Weyl Expansion for Symmetric Potentials

We present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately evaluated using the Wigner transforms of the projection operators. For discrete symmetries the expansion yields a formally exact but asymptotic series in $\hbar$, while for the rotational $SO(n)$ symmetries the expansion requires averaging over angular momentum as well as energy. A numerical example is given in two dimensions, in which we calculate the leading terms of the Weyl expansion as well as the leading periodic orbit contributions to the symmetry reduced level density.Comment: Four of the five figures are appended as a postscript file. The fifth figure is available by snail mail

Characterizing the Rigidly Rotating Magnetosphere Stars HD 345439 and HD 23478

The SDSS III APOGEE survey recently identified two new $\sigma$ Ori E type candidates, HD 345439 and HD 23478, which are a rare subset of rapidly rotating massive stars whose large (kGauss) magnetic fields confine circumstellar material around these systems. Our analysis of multi-epoch photometric observations of HD 345439 from the KELT, SuperWASP, and ASAS surveys reveals the presence of a $\sim$0.7701 day period in each dataset, suggesting the system is amongst the faster known $\sigma$ Ori E analogs. We also see clear evidence that the strength of H-alpha, H I Brackett series lines, and He I lines also vary on a $\sim$0.7701 day period from our analysis of multi-epoch, multi-wavelength spectroscopic monitoring of the system from the APO 3.5m telescope. We trace the evolution of select emission line profiles in the system, and observe coherent line profile variability in both optical and infrared H I lines, as expected for rigidly rotating magnetosphere stars. We also analyze the evolution of the H I Br-11 line strength and line profile in multi-epoch observations of HD 23478 from the SDSS-III APOGEE instrument. The observed periodic behavior is consistent with that recently reported by Sikora and collaborators in optical spectra.Comment: Accepted in ApJ

Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

Circumstellar Na I and Ca II lines of type Ia supernovae in symbiotic scenario

Formation of circumstellar lines of Na I and Ca II in type Ia supernovae is studied for the case, when supernova explodes in a binary system with a red giant. The model suggests a spherically-symmetric wind and takes into account ionization and heating of the wind by X-rays from the shock wave and by gamma-quanta of ^{56}Ni radioactive decay. For the wind density typical of the red giant the expected optical depth of the wind in Na I lines turnes out too low (\tau<0.001}) to detect the absorption. For the same wind densities the predicted optical depth of Ca II 3934 \AA is sufficient for the detection (\tau>0.1). I conclude that the absorption lines detected in SN 2006X cannot form in the red giant wind; they are rather related to clouds at distances larger than the dust evaporation radius (r>10^{17} cm). From the absence in SN 2006X of Ca II absorption lines not related with the similar Na I components I derive the upper limit of the mass loss rate by the wind with velocity u: \dot{M}<10^{-8}(u/10 km/s) M_{\odot} yr^{-1}.Comment: 10 pages, 6 figures, Astronomy Letters (accepted

Variability of the X-ray P Cygni Line Profiles from Circinus X-1 Near Zero Phase

The luminous X-ray binary Circinus X-1 has been observed twice near zero orbital phase using the High-Energy Transmission Grating Spectrometer (HETGS) onboard Chandra. The source was in a high-flux state during a flare for the first observation, and it was in a low-flux state during a dip for the second. Spectra from both flux states show clear P Cygni lines, predominantly from H-like and He-like ion species. These indicate the presence of a high-velocity outflow from the Cir X-1 system which we interpret as an equatorial accretion-disk wind, and from the blueshifted resonance absorption lines we determine outflow velocities of 200 - 1900 km/s with no clear velocity differences between the two flux states. The line strengths and profiles, however, are strongly variable both between the two observations as well as within the individual observations. We characterize this variability and suggest that it is due to both changes in the amount of absorbing material along the line of sight as well as changes in the ionization level of the wind. We also refine constraints on the accretion-disk wind model using improved plasma diagnostics such as the He-like Mg XI triplet, and we consider the possibility that the X-ray absorption features seen from superluminal jet sources can generally be explained via high-velocity outflows.Comment: 12 pages, 8 figures, accepted by ApJ (Main

Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards

We demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than $l$ increases as $\pi b_0l^2/\langle a(l) \rangle$, where $b_0$ is a constant and $\langle a(l) \rangle$ is the average area occupied by these families. We also find that $\langle a(l) \rangle$ increases with $l$ before saturating. Finally, we show that periodic orbits provide a good estimate of spectral correlations in the corresponding quantum spectrum and thus conclude that diffraction effects are not as significant in such studies.Comment: 13 pages in RevTex including 5 figure