The dynamical mass and evolutionary status of the type-II Cepheid in the eclipsing binary system OGLE-LMC-T2CEP-211 with a double-ring disk

We present the analysis of a peculiar W~Virginis (pWVir) type-II Cepheid, OGLE-LMC-T2CEP-211 ($P_{puls}=9.393\,d$), in a double-lined binary system ($P_{orb}=242\,d$), which shed light on virtually unknown evolutionary status and structure of pWVir stars. The dynamical mass of the Cepheid (first ever for a type-II Cepheid) is $0.64\pm{}0.02\,M_\odot$ and the radius $R=25.1\pm{}0.3\,R_\odot$. The companion is a massive ($5.67\,M_\odot$) main-sequence star obscured by a disk. Such configuration suggests a mass transfer in the system history. We found that originally the system ($P_{orb}^{init}=12\,d$) was composed of $3.5$ and $2.8\,M_\odot$ stars, with the current Cepheid being more massive. The system age is now $\sim{}$200 My, and the Cepheid is almost completely stripped of hydrogen, with helium mass of $\sim{}92\%$ of the total mass. It finished transferring the mass 2.5 My ago and is evolving towards lower temperatures passing through the instability strip. Comparison with observations indicate a reasonable $2.7\cdot{}10^{-8}\,M_\odot/y$ mass loss from the Cepheid. The companion is most probably a Be main-sequence star with $T=22000\,K$ and $R=2.5\,R_\odot$. Our results yield a good agreement with a pulsation theory model for a hydrogen-deficient pulsator, confirming the described evolutionary scenario. We detected a two-ring disk ($R_{disk}\sim\,116\,R_{\odot}$) and a shell ($R_{shell}\sim\,9\,R_{\odot}$) around the companion, that is probably a combination of the matter from the past mass transfer, the mass being lost by the Cepheid due to wind and pulsations, and a decretion disk around a rapidly rotating secondary. Our study together with observational properties of pWVir stars suggests that their majority are products of a similar binary evolution interaction.Comment: 21 pages, 14 figures, 6 tables, accepted for publication in Ap

Affine sl(2|1) and D(2|1;alpha) as Vertex Operator Extensions of Dual Affine sl(2) Algebras

We discover a realisation of the affine Lie superalgebra sl(2|1) and of the exceptional affine superalgebra D(2|1;alpha) as vertex operator extensions of two affine sl(2) algebras with dual levels (and an auxiliary level 1 sl(2) algebra). The duality relation between the levels is (k+1)(k'+1)=1. We construct the representation of sl(2|1) at level k' on a sum of tensor products of sl(2) at level k, sl(2) at level k' and sl(2) at level 1 modules and decompose it into a direct sum over the sl(2|1) spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to the affine D(2|1;k') at level k is traced to properties of sl(2)+sl(2)+sl(2) embeddings into D(2|1;alpha) and their relation with the dual sl(2) pairs. Conversely, we show how the level k' sl(2) representations are constructed from level k sl(2|1) representations.Comment: 50 pages, Latex2e, 2 figures, acknowledgements adde

Imidazolium bromide substituted magnesium phthalocyanine polymers: New promising materials for CO2 conversion

The conversion of CO2 with epoxides into the corresponding cyclic carbonates represents a green approach to transform a waste into value-added products. To promote this conversion, a catalyst in needed. This study presents the synthesis of two cross-linked materials composed of magnesium phthalocyanine and imidazolium bromide moieties: MgPc-BIBI-Br and MgPc-SIBI-Br. Magnesium phthalocyanines are cost-effective and versatile catalysts, synthesized in high yield from low-cost precursors and can be easily modified for specific needs. Imidazolium bromide groups play a crucial role as well, acting as a nucleophile source essential to promote the ring-opening process of the epoxide. The materials have been extensively characterized through analytical and spectroscopic techniques and tested as catalysts in the conversion of epichlorohydrin into 4-chloromethyl-1,3-dioxalan-2-one. They both achieved excellent catalytic performance (maximal TON values of 3070 for MgPc-SIBI-Br and 1903 for MgPc-BIBI-Br) and recyclability (both recyclable at least for 4 cycles). The reported results represent an improvement if compared to similar materials already reported in the literature in which the addition of external nucleophilic species (e.g. TBAB, BMIM-Br, etc.) is needed. To the best of our knowledge, this work is the first example in which imidazolium bromide and magnesium phthalocyanine moieties are combined in bifunctional polymeric materials that convert CO2 into cyclic carbonates via heterogeneous catalysis

First Evidence of Tris(catecholato)silicate Formation from Hydrolysis of an Alkyl Bis(catecholato)silicate

The hydrolysis of 3-ammoniumpropylbis(catecholato)silicate 1, giving two different silica-based materials containing different amounts of tris(catecholato)silicate, is reported. The latter species can be formed through an attack of catechol to the silicon atom in the pentacoordinate complex, in which the silicon-carbon bond is further activated toward electrophilic proton cleavage. The Knoevenagel reaction was used as a probe in order to test the availability of functional groups on the surface of such materials

