Coloured peak algebras and Hopf algebras

For $G$ a finite abelian group, we study the properties of general equivalence relations on G_n=G^n\rtimes \SG_n, the wreath product of $G$ with the symmetric group \SG_n, also known as the $G$-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of \k G_n as well as graded connected Hopf subalgebras of \bigoplus_{n\ge o} \k G_n. In particular we construct a $G$-coloured peak subalgebra of the Mantaci-Reutenauer algebra (or $G$-coloured descent algebra). We show that the direct sum of the $G$-coloured peak algebras is a Hopf algebra. We also have similar results for a $G$-colouring of the Loday-Ronco Hopf algebras of planar binary trees. For many of the equivalence relations under study, we obtain a functor from the category of finite abelian groups to the category of graded connected Hopf algebras. We end our investigation by describing a Hopf endomorphism of the $G$-coloured descent Hopf algebra whose image is the $G$-coloured peak Hopf algebra. We outline a theory of combinatorial $G$-coloured Hopf algebra for which the $G$-coloured quasi-symmetric Hopf algebra and the graded dual to the $G$-coloured peak Hopf algebra are central objects.Comment: 26 pages latex2

Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem

We consider the numbers arising in the problem of normal ordering of expressions in canonical boson creation and annihilation operators. We treat a general form of a boson string which is shown to be associated with generalizations of Stirling and Bell numbers. The recurrence relations and closed-form expressions (Dobiski-type formulas) are obtained for these quantities by both algebraic and combinatorial methods. By extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs. This link provides a combinatorial interpretation of the numbers arising in this normal ordering problem.Comment: 10 pages, 5 figure

The Advantage of Increased Resolution in the Study of Quasar Absorption Systems

We compare a new R = 120,000 spectrum of PG1634+706 (z_QSO = 1.337,m_V = 14.9) obtained with the HDS instrument on Subaru to a R = 45, 000 spectrum obtained previously with HIRES/Keck. In the strong MgII system at z = 0.9902 and the multiple cloud, weak MgII system at z = 1.0414, we find that at the higher resolution, additional components are resolved in a blended profile. We find that two single-cloud weak MgII absorbers were already resolved at R = 45,000, to have b = 2 - 4 km/s. The narrowest line that we measure in the R = 120, 000 spectrum is a component of the Galactic NaI absorption, with b = 0.90+/-0.20 km/s. We discuss expectations of similarly narrow lines in various applications, including studies of DLAs, the MgI phases of strong MgII absorbers, and high velocity clouds. By applying Voigt profile fitting to synthetic lines, we compare the consistency with which line profile parameters can be accurately recovered at R = 45,000 and R = 120,000. We estimate the improvement gained from superhigh resolution in resolving narrowly separated velocity components in absorption profiles. We also explore the influence of isotope line shifts and hyperfine splitting in measurements of line profile parameters, and the spectral resolution needed to identify these effects. Super high resolution spectra of quasars, which will be routinely possible with 20-meter class telescopes, will lead to greater sensitivity for absorption line surveys, and to determination of more accurate physical conditions for cold phases of gas in various environments.Comment: To appear in AJ. Paper with better resolution images available at http://www.astro.psu.edu/users/anand/superhigh.AJ.pd

Detailed Spectroscopic and Photometric Analysis of DQ White Dwarfs

We present an analysis of spectroscopic and photometric data for cool DQ white dwarfs based on improved model atmosphere calculations. In particular, we revise the atmospheric parameters of the trigonometric parallax sample of Bergeron et al.(2001), and discuss the astrophysical implications on the temperature scale and mean mass, as well as the chemical evolution of these stars. We also analyze 40 new DQ stars discovered in the first data release of the Sloan Digital Sky Survey.Comment: 6 pages,3 figures, 14th European Workshop on White Dwarfs, ASP Conference Series, in pres

