Spectral synthesis and topologies on ideal spaces for Banach *-algebras

This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G).

Spectral synthesis for Banach Algebras II

This paper continues the study of spectral synthesis and the topologies tau-infinity and tau-r on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C*-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of tau_infinity. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of tau_r.

First stars XI. Chemical composition of the extremely metal-poor dwarfs in the binary CS 22876-032

Context. Unevolved metal-poor stars constitute a fossil record of the early Galaxy, and can provide invaluable information on the properties of the first generations of stars. Binary systems also provide direct information on the stellar masses of their member stars. Aims. The purpose of this investigation is a detailed abundance study of the double-lined spectroscopic binary CS 22876-032, which comprises the two most metal-poor dwarfs known. Methods. We used high-resolution, high-S/N ratio spectra from the UVES spectrograph at the ESO VLT telescope. Long-term radial-velocity measurements and broad-band photometry allowed us to determine improved orbital elements and stellar parameters for both components. We used OSMARCS 1D models and the TURBOSPECTRUM spectral synthesis code to determine the abundances of Li, O, Na, Mg, Al, Si, Ca, Sc, Ti, Cr, Mn, Fe, Co and Ni. We also used the (COBOLD)-B-5 model atmosphere code to compute the 3D abundance corrections, notably for Li and O. Results. We find a metallicity of [Fe/H] similar to -3.6 for both stars, using 1D models with 3D corrections of similar to -0.1 dex from averaged 3D models. We determine the oxygen abundance from the near-UV OH bands; the 3D corrections are large, -1 and -1.5 dex for the secondary and primary respectively, and yield [O/Fe] similar to 0.8, close to the high-quality results obtained from the [OI] 630 nm line in metal-poor giants. Other [alpha/Fe] ratios are consistent with those measured in other dwarfs and giants with similar [Fe/H], although Ca and Si are somewhat low ([X/Fe] less than or similar to 0). Other element ratios follow those of other halo stars. The Li abundance of the primary star is consistent with the Spite plateau, but the secondary shows a lower abundance; 3D corrections are small. Conclusions. The Li abundance in the primary star supports the extension of the Spite Plateau value at the lowest metallicities, without any decrease. The low abundance in the secondary star could be explained by endogenic Li depletion, due to its cooler temperature. If this is not the case, another, yet unknown mechanism may be causing increased scatter in A( Li) at the lowest metallicities.

Alpha element abundances and gradients in the Milky Way bulge from FLAMES-GIRAFFE spectra of 650 K giants

Aims. We present the analysis of the [alpha/Fe] abundance ratios for a large number of stars at several locations in the Milky Way bulge with the aim of constraining its formation scenario. Methods. We obtained FLAMES-GIRAFFE spectra (R = 22 500) at the ESO Very Large Telescope for 650 bulge red giant branch (RGB) stars and performed spectral synthesis to measure Mg, Ca, Ti, and Si abundances. This sample is composed of 474 giant stars observed in 3 fields along the minor axis of the Galactic bulge and at latitudes b = -4 degrees, b = -6 degrees, b = -12 degrees. Another 176 stars belong to a field containing the globular cluster NGC 6553, located at b = -3 degrees and 5 degrees away from the other three fields along the major axis. Stellar parameters and metallicities for these stars were presented in Zoccali et al. (2008, A&A, 486, 177). We have also re-derived stellar parameters and abundances for the sample of thick and thin disk red giants analyzed in Alves-Brito et al. (2010, A&A, 513, A35). Therefore using a homogeneous abundance database for the bulge, thick and thin disk, we have performed a differential analysis minimizing systematic errors, to compare the formation scenarios of these Galactic components. Results. Our results confirm, with large number statistics, the chemical similarity between the Galactic bulge and thick disk, which are both enhanced in alpha elements when compared to the thin disk. In the same context, we analyze [alpha/Fe] vs. [Fe/H] trends across different bulge regions. The most metal rich stars, showing low [alpha/Fe] ratios at b = -4 degrees disappear at higher Galactic latitudes in agreement with the observed metallicity gradient in the bulge. Metal-poor stars ([Fe/H] < -0.2) show a remarkable homogeneity at different bulge locations. Conclusions. We have obtained further constrains for the formation scenario of the Galactic bulge. A metal-poor component chemically indistinguishable from the thick disk hints for a fast and early formation for both the bulge and the thick disk. Such a component shows no variation, neither in abundances nor kinematics, among different bulge regions. A metal-rich component showing low [alpha/Fe] similar to those of the thin disk disappears at larger latitudes. This allows us to trace a component formed through fast early mergers (classical bulge) and a disk/bar component formed on a more extended timescale.

