Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase

Schwinger's finite (D) dimensional periodic Hilbert space representations are studied on the toroidal lattice {\ee Z}_{D} \times {\ee Z}_{D} with specific emphasis on the deformed oscillator subalgebras and the generalized representations of the Wigner function. These subalgebras are shown to be admissible endowed with the non-negative norm of Hilbert space vectors. Hence, they provide the desired canonical basis for the algebraic formulation of the quantum phase problem. Certain equivalence classes in the space of labels are identified within each subalgebra, and connections with area-preserving canonical transformations are examined. The generalized representations of the Wigner function are examined in the finite-dimensional cyclic Schwinger basis. These representations are shown to conform to all fundamental conditions of the generalized phase space Wigner distribution. As a specific application of the Schwinger basis, the number-phase unitary operator pair in {\ee Z}_{D} \times {\ee Z}_{D} is studied and, based on the admissibility of the underlying q-oscillator subalgebra, an {\it algebraic} approach to the unitary quantum phase operator is established. This being the focus of this work, connections with the Susskind-Glogower- Carruthers-Nieto phase operator formalism as well as standard action-angle Wigner function formalisms are examined in the infinite-period limit. The concept of continuously shifted Fock basis is introduced to facilitate the Fock space representations of the Wigner function.Comment: 19 pages, no figure

Milky Way potentials in CDM and MOND. Is the Large Magellanic Cloud on a bound orbit?

We compute the Milky Way potential in different cold dark matter (CDM) based models, and compare these with the modified Newtonian dynamics (MOND) framework. We calculate the axis ratio of the potential in various models, and find that isopotentials are less spherical in MOND than in CDM potentials. As an application of these models, we predict the escape velocity as a function of the position in the Galaxy. This could be useful in comparing with future data from planned or already-underway kinematic surveys (RAVE, SDSS, SEGUE, SIM, GAIA or the hypervelocity stars survey). In addition, the predicted escape velocity is compared with the recently measured high proper motion velocity of the Large Magellanic Cloud (LMC). To bind the LMC to the Galaxy in a MOND model, while still being compatible with the RAVE-measured local escape speed at the Sun's position, we show that an external field modulus of less than $0.03 a_0$ is needed.Comment: Accepted for publication in MNRAS, 13 pages, 7 figures, 3 table

A Study of the Populations of X-ray Sources in the Small Magellanic Cloud with ASCA

The Advanced Satellite for Cosmology and Astrophysics (ASCA) has made multiple observations of the Small Magellanic Cloud (SMC). X-ray mosaic images in the soft (0.7--2.0 keV) and hard (2.0--7.0 keV) bands are separately constructed, and the latter provides the first hard X-ray view of the SMC. We extract 39 sources from the two-band images with a criterion of S/N>5, and conduct timing and spectral analyses for all of these sources. Coherent pulsations are detected from 12 X-ray sources; five of which are new discoveries. Most of the 12 X-ray pulsars are found to exhibit long-term flux variabilities, hence they are likely to be X-ray binary pulsars (XBPs). On the other hand, we classify four supernova remnants (SNRs) as thermal SNRs, because their spectra exhibit emission lines from highly ionized atoms. We find that XBPs and thermal SNRs in the SMC can be clearly separated by their hardness ratio (the ratio of the count rate between the hard and soft bands). Using this empirical grouping, we find many XBP candidates in the SMC, although no pulsations have yet been detected from these sources. Possible implications on the star-formation history and evolution of the SMC are presented by a comparison of the source populations in the SMC and our Galaxy.Comment: 11 pages, 39 Figures, to be published in ApJ Supplement. Tables (body and figures also) are available at http://www-cr.scphys.kyoto-u.ac.jp/member/jun/job

Magellanic Cloud Structure from Near-IR Surveys II: Star Count Maps and the Intrinsic Elongation of the LMC

I construct a near-IR star count map of the LMC and demonstrate, using the viewing angles derived in Paper I, that the LMC is intrinsically elongated. I argue that this is due to the tidal force from the Milky Way. The near-IR data from the 2MASS and DENIS surveys are used to create a star count map of RGB and AGB stars, which is interpreted through ellipse fitting. The radial number density profile is approximately exponential with a scale-length 1.3-1.5 kpc. However, there is an excess density at large radii that may be due to the tidal effect of the Milky Way. The position angle and ellipticity profile converge to PA_maj = 189.3 +/- 1.4 degrees and epsilon = 0.199 +/- 0.008 for r > 5 deg. At large radii there is a drift of the center of the star count contours towards the near side of the plane, which can be undrestood as due to viewing perspective. The fact that PA_maj differes from the line of nodes position angle Theta = 122.5 +/- 8.3 (cf. Paper I) indicates that the LMC disk is not circular, but has an intrinsic ellipticity of 0.31. The LMC is elongated in the general direction of the Galactic center, and is elongated perpendicular to the Magellanic Stream and the velocity vector of the LMC center of mass. This suggests that the elongation of the LMC has been induced by the tidal force of the Milky Way. The position angle of the line of nodes differs from the position angle Theta_max of the line of maximum line of sight velocity gradient: Theta_max - Theta = 20-60 degrees. This could be due to: (a) streaming along non-circular orbits in the elongated disk; (b) uncertainties in the transverse motion of the LMC center of mass; (c) precession and nutation of the LMC disk as it orbits the Milky Way (expected on theoretical grounds). [Abridged]Comment: Astronomical Journal, in press. 34 pages, LaTeX, with 7 PostScript figures. Contains minor revisions with respect to previously posted version. Check out http://www.stsci.edu/~marel/lmc.html for a large scale (23x21 degree) stellar number-density image of the LMC constructed from RGB and AGB stars in the 2MASS and DENIS surveys. The paper is available with higher resolution color figures from http://www.stsci.edu/~marel/abstracts/abs_R32.htm