Radial velocity measurements of white dwarfs

We present 594 radial velocity measurements for 71 white dwarfs obtained during our search for binary white dwarfs and not reported elsewhere. We identify three excellent candidate binaries, which require further observations to confirm our preliminary estimates for their orbital periods, and one other good candidate. We investigate whether our data support the existence of a population of single, low mass (<~0.5 solar masses) white dwarfs (LMWDs). These stars are difficult to explain in standard models of stellar evolution. We find that a model with a mixed single/binary population is at least ~20 times more likely to explain our data than a pure binary population. This result depends on assumed period distributions for binary LMWDs, assumed companion masses and several other factors. Therefore, the evidence in favour of the existence of a population of single LMWDs is not sufficient, in our opinion, to firmly establish the existence of such a population, but does suggest that extended observations of LMWDs to obtain a more convincing result would be worthwhile .Comment: 14 pages, 4 Figures. Accepted for publication in MNRAS. Added Institutio

Highly Ionized High Velocity Clouds: Intergalactic Gas in the Local Group or Distant Gas in the Galactic Halo?

We have recently identified several high velocity (V < -100 km/s) clouds in the directions of Mrk 509 and PKS 2155-304 that have unusual ionization properties. The clouds exhibit strong C IV absorption with little or no detectable low ion (C II, Si II) absorption or H I 21cm emission. As the closest known analog to the outer diffuse halos of damped Ly-alpha absorbers and the low H I column density metal line absorption systems seen in the spectra of high redshift quasars, these "C IV-HVCs" present unique opportunities for relating the conditions within the Milky Way halo and nearby intergalactic gas to the properties of galactic halos at higher redshift. The C IV-HVCs have ionization properties consistent with photoionization by extragalactic background radiation, though some contribution by collisional ionization within a hot plasma cannot be ruled out. The clouds are probably low density [n(H) ~ 10^-4 cm^-3], large [greater than several kiloparsecs], and mostly ionized [n(HI)/n(H) ~ 10^-3] regions located well beyond the neutral gas layer of the Galaxy. The presence of weak H I-HVCs detected through 21cm emission near both sight lines indicates that the C IV-HVCs trace the extended, ionized, low density regions of the H I-HVCs. Several lines of evidence, including very low thermal pressures (P/k ~ 2 cm^-3 K), favor a location for the C IV-HVCs in the Local Group or very distant Galactic halo.Comment: AASTEX manuscript and tables, 55 pages, 8 postscript figures. Astrophysical Journal, in pres

The Discovery of the Most Metal-Rich White Dwarf: Composition of a Tidally Disrupted Extrasolar Dwarf Planet

Cool white dwarf stars are usually found to have an outer atmosphere that is practically pure in hydrogen or helium. However, a small fraction have traces of heavy elements that must originate from the accretion of extrinsic material, most probably circumstellar matter. Upon examining thousands of Sloan Digital Sky Survey spectra, we discovered that the helium-atmosphere white dwarf SDSS J073842.56+183509.6 shows the most severe metal pollution ever seen in the outermost layers of such stars. We present here a quantitative analysis of this exciting star by combining high S/N follow-up spectroscopic and photometric observations with model atmospheres and evolutionary models. We determine the global structural properties of our target star, as well as the abundances of the most significant pollutants in its atmosphere, i.e., H, O, Na, Mg, Si, Ca, and Fe. The relative abundances of these elements imply that the source of the accreted material has a composition similar to that of Bulk Earth. We also report the signature of a circumstellar disk revealed through a large infrared excess in JHK photometry. Combined with our inferred estimate of the mass of the accreted material, this strongly suggests that we are witnessing the remains of a tidally disrupted extrasolar body that was as large as Ceres.Comment: 7 pages in emulateapj, 5 figures, accepted for publication in Ap

High-resolution FUSE and HST ultraviolet spectroscopy of the white dwarf central star of Sh 2-216

