CO J = 2 - 1 Emission from Evolved Stars in the Galactic Bulge

We observe a sample of 8 evolved stars in the Galactic Bulge in the CO J = 2 - 1 line using the Submillimeter Array (SMA) with angular resolution of 1 - 4 arcseconds. These stars have been detected previously at infrared wavelengths, and several of them have OH maser emission. We detect CO J = 2 - 1 emission from three of the sources in the sample: OH 359.943 +0.260, [SLO2003] A12, and [SLO2003] A51. We do not detect the remaining 5 stars in the sample because of heavy contamination from the galactic foreground CO emission. Combining CO data with observations at infrared wavelengths constraining dust mass loss from these stars, we determine the gas-to-dust ratios of the Galactic Bulge stars for which CO emission is detected. For OH 359.943 +0.260, we determine a gas mass-loss rate of 7.9 (+/- 2.2) x 10^-5 M_Sun/year and a gas-to-dust ratio of 310 (+/- 89). For [SLO2003] A12, we find a gas mass-loss rate of 5.4 (+/- 2.8) x 10^-5 M_Sun/year and a gas-to-dust ratio of 220 (+/- 110). For [SLO2003] A51, we find a gas mass-loss rate of 3.4 (+/- 3.0) x 10^-5 M_Sun/year and a gas-to-dust ratio of 160 (+/- 140), reflecting the low quality of our tentative detection of the CO J = 2 - 1 emission from A51. We find the CO J = 2 - 1 detections of OH/IR stars in the Galactic Bulge require lower average CO J = 2 - 1 backgrounds.Comment: 40 pages, 16 figures, appeared in the 1 March 2013 issue of the Astrophysical Journa

Classical and quantum three-dimensional integrable systems with axial symmetry

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of a kinetic part plus a potential dependent on the position only, the $z$-component of the angular momentum, $L$, and a Hamiltonian-like constant, $\widetilde H$, for which the kinetic part is quadratic in the momenta. We find the explicit form of these potentials compatible with complete integrability. The classical equations of motion, written in terms of two arbitrary potential functions, is separated in oblate spheroidal coordinates. The quantization of such systems leads to a set of two differential equations that can be presented in the form of spheroidal wave equations.Comment: 17 pages, 3 figure