Spectroscopic variabilities in lambda Pavonis

Aims. We investigate the time-varying patterns in line profiles, V/R, and radial velocity of the Be star HD 173948 (lambda Pavonis). Methods. Time series analyses of radial velocity, V/R, and line profiles of He I, Fe II, and Si II were performed with the Cleanest algorithm. An estimate of the stellar rotation frequency was derived from the stellar mass and radius in the Roche limit by adopting an aspect angle i derived from the fittings of non-LTE model spectra affected by rotation. The projected rotation velocity, necessary as input for the spectral synthesis procedure, was evaluated from the Fourier transform of the rotation profiles of all neutral helium lines in the optical range. Results. Emission episodes in Balmer and He i lines, as well as V/R cyclic variations, are reported for spectra observed in year 1999, followed by a relatively quiescent phase (2000) and then again a new active epoch (2001). From time series analyses of line profiles, radial velocities, and V/R ratios, four signals with high confidence levels are detected: nu(1) = 0.17 +/- 0.02, nu(2) = 0.49 +/- 0.05, nu(3) = 0.82 +/- 0.03, and nu(4) = 1.63 +/- 0.04 c/d. We interpret nu 4 as a non-radial pulsation g-mode, nu 3 as a signal related to the orbital timescale of ejected material, which is near the theoretical rotation frequency 0.81 c/d inferred from the fitting of the models taken into account for gravity darkening. The signals nu(1) and nu(2) are viewed as aliases of nu(3) and nu(4).

Li-rich red giant branch stars in the Galactic bulge

Aims. We present lithium abundance determination for a sample of K giant stars in the Galactic bulge. The stars presented here are the only 13 stars with a detectable lithium line (6767.18 angstrom) among similar to 400 stars for which we have spectra in this wavelength range, half of them in Baade's Window (b = -4 degrees) and half in a field at b = -6 degrees. Methods. The stars were observed with the GIRAFFE spectrograph of FLAMES mounted on VLT, with a spectral resolution of R similar to 20 000. Abundances were derived from spectral synthesis and the results are compared with those of stars with similar parameters, but no detectable Li line. Results. We find 13 stars with a detectable Li line, among which 2 have abundances A(Li) > 2.7. No clear correlations were found between the Li abundance and those of other elements. With the exception of the two most Li rich stars, the others follow a fairly tight A(Li) - T(eff) correlation. Conclusions. There is strong indication of a Li production phase during the red giant branch (RGB), acting either on a very short timescale, or selectively only in some stars. That the proposed Li production phase is associated with the RGB bump cannot be excluded, although our targets are significantly brighter than the predicted RGB bump magnitude for a population at 8 kpc.