LS V +4621 is the DAO-type central star of the planetary nebula Sh 2-216. We perform a comprehensive spectral analysis of high-resolution, high-S/N ultraviolet observations obtained with FUSE and STIS aboard the HST as well as the optical spectrum of LS V +4621 by means of state-of-the-art NLTE model-atmosphere techniques in order to compare its photospheric properties to theoretical predictions from stellar evolution theory as well as from diffusion calculations. From the N IV - NV, O IV - O VI, Si IV - Si V, and Fe V - Fe VII ionization equilibria, we determined an effective temperature of 95 +/- 2 kK with high precision. The surface gravity is log g = 6.9 +/- 0.2. An unexplained discrepancy appears between the spectroscopic distance d = 224 +46/-58 pc and the parallax distance d = 129 +6/-5 pc of LS V +4621. For the first time, we have identified Mg IV and Ar VI absorption lines in the spectrum of a hydrogen-rich central star and determined the Mg and Ar abundances as well as the individual abundances of iron-group elements (Cr, Mn, Fe, Co, and Ni). With the realistic treatment of metal opacities up to the iron group in the model-atmosphere calculations, the so-called Balmer-line problem (found in models that neglect metal-line blanketing) vanishes. Spectral analysis by means of NLTE model atmospheres has presently arrived at a high level of sophistication, which is now hampered largely by the lack of reliable atomic data and accurate line-broadening tables. Strong efforts should be made to improve upon this situation.Comment: 13 pages, 20 figure

Spectroscopic Analysis of H I Absorption Line Systems in 40 HIRES Quasars

We list and analyze H I absorption lines at redshifts 2 < z < 4 with column density (12 < log(N_HI) < 19) in 40 high-resolutional (FWHM = 8.0 km/s) quasar spectra obtained with the Keck+HIRES. We de-blend and fit all H I lines within 1,000 km/s of 86 strong H I lines whose column densities are log(N_HI/[cm^-2]) > 15. Unlike most prior studies, we use not only Lya but also all visible higher Lyman series lines to improve the fitting accuracy. This reveals components near to higher column density systems that can not be seen in Lya. We list the Voigt profile fits to the 1339 H I components that we found. We examined physical properties of H I lines after separating them into several sub-samples according to their velocity separation from the quasars, their redshift, column density and the S/N ratio of the spectrum. We found two interesting trends for lines with 12 < log(N_HI) < 15 which are within 200-1000 km/s of systems with log(N_HI) > 15. First, their column density distribution becomes steeper, meaning relatively fewer high column density lines, at z < 2.9. Second, their column density distribution also becomes steeper and their line width becomes broader by about 2-3 km/s when they are within 5,000 km/s of their quasar.Comment: 32 pages, 14 figures, accepted for publication in the Astronomical Journal. A complete version with all tables and figures is available at http://www.astro.psu.edu/users/misawa/pub/Paper/40hires.ps.g

On the Spectral Evolution of Cool, Helium-Atmosphere White Dwarfs: Detailed Spectroscopic and Photometric Analysis of DZ Stars

We present a detailed analysis of a large spectroscopic and photometric sample of DZ white dwarfs based on our latest model atmosphere calculations. We revise the atmospheric parameters of the trigonometric parallax sample of Bergeron, Leggett, & Ruiz (12 stars) and analyze 147 new DZ white dwarfs discovered in the Sloan Digital Sky Survey. The inclusion of metals and hydrogen in our model atmosphere calculations leads to different atmospheric parameters than those derived from pure helium models. Calcium abundances are found in the range from log (Ca/He) = -12 to -8. We also find that fits of the coolest objects show peculiarities, suggesting that our physical models may not correctly describe the conditions of high atmospheric pressure encountered in the coolest DZ stars. We find that the mean mass of the 11 DZ stars with trigonometric parallaxes, = 0.63 Mo, is significantly lower than that obtained from pure helium models, = 0.78 Mo, and in much better agreement with the mean mass of other types of white dwarfs. We determine hydrogen abundances for 27% of the DZ stars in our sample, while only upper limits are obtained for objects with low signal-to-noise ratio spectroscopic data. We confirm with a high level of confidence that the accretion rate of hydrogen is at least two orders of magnitude smaller than that of metals (and up to five in some cases) to be compatible with the observations. We find a correlation between the hydrogen abundance and the effective temperature, suggesting for the first time empirical evidence of a lower temperature boundary for the hydrogen screening mechanism. Finally, we speculate on the possibility that the DZA white dwarfs could be the result of the convective mixing of thin hydrogen-rich atmospheres with the underlying helium convection zone.Comment: 67 pages, 32 figures, accepted for publication in Ap