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In this paper we prove that the etale sheafification of the functor arising from the quotient of an algebraic supergroup by a closed subsupergroup is representable by a smooth superscheme.

We study SUSY $N$-supergroups, $N=1,2$, their classification and explicit realization, together with their real forms. In the end, we give the supergroup of SUSY preserving automorphism of $\mathbf{C}^{1|1}$ and we identify it with a subsupergroup of the SUSY preserving automorphisms of $\mathbf{P}^{1|1}$.

We study a generalization of the results \in \cite{cfk} to the case of $SU(1|1)$ interpreted as the supercircle $S^{1|2}$. We describe all of its finite dimensional complex irreducible representations, we give a reducibility result for representations not containing the trivial character, and we compute explicitly the corresponding matrix elements. In the end we give the Peter-Weyl theorem for $S^{1|2}$.

The purpose of this paper is to describe the projective linear supergroup, its relation with the automorphisms of the projective superspace and to determine the supergroup of SUSY preserving automorphisms of ${\mathbf P}^{1|1}$

The real compact supergroup $S^{1|1}$ is analized from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of $({\mathbf C}^{1|1})^\times$ with reduced Lie group $S^1$, and a link with SUSY structures on ${\mathbf C}^{1|1}$ is established. We describe a large family of complex semisimple representations of $S^{1|1}$ and we show that any $S^{1|1}$-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for $S^{1|1}$.

In this note we give a summary of some elementary results in the theory of super Riemann surfaces (SUSY curves).

NGC 2392 is a young double-shell planetary nebula (PN). Its intrinsic structure and shaping mechanism are still not fully understood. In this paper we present new spectroscopic observations of NGC 2392. The slits were placed at two different locations to obtain the spectra of the inner and outer regions. Several [Fe III] lines are clearly detected in the inner region. We infer that NGC 2392 might have an intrinsic structure similar to the bipolar nebula Mz 3, which also exhibits a number of [Fe III}] lines arising from the central regions. In this scenario, the inner and outer regions of NGC 2392 correspond to the inner lobes and the outer outflows of Mz 3, respectively. We construct a three-dimensional morpho-kinematic model to examine our hypothesis. We also compare the physical conditions and chemical composition of the inner and outer regions, and discuss the implications on the formation of this type of PN., Comment: 41 pages, 13 figures, Accepted for publication in ApJ

We present the result of radio observations of red supergiants in the star cluster, Stephenson's #2, and candidates for red supergiants in the star clusters, Mercer et al. (2005)'s #4, #8, and #13, in the SiO and H$_2$O maser lines.The Stephenson's #2 cluster and nearby aggregation at the South-West contain more than 15 red supergiants. We detected one at the center of Stephenson's #2 and three in the south-west aggregation in the SiO maser line, and three of these 4 were also detected in the H2O maser line. The average radial velocity of the 4 detected objects is 96 km s^{-1}, giving a kinematic distance of 5.5 kpc, which locates this cluster near the base of the Scutum-Crux spiral arm. We also detected 6 SiO emitting objects associated with the other star clusters. In addition, mapping observations in the CO J=1--0 line toward these clusters revealed that an appreciable amount of molecular gas still remains around Stephenson's #2 cluster in contrast to the prototypical red-supergiant cluster, Bica et al.'s #122. It indicates that a time scale of gas expulsion differs considerably in individual clusters., Comment: high res. figures available at http://www.nro.nao.ac.jp/~lib_pub/report/data/no674.pdf. PASJ 62, No.2 (2010, April 25 issue) in press

We investigate the physical and chemical conditions in a typical star forming region, including an unbiased search for new molecules in a spectral region previously unobserved. Due to its proximity, the Orion KL region offers a unique laboratory of molecular astrophysics in a chemically rich, massive star forming region. Several ground-based spectral line surveys have been made, but due to the absorption by water and oxygen, the terrestrial atmosphere is completely opaque at frequencies around 487 and 557 GHz. To cover these frequencies we used the Odin satellite to perform a spectral line survey in the frequency ranges 486-492 GHz and 541-577 GHz, filling the gaps between previous spectral scans. Odin's high main beam efficiency and observations performed outside the atmosphere make our intensity scale very well determined. We observed 280 spectral lines from 38 molecules including isotopologues, and, in addition, 64 unidentified lines. The beam-averaged emission is dominated by CO, H2O, SO2, SO, 13CO and CH3OH. Species with the largest number of lines are CH3OH, (CH33)2O, SO2, 13CH3OH, CH3CN and NO. Six water lines are detected including the ground state rotational transition o-H2O, its isotopologues o-H218O and o-H217O, the Hot Core tracing p-H2O transition 6(2,4)-7(1,7), and the 2(0, 2)-1(1,1) transition of HDO. Other lines of special interest are the 1_0-0_0 transition of NH3 and its isotopologue 15NH3. Isotopologue abundance ratios of D/H, 12C/13C, 32S/34S, 34S/33S, and 18O/17O are estimated. The temperatures, column densities and abundances in the various subregions are estimated, and we find very high gas-phase abundances of H2O, NH3, SO2, SO, NO, and CH3OH. A comparison with the ice inventory of ISO sheds new light on the origin of the abundant gas-phase molecules., Comment: 51 pages, 47 figures, 35 tables, accepted for publication in Astronomy and Astrophysics 17 September 2007

Spectral line surveys are useful since they allow identification of new molecules and new lines in uniformly calibrated data sets. Nonetheless, large portions of the sub-millimetre spectral regime remain unexplored due to severe absorptions by H2O and O2 in the terrestrial atmosphere. The purpose of the measurements presented here is to cover wavelength regions at and around 0.55 mm -- regions largely unobservable from the ground. Using the Odin astronomy/aeronomy satellite, we performed the first spectral survey of the Orion KL molecular cloud core in the bands 486--492 and 541--576 GHz with rather uniform sensitivity (22--25 mK baseline noise). Odin's 1.1 m size telescope, equipped with four cryo-cooled tuneable mixers connected to broad band spectrometers, was used in a satellite position-switching mode. Two mixers simultaneously observed different 1.1 GHz bands using frequency steps of 0.5 GHz (25 hours each). An on-source integration time of 20 hours was achieved for most bands. The entire campaign consumed ~1100 orbits, each containing one hour of serviceable astro-observation. We identified 280 spectral lines from 38 known interstellar molecules (including isotopologues) having intensities in the range 80 to 0.05 K. An additional 64 weak lines remain unidentified. Apart from the ground state rotational 1(1,0)--1(0,1) transitions of ortho-H2O, H218O and H217O, the high energy 6(2,4)--7(1,7) line of para-H2O and the HDO(2,0,2--1,1,1) line have been observed, as well as the 1,0--0,1 lines from NH3 and its rare isotopologue 15NH3. We suggest assignments for some unidentified features, notably the new interstellar molecules ND and SH-. Severe blends have been detected in the line wings of the H218O, H217O and 13CO lines changing the true linewidths of the outflow emission., Comment: 21 pages, 10 figures, 7 tables, accepeted for publication in Astronomy and Astrophysics 30 August 2007

We have used the He I discontinuities at 3421A to determine the electron temperatures, designated Te(He I), for a sample of five Galactic planetary nebulae (PNe). We compared Te(He I) with the electron temperatures derived from the hydrogen Balmer jump at 3646A, designated Te(H I), and found that Te(He I) are generally lower than Te(H I). There are two possible interpretations, a) the presence of substantial He+2 zone, or b) the presence of hydrogen-deficient cold clumps within diffuse nebulae. A series of photoionization models were constructed to test the two scenarios. We found that the observed Te(He I)/Te(H I) discrepancies are beyond the predictions of chemically homogeneous models. Our modelling shows that the presence of a small amount of hydrogen-deficient inclusions seems to be able to reproduce the observed intensities of He I discontinuities. We stress the value of He I discontinuities in investigating nebular physical conditions. Albeit with some observational and technical limitations, He I discontinuities should be considered in future modelling work., Comment: 19 pages, 6 figures. Accepted for publication in ApJ