AUTOMATED DETERMINATION OF [Fe/H] AND [C/Fe] FROM LOW-RESOLUTION SPECTROSCOPY

We develop an automated spectral synthesis technique for the estimation of metallicities ([Fe/H]) and carbon abundances ([C/Fe]) for metal-poor stars, including carbon-enhanced metal-poor stars, for which other methods may prove insufficient. This technique, autoMOOG, is designed to operate on relatively strong features visible in even low- to medium-resolution spectra, yielding results comparable to much more telescope-intensive high-resolution studies. We validate this method by comparison with 913 stars which have existing high-resolution and low- to medium-resolution to medium-resolution spectra, and that cover a wide range of stellar parameters. We find that at low metallicities ([Fe/H] less than or similar to -2.0), we successfully recover both the metallicity and carbon abundance, where possible, with an accuracy of similar to 0.20 dex. At higher metallicities, due to issues of continuum placement in spectral normalization done prior to the running of autoMOOG, a general underestimate of the overall metallicity of a star is seen, although the carbon abundance is still successfully recovered. As a result, this method is only recommended for use on samples of stars of known sufficiently low metallicity. For these low- metallicity stars, however, autoMOOG performs much more consistently and quickly than similar, existing techniques, which should allow for analyses of large samples of metal-poor stars in the near future. Steps to improve and correct the continuum placement difficulties are being pursued.

Mn, Cu, and Zn abundances in barium stars and their correlations with neutron capture elements

Barium stars are optimal sites for studying the correlations between the neutron-capture elements and other species that may be depleted or enhanced, because they act as neutron seeds or poisons during the operation of the s-process. These data are necessary to help constrain the modeling of the neutron-capture paths and explain the s-process abundance curve of the solar system. Chemical abundances for a large number of barium stars with different degrees of s-process excesses, masses, metallicities, and evolutionary states are a crucial step towards this goal. We present abundances of Mn, Cu, Zn, and various light and heavy elements for a sample of barium and normal giant stars, and present correlations between abundances contributed to different degrees by the weak-s, mains, and r-processes of neutron capture, between Fe-peak elements and heavy elements. Data from the literature are also considered in order to better study the abundance pattern of peculiar stars. The stellar spectra were observed with FEROS/ESO. The stellar atmospheric parameters of the eight barium giant stars and six normal giants that we analyzed lie in the range 4300 < T(eff)/K < 5300, -0.7 < [Fe/H] <= 0.12 and 1.5 <= log g < 2.9. Carbon and nitrogen abundances were derived by spectral synthesis of the molecular bands of C(2), CH, and CN. For all other elements we used the atomic lines to perform the spectral synthesis. A very large scatter was found mainly for the Mn abundances when data from the literature were considered. We found that [Zn/Fe] correlates well with the heavy element excesses, its abundance clearly increasing as the heavy element excesses increase, a trend not shown by the [Cu/Fe] and [Mn/Fe] ratios. Also, the ratios involving Mn, Cu, and Zn and heavy elements usually show an increasing trend toward higher metallicities. Our results suggest that a larger fraction of the Zn synthesis than of Cu is owed to massive stars, and that the contribution of the main-s process to the synthesis of both elements is small. We also conclude that Mn is mostly synthesized by SN Ia, and that a non-negligible fraction of the synthesis of Mn, Cu, and Zn is owed to the weak s-process.

Towards the main sequence: detailed analysis of weak line and post-T Tauri stars

A detailed study was performed for a sample of low-mass pre-main-sequence (PMS) stars, previously identified as weak-line T Tauri stars, which are compared to members of the Tucanae and Horologium Associations. Aiming to verify if there is any pattern of abundances when comparing the young stars at different phases, we selected objects in the range from 1 to 100 Myr, which covers most of PMS evolution. High-resolution optical spectra were acquired at European Southern Observatory and Observatorio do Pico dos Dias. The stellar fundamental parameters effective temperature and gravity were calculated by excitation and ionization equilibria of iron absorption lines. Chemical abundances were obtained via equivalent width calculations and spectral synthesis for 44 per cent of the sample, which shows metallicities within 0.5 dex solar. A classification was developed based on equivalent width of Li I 6708 angstrom and Ha lines and spectral types of the studied stars. This classification allowed a separation of the sample into categories that correspond to different evolutive stages in the PMS. The position of these stars in the Hertzsprung-Russell diagram was also inspected in order to estimate their ages and masses. Among the studied objects, it was verified that our sample actually contains seven weak-line T Tauri stars, three are Classical T Tauri, 12 are Fe/Ge PMS stars and 21 are post-T Tauri or young main-sequence stars. An estimation of circumstellar luminosity was obtained using a disc model to reproduce the observed spectral energy distribution. Most of the stars show low levels of circumstellar emission, corresponding to less than 30 per cent of the total emission.

