Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane

We study α-harmonic functions on the complement of the sphere and on the complement of the hyperplane in Euclidean spaces of dimension bigger than one, for α ∈ (1,2). We describe the corresponding Hardy spaces and prove the Fatou theorem for α-harmonic functions. We also give explicit formulas for the Martin kernel of the complement of the sphere and for the harmonic measure, Green function and Martