Sub-millimeter images of a dusty Kuiper belt around eta Corvi

We present sub-millimeter and mid-infrared images of the circumstellar disk around the nearby F2V star eta Corvi. The disk is resolved at 850um with a size of ~100AU. At 450um the emission is found to be extended at all position angles, with significant elongation along a position angle of 130+-10deg; at the highest resolution (9.3") this emission is resolved into two peaks which are to within the uncertainties offset symmetrically from the star at 100AU projected separation. Modeling the appearance of emission from a narrow ring in the sub-mm images shows the observed structure cannot be caused by an edge-on or face-on axisymmetric ring; the observations are consistent with a ring of radius 150+-20AU seen at 45+-25deg inclination. More face-on orientations are possible if the dust distribution includes two clumps similar to Vega; we show how such a clumpy structure could arise from the migration over 25Myr of a Neptune mass planet from 80-105AU. The inner 100AU of the system appears relatively empty of sub-mm emitting dust, indicating that this region may have been cleared by the formation of planets, but the disk emission spectrum shows that IRAS detected an additional hot component with a characteristic temperature of 370+-60K (implying a distance of 1-2AU). At 11.9um we found the emission to be unresolved with no background sources which could be contaminating the fluxes measured by IRAS. The age of this star is estimated to be ~1Gyr. It is very unusual for such an old main sequence star to exhibit significant mid-IR emission. The proximity of this source makes it a perfect candidate for further study from optical to mm wavelengths to determine the distribution of its dust.Comment: 22 pages, 4 figures. Scheduled for publication in ApJ 10 February 2005 issu

Spitzer/MIPS Observations of Stars in the Beta Pictoris Moving Group

We present Multiband Imaging Photometer for Spitzer (MIPS) observations at 24 and 70 microns for 30 stars, and at 160 microns for a subset of 12 stars, in the nearby (~30 pc), young (~12 Myr) Beta Pictoris Moving Group (BPMG). In several cases, the new MIPS measurements resolve source confusion and background contamination issues in the IRAS data for this sample. We find that 7 members have 24 micron excesses, implying a debris disk fraction of 23%, and that at least 11 have 70 micron excesses (disk fraction of >=37%). Five disks are detected at 160 microns (out of a biased sample of 12 stars observed), with a range of 160/70 flux ratios. The disk fraction at 24 and 70 microns, and the size of the excesses measured at each wavelength, are both consistent with an "inside-out" infrared excess decrease with time, wherein the shorter-wavelength excesses disappear before longer-wavelength excesses, and consistent with the overall decrease of infrared excess frequency with stellar age, as seen in Spitzer studies of other young stellar groups. Assuming that the infrared excesses are entirely due to circumstellar disks, we characterize the disk properties using simple models and fractional infrared luminosities. Optically thick disks, seen in the younger TW Hya and eta Cha associations, are entirely absent in the BPMG. Additional flux density measurements at 24 and 70 microns are reported for nine Tucanae-Horologium Association member stars. Since this is <20% of the association membership, limited analysis on the complete disk fraction of this association is possible.Comment: Accepted for Ap

Atomic and molecular interstellar absorption lines toward the high galactic latitude stars HD~141569 and HD~157841 at ultra-high resolution

We present ultra-high resolution (0.32 km/s) spectra obtained with the 3.9m Anglo-Australian Telescope (AAT) and Ultra-High-Resolution Facility (UHRF), of interstellar NaI D1, D2, Ca II K, K I and CH absorption toward two high galactic latitude stars HD141569 and HD157841. We have compared our data with 21-cm observations obtained from the Leiden/Dwingeloo HI survey. We derive the velocity structure, column densities of the clouds represented by the various components and identify the clouds with ISM structures seen in the region at other wavelengths. We further derive abundances, linear depletions and H2 fractional abundances for these clouds, wherever possible. Toward HD141569, we detect two components in our UHRF spectra : a weak, broad component at - 15 km/s, seen only in CaII K absorption and another component at 0 km/s, seen in NaI D1, D2, Ca II K, KI and CH absorption. In the case of the HD157841 sightline, a total of 6 components are seen on our UHRF spectra in NaI D1, D2 Ca II K, K I and CH absorption. 2 of these 6 components are seen only in a single species.Comment: 16 pages, Latex, 4 figures, ps files Astrophysical Journal (in press

Highest weight Macdonald and Jack Polynomials

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio

The Sylvester equation and the elliptic Korteweg-de Vries system

The elliptic potential Korteweg-de Vries lattice system is a multi-component extension of the lattice potential Korteweg-de Vries equation, whose soliton solutions are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus). In this paper we generalize the class of solutions by allowing the spectral parameter to be a full matrix obeying a matrix version of the equation of the elliptic curve, and for the Cauchy matrix to be a solution of a Sylvester type matrix equation subject to this matrix elliptic curve equation. The construction involves solving the matrix elliptic curve equation by using Toeplitz matrix techniques, and analysing the solution of the Sylvester equation in terms of Jordan normal forms. Furthermore, we consider the continuum limit system associated with the elliptic potential Korteweg-de Vries system, and analyse the dynamics of the soliton solutions, which reveals some new features of the elliptic system in comparison to the non-elliptic case

Spitzer/IRS spectroscopy of high mass precursors to planetary nebulae

We present Spitzer/IRS observations of a small sample of heavily obscured IRAS sources displaying both the infrared and OH maser emission characteristic of OH/IR stars on the asymptotic giant branch (AGB), but also radio continuum emission typical of ionized planetary nebulae (PNe), the so-called OHPNe. Our observations show that their mid-infrared spectra are dominated by the simultaneous presence of strong and broad amorphous silicate absorption features together with crystalline silicate features, originated in their O-rich circumstellar shells. Out of the five sources observed, three of them are clearly non-variable at infrared wavelengths, confirming their post-AGB status, while the remaining two still show strong photometric fluctuations, and may still have not yet departed from the AGB. One of the non-variable sources in the sample, IRAS 17393-2727, displays a strong [Ne II] nebular emission at 12.8 microns, indicating that the ionization of its central region has already started. This suggests a rapid evolution from the AGB to the PN stage. We propose that these heavily obscured OHPNe represent the population of high mass precursors to PNe in our Galaxy.Comment: To appear in The Astrophysical Journal Letters (scheduled in the 2007 September 1 issue

Geometric torsions and invariants of manifolds with triangulated boundary

Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a manifold with a triangulated boundary. These invariants can be naturally united in a vector, and a change of the boundary triangulation corresponds to a linear transformation of this vector. Moreover, when two manifolds are glued by their common boundary, these vectors undergo scalar multiplication, i.e., they work according to M. Atiyah's axioms for a topological quantum field theory.Comment: 18 pages, 4 figure

Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of $n$ spins with pairwise coupling, the scheme concatenates $cn$ intervals of system evolution and uses at most $c n^2$ pulses where $c \approx 1$. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.Comment: 7 pages, 4 figures, mypsfig2, revtex, submitted April 27, 199

Modeling the gas-phase chemistry of the transitional disk around HD 141569A

Aims: The chemistry, distribution and mass of the gas in the transitional disk around the 5 Myr old B9.5 V star HD 141569A are constrained. Methods: A quasi 2-dimensional (2D) chemistry code for photon dominated regions (PDR) is used to calculate the chemistry and gas temperatures in the disk. The calculations are performed for several gas distributions, PAH abundances and values of the total gas mass. The resulting CO J=2-1 and J=3-2 emission lines are computed with a 2D radiative transfer code and are compared to observations. Results: The CO abundance is very sensitive to the total disk mass because the disk is in a regime where self-shielding just sets in. The observed CO emission lines are best fit by a power-law gas distribution of 80 M_earth starting at 80 AU from the central star, indicating that there is some gas in the inner hole. Predictions are made for intensities of atomic fine-structure lines. [C I], which is the dominant form of carbon in large parts of the disk, is found to be a good alternative tracer of the gas mass.Comment: 11 pages, 9 figures. Accepted for publication in A&

Sub-mm observations and modelling of Vega type stars

We present new sub-mm observations and modelling of Vega excess stars, using realistic dust grain models. For resolved disks, we find that different objects require very different dust grain properties in order to simultaneously fit the image data and SED. Fomalhaut and Vega require solid dust grains, whilst HR4796 and HD141569 can only be fitted using porous grains. The older stars tend to have less porous grains than younger stars, which may indicate that collisions have compacted the dust grains. Eps Eri appears to be deficient in small dust grains compared to our best fitting model. This may be due to factors which affect the size distribution of grains close to the radiation pressure blowout limit. Alternatively, this discrepancy may be due to some external influence on the disk (e.g. a planet). When the model is applied to unresolved targets, an estimate of the disk size can be made. However, the large diversity in dust composition for the resolved disks means that we cannot make a reliable assumption as to the composition of the grains in an unresolved disk, and there is corresponding uncertainty in the disk size. In addition, the poor fit for Eps Eri shows that the model cannot always account for the SED even if the disk size is known. These two factors mean that it may not be possible to determine a disk's size without actually resolving it.Comment: 15 pages, 15 figures, accepted by MNRAS. Revised Eps Eri modelling to show larger range of minimum size cutoffs with porous grains, Figure