Compactification of a Drinfeld Period Domain over a Finite Field

We study a certain compactification of the Drinfeld period domain over a finite field which arises naturally in the context of Drinfeld moduli spaces. Its boundary is a disjoint union of period domains of smaller rank, but these are glued together in a way that is dual to how they are glued in the compactification by projective space. This compactification is normal and singular along all boundary strata of codimension $\ge2$. We study its geometry from various angles including the projective coordinate ring with its Hilbert function, the cohomology of twisting sheaves, the dualizing sheaf, and give a modular interpretation for it. We construct a natural desingularization which is smooth projective and whose boundary is a divisor with normal crossings. We also study its quotients by certain finite groups

Atomic Carbon in M82: Physical conditions derived from simultaneous observations of the [CI] fine structure submillimeter wave transitions

We report the first extragalactic detection of the neutral carbon [CI] 3P2-3P1 fine structure line at 809 GHz. The line was observed towards M82 simultaneously with the 3P1-3P0 line at 492 GHz, providing a precise measurement of the J=2-1/J=1-0 integrated line ratio of 0.96 (on a [K km s^-1] -scale). This ratio constrains the [CI] emitting gas to have a temperature of at least 50 K and a density of at least 10^4 cm^-3. Already at this minimum temperature and density, the beam averaged CI-column density is large, 2.1 10^18 cm^-2, confirming the high CI/CO abundance ratio of approximately 0.5 estimated earlier from the 492 GHz line alone. We argue that the [CI] emission from M82 most likely arises in clouds of linear size around a few pc with a density of about 10^4 cm^-3 or slightly higher and temperatures of 50 K up to about 100 K.Comment: 4 pages, 2 figures, ApJL in press, postscript also available at ftp://apollo.ph1.uni-koeln.de/pub/stutzki/m82_pap.ps.gz e-mail-contact:[email protected]

The Antarctic Submillimeter Telescope and Remote Observatory (AST/RO)

AST/RO, a 1.7 m diameter telescope for astronomy and aeronomy studies at wavelengths between 200 and 2000 microns, was installed at the South Pole during the 1994-1995 Austral summer. The telescope operates continuously through the Austral winter, and is being used primarily for spectroscopic studies of neutral atomic carbon and carbon monoxide in the interstellar medium of the Milky Way and the Magellanic Clouds. The South Pole environment is unique among observatory sites for unusually low wind speeds, low absolute humidity, and the consistent clarity of the submillimeter sky. Four heterodyne receivers, an array receiver, three acousto-optical spectrometers, and an array spectrometer are installed. A Fabry-Perot spectrometer using a bolometric array and a Terahertz receiver are in development. Telescope pointing, focus, and calibration methods as well as the unique working environment and logistical requirements of the South Pole are described.Comment: 57 pages, 15 figures. Submitted to PAS

Photon Dominated Regions in NGC 3603

Aims: We aim at deriving the excitation conditions of the interstellar gas as well as the local FUV intensities in the molecular cloud surrounding NGC 3603 to get a coherent picture of how the gas is energized by the central stars. Methods: The NANTEN2-4m submillimeter antenna is used to map the [CI] 1-0, 2-1 and CO 4-3, 7-6 lines in a 2' x 2' region around the young OB cluster NGC 3603 YC. These data are combined with C18O 2-1 data, HIRES-processed IRAS 60 and 100 micron maps of the FIR continuum, and Spitzer/IRAC maps. Results: The NANTEN2 observations show the presence of two molecular clumps located south-east and south-west of the cluster and confirm the overall structure already found by previous CS and C18O observations. We find a slight position offset of the peak intensity of CO and [CI], and the atomic carbon appears to be further extended compared to the molecular material. We used the HIRES far-infrared dust data to derive a map of the FUV field heating the dust. We constrain the FUV field to values of \chi = 3 - 6 \times 10^3 in units of the Draine field across the clouds. Approximately 0.2 to 0.3 % of the total FUV energy is re-emitted in the [CII] 158 {\mu}m cooling line observed by ISO. Applying LTE and escape probability calculations, we derive temperatures (TMM1 = 43 K, TMM2 = 47 K), column densities (N(MM1) = 0.9 \times 10^22 cm^-2, N(MM2) = 2.5 \times 10^22 cm^-2) and densities (n(MM1) = 3 \times 10^3 cm^-3, n(MM2) = 10^3 -10^4 cm^-3) for the two observed molecular clumps MM1 and MM2. Conclusions: The cluster is strongly interacting with the ambient molecular cloud, governing its structure and physical conditions. A stability analysis shows the existence of gravitationally collapsing gas clumps which should lead to star formation. Embedded IR sources have already been observed in the outskirts of the molecular cloud and seem to support our conclusions.Comment: 13 pages, 10 figures, accepted for publication by A&

