130 research outputs found
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
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