Evolution of the stellar-merger red nova V1309 Scorpii: SED analysis

One very important object for understanding the nature of red novae is V1309 Sco. Its pre-outburst observations showed that, before its red-nova eruption in 2008, it was a contact binary quickly evolving to the merger of the components. It thus provided us with a direct evidence that the red novae result from stellar mergers. We analyse the spectral energy distribution (SED) of the object and its evolution with time. From various optical and infrared surveys and observing programmes carried out with OGLE, HST, VVV, Gemini South, WISE, Spitzer, and Herschel we constructed observed SED in 2010 and 2012. Some limited data are also available for the red-nova progenitor in 2007. We analyse the data with our model of a dusty envelope surrounding a central star. Dust was present in the pre-outburst state of V1309 Sco. Its high temperature (900-1000 K) suggests that this was a freshly formed dust in a presumable mass-loss from the spiralling-in binary. Shortly after its 2008 eruption, V1309~Sco became almost completely embedded in dust. The parameters (temperature, dimensions) of the dusty envelope in 2010 and 2012 evidence that we then observed matter lost by the object during the 2008 outburst. Its mass is at least $10^{-3}\,M_\odot$. The object remains quite luminous, although since its maximum brightness in September 2008, it has faded in luminosity by a factor of ~50 (in 2012). Far infrared data from Herschel reveal presence of a cold (~30 K) dust at a distance of a few thousand AU from the object. This conclusion could be verified by submillimeter interferometric observations.Comment: 12 pages, 7 figures, accepted in Astronomy & Astrophysisc

Optical spectropolarimetry of V4332 Sagittarii

The eruption of V4332 Sgr was observed in 1994. During the outburst, the object became extremely red, so it has been considered as to belong to red transients of the V838 Mon type. Optical spectroscopy obtained a few years after the eruption showed a faint M-type stellar spectrum underlying numerous molecular and atomic emission features. It has recently been suggested that the central object in V4332 Sgr is now hidden in a dusty disc and that the photospheric spectrum of this object observed in the optical results from scattering of the radiation of the central star on dust grains in the circumstellar matter. Recent polarimetric photometry has shown that the optical radiation of the object is indeed strongly polarized. We present and analyse our spectropolarimetric observations of V4332 Sgr obtained with the VLT in the optical region. The optical continuum of V4332 Sgr is linearly polarized with a typical degree of 16.6%. A clear depolarization is observed in the spectral regions where emission features contribute significantly to the observed flux. The only prominent exception is the CaI 6573 emission line, which is polarized in 21%. The results of our spectropolarimetric observations are in accord with the proposed geometry of the system and the advocated nature of the observed optical spectrum of V4332 Sgr. The continuum is not seen directly but results from scattering on dust within the disc and polar outflow, while most of the gas emission comes from the polar outflow excited by the radiation field of the central source. Additionally, the observed polarization patterns suggest a stratification of the outflow.Comment: accepted for publication in Astronomy & Astrophysic

High-resolution optical spectroscopy of V838 Monocerotis in 2009

V838 Mon erupted at the beginning of 2002. In the course of the outburst the object evolved to low effective temperatures and declined as a very late M-type supergiant. Among various scenarios proposed to explain the nature of the outburst, the most promising is a stellar merger event. We aim at studying the structure and evolution of the object in the decline from the 2002 eruption. We obtained spectroscopic observations of V838 Mon in January--March 2009 with UVES/VLT. The results are analysed and compared with similar observations obtained in October 2005 with HIRES/Keck. The most striking difference between 2009 and 2005 is a complete absence of the B3V component and of the [FeII] emission lines in 2009. The present spectrum displays only the spectrum of the 2002 eruption remnant. It resembles that of an M6 giant, although the molecular bands in V838 Mon are deeper than those in standard stellar spectra of a similar spectral class. Several atomic lines, which displayed P-Cyg profiles in 2005, are now dominated by pure absorptions. Some of these lines, however, show a narrow emission component, which, as we argue, measures the radial velocity of V838 Mon. The resulting heliocentric velocity is 71 km/s, which very well agrees with the velocity obtained from SiO maser observations. The atomic lines and the molecular bands show very complex kinematics. In some atomic lines and high-excitation molecular bands we observe matter infalling in the object atmosphere. The infall components were already observed in 2005, but were less pronounced and present in fewer lines than in 2009. We argue that the most negative radial velocity components seen in the resonance atomic lines and in the low-excitation molecular bands were formed in the ejecta of the 2002 eruption. The B3V companion most probably became engulfed in an opaque dusty matter of the 2002 V838 Mon ejecta.Comment: A&A, in pres

Quantum constraints, Dirac observables and evolution: group averaging versus Schroedinger picture in LQC

A general quantum constraint of the form $C= - \partial_T^2 \otimes B - I\otimes H$ (realized in particular in Loop Quantum Cosmology models) is studied. Group Averaging is applied to define the Hilbert space of solutions and the relational Dirac observables. Two cases are considered. In the first case, the spectrum of the operator $(1/2)\pi^2 B - H$ is assumed to be discrete. The quantum theory defined by the constraint takes the form of a Schroedinger-like quantum mechanics with a generalized Hamiltonian $\sqrt{B^{-1} H}$. In the second case, the spectrum is absolutely continuous and some peculiar asymptotic properties of the eigenfunctions are assumed. The resulting Hilbert space and the dynamics are characterized by a continuous family of the Schroedinger-like quantum theories. However, the relational observables mix different members of the family. Our assumptions are motivated by new Loop Quantum Cosmology models of quantum FRW spacetime. The two cases considered in the paper correspond to the negative and, respectively, positive cosmological constant. Our results should be also applicable in many other general relativistic contexts.Comment: RevTex4, 32 page

Widespread HCN maser emission in carbon-rich evolved stars

Context. HCN is a major constituent of the circumstellar envelopes of carbon-rich evolved stars, and rotational lines from within its vibrationally excited states probe parts of these regions closest to the stellar surface. A number of such lines are known to show maser action. Historically, in one of them, the 177 GHz $J=2\rightarrow1$ line in the $l$-doubled bending mode has been found to show relatively strong maser action, with results only published for a single object, the archetypical high-mass loss asymptotic giant branch (AGB) star IRC+10216. Aims. To examine how common 177 GHz HCN maser emission is, we conducted an exploratory survey for this line toward a select sample of carbon-rich asymptotic giant branch stars that are observable from the southern hemisphere. Methods. We used the Atacama Pathfinder Experiment 12 meter submillimeter Telescope (APEX) equipped with a new receiver to simultaneously observe three $J=2\rightarrow1$ HCN rotational transitions, the $(0,1^{{1}_{\rm c}},0)$ and $(0,1^{{1}_{\rm d}},0)$ $l$-doublet components, and the line from the (0,0,0) ground state. Results. The $(0,1^{{1}_{\rm c}},0)$ maser line is detected toward 11 of 13 observed sources, which all show emission in the (0,0,0) transition. In most of the sources, the peak intensity of the $(0,1^{{1}_{\rm c}},0)$ line rivals that of the (0,0,0) line; in two sources, it is even stronger. Except for the object with the highest mass-loss rate, IRC+10216, the $(0,1^{{1}_{\rm c}},0)$ line covers a smaller velocity range than the (0,0,0) line. Conclusions. Maser emission in the 177 GHz $J=2\rightarrow1$ $(0,1^{{1}_{\rm c}},0)$ line of HCN appears to be common in carbon-rich AGB stars. (Abbreviated)Comment: 12 pages (including appendix), 3 figures / Astronomy & Astrophysics (in press

Towards uniqueness of degenerate axially symmetric Killing horizon

We examine the linearized equations around extremal Kerr horizon and give some arguments towards stability of the horizon with respect to generic (non-symmetric) linear perturbation of near horizon geometry.Comment: 17 page

Space-time directional Lyapunov exponents for cellular automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved

Reconfiguration of Dominating Sets

We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph $G$ is a set $S$ of vertices such that each vertex is either in $S$ or has a neighbour in $S$. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions $s$ and $t$ such that each pair of consecutive solutions is adjacent according to a specified adjacency relation. Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex. For various values of $k$, we consider properties of $D_k(G)$, the graph consisting of a vertex for each dominating set of size at most $k$ and edges specified by the adjacency relation. Addressing an open question posed by Haas and Seyffarth, we demonstrate that $D_{\Gamma(G)+1}(G)$ is not necessarily connected, for $\Gamma(G)$ the maximum cardinality of a minimal dominating set in $G$. The result holds even when graphs are constrained to be planar, of bounded tree-width, or $b$-partite for $b \ge 3$. Moreover, we construct an infinite family of graphs such that $D_{\gamma(G)+1}(G)$ has exponential diameter, for $\gamma(G)$ the minimum size of a dominating set. On the positive side, we show that $D_{n-m}(G)$ is connected and of linear diameter for any graph $G$ on $n$ vertices having at least $m+1$ independent edges.Comment: 12 pages, 4 figure

Reconfiguring Independent Sets in Claw-Free Graphs

We present a polynomial-time algorithm that, given two independent sets in a claw-free graph $G$, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex $v$ from the current independent set $S$ and to add a new vertex $w$ (not in $S$) such that the result is again an independent set. We also consider the more restricted model where $v$ and $w$ have to be adjacent