The Lambda-structure Of The Representation Rings Of The Classical Weyl Groups

First, we introduce a class of operations, called {dollar}\phi{dollar}-operations, on the representation rings of the classical Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar}. These operations are shown to generate the exterior power operations in the representation rings {dollar}R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} and {dollar}R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})).{dollar} Given integers l, h satisfying {dollar}l + h=k{dollar}, let {dollar}\beta{dollar} be a partition of l and {dollar}\alpha{dollar} be a partition of h. The main theorem shows that induced representations of the form {dollar}{dollar}Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,\alpha{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1,{dollar}{dollar}where {dollar}{lcub}\cal W{rcub}\sb{lcub}B,a{rcub}=\prod{lcub}\cal W{rcub}(B\sb{lcub}B{rcub})\times\prod{lcub}\cal W{rcub}(A\sb{lcub}a{rcub}),{dollar} can be expressed as an algebraic combination of {dollar}\phi{dollar}-operations acting on the two canonical induced representations {dollar}{dollar}\eqalign{lcub}X\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub})\times{lcub}\cal W{rcub}(B\sb1){rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1\cr\cr Y\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub}){rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1.\cr{rcub}{dollar}{dollar};Next, we show that the set {dollar}{dollar}\left\{lcub}1 \otimes Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,a{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1\right\{rcub}{dollar}{dollar}is a basis of {dollar}\doubq \otimes R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar}. Since the {dollar}\phi{dollar}-operations generate the {dollar}\lambda{dollar}-operations, one can deduce that {dollar}\doubq\otimes R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} is generated as a {dollar}\lambda{dollar}-ring over {dollar}\doubq{dollar} by the elements {dollar}1 \otimes X\sb{lcub}k{rcub}{dollar} and {dollar}1 \otimes Y\sb{lcub}k{rcub}{dollar}. By applying a result of Lusztig which characterizes the irreducible representations of the Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar} it follows, as a corollary, that {dollar}\doubq\otimes R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})){dollar} is generated by two elements as a {dollar}\lambda{dollar}-ring over {dollar}\doubq{dollar}

A Spitzer IRS Study of Debris Disks Around Planet-Host Stars

Since giant planets scatter planetesimals within a few tidal radii of their orbits, the locations of existing planetesimal belts indicate regions where giant planet formation failed in bygone protostellar disks. Infrared observations of circumstellar dust produced by colliding planetesimals are therefore powerful probes of the formation histories of known planets. Here we present new Spitzer IRS spectrophotometry of 111 Solar-type stars, including 105 planet hosts. Our observations reveal 11 debris disks, including two previously undetected debris disks orbiting HD 108874 and HD 130322. Combining our 32 micron spectrophotometry with previously published MIPS photometry, we find that the majority of debris disks around planet hosts have temperatures in the range 60 < T < 100 K. Assuming a dust temperature T = 70 K, which is representative of the nine debris disks detected by both IRS and MIPS, we find that debris rings surrounding Sunlike stars orbit between 15 and 240 AU, depending on the mean particle size. Our observations imply that the planets detected by radial-velocity searches formed within 240 AU of their parent stars. If any of the debris disks studied here have mostly large, blackbody emitting grains, their companion giant planets must have formed in a narrow region between the ice line and 15 AU.Comment: Accepted for publication in the Astronomical Journal. 14 pages, including five figures and two table

Accurate Coordinates and 2MASS Cross-IDs for (Almost) All Gliese Catalog Stars

We provide precise J2000, epoch 2000 coordinates and cross-identifications to sources in the 2MASS point source catalog for nearly all stars in the Gliese, Gliese and Jahreiss, and Woolley catalogs of nearby stars. The only Gliese objects where we were not successful are two Gliese sources that are actually QSOs, two proposed companions to brighter stars which we believe do not exist, four stars included in one of the catalogs but identified there as only optical companions, one probable plate flaw, and two stars which simply remain un-recovered. For the 4251 recovered stars, 2693 have coordinates based on Hipparcos positions, 1549 have coordinates based on 2MASS data, and 9 have positions from other astrometric sources. All positions have been calculated at epoch 2000 using proper motions from the literature, which are also given here.Comment: accepted to PASP, Full version of Table 1 available electronicall

Far Infrared Prperties of M Dwarfs

We report the mid- and far-infrared properties of nearby M dwarfs. Spitzer/MIPS measurements were obtained for a sample of 62 stars at 24 um, with subsamples of 41 and 20 stars observed at 70 um and 160 um respectively. We compare the results with current models of M star photospheres and look for indications of circumstellar dust in the form of significant deviations of K-[24 um] colors and 70 um / 24 um flux ratios from the average M star values. At 24 um, all 62 of the targets were detected; 70 um detections were achieved for 20 targets in the subsample observed; and no detections were seen in the 160 um subsample. No clear far-infrared excesses were detected in our sample. The average far infrared excess relative to the photospheric emission of the M stars is at least four times smaller than the similar average for a sample of solar-type stars. However, this limit allows the average fractional infrared luminosity in the M-star sample to be similar to that for more massive stars. We have also set low limits for the maximum mass of dust possible around our stars.Comment: 28 pages, 4 figures, to be published in The Astrophysical Journa

Investigating planet formation in circumstellar disks: CARMA observations of RY Tau and DG Tau

(Abridged) We present CARMA observations of the thermal dust emission from the circumstellar disks around the young stars RYTau and DGTau at wavelengths of 1.3mm and 2.8mm. The angular resolution of the maps is as high as 0.15arcsec, or 20AU at the distance of the Taurus cloud, which is a factor of 2 higher than has been achieved to date at these wavelengths. The unprecedented detail of the resulting disk images enables us to address three important questions related to the formation of planets. (1) What is the radial distribution of the circumstellar dust? (2) Does the dust emission show any indication of gaps that might signify the presence of (proto-)planets? (3) Do the dust properties depend on the orbital radius? We find that modeling the disk surface density in terms of either a classical power law or the similarity solution for viscous disk evolution, reproduces the observations well. The 1.3mm image from RYTau shows two peaks separated by 0.2arcsec with a decline in the dust emission toward the stellar position, which is significant at about 2-4sigma. For both RYTau and DGTau, the dust emission at radii larger than 15 AU displays no significant deviation from an unperturbed viscous disk model. In particular, no radial gaps in the dust distribution are detected. Under reasonable assumptions, we exclude the presence of planets more massive than 5 Jupiter masses orbiting either star at distances between about 10 and 60 AU. The radial variation of the dust opacity slope, beta, was investigated by comparing the 1.3mm and 2.8mm observations. We find mean values of beta of 0.5 and 0.7 for DGTau and RYTau respectively. Variations in beta are smaller than 0.7 between 20 and 70 AU. These results confirm that the circumstellar dust throughout these disks differs significantly from dust in the interstellar medium.Comment: ApJ in press

HST and Spitzer Observations of the HD 207129 Debris Ring

A debris ring around the star HD 207129 (G0V; d = 16.0 pc) has been imaged in scattered visible light with the ACS coronagraph on the Hubble Space Telescope and in thermal emission using MIPS on the Spitzer Space Telescope at 70 microns (resolved) and 160 microns (unresolved). Spitzer IRS (7-35 microns) and MIPS (55-90 microns) spectrographs measured disk emission at >28 microns. In the HST image the disk appears as a ~30 AU wide ring with a mean radius of ~163 AU and is inclined by 60 degrees from pole-on. At 70 microns it appears partially resolved and is elongated in the same direction and with nearly the same size as seen with HST in scattered light. At 0.6 microns the ring shows no significant brightness asymmetry, implying little or no forward scattering by its constituent dust. With a mean surface brightness of V=23.7 mag per square arcsec, it is the faintest disk imaged to date in scattered light.Comment: 28 pages, 8 figure