Constraints on Intervening Stellar Populations Toward the Large Magellanic Cloud

The suggestion by Zaritsky & Lin that a vertical extension of the red clump feature in color-magnitude diagrams of the Large Magellanic Cloud (LMC) is consistent with a significant population of foreground stars to the LMC that could account for the observed microlensing optical depth has been challenged by various investigators. We respond by (1) examining each of the challenges presented and (2) presenting new photometric and spectroscopic data. We conclude that although the CMD data do not mandate the existence of a foreground population, they are entirely consistent with a foreground population associated with the LMC that contributes significantly (~ 50%) to the observed microlensing optical depth. From our new data, we conclude that <~ 40% of the VRC stars are young, massive red clump stars because (1) synthetic color-magnitude diagrams created using the star formation history derived indepdently from HST data suggest that < 50% of the VRC stars are young, massive red clump stars, (2) the angular distribution of the VRC stars is more uniform than that of the young (age < 1 Gyr) main sequence stars, and (3) the velocity dispersion of the VRC stars in the region of the LMC examined by ZL is inconsistent with the expectation for a young disk population. Each of these arguments is predicated on assumptions and the conclusions are uncertain. Therefore, an exact determination of the contribution to the microlensing optical depth by the various hypothesized foreground populations, and the subsequent conclusions regarding the existence of halo MACHOs, requires a detailed knowledge of many complex astrophysical issues, such as the IMF, star formation history, and post-main sequence stellar evolution. (abridged)Comment: Scheduled for publication in AJ in May 199

A New Look at the Kinematics of Neutral Hydrogen in the Small Magellanic Cloud

We have used the latest HI observations of the Small Magellanic Cloud (SMC), obtained with the Australia Telescope Compact Array and the Parkes telescope, to re-examine the kinematics of this dwarf, irregular galaxy. A large velocity gradient is found in the HI velocity field with a significant symmetry in iso-velocity contours, suggestive of a differential rotation. A comparison of HI data with the predictions from tidal models for the SMC evolution suggests that the central region of the SMC corresponds to the central, disk- or bar-like, component left from the rotationally supported SMC disk prior to its last two encounters with the Large Magellanic Cloud. In this scenario, the velocity gradient is expected as a left-over from the original, pre-encounter, angular momentum. We have derived the HI rotation curve and the mass model for the SMC. This rotation curve rapidly rises to about 60 km/s up to the turnover radius of ~3 kpc. A stellar mass-to-light ratio of about unity is required to match the observed rotation curve, suggesting that a dark matter halo is not needed to explain the dynamics of the SMC. A set of derived kinematic parameters agrees well with the assumptions used in tidal theoretical models that led to a good reproduction of observational properties of the Magellanic System. The dynamical mass of the SMC, derived from the rotation curve, is 2.4x10^9 Msolar.Comment: To appear in ApJ, March 20 2004, 11 figure

Magellanic Cloud Structure from Near-IR Surveys I: The Viewing Angles of the LMC

We present a detailed study of the viewing angles of the LMC disk plane. We find that our viewing direction differs considerably from the commonly accepted values, which has important implications for the structure of the LMC. The discussion is based on an analysis of spatial variations in the apparent magnitude of features in the near-IR color-magnitude diagrams extracted from the DENIS and 2MASS surveys. Sinusoidal brightness variations with a peak-to-peak amplitude of approximately 0.25 mag are detected as function of position angle, for both AGB and RGB stars. This is naturally interpreted as the result of distance variations, due to one side of the LMC plane being closer to us than the opposite side. The best fitting geometric model of an inclined plane yields an inclination angle i = 34.7 +/- 6.2 degrees and line-of-nodes position angle Theta = 122.5 +/- 8.3 degrees. There is tentative evidence that the LMC disk plane may be warped. Traditional methods to estimate the position angle of the line of nodes have used either the major axis position angle Theta_maj of the spatial distribution of tracers on the sky, or the position angle Theta_max of the line of maximum gradient in the velocity field, given that for a circular disk Theta_maj = Theta_max = Theta. The present study does not rely on the assumption of circular symmetry, and is considerably more accurate than previous studies of its kind. We find that the actual position angle of the line of nodes differs considerably from both Theta_maj and Theta_max, for which measurements have fallen in the range 140-190 degrees. This indicates that the intrinsic shape of the LMC disk is not circular, but elliptical, as discussed further in Paper II. [Abridged]Comment: Astronomical Journal, in press. 44 pages, LaTeX, with 8 PostScript figures. Contains minor revisions with respect to previously posted version. Check out http://www.stsci.edu/~marel/lmc.html for a large scale (23x21 degree) stellar number-density image of the LMC constructed from RGB and AGB stars in the 2MASS and DENIS surveys. The paper is available with higher resolution figures from http://www.stsci.edu/~marel/abstracts/abs_R31.htm