Mass and p-factor of the type II Cepheid OGLE-LMC-T2CEP-098 in a binary system

We present the results of a study of the type II Cepheid ($P_{puls} = 4.974 d$) in the eclipsing binary system OGLE-LMC-T2CEP-098 ($P_{orb} = 397.2 d$). The Cepheid belongs to the peculiar W Vir group, for which the evolutionary status is virtually unknown. It is the first single-lined system with a pulsating component analyzed using the method developed by Pilecki et al. (2013). We show that the presence of a pulsator makes it possible to derive accurate physical parameters of the stars even if radial velocities can be measured for only one of the components. We have used four different methods to limit and estimate the physical parameters, eventually obtaining precise results by combining pulsation theory with the spectroscopic and photometric solutions. The Cepheid radius, mass and temperature are $25.3 \pm 0.2 R_\odot$, $1.51 \pm 0.09 M_\odot$ and $5300 \pm 100 K$, respectively, while its companion has similar size ($26.3 R_\odot$), but is more massive ($6.8 M_\odot$) and hotter ($9500 K$). Our best estimate for the p-factor of the Cepheid is $1.30 \pm 0.03$. The mass, position on the period-luminosity diagram, and pulsation amplitude indicate that the pulsating component is very similar to the Anomalous Cepheids, although it has a much longer period and is redder in color. The very unusual combination of the components suggest that the system has passed through a mass transfer phase in its evolution. More complicated internal structure would then explain its peculiarity.Comment: 23 pages, 17 figures, accepted for publication in Ap

Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities

Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are obtained. Dilogarithm identities producing corresponding effective central charges and secondary effective central charges are derived. Several ways of constructing more general fermionic representations are discussed.Comment: 14 pages, LaTex; minor correction

Discovery of a binary-origin classical Cepheid in a binary system with a 59-day orbital period

We report the discovery of a surprising binary configuration of the double-mode Cepheid OGLE-LMC-CEP-1347 pulsating in the first (P_1=0.690d) and second overtone (P_2=0.556d) modes. The orbital period (P_orb=59d) of the system is five times shorter than the shortest known to date (310d) for a binary Cepheid. The Cepheid itself is also the shortest-period one ever found in a binary system and the first double-mode Cepheid in a spectroscopically double-lined binary. OGLE-LMC-CEP-1347 is most probably on its first crossing through the instability strip, as inferred from both its short period and fast period increase, consistent with evolutionary models, and from the short orbital period (not expected for binary Cepheids whose components have passed through the red giant phase). Our evolutionary analysis yielded a first-crossing Cepheid with a mass in a range of 2.9-3.4 Msun (lower than any measured Cepheid mass), consistent with observations. The companion is a stable star, at least two times fainter and less massive than the Cepheid (preliminary mass ratio q=0.55), while also redder and thus at the subgiant or more advanced evolutionary stage. To match these characteristics, the Cepheid has to be a product of binary interaction, most likely a merger of two less massive stars, which makes it the second known classical Cepheid of binary origin. Moreover, further evolution of the components may lead to another binary interaction.Comment: 6 pages, 4 figures, 1 table, published in The Astrophysical Journal Letter

The Araucaria Project: A study of the classical Cepheid in the eclipsing binary system OGLE LMC562.05.9009 in the Large Magellanic Cloud

We present a detailed study of the classical Cepheid in the double-lined, highly eccentric eclipsing binary system OGLE-LMC562.05.9009. The Cepheid is a fundamental mode pulsator with a period of 2.988 days. The orbital period of the system is 1550 days. Using spectroscopic data from three 4-8-m telescopes and photometry spanning 22 years, we were able to derive the dynamical masses and radii of both stars with exquisite accuracy. Both stars in the system are very similar in mass, radius and color, but the companion is a stable, non-pulsating star. The Cepheid is slightly more massive and bigger (M_1 = 3.70 +/- 0.03M_sun, R_1 = 28.6 +/- 0.2R_sun) than its companion (M_2 = 3.60 +/- 0.03M_sun, R_2 = 26.6 +/- 0.2R_sun). Within the observational uncertainties both stars have the same effective temperature of 6030 +/- 150K. Evolutionary tracks place both stars inside the classical Cepheid instability strip, but it is likely that future improved temperature estimates will move the stable giant companion just beyond the red edge of the instability strip. Within current observational and theoretical uncertainties, both stars fit on a 205 Myr isochrone arguing for their common age. From our model, we determine a value of the projection factor of p = 1.37 +/- 0.07 for the Cepheid in the OGLE-LMC562.05.9009 system. This is the second Cepheid for which we could measure its p-factor with high precision directly from the analysis of an eclipsing binary system, which represents an important contribution towards a better calibration of Baade-Wesselink methods of distance determination for Cepheids.Comment: Accepted to be published in Ap