The evolution of the mass-metallicity relation in SDSS galaxies uncovered by astropaleontology

We have obtained the mass-metallicity (M-Z) relation at different lookback times for the same set of galaxies from the Sloan Digital Sky Survey, using the stellar metallicities estimated with our spectral synthesis code STARLIGHT. We have found that this relation steepens and spans a wider range in both mass and metallicity at higher redshifts. We have modelled the time evolution of stellar metallicity with a closed-box chemical evolution model, for galaxies of different types and masses. Our results suggest that the M-Z relation for galaxies with present-day stellar masses down to 10(10) M(circle dot) is mainly driven by the history of star formation and not by inflows or outflows.

The star formation history of CALIFA galaxies: Radial structures

We have studied the radial structure of the stellar mass surface density (μ∗) and stellar population age as a function of the total stellar mass and morphology for a sample of 107 galaxies from the CALIFA survey. We applied the fossil record method based on spectral synthesis techniques to recover the star formation history (SFH), resolved in space and time, in spheroidal and disk dominated galaxies with masses from 10^9 to 10^12 M_⊙. We derived the half-mass radius, and we found that galaxies are on average 15% more compact in mass than in light. The ratio of half-mass radius to half-light radius (HLR) shows a dual dependence with galaxy stellar mass; it decreases with increasing mass for disk galaxies, but is almost constant in spheroidal galaxies. In terms of integrated versus spatially resolved properties, we find that the galaxy-averaged stellar population age, stellar extinction, and μ_∗ are well represented by their values at 1 HLR. Negative radial gradients of the stellar population ages are present in most of the galaxies, supporting an inside-out formation. The larger inner (≤1 HLR) age gradients occur in the most massive (10^11 M_⊙) disk galaxies that have the most prominent bulges; shallower age gradients are obtained in spheroids of similar mass. Disk and spheroidal galaxies show negative μ∗ gradients that steepen with stellar mass. In spheroidal galaxies, μ∗ saturates at a critical value (~7 × 10^2 M_⊙/pc^2 at 1 HLR) that is independent of the galaxy mass. Thus, all the massive spheroidal galaxies have similar local μ_∗ at the same distance (in HLR units) from the nucleus. The SFH of the regions beyond 1 HLR are well correlated with their local μ_∗, and follow the same relation as the galaxy-averaged age and μ_∗; this suggests that local stellar mass surface density preserves the SFH of disks. The SFH of bulges are, however, more fundamentally related to the total stellar mass, since the radial structure of the stellar age changes with galaxy mass even though all the spheroid dominated galaxies have similar radial structure in μ_∗. Thus, galaxy mass is a more fundamental property in spheroidal systems, while the local stellar mass surface density is more important in disks.

The ionized gas in the CALIFA early-type galaxies I. Mapping two representative cases: NGC 6762 and NGC 5966

