On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

High-resolution spectroscopic observations of B-type stars from the Edinburgh-Cape Survey - III. Completion of a magnitude range limited survey

High spectral resolution (R similar to 40 000) and signal-to- noise ratio observations of five high Galactic latitude early- type stars taken from the Edinburgh-Cape (EC) Faint Blue Object Survey are presented. These were required to complete a magnitude range-limited survey of young B-type objects with 11 <V <15. Of the five stars, four were rejected on the grounds that they are either subluminous (subdwarf or horizontal branch), were part of a binary system or possessed colours later than the (U - B) = -0.5 cut-off employed. The remaining star in the data set, EC 19596-5356, is found to exhibit normal young B-type stellar properties. A kinematic analysis reveals that an origin in the Galactic disc appears likely for all the stars in the sample. Some statistics are drawn about the number density of young stars in the Galactic halo.

Chemical compositions of four B-type supergiants in the SMC wing

High-resolution UCLES/AAT spectra of four B-type supergiants in the SMC South East Wing have been analysed using non-LTE model atmosphere techniques to determine their atmospheric parameters and chemical compositions. The principle aim of this analysis was to determine whether the very low metal abundances (-1.1 dex compared with Galactic value) previously found in the Magellanic Inter Cloud region (ICR) were also present in the SMC Wing. The chemical compositions of the four targets are similar to those found in other SMC objects and appear to be incompatible with those deduced previously for the ICR. Given the close proximity of the Wing to the ICR, this is difficult to understand and some possible explanations are briefly discussed.

B-type supergiants in the SMC: Chemical compositions and comparison of static and unified models

High-resolution UCLES/AAT spectra are presented for nine B-type supergiants in the SMC, chosen on the basis that they may show varying amounts of nuclear-synthetically processed material mixed to their surface. These spectra have been analysed using a new grid of approximately 12 000 non-LTE line blanketed tlusty model atmospheres to estimate atmospheric parameters and chemical composition. The abundance estimates for O, Mg and Si are in excellent agreement with those deduced from other studies, whilst the low estimate for C may reflect the use of the C II doublet at 4267 Å. The N estimates are approximately an order of magnitude greater than those found in unevolved B-type stars or H II regions but are consistent with the other estimates in AB-type supergiants. These results have been combined with results from a unified model atmosphere analysis of UVES/VLT spectra of B-type supergiants (Trundle et al. 2004, A&A, 417, 217) to discuss the evolutionary status of these objects. For two stars that are in common with those discussed by Trundle et al., we have undertaken a careful comparison in order to try to understand the relative importance of the different uncertainties present in such analyses, including observational errors and the use of static or unified models. We find that even for these relatively luminous supergiants, tlusty models yield atmospheric parameters and chemical compositions similar to those deduced from the unified code fastwind.

A non-LTE analysis of the spectra of two narrow lined main sequence stars in the SMC

An analysis of high-resolution VLT/UVES spectra of two B-type main sequence stars, NGC 346-11 and AV 304, in the Small Magellanic Cloud (SMC), has been undertaken, using the non-LTE tlusty model atmospheres to derive the stellar parameters and chemical compositions of each star. The chemical compositions of the two stars are in reasonable agreement. Moreover, our stellar analysis agrees well with earlier analyses of H II regions. The results derived here should be representative of the current base-line chemical composition of the SMC interstellar medium as derived from B-type stars.

A search for star formation around the Galactic halo B-type star PHL 346 with the 2dF spectrograph

A preliminary search for stars that may have formed coevally with the apparently young halo B-type star PHL 346 has been performed with the 2dF multifibre spectrograph on the Anglo- Australian Telescope (AAT). Candidates were selected for spectroscopy from APM scans of B and R Schmidt plates centred on PHL 346. A total of 476 stars of spectral type A or F were found; radial velocity estimates and more accurate spectral type assignments narrowed the number of possible coeval candidates to 6 A-type and 14 F-type stars. A statistical analysis of these results using a comparison with a control field suggests that the number of A-type or F-type candidate stars around PHL 346 is not unexpected, and that they need not be associated with PHL 346. A number of ways to improve the project are suggested.

Early-type stars in the Galactic halo from the Palomar-Green survey - III. Completion of a magnitude range limited sample

High-resolution (R approximate to 40 000) echelle spectroscopic observations of 13 high-latitude early-type stars are presented. These stars comprise the final part of a complete magnitude range limited sample based on low-resolution spectroscopy of targets drawn from the Palomar-Green survey. The magnitude range under consideration is 13 less than or equal to B-PG less than or equal to 14.6, corresponding to an approximate distance limit for main-sequence B-type objects of 5 less than or equal to d less than or equal to 40 kpc. Three stars are found to be apparently normal, young stars, based on their positions on the (T-eff, log g) diagram, normal abundance patterns and relatively large projected rotational velocities. A further star, PG 1209+263, was found to belong to the chemically peculiar (CP) silicon star class of objects. The remainder are evolved subluminous stars lying on post- horizontal branch (post-HB) tracks, with the exception of PG 2120+062, which appears to be in a post-asymptotic giant branch evolutionary stage. For the young stars in the sample, we have derived distance and age estimates through comparison of the atmospheric parameters with recent theoretical evolutionary models. We discuss formation scenarios by comparing times-of- flight and evolutionary time-scales. It is found that all stars could have formed in the Galactic disc and been ejected from there soon after their birth, with the exception of PG 1209+263. The adopted proper motion is found to be a crucial factor in the kinematical analysis. We also present some number densities for young B-type halo stars, which indicate that they are extremely scarce objects.