A consistent quantum model for continuous photodetection processes

We are modifying some aspects of the continuous photodetection theory, proposed by Srinivas and Davies [Optica Acta 28, 981 (1981)], which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the `annihilation' and `creation' operators that enter in the photocount superoperators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to Srinivas and Davies precepts, but also avoids some weird result appearing when previous definitions are used.Comment: 12 pages, 4 figure

Adult infiltrating gliomas with WHO 2016 integrated diagnosis: additional prognostic roles of ATRX and TERT

The “integrated diagnosis” for infiltrating gliomas in the 2016 revised World Health Organization (WHO) classification of tumors of the central nervous system requires assessment of the tumor for IDH mutations and 1p/19q codeletion. Since TERT promoter mutations and ATRX alterations have been shown to be associated with prognosis, we analyzed whether these tumor markers provide additional prognostic information within each of the five WHO 2016 categories. We used data for 1206 patients from the UCSF Adult Glioma Study, the Mayo Clinic and The Cancer Genome Atlas (TCGA) with infiltrative glioma, grades II-IV for whom tumor status for IDH, 1p/19q codeletion, ATRX, and TERT had been determined. All cases were assigned to one of 5 groups following the WHO 2016 diagnostic criteria based on their morphologic features, and IDH and 1p/19q codeletion status. These groups are: (1) Oligodendroglioma, IDH-mutant and 1p/19q-codeleted; (2) Astrocytoma, IDH-mutant; (3) Glioblastoma, IDH-mutant; (4) Glioblastoma, IDH-wildtype; and (5) Astrocytoma, IDH-wildtype. Within each group, we used univariate and multivariate Cox proportional hazards models to assess associations of overall survival with patient age at diagnosis, grade, and ATRX alteration status and/or TERT promoter mutation status. Among Group 1 IDH-mutant 1p/19q-codeleted oligodendrogliomas, the TERT-WT group had significantly worse overall survival than the TERT-MUT group (HR: 2.72, 95% CI 1.05–7.04, p&nbsp;=&nbsp;0.04). In both Group 2, IDH-mutant astrocytomas and Group 3, IDH-mutant glioblastomas, neither TERT mutations nor ATRX alterations were significantly associated with survival. Among Group 4, IDH-wildtype glioblastomas, ATRX alterations were associated with favorable outcomes (HR: 0.36, 95% CI 0.17–0.81, p&nbsp;=&nbsp;0.01). Among Group 5, IDH-wildtype astrocytomas, the TERT-WT group had significantly better overall survival than the TERT-MUT group (HR: 0.48, 95% CI 0.27–0.87), p&nbsp;=&nbsp;0.02). Thus, we present evidence that in certain WHO 2016 diagnostic groups, testing for TERT promoter mutations or ATRX alterations may provide additional useful prognostic information

The Magellanic Stream, High-Velocity Clouds and the Sculptor Group

The Magellanic Stream is a 100\deg x 10\deg filament of gas which lies within the Galactic halo and contains ~ 2 x 10^8 \Msun of neutral hydrogen. We present data from the HI Parkes All Sky Survey (HIPASS) in the first complete survey of the entire Magellanic Stream and its surroundings. We also present a summary of the reprocessing techniques used to recover large-scale structure in the Stream. The Stream properties revealed include: bifurcation along the main Stream filament; dense, isolated clouds which follow the entire length of the Stream; head-tail structures; and a complex filamentary web at the head where gas is being freshly stripped away from the Small Magellanic Cloud and the Bridge. Debris which appears to be of Magellanic origin extends out to 20\deg from the main Stream filaments. The large number of elongated Stream clouds suggests the presence of shearing motions within the Stream, arising from tidal forces or interaction with the tenuous Galactic halo. Clouds along the sightline to the less distant half of the Sculptor Group, show anomalous properties. We argue that these clouds represent halo material, and are not distant Sculptor Group clouds. This result has significant implications for the hypothesis that there might exist distant, massive HVCs within the Local Group. (abridged