On the nature of the transition disk around LkCa 15

We present CARMA 1.3 mm continuum observations of the T Tauri star LkCa 15,which resolve the circumstellar dust continuum emission on angular scales between 0.2-3 arcsec, corresponding to 28-420 AU at the distance of the star. The observations resolve the inner gap in the dust emission and reveal an asymmetric dust distribution in the outer disk. (Abridge) We calculate that 90% of the dust emission arises from an azimuthally symmetric ring that contains about 5x10^{-4} M_sun of dust. A low surface-brightness tail that extends to the northwest out to a radius of about 300 AU contains the remaining 10% of the observed continuum emission. The ring is modeled with a rather flat surface density profile between 40 and 120 AU, while the inner cavity is consistent with either a sharp drop of the 1.3 mm dust optical depth at about 42 AU or a smooth inward decrease between 3 and 85 AU. (Abridge). Within 40 AU, the observations constrain the amount of dust between 10^{-6} and 7 Earth masses, where the minimum and maximum limits are set by the near-IR SED modeling and by the mm-wave observations of the dust emission respectively. In addition, we confirm the discrepancy in the outer disk radius inferred from the dust and gas, which corresponds to 150 AU and 900 AU respectively. We cannot reconcile this difference by adopting an exponentially tapered surface density profile as suggested for other systems, but we instead suggest that the gas surface density in the outer disk decreases less steeply than that predicted by model fits to the dust continuum emission. The lack of continuum emission at radii lager than 120 AU suggests a drop of at least a factor of 5 in the dust-to-gas ratio, or in the dust opacity. We show that a sharp dust opacity drop of this magnitude is consistent with a radial variation of the grain size distribution as predicted by existing grain growth models.Comment: Accepted for publication on ApJ, 13 pages, 11 figure

Debris Disks of Members of the Blanco 1 Open Cluster

We have used the Spitzer Space Telescope to obtain Multiband Imaging Photometer for Spitzer (MIPS) 24 um photometry for 37 members of the ~100 Myr old open cluster Blanco 1. For the brightest 25 of these stars (where we have 3sigma uncertainties less than 15%), we find significant mid-IR excesses for eight stars, corresponding to a debris disk detection frequency of about 32%. The stars with excesses include two A stars, four F dwarfs and two G dwarfs. The most significant linkage between 24 um excess and any other stellar property for our Blanco 1 sample of stars is with binarity. Blanco 1 members that are photometric binaries show few or no detected 24 um excesses whereas a quarter of the apparently single Blanco 1 members do have excesses. We have examined the MIPS data for two other clusters of similar age to Blanco 1 -- NGC 2547 and the Pleiades. The AFGK photometric binary star members of both of these clusters also show a much lower frequency of 24 um excesses compared to stars that lie near the single-star main sequence. We provide a new determination of the relation between V-Ks color and Ks-[24] color for main sequence photospheres based on Hyades members observed with MIPS. As a result of our analysis of the Hyades data, we identify three low mass Hyades members as candidates for having debris disks near the MIPS detection limit.Comment: Accepted to Ap

Exploring the Effects of Stellar Rotation and Wind Clearing: Debris Disks around F Stars

We have conducted a study of debris disks around F stars in order to explore correlations between rotation, stellar winds, and circumstellar disks. We obtained new 24 μm photometry from the Multiband Imaging Photometer for Spitzer (MIPS) camera for a sample of 188 relatively nearby F dwarfs with various rotation rates and optical colors, and combined it with archival MIPS data for 66 more F stars, as well as Wide-field Infrared Survey Explorer data for the entire sample, plus 9 more F stars. Based on the objects' K_s – [24] and [3.4] – [22] colors, we identify 22 stars in our sample as having 22 and/or 24 μm excesses above our detection limit, 13 of which are new discoveries. Our overall disk detection rate is 22/263, or 8%, consistent with previous determinations of disk fractions in the solar neighborhood. While fast-rotating stars are expected to have strong winds capable of efficiently removing dust, we find no correlation between rotational velocity and infrared excess. Similarly, we find no significant difference in excess detection rate between late-type F stars, which have convective surfaces, and early-type F stars, which have fully radiative envelopes. However, the essentially unknown range of ages in this sample may be washing out any effects relating rotation, winds, and disks