Aims: Spectrally resolved circumstellar H2O(1_10 - 1_01) lines have been obtained towards three M-type AGB stars using the Odin satellite. This provides additional strong constrains on the properties of circumstellar H2O and the circumstellar envelope. Methods: ISO and Odin satellite H2O line data are used as constraints for radiative transfer models. Special consideration is taken to the spectrally resolved Odin line profiles, and the effect of excitation to the first excited vibrational states of the stretching modes (nu1=1 and nu3=1) on the derived abundances is estimated. A non-local, radiative transfer code based on the ALI formalism is used. Results: The H2O abundance estimates are in agreement with previous estimates. The inclusion of the Odin data sets stronger constraints on the size of the H2O envelope. The H2O(1_10 - 1_01) line profiles require a significant reduction in expansion velocity compared to the terminal gas expansion velocity determined in models of CO radio line emission, indicating that the H2O emission lines probe a region where the wind is still being accelerated. Including the nu3=1 state significantly lowers the estimated abundances for the low-mass-loss-rate objects. This shows the importance of detailed modelling, in particular the details of the infrared spectrum in the range 3 to 6 micron, to estimate accurate circumstellar H2O abundances. Conclusions: Spectrally resolved circumstellar H2O emission lines are important probes of the physics and chemistry in the inner regions of circumstellar envelopes around asymptotic giant branch stars. Predictions for H2O emission lines in the spectral range of the upcoming Herschel/HIFI mission indicate that these observations will be very important in this context., Comment: accepted in A&A, 10 pages, 8 figures

We present the results of our spectral line surveys in the 2 mm and 1.3 mm windows toward the carbon rich envelope of IRC +10216. Totally 377 lines are detected, among which 360 lines are assigned to 57 known molecules (including 29 rare isotopomers and 2 cyclic isomers). Only 17 weak lines remain unidentified. Rotational lines of isotopomers 13CCH and HN13C are detected for the first time in IRC +10216. The detection of the formaldehyde lines in this star is also confirmed. Possible abundance difference among the three 13C substituted isotopic isomers of HC3N is reported. Isotopic ratios of C and O are confirmed to be non-solar while those of S and Si to be nearly solar. Column densities have been estimated for 15 molecular species. Modified spectroscopic parameters have been calculated for NaCN, Na13CN, KCN and SiC2. Transition frequencies from the present observations were used to improve the spectroscopic parameters of Si13CC, 29SiC2 and 30SiC2., Comment: 17 pages of text, 18 pages of 14 tables, 35 pages of 4 figures, a typo corrected in Abstract

We present interferometric observations of $^{12}$CO and $^{13}$CO $J$=2$-$1 emission from the butterfly-shaped, young planetary nebula NGC 6302. The high angular resolution and high sensitivity achieved in our observations allow us to resolve the nebula into two distinct kinematic components: (1) a massive expanding torus seen almost edge-on and oriented in the North-South direction, roughly perpendicular to the optical nebula axis. The torus exhibits very complex and fragmentated structure; (2) high velocity molecular knots moving at high velocity, higher than 20 \kms, and located in the optical bipolar lobes. These knots show a linear position-velocity gradient (Hubble-like flow), which is characteristic of fast molecular outflow in young planetary nebulae. From the low but variable $^{12}$CO/$^{13}$CO $J$=2$-$1 line intensity ratio we conclude that the $^{12}$CO $J$=2$-$1 emission is optically thick over much of the nebula. Using the optically thinner line $^{13}$CO $J$=2$-$1 we estimate a total molecular gas mass of $\sim$ 0.1 M$_\odot$, comparable to the ionized gas mass; the total gas mass of the NGC 6302 nebula, including the massive ionized gas from photon dominated region, is found to be $\sim$ 0.5 M$_\odot$. From radiative transfer modelling we infer that the torus is seen at inclination angle of 75$^\circ$ with respect to the plane of the sky and expanding at velocity of 15 \kms. Comparison with recent observations of molecular gas in NGC 6302 is also discussed., Comment: 24 pages, 7 figures, accepted for publication in Astrophysical Journal

Using the 3.6/4.5/5.8/8.0 micron images with 1.2 arcsec pixel resolution from the Spitzer/GLIMPSE survey, we investigated 23 masing and 18 very red objects that were not identified in the 2MASS survey. Counterparts for all selected objects were found in the GLIMPSE images. Color indices in these IR bands suggest the presence of a high-extinction layer of more than a few tenths of a solar mass in front of the central star. Furthermore, radio observations in the SiO and H2O maser lines found characteristic maser-line spectra of the embedded objects, e.g., the SiO J=1-0 line intensity in the v=2 state stronger than that of the v=1 state, or very widespread H2O maser emission spectra. This indicates that these objects are actually enshrouded by very thick circumstellar matter, some of which cannot be ascribed to the AGB wind of the central star. Individually interesting objects are discussed, including two newly found water fountains and an SiO source with nebulosity., Comment: High resolution figures available at ftp://ftp.nro.nao.ac.jp/nroreport/no653.pdf.gz. ApJ No. 655 no.1 issue in press