The origin of the [C II] emission in the S140 PDRs - new insights from HIFI

Using Herschel's HIFI instrument we have observed [C II] along a cut through S140 and high-J transitions of CO and HCO+ at two positions on the cut, corresponding to the externally irradiated ionization front and the embedded massive star forming core IRS1. The HIFI data were combined with available ground-based observations and modeled using the KOSMA-tau model for photon dominated regions. Here we derive the physical conditions in S140 and in particular the origin of [C II] emission around IRS1. We identify three distinct regions of [C II] emission from the cut, one close to the embedded source IRS1, one associated with the ionization front and one further into the cloud. The line emission can be understood in terms of a clumpy model of photon-dominated regions. At the position of IRS1, we identify at least two distinct components contributing to the [C II] emission, one of them a small, hot component, which can possibly be identified with the irradiated outflow walls. This is consistent with the fact that the [C II] peak at IRS1 coincides with shocked H2 emission at the edges of the outflow cavity. We note that previously available observations of IRS1 can be well reproduced by a single-component KOSMA-tau model. Thus it is HIFI's unprecedented spatial and spectral resolution, as well as its sensitivity which has allowed us to uncover an additional hot gas component in the S140 region.Comment: accepted for publication in Astronomy and Astrophysics (HIFI special issue

Clumpy photon-dominated regions in Carina. I. [CI] and mid-J CO lines in two 4'x4' fields

The Carina region is an excellent astrophysical laboratory for studying the feedback mechanisms of newly born, very massive stars within their natal giant molecular clouds (GMCs) at only 2.35 kpc distance. We use a clumpy PDR model to analyse the observed intensities of atomic carbon and CO and to derive the excitation conditions of the gas. The NANTEN2-4m submillimeter telescope was used to map the [CI] 3P1-3P0, 3P2-3P1 and CO 4-3, 7-6 lines in two 4'x4' regions of Carina where molecular material interfaces with radiation from the massive star clusters. One region is the northern molecular cloud near the compact OB cluster Tr14, and the second region is in the molecular cloud south of etaCar and Tr16. These data were combined with 13CO SEST spectra, HIRES/IRAS 60um and 100um maps of the FIR continuum, and maps of 8um IRAC/Spitzer and MSX emission. We used the HIRES far-infrared dust data to create a map of the FUV field heating the gas. The northern region shows an FUV field of a few 1000 in Draine units while the field of the southern region is about a factor 10 weaker. We constructed models consisting of an ensemble of small spherically symmetric PDR clumps within the 38" beam (0.43pc), which follow canonical power-law mass and mass-size distributions. We find that an average local clump density of 2x10**5 cm-3 is needed to reproduce the observed line emission at two selected interface positions. Stationary, clumpy PDR models reproduce the observed cooling lines of atomic carbon and CO at two positions in the Carina Nebula.Comment: accepted by A&

Picard-Lefschetz Oscillators for the Drinfeld-Lafforgue-Vinberg Compactification

We study the singularities of the Drinfeld-Lafforgue-Vinberg compactification of the moduli stack of G-bundles on a smooth projective curve for a reductive group G. The study of these compactifications was initiated by V. Drinfeld (for G=GL_2) and continued by L. Lafforgue (for G=GL_n) in their work on the Langlands correspondence for function fields; unlike the work of Drinfeld and Lafforgue, however, we focus on questions about the singularities of these compactifications which arise naturally in the geometric Langlands program. A definition of the compactification for a general reductive group G is also due to Drinfeld (unpublished) and relies on the Vinberg semigroup of G; this case will be dealt with in the forthcoming work [Sch]. In the present work we focus on the case G=SL_2. In this case the compactification can alternatively be viewed as a canonical one-parameter degeneration of the moduli space of SL_2-bundles. We study the singularities of this one-parameter degeneration via the weight-monodromy theory of the associated nearby cycles construction: We give an explicit description of the nearby cycles sheaf together with its monodromy action in terms of certain novel perverse sheaves which we call "Picard-Lefschetz oscillators", and then use this description to determine the intersection cohomology sheaf and other invariants of the singularities. Our proofs rely on the construction of certain local models for the one-parameter degeneration which themselves form one-parameter families of spaces which are factorizable in the sense of Beilinson and Drinfeld. We also include a first application on the level of functions.Mathematic