As part of the ongoing CALIFA survey, we have conducted a thorough bidimensional analysis of the ionized gas in two E/S0 galaxies, NGC 6762 and NGC 5966, aiming to shed light on the nature of their warm ionized ISM. Specifically, we present optical (3745–7300 Å) integral field spectroscopy obtained with the PMAS/PPAK integral field spectrophotometer. Its wide field-of-view (1′ × 1′) covers the entire optical extent of each galaxy down to faint continuum surface brightnesses. To recover the nebular lines, we modeled and subtracted the underlying stellar continuum from the observed spectra using the STARLIGHT spectral synthesis code. The pure emission-line spectra were used to investigate the gas properties and determine the possible sources of ionization. We show the advantages of IFU data in interpreting the complex nature of the ionized gas in NGC 6762 and NGC 5966. In NGC 6762, the ionized gas and stellar emission display similar morphologies, while the emission line morphology is elongated in NGC 5966, spanning ~6 kpc, and is oriented roughly orthogonal to the major axis of the stellar continuum ellipsoid. Whereas gas and stars are kinematically aligned in NGC 6762, the gas is kinematically decoupled from the stars in NGC 5966. A decoupled rotating disk or an “ionization cone” are two possible interpretations of the elongated ionized gas structure in NGC 5966. The latter would be the first “ionization cone” of such a dimension detected within a weak emission-line galaxy. Both galaxies have weak emission-lines relative to the continuum[EW(Hα) ≲ 3 Å] and have very low excitation, log([OIII]λ5007/Hβ) ≲ 0.5. Based on optical diagnostic ratios ([OIII]λ5007/Hβ, [NII]λ6584/Hα, [SII]λ6717, 6731/Hα, [OI]λ6300/Hα), both objects contain a LINER nucleus and an extended LINER-like gas emission. The emission line ratios do not vary significantly with radius or aperture, which indicates that the nebular properties are spatially homogeneous. The gas emission in NGC 6762 can be best explained by photoionization by pAGB stars without the need of invoking any other excitation mechanism. In the case of NGC 5966, the presence of a nuclear ionizing source seems to be required to shape the elongated gas emission feature in the “ionization cone” scenario, although ionization by pAGB stars cannot be ruled out. Further study of this object is needed to clarify the nature of its elongated gas structure.

On the Equality of Sharp and Germ - Fields for Gaussian Processes and Fields

2000 Mathematics Subject Classification: 60G15, 60G60; secondary 31B15, 31B25, 60H15

Synthesis and spectral investigation of Al(III) catechin/beta-cyclodextrin and Al(III) quercetin/beta-cyclodextrin inclusion compounds

Al-catechin/beta-cyclodextrin and Al-quercetin/beta-cyclodextrin (beta-CD) inclusion compounds were synthesized and characterized by IR, UV-vis, H-1 and C-13 NMR and TG and DTA analyses. Because quercetin is sparingly soluble in water, the stability constants of the Al-quercetin/beta-CD and Al-catechin/beta-CD compounds were determined by phase solubility studies. The A(L)-type diagrams indicated the formation of 1:1 inclusion compounds and allowed calculation of the stability constants. The thermodynamic parameters were obtained from the dependence of the stability constants on temperature and results indicated that the formation of the inclusion compounds is an enthalpically driven process. The thermal decomposition of the solid Al-quercetin/beta-CD and Al-catcchin/beta-CD inclusion compounds took place at different stages, compared with the respective precursors, proving that an inclusion complexation process really occurred. (C) 2007 Published by Elsevier B.V.

Synthesis and spectral studies of methyl heterocylic systems

2-Carboxy-2?-methyldiphenyl sulfide was prepared by the Ullmann reaction and cyclodehydrated by sulfuric acid to afford 4-methylthioxanthone. 1-Methylthioxanthone was separated from the reaction mixture obtained upon cyclodehydration of 2-carboxy-3f-methyldiphenyl sulfide. In addition, 1-, 2-, 3- and 4-methylthioxanthone 10,10-dioxides were synthesized by oxidation of the corresponding thioxanthones. o-, m- and p-N-Tolylanthranilic acids were prepared by the Ullmann reaction and used as precursors for the preparation of 1-, 2- and 4- methyl-9-chloroacridine and finally 1-, 2-, 3- and 4-methylacridone. High resolution, 60 MHz PMR spectra were obtained on the four monomethyl isomers of xanthone, thioxanthone, thioxanthone 10,10-dioxide and acridone, and on 1-, 2- and 4-methyl-9-chloroacridine. For some compounds, coupling of all three different aromatic protons to the methyl was observed, two of the couplings typically being smaller than the third. With the large (ortho) coupling being on the order of 0.5 to 1.0 Hz, it was necessary to decouple the aromatic part of the spectrum. The magnitude of the ortho benzylic constant may be related to an incomplete Tr-bond delocalization in the molecules.