We report our search for optically thick radio cores in sixteen narrow-waist bipolar nebulae. Optically thick cores are a characteristic signature of collimated ionized winds. Eleven northern nebulae were observed with the Very Large Array (VLA) at 1.3 cm and 0.7 cm, and five southern nebulae were observed with the Australia Telescope Compact Array (ATCA) at 6 cm and 3.6 cm. Two northern objects, 19W32 and M 1-91, and three southern objects, He 2-25, He 2-84 and Mz 3, were found to exhibit a compact radio core with a rising spectrum consistent with an ionized jet. Such jets have been seen in M 2-9 and may be responsible for shaping bipolar structure in planetary nebulae., Comment: 29 pages, accepted for publication in ApJ

Molecular oxygen, O2 has been expected historically to be an abundant component of the chemical species in molecular clouds and, as such, an important coolant of the dense interstellar medium. However, a number of attempts from both ground and from space have failed to detect O2 emission. The work described here uses heterodyne spectroscopy from space to search for molecular oxygen in the interstellar medium. The Odin satellite carries a 1.1 m sub-millimeter dish and a dedicated 119 GHz receiver for the ground state line of O2. Starting in 2002, the star forming molecular cloud core rho Oph A was observed with Odin for 34 days during several observing runs. We detect a spectral line at v(LSR) = 3.5 km/s with dv(FWHM) = 1.5 km/s, parameters which are also common to other species associated with rho Ohp A. This feature is identified as the O2 (N_J = 1_1 - 1_0) transition at 118 750.343 MHz. The abundance of molecular oxygen, relative to H2,, is 5E-8 averaged over the Odin beam. This abundance is consistently lower than previously reported upper limits., Comment: 10 pages, 11 figures, accepted for publication in A&A

We present millimeter interferometric observations of the molecular envelope around the red supergiant VY CMa with the SubMillimeter Array (SMA). The high angular resolution (< 2'') allows us to derive the structure of the envelope as observed in the 1.3 mm continuum, 12CO(2-1), 13CO(2-1) and SO(6,5-5,4) lines emission. The circumstellar envelope is resolved into three components: a dense, compact and dusty central component, embedded in a more diffuse and extended envelope plus a high velocity component. We construct a simple model, consisting of a spherically symmetric slowly expanding envelope and bipolar outflows with a wide opening angle (~ 120 deg.) viewed close to the line of sight (i = 15 deg.). Our model can explain the main features of the SMA data and previous single-dish CO multi-line observations. An episode of enhanced mass loss along the bipolar direction is inferred from our modelling. The SMA data provide a better understanding of the complicated morphology seen in the optical/IR high resolution observations., Comment: accepted for publication in ApJ

The effects of dust extinction on the departure from axi-symmetry in the morphology of planetary nebulae (PNs) are investigated through a comparison of the radio free-free emission and hydrogen recombination line images. The dust exctinction maps of five compact PNs are derived using high-resolution (~ 0".1) H-alpha and radio images maps of the HST and VLA. These extinction maps are then analyzed by an ellipsoidal shell ionization model including the effects of dust extinction to infer the nebulae's intrinsic structure and orientation in the sky. This method provides a quantitative analysis of the morphological structure of PNs and represents a step beyond qualitative classification of morphological types of PNs., Comment: 39 pages, including 21 figure pages and 1 table page; accepted for publication in the Astrophysical Journal; figure quality reduced; full resolution copy available at http://www.noao.edu/staff/thlee/cv/thlee05.pdf.gz

