Tracing the development of dust around evolved stars: The case of 47 Tuc

We observed mid-infrared (7.5-22 mum) spectra of AGB stars in the globular cluster 47 Tuc with the Spitzer telescope and find significant dust features of various types. Comparison of the characteristics of the dust spectra with the location of the stars in a logP-K-diagram shows that dust mineralogy and position on the AGB are related. A 13 mum feature is seen in spectra of low luminosity AGB stars. More luminous AGB stars show a broad feature at 11.5 mum. The spectra of the most luminous stars are dominated by the amorphous silicate bending vibration centered at 9.7 mum. For 47 Tuc AGB stars, we conclude that early on the AGB dust consisting primarily of Mg-, Al- and Fe oxides is formed. With further AGB evolution amorphous silicates become the dominant species.Comment: 2 figures, accepted for publication in ApJ Letter

On the Submillimeter Opacity of Protoplanetary Disks

Solid particles with the composition of interstellar dust and power-law size distribution dn/da propto a^{-p} for a 3 lambda and 3 < p < 4 will have submm opacity spectral index beta(lambda) = dln(kappa)/dln(nu) approx (p-3) beta_{ism}, where beta_{ism} approx 1.7 is the opacity spectral index of interstellar dust material in the Rayleigh limit. For the power-law index p approx 3.5 that characterizes interstellar dust, and that appears likely for particles growing by agglomeration in protoplanetary disks, grain growth to sizes a > 3 mm will result in beta(1 mm) < ~1. Grain growth can naturally account for beta approx 1 observed for protoplanetary disks, provided that a_{max} > ~ 3 lambda.Comment: Submitted to ApJ. 17 pages, 6 figure

An eccentrically perturbed Tonks-Girardeau gas

We investigate the static and dynamic properties of a Tonks-Girardeau gas in a harmonic trap with an eccentric $\delta$-perturbation of variable strength. For this we first find the analytic eigensolution of the single particle problem and use this solution to calculate the spatial density and energy profiles of the many particle gas as a function of the strength and position of the perturbation. We find that the crystal nature of the Tonks state is reflected in both the lowest occupation number and momentum distribution of the gas. As a novel application of our model, we study the time evolution of the the spatial density after a sudden removal of the perturbation. The dynamics exhibits collapses and revivals of the original density distribution which occur in units of the trap frequency. This is reminiscent of the Talbot effect from classical optics.Comment: Comments and suggestions are welcom

Ion induced density bubble in a strongly correlated one dimensional gas

We consider a harmonically trapped Tonks-Girardeau gas of impenetrable bosons in the presence of a single embedded ion, which is assumed to be tightly confined in a RF trap. In an ultracold ion-atom collision the ion's charge induces an electric dipole moment in the atoms which leads to an attractive $r^{-4}$ potential asymptotically. We treat the ion as a static deformation of the harmonic trap potential and model its short range interaction with the gas in the framework of quantum defect theory. The molecular bound states of the ionic potential are not populated due to the lack of any possible relaxation process in the Tonks-Girardeau regime. Armed with this knowledge we calculate the density profile of the gas in the presence of a central ionic impurity and show that a density \textit{bubble} of the order of a micron occurs around the ion for typical experimental parameters. From these exact results we show that an ionic impurity in a Tonks gas can be described using a pseudopotential, allowing for significantly easier treatment.Comment: Accepted for publication in Physical Review A (Rapid Communications)

Orbital stability of periodic waves for the nonlinear Schroedinger equation

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.Comment: 34 pages, 7 figure

On the Ricci tensor in type II B string theory

Let $\nabla$ be a metric connection with totally skew-symmetric torsion \T on a Riemannian manifold. Given a spinor field $\Psi$ and a dilaton function $\Phi$, the basic equations in type II B string theory are \bdm \nabla \Psi = 0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi = b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations between the length ||\T||^2 of the torsion form, the scalar curvature of $\nabla$, the dilaton function $\Phi$ and the parameters $a,b,\mu$. The main results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the connection. In particular, if the supersymmetry $\Psi$ is non-trivial and if the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d \T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is divergence-free. We show that the latter condition is satisfied in many examples constructed out of special geometries. A special case is $a = b$. Then the divergence of the energy-momentum tensor vanishes if and only if one condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T = 0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq 0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2

Sub-Hz line width diode lasers by stabilization to vibrationally and thermally compensated ULE Fabry-Perot cavities

We achieved a 0.5 Hz optical beat note line width with ~ 0.1 Hz/s frequency drift at 972 nm between two external cavity diode lasers independently stabilized to two vertically mounted Fabry-Perot (FP) reference cavities. Vertical FP reference cavities are suspended in mid-plane such that the influence of vertical vibrations to the mirror separation is significantly suppressed. This makes the setup virtually immune for vertical vibrations that are more difficult to isolate than the horizontal vibrations. To compensate for thermal drifts the FP spacers are made from Ultra-Low-Expansion (ULE) glass which possesses a zero linear expansion coefficient. A new design using Peltier elements in vacuum allows operation at an optimal temperature where the quadratic temperature expansion of the ULE could be eliminated as well. The measured linear drift of such ULE FP cavity of 63 mHz/s was due to material aging and the residual frequency fluctuations were less than 40 Hz during 16 hours of measurement. Some part of the temperature-caused drift is attributed to the thermal expansion of the mirror coatings. High-frequency thermal fluctuations that cause vibrations of the mirror surfaces limit the stability of a well designed reference cavity. By comparing two similar laser systems we obtain an Allan instability of 2*10-15 between 0.1 and 10 s averaging time, which is close to the theoretical thermal noise limit.Comment: submitted to Applied Physics

Absorption Line Survey of H3+ toward the Galactic Center Sources III. Extent of the Warm and Diffuse Clouds

We present follow-up observations to those of Geballe & Oka (2010), who found high column densities of H3+ ~100 pc off of the Galactic center (GC) on the lines of sight to 2MASS J17432173-2951430 (J1743) and 2MASS J17470898-2829561 (J1747). The wavelength coverages on these sightlines have been extended in order to observe two key transitions of H3+, R(3,3)l and R(2,2)l, that constrain the temperatures and densities of the environments. The profiles of the H3+ R(3,3)l line, which is due only to gas in the GC, closely matches the differences between the H3+ R(1,1)l and CO line profiles, just as it does for previously studied sightlines in the GC. Absorption in the R(2,2)l line of H3+ is present in J1747 at velocities between -60 and +100 km/s. This is the second clear detection of this line in the interstellar medium after GCIRS 3 in the Central Cluster. The temperature of the absorbing gas in this velocity range is 350 K, significantly warmer than in the diffuse clouds in other parts of the Central Molecular Zone. This indicates that the absorbing gas is local to Sgr B molecular cloud complex. The warm and diffuse gas revealed by Oka et al. (2005) apparently extends to ~100 pc, but there is a hint that its temperature is somewhat lower in the line of sight to J1743 than elsewhere in the GC. The observation of H3+ toward J1747 is compared with the recent Herschel observation of H2O+ toward Sgr B2 and their chemical relationship and remarkably similar velocity profiles are discussed.Comment: 6 pages, 3 figures, 2 tables, Accepted for publication in Publications of the Astronomical Society of Japa