Model atmosphere and kinematical analyses of early-type stars from the Edinburgh-Cape Survey

We present high-resolution spectroscopic observations of 21 B- type stars, selected from the Edinburgh-Cape Blue Object Survey. Model atmosphere analyses confirm that 14 of these stars are young, main-sequence B-type objects with Population I chemical compositions. The remaining seven are found to be evolved objects, including subdwarfs, horizontal branch and post-AGB objects. A kinematical analysis shows that all 14 young main-sequence stars could have formed in the disc and subsequently been ejected into the halo. These results are combined with the analysis of a previous subsample of stars taken from the Survey. Of the complete sample, 31 have been found to be young, main-sequence objects, with formation in the disc, and subsequent ejection into the halo, again being found to be a plausible scenario.

Early-type stars observed in the ESO UVES Paranal Observatory Project - I. Interstellar NaIUV, TiII and CaIIKobservations

We present an analysis of interstellar NaI (lambda(air) = 3302.37 and 3302.98 angstrom), TiII (lambda(air) = 3383.76 angstrom) and CaII K (lambda(air) = 3933.66 angstrom) absorption features for 74 sightlines towards O- and B-type stars in the Galactic disc. The data were obtained from the Ultraviolet and Visual Echelle Spectrograph Paranal Observatory Project, at a spectral resolution of 3.75 km s(-1) and with mean signal-to-noise ratios per pixel of 260, 300 and 430 for the NaI, TiII and CaII observations, respectively. Interstellar features were detected in all but one of the TiII sightlines and all of the CaII sightlines. The dependence of the column density of these three species with distance, height relative to the Galactic plane, HI column density, reddening and depletion relative to the solar abundance has been investigated. We also examine the accuracy of using the NaI column density as an indicator of that for HI. In general, we find similar strong correlations for both Ti and Ca, and weaker correlations for Na. Our results confirm the general belief that Ti and Ca occur in the same regions of the interstellar medium ( ISM) and also that the TiII/CaII ratio is constant over all parameters. We hence conclude that the absorption properties of Ti and Ca are essentially constant under the general ISM conditions of the Galactic disc.

A chemical analysis of five hot stars towards the Galactic centre

High resolution echelle spectroscopy is presented for thirteen stars lying in the direction of the Galactic centre which, on the basis of photographic photometry and low dispersion spectroscopy, have been classified as early-B-type. Eight of these stars have large rotational velocities which preclude a detailed analysis. The five stars with moderate to low projected rotational velocities have been analysed using model atmosphere techniques to determine atmospheric parameters and chemical compositions. Two of these stars appear to be evolved blue horizontal branch objects on the basis of their chemical compositions and small projected rotational velocity. The evolutionary status of a third is ambiguous but it is probably a post-asymptotic-giant branch star. The remaining two objects are probably young massive stars and show enhanced abundances of N, C, Mg and Si, consistent with their formation in the inner part of the Galactic disk. However their O abundances are normal, confirming results found previously for other early- type stars, which would imply a flat abundance gradient for this element in the inner region of our Galaxy.

A non-LTE abundance analysis of the post-AGB star ROA 5701

An analysis of high-resolution Anglo-Australian Telescope (AAT)/University College London Echelle Spectrograph (UCLES) optical spectra for the ultraviolet (UV)-bright star ROA 5701 in the globular cluster omega Cen (NGC 5139) is performed, using non-local thermodynamic equilibrium (non-LTE) model atmospheres to estimate stellar atmospheric parameters and chemical composition. Abundances are derived for C, N, O, Mg, Si and S, and compared with those found previously by Moehler et al. We find a general metal underabundance relative to young B-type stars, consistent with the average metallicity of the cluster. Our results indicate that ROA 5701 has not undergone a gas-dust separation scenario as previously suggested. However, its abundance pattern does imply that ROA 5701 has evolved off the asymptotic giant branch (AGB) prior to the onset of the third dredge-up.