We present Odin observations of the AGB star W Hya in the ground-state transition of ortho-H2O, 1(10)-1(01), at 557GHz. The line is clearly of circumstellar origin. Radiative transfer modelling of the water lines observed by Odin and ISO results in a mass-loss rate of (2.5 +/- 0.5)E-7 Msol/yr, and a circumstellar H2O abundance of (2.0 +/- 1.0)E-3. The inferred mass-loss rate is consistent with that obtained from modelling the circumstellar CO radio line emission, and also with that obtained from the dust emission modelling combined with a dynamical model for the outflow. The very high water abundance, higher than the cosmic oxygen abundance, can be explained by invoking an injection of excess water from evaporating icy bodies in the system. The required extra mass of water is quite small, on the order of ~ 0.1 earth mass., Comment: 7 pages, 6 figures Accepted for publication in Astronomy and Astrophysics

An Artificial Neural Network (ANN) has been employed using a supervised back-propagation scheme to classify 2000 bright sources from the Calgary database of IRAS (Infrared Astronomy Satellite) spectra in the wavelength region of 8-23 microns. The data base has been classified into 17 pre-determined classes based on spectral morphology. We have been able to classify more than 80 percent of the 2000 sources correctly at the first instance. The speed and robustness of the scheme will allow us to classify the whole of LRS database, containing more than 50,000 sources in the future., Comment: 26 pages, To appear in ApJS after July 2004

Odin has successfully observed the molecular core rho Oph A in the 572.5 GHz rotational ground state line of ammonia, NH3 (J,K = 1,0 - 0,0). The interpretation of this result makes use of complementary molecular line data obtained from the ground (C17O and CH3OH) as part of the Odin preparatory work. Comparison of these observations with theoretical model calculations of line excitation and transfer yields a quite ordinary abundance of methanol, X(CH3OH) = 3e-9. Unless NH3 is not entirely segregated from C17O and CH3OH, ammonia is found to be significantly underabundant with respect to typical dense core values, viz. X(NH3) = 8e-10., Comment: 4 pages, 2 figures, 2 tables, to appear in Astron. Astrophys. Letters

We have mapped the submillimeter emission from the 1(10)-1(01) transition of ortho-water in the W3 star-forming region. A 5'x5' map of the W3 IRS4 and W3 IRS5 region reveals strong water lines at half the positions in the map. The relative strength of the Odin lines compared to previous observations by SWAS suggests that we are seeing water emission from an extended region. Across much of the map the lines are double-peaked, with an absorption feature at -39 km/s; however, some positions in the map show a single strong line at -43 km/s. We interpret the double-peaked lines as arising from optically thick, self-absorbed water emission near the W3 IRS5, while the narrower blue-shifted lines originate in emission near W3 IRS4. In this model, the unusual appearance of the spectral lines across the map results from a coincidental agreement in velocity between the emission near W3 IRS4 and the blue peak of the more complex lines near W3 IRS5. The strength of the water lines near W3 IRS4 suggests we may be seeing water emission enhanced in a photon-dominated region., Comment: Accepted to A&A Letters as part of the special Odin issue; 4 pages

Odin has successfully observed three regions in the Orion A cloud, i.e. Ori KL, Ori S and the Orion Bar, in the 572.5 GHz rotational ground state line of ammonia, ortho-NH3 (J,K) = (1,0) -> (0,0), and the result for the Orion Bar represents the first detection in an ammonia line. Several velocity components are present in the data. Specifically, the observed line profile from the Orion Bar can be decomposed into two components, which are in agreement with observations in high-J CO lines by Wilson et al. 2001. Using the source model for the Orion Bar by these authors, our Odin observation implies a total ammonia abundance of NH3/H2 = 5E-9., Comment: 4 pages with 2 figures, accepted for publication in A&A

We report NICMOS wide-band and polarimetric observations of four proto-planetary nebulae. Molecular hydrogen emission is detected near the ends of the bipolar lobes of IRAS 17150-3224, which is evidence for the interaction of a fast, collimated outflow with the remnant of the asymptotic giant branch wind., Comment: To appear in ``Asymmetrical Planetary Nebulae II: from Origins to Microstructures,'' ASP Conference Series, Vol. 199, 2000; J.H. Kastner, N. Soker, & S.A. Rappaport, eds

We have fitted the HST images and the spectral energy distributions (SEDs) of three proto-planetary nebulae (PPN) with a 2-D radiation transfer model. The geometric and mass loss properties of these PPN are also derived., Comment: To appear in ``Asymmetrical Planetary Nebulae II: from Origins to Microstructures,'' ASP Conference Series, Vol. 199, 2000; J.H. Kastner, N. Soker, & S.A. Rappaport, eds