-type galaxies NGC1087, NGC2967, NGC3023, NGC4030, NGC4123, and NGC4517A were observed with the South African Large Telescope (SALT). In all 34 H II regions, oxygen abundances were determined through the "counterpart" method (C method). Additionally, in two H II regions in which the auroral lines were detected oxygen abundances were measured through the classic Te method. We also estimated the abundances in our H II regions using the O3N2 and N2 calibrations and compared those with the C-based abundances. With these data we examined the radial abundance distributions in the disks of our target galaxies. We derived surface-brightness profiles and other characteristics of the disks (the surface brightness at the disk center and the disk scale length) in three photometric bands for each galaxy using publicly available photometric imaging data. The radial distributions of the oxygen abundances predicted by the relation between abundance and disk surface brightness in the W1 band obtained for spiral galaxies in our previous study are close to the radial distributions of the oxygen abundances determined from the analysis of the emission line spectra for four galaxies where this relation is applicable. Hence, when the surface-brightness profile of a late-type galaxy is known, this parametric relation can be used to estimate the likely present-day oxygen abundance in its disk.Comment: 15 pages, 11 figures; Accepted for publication in Astronomy & Astrophysic

Detection of a new methanol maser line with ALMA

Aims. We aimed at investigating the structure and kinematics of the gaseous disk and outflows around the massive YSO S255 NIRS3 in the S255IR-SMA1 dense clump. Methods. Observations of the S255IR region were carried out with ALMA at two epochs in the compact and extended configurations. Results. We serendipitously detected a new, never predicted, bright maser line at about 349.1 GHz, which most probably represents the CH$_3$OH $14_{1} - 14_{0}$ A$^{- +}$ transition. The emission covers most of the 6.7 GHz methanol maser emission area of almost 1$^{\prime\prime}$ in size and shows a velocity gradient in the same sense as the disk rotation. No variability was found on the time interval of several months. It is classified as Class II maser and probably originates in a ring at a distance of several hundreds AU from the central star.Comment: 4 pages, 4 figures, accepted by Astronomy and Astrophysic

A Search for Small-Scale Clumpiness in Dense Cores of Molecular Clouds

We have analyzed HCN(1-0) and CS(2-1) line profiles obtained with high signal-to-noise ratios toward distinct positions in three selected objects in order to search for small-scale structure in molecular cloud cores associated with regions of high-mass star formation. In some cases, ripples were detected in the line profiles, which could be due to the presence of a large number of unresolved small clumps in the telescope beam. The number of clumps for regions with linear scales of ~0.2-0.5 pc is determined using an analytical model and detailed calculations for a clumpy cloud model; this number varies in the range: ~2 10^4-3 10^5, depending on the source. The clump densities range from ~3 10^5-10^6 cm^{-3}, and the sizes and volume filling factors of the clumps are ~(1-3) 10^{-3} pc and ~0.03-0.12. The clumps are surrounded by inter-clump gas with densities not lower than ~(2-7) 10^4 cm^{-3}. The internal thermal energy of the gas in the model clumps is much higher than their gravitational energy. Their mean lifetimes can depend on the inter-clump collisional rates, and vary in the range ~10^4-10^5 yr. These structures are probably connected with density fluctuations due to turbulence in high-mass star-forming regions.Comment: 23 pages including 4 figures and 4 table