On the characterisation of paired monotone metrics

Hasegawa and Petz introduced the notion of dual statistically monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the dual family. In this paper we show that the characterisation theorem holds true under more general hypotheses.Comment: 12 pages, to appear on Ann. Inst. Stat. Math.; v2: changes made to conform to accepted version, title changed as wel

Integral-Field Spectroscopy of the Post Red Supergiant IRC +10420: evidence for an axi-symmetric wind

We present NAOMI/OASIS adaptive-optics assisted integral-field spectroscopy of the transitional massive hypergiant IRC +10420, an extreme mass-losing star apparently in the process of evolving from a Red Supergiant toward the Wolf-Rayet phase. To investigate the present-day mass-loss geometry of the star, we study the appearance of the line-emission from the inner wind as viewed when reflected off the surrounding nebula. We find that, contrary to previous work, there is strong evidence for wind axi-symmetry, based on the equivalent-width and velocity variations of H$\alpha$ and Fe {\sc ii} $\lambda$6516. We attribute this behaviour to the appearance of the complex line-profiles when viewed from different angles. We also speculate that the Ti {\sc ii} emission originates in the outer nebula in a region analogous to the Strontium Filament of $\eta$ Carinae, based on the morphology of the line-emission. Finally, we suggest that the present-day axisymmetric wind of IRC +10420, combined with its continued blueward evolution, is evidence that the star is evolving toward the B[e] supergiant phase.Comment: 22 pages, 9 figures, accepted for publication in ApJ. B&W-optimized version can be downloaded from http://www.cis.rit.edu/~bxdpci/pubs.htm

Two New LBV Candidates in the M33 Galaxy

We present two new luminous blue variable (LBV) candidate stars discovered in the M33 galaxy. We identified these stars (Valeev et al. 2010) as massive star candidates at the final stages of evolution, presumably with a notable interstellar extinction. The candidates were selected from the Massey et al. (2006) catalog based on the following criteria: emission in Halpha, V<18.5 and 0.35<(B-V)<1.2. The spectra of both stars reveal a broad and strong Halpha emission with extended wings (770 and 1000 km/s). Based on the spectra we estimated the main parameters of the stars. Object N45901 has a bolometric luminosity log(L/Lsun)=6.0-6.2 with the value of interstellar extinction Av=2.3+-0.1. The temperature of the star's photosphere is estimated as Tstar~13000-15000K its probable mass on the Zero Age Main Sequence is M~60-80Msun. The infrared excess in N45901 corresponds to the emission of warm dust with the temperature Twarm~1000K, and amounts to 0.1% of the bolometric luminosity. A comparison of stellar magnitude estimates from different catalogs points to the probable variability of the object N45901. Bolometric luminosity of the second object, N125093, is log(L/Lsun)=6.3-6.6, the value of interstellar extinction is Av=2.75+-0.15. We estimate its photosphere's temperature as Tstar~13000-16000K, the initial mass as M~90-120Msun. The infrared excess in N125093 amounts to 5-6% of the bolometric luminosity. Its spectral energy distribution reveals two thermal components with the temperatures Twarm~1000K and Tcold~480K. The [CaII] lines (7291A and 7323A), observed in LBV-like stars VarA and N93351 in M33, are also present in the spectrum of N125093. These lines indicate relatively recent gas eruptions and dust activity linked with them. High bolometric luminosity of these stars and broad Halpha emissions allow classifying the studied objects as LBV candidates.Comment: 14 pages, 4 figure

Observations of Lick Standard Stars Using the SCORPIO Multi-Slit Unit at the SAO 6-m Telescope

We present Lick line-index measurements of standard stars from the list of Worthey. The spectra were taken with the multi-slit unit of the SCORPIO spectrograph at the 6-m Special Astrophysical observatory telescope. We describe in detail our method of analysis and explain the importance of using the Lick index system for studying extragalactic globular clusters. Our results show that the calibration of our instrumental system to the standard Lick system can be performed with high confidence.Comment: 12 pages, 3 figure

Optical spectrum of the post-AGB star HD56126 in the region 4010-8790 AA

We studied in detail the optical spectrum of the post-AGB star HD56126 (IRAS07134+1005). We use high resolution spectra (R=25000 and 60000) obtained with the echelle spectrographs of the 6-m telescope. About one and a half thousand absorptions of neutral atoms and ions, absorption bands of C_2, CN, and CH molecules, and interstellar bands (DIBs) are identified in the 4010 to 8790 AA wavelength region, and the depths and radial velocities of these spectral features are measured. Differences are revealed between the variations of the radial velocities measured from spectral features of different excitation. In addition to the well-known variability of the Halpha profile, we found variations in the profiles of a number of FeII, YII, and BaII lines. We also produce an atlas of the spectrum of HD56126 and its comparison staralpha Per. The full version of the atlas is available in electronic form from Web-address: http://www.sao.ru/hq/ssl/Atlas/Atlas.htmlComment: 42 pages, 6 figure