Chemical abundances and winds of massive stars in M31: a B-type supergiant and a WC star in OB 10

We present high quality spectroscopic data for two massive stars in the OB 10 association of M31, OB 10-64 (B0 la) and OB 10-WRI (WC6). Medium resolution spectra of both stars were obtained using the ISIS spectrograph on the William Herschel Telescope. This is supplemented with Hubble Space Telescope STIS UV spectroscopy and Keck I HIRES data for OB 10-64. A non- local thermodynamic equilibrium (LTE) model atmosphere and abundance analysis for OB 10-64 is presented, indicating that this star has similar photospheric CNO, Mg and Si abundances to solar neighbourhood massive stars. A wind analysis of this early B-type supergiant reveals a mass-loss rate of (M)over dot = 1.6 x 10(-6) M-circle dot yr(-1), and v(infinity) = 1650 km s(-1). The corresponding wind momentum is in good agreement with the wind momentum-luminosity relationship found for Galactic early-B supergiants. Observations of OB 10-WRI are analysed using a non-LTE, line-blanketed code, to reveal approximate stellar parameters of log L/L-circle dot similar to 5.7, T-* - 75 kK, v(infinity) similar to 3000 km s(-1), (M)over dot/(M-circle dot yr(-1)) similar to 10(-4.3) adopting a clumped wind with a filling factor of 10 per cent. Quantitative comparisons are made with the Galactic WC6 star HD 92809 (WR23) revealing that OB 10-WR1 is 0.4 dex more luminous, though it has a much lower C/He ratio (similar to0.1 versus 0.3 for HD 92809). Our study represents the first detailed, chemical model atmosphere analysis for either a B-type supergiant or a Wolf- Rayet (WR) star in Andromeda, and shows the potential of how such studies can provide new information on the chemical evolution of galaxies and the evolution of massive stars in the local Universe.

The present-day chemical composition of the SMC from UVES spectra of the sharp-lined, B-type dwarf AV 304

High-resolution spectroscopic VLT/UVES observations are presented for the B-type main-sequence star, AV 304, in the Small Magellanic Cloud (SMC). These spectra have been analysed using LTE model-atmosphere techniques, to derive stellar atmospheric parameters and chemical compositions. As AV 304 is located within the hydrogen burning main-sequence band, its chemical composition should reflect that of the SMC interstellar medium (ISM). A detailed line-by-line differential analysis has been undertaken relative to a Galactic comparison star. A general metal deficiency for the a-process elements O, Si & S of -0.43 +/- 0.05 dex is found for AV 304, with iron having a similar underabundance. Oxygen may be relatively over- abundant by similar to0.1 dex and carbon and aluminium underabundant by similar to0.2 dex. A large nitrogen underabundance (of -1.2 dex relative to hydrogen and -0.7 dex relative to iron) is found. This is interpreted in terms of the CNO bi-cycle having been suppressed in the SMC. Furthermore, the large nitrogen deficiency is in excellent agreement with that found for SMC H II regions. Indeed, this represents a first for stellar astrophysics - confirming the low base-line nitrogen composition of the SMC ISM (viz. 12+log(N/H) similar to 6.66 +/- 0.10 dex).

Chemical composition of B-type supergiants in the OB 8, OB 10, OB 48, OB 78 associations of M 31

Absolute and differential chemical abundances are presented for the largest group of massive stars in M31 studied to date. These results were derived from intermediate resolution spectra of seven B-type supergiants, lying within four OB associations covering a galactocentric distance of 5-12 kpc. The results are mainly based on an LTE analysis, and we additionally present a full non-LTE, unified model atmosphere analysis of one star (OB 78-277) to demonstrate the reliability of the differential LTE technique. A comparison of the stellar oxygen abundance with that of previous nebular results shows that there is an off set of between similar to0.15-0.4 dex between the two methods which is critically dependent on the empirical calibration adopted for the R 23 parameter with [O/H]. However within the typical errors of the stellar and nebular analyses (and given the strength of dependence of the nebular results on the calibration used) the oxygen abundances determined in each method are fairly consistent. We determine the radial oxygen abundance gradient from these stars, and do not detect any systematic gradient across this galactocentric range. We find that the inner regions of M31 are not, as previously thought, very "metal rich". Our abundances of C, N, O, Mg, Si, Al, S and Fe in the M31 supergiants are very similar to those of massive stars in the solar neighbourhood.

Interplay between proton ordering and ferroelectric polarization in H-bonded KDP-type crystals

The origin of ferroelectricity in KH2PO4 (KDP) is studied by first-principles electronic structure calculations. In the low-temperature phase, the collective off-centre ordering of the protons is accompanied by an electronic charge delocalization from the near and localization at the far oxygen within the O-H...O bonds. Electrostatic forces. then, push the K+ ions towards off-centre positions, and induce a macroscopic polarization. The analysis of the correlation between different geometrical and electronic quantities, in connection with experimental data. supports the idea that the role of tunnelling in isotopic effects is irrelevant. Instead, geometrical quantum effects appear to play a central role. (C) 2001 Elsevier Science B.V. All rights reserved.