The PHASES Differential Astrometry Data Archive. I. Measurements and Description

The Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES) monitored 51 sub-arcsecond binary systems to determine precision binary orbits, study the geometries of triple and quadruple star systems, and discover previously unknown faint astrometric companions as small as giant planets. PHASES measurements made with the Palomar Testbed Interferometer (PTI) from 2002 until PTI ceased normal operations in late 2008 are presented. Infrared differential photometry of several PHASES targets were measured with Keck Adaptive Optics and are presented.Comment: 33 pages emulateapj, Accepted to A

Masses, luminosities, and orbital coplanarities of the µ Orionis quadruple-star system from phases differential astrometry

μ Orionis was identified by spectroscopic studies as a quadruple-star system. Seventeen high-precision differential astrometry measurements of μ Ori have been collected by the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES). These show both the motion of the long-period binary orbit and short-period perturbations superimposed on that caused by each of the components in the long-period system being themselves binaries. The new measurements enable the orientations of the long-period binary and short-period subsystems to be determined. Recent theoretical work predicts the distribution of relative inclinations between inner and outer orbits of hierarchical systems to peak near 40 and 140 degrees. The degree of coplanarity of this complex system is determined, and the angle between the planes of the A–B and Aa–Ab orbits is found to be 136.7 ± 8.3 degrees, near the predicted distribution peak at 140 degrees; this result is discussed in the context of the handful of systems with established mutual inclinations. The system distance and masses for each component are obtained from a combined fit of the PHASES astrometry and archival radial velocity observations. The component masses have relative precisions of 5% (component Aa), 15% (Ab), and 1.4% (each of Ba and Bb). The median size of the minor axes of the uncertainty ellipses for the new measurements is 20 micro-arcseconds (μas). Updated orbits for δ Equulei, κ Pegasi, and V819 Herculis are also presented

On the algebra of local unitary invariants of pure and mixed quantum states

We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically independent generators with homogenous degree 2m equals the number of conjugacy classes of index m subgroups in a free group on k-1 generators. Similarly, we conjecture that the inverse limit in the case of k-partite mixed state invariants is free and the number of algebraically independent generators with homogenous degree m equals the number of conjugacy classes of index m subgroups in a free group on k generators. The two conjectures are shown to be equivalent. To illustrate the equivalence, using the representation theory of the unitary groups, we obtain all invariants in the m=2 graded parts and express them in a simple form both in the case of mixed and pure states. The transformation between the two forms is also derived. Analogous invariants of higher degree are also introduced.Comment: 14 pages, no figure

Unusual metallic phase in a chain of strongly interacting particles

We consider a one-dimensional lattice model with the nearest-neighbor interaction $V_1$ and the next-nearest neighbor interaction $V_2$ with filling factor 1/2 at zero temperature. The particles are assumed to be spinless fermions or hard-core bosons. Using very simple assumptions we are able to predict the basic structure of the insulator-metal phase diagram for this model. Computations of the flux sensitivity support the main features of the proposed diagram and show that the system maintains metallic properties at arbitrarily large values of $V_1$ and $V_2$ along the line $V_1-2V_2=\gamma J$, where $J$ is the hopping amplitude, and $\gamma\approx1.2$. We think that close to this line the system is a ``weak'' metal in a sense that the flux sensitivity decreases with the size of the system not exponentially but as $1/L^\alpha$ with $\alpha>1$.Comment: To appear in J. Phys. C; 9 revtex preprint pages + 4 ps figures, uuencode

Silicon isotopes in Antarctic sponges : an interlaboratory comparison

Cycling of deepwater silicon (Si) within the Southern Ocean, and its transport into other ocean basins, may be an important player in the uptake of atmospheric carbon, and global climate. Recent work has shown that the Si isotope (denoted by δ29Si or δ30Si) composition of deep sea sponges reflects the availability of dissolved Si during growth, and is a potential proxy for past deep and intermediate water silicic acid concentrations. As with any geochemical tool, it is essential to ensure analytical precision and accuracy, and consistency between methodologies and laboratories. Analytical bias may exist between laboratories, and sponge material may have matrix effects leading to offsets between samples and standards. Here, we report an interlaboratory evaluation of Si isotopes in Antarctic and sub-Antarctic sponges. We review independent methods for measuring Si isotopes in sponge spicules. Our results show that separate subsamples of non-homogenized sponges measured by three methods yield isotopic values within analytical error for over 80% of specimens. The relationship between δ29Si and δ30Si in sponges is consistent with kinetic fractionation during biomineralization. Sponge Si isotope analyses show potential as palaeoceaongraphic archives, and we suggest Southern Ocean sponge material would form a useful additional reference standard for future spicule analyses