Evolutionary stage of the spectral variable BD+48 1220=IRAS 05040+4820

Based on high-resolution observations (R=60000 and 75000), we have studied the optical spectral variability of the star BD+48 1220 (IRAS05040+4820). We have measured the equivalent widths of numerous absorption lines of neutral atoms and ions at wavelengths from 4500 to 6760 AA, as well as the corresponding radial velocities. We use model atmospheres to determine Teff=7900K, log g=0.0, microturbulence velocity xi_t=6.0, and the abundances for 16 elements. The star's metallicity differs little from the solar value: [Fe/H]=-0.10 dex. The main peculiarity of the chemical composition of the star is a large He-excess, derived from the HeI 5876 A absorption, [He/H]=+1.04, and the equally large O-excess, [O/Fe]=+0.72 dex. The C-excess is small, [C/Fe]=+0.09 dex, and the ratio [C/O]$\le$ 1. We obtained a revised relation for the light-metal abundances: [Na/Fe]=+0.87 with [Mg/Fe]=-0.31. The barium abundance is low, [Ba/Fe]=-0.84. The radial velocity of the star measured from photospheric absorption lines over three years of observations varies in the interval V_sun = -(7 - 15) km/s. Time variable differential line shifts have been revealed. The entire set of available data (the luminosity Mv~-5m, velocity V_lsr~-20 km/s, metallicity [Fe/H]=-0.10, and peculiarities of the optical spectrum and chemical composition) confirms the status of BD+48 1220 as a post-AGB star with He- and O-excesses belonging to the Galactic disk.Comment: 42 pages, 7 figures, 6 tables, accepted by Astronomy Report

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

The evolutionary status of the semiregular variable QYSge

Repeated spectroscopic observations made with the 6m telescope of yielded new data on the radial-velocity variability of the anomalous yellow supergiant QYSge. The strongest and most peculiar feature in its spectrum is the complex profile of NaI D lines, which contains a narrow and a very wide emission components. The wide emission component can be seen to extend from -170 to +120 km/s, and at its central part it is cut by an absorption feature, which, in turn, is split into two subcomponents by a narrow (16km/s at r=2.5) emission peak. An analysis of all the Vr values leads us to adopt for the star a systemic velocity of Vr=-21.1 km/s, which corresponds to the position of the narrow emission component of NaI. The locations of emission-line features of NaI D lines are invariable, which point to their formation in regions that are external to the supergiant's photosphere. Differential line shifts of about 10km/s are revealed. The absorption lines in the spectrum of QYSge have a substantial width of FWHM~45 km/s. The method of model atmospheres is used to determine the following parameters: Teff=6250K, lg g=2.0, and microturbulence Vt=4.5km/s. The metallicity of the star is found to be somewhat higher than the solar one with an average overabundance of iron-peak elements of [Met/H]=+0.20. The star is found to be slightly overabundant in carbon and nitrogen, [C/Fe]=+0.25, [N/Fe]=+0.27. The alpha-process elements Mg, Si, and Ca are slightly overabundant [alpha/H]=+0.12. The strong sodium excess, [Na/Fe]=+0.75, is likely to be due to the dredge-up of the matter processed in the NeNa cycle. Heavy elements of the s-process are underabundant relative to the Sun. On the whole, the observed properties of QYSge do not give grounds for including this star into the group of RCrB or RVTau-type type objects.Comment: 29 pages, 8 figures, 4 tables; accepted by Astrophys. Bulleti

V2324Cyg - an F-type star with fast wind

For the first time high-resolution optical spectroscopy of the variable star V2324Cyg associated with the IR-source IRAS20572+4919 is made. More than 200 absorption features (mostly FeII, TiII, CrII, YII, BaII, and YII) are identified within the wavelength interval 4549-7880AA. The spectral type and rotation velocity of the star are found to be F0III and Vsini=69km/s, respectively. HI and NaID lines have complex PCyg-type profiles with an emission component. Neither systematic trend of radial velocity Vr with line depth Ro nor temporal variability of Vr have been found. We determined the average heliocentric radial velocity Vr=-16.8\pm 0.6km/s. The radial velocities inferred from the cores of the absorption components of the H$\beta$ and NaI wind lines vary from -140 to -225km/s (and the expansion velocities of the corresponding layers, from about 120 to 210km/s). The maximum expansion velocity is found for the blue component of the split H$\alpha$ absorption: 450km/s for December 12, 1995. The model atmospheres method is used to determine the star's parameters: Teff=7500K, log g=2.0, $\xi_t$=6.0km/s, and metallicity, which is equal to the solar value. The main peculiarity of the chemical abundances pattern is the overabundance of lithium and sodium. The results cast some doubt on the classification of V2324Cyg as a post-AGB star.Comment: 28 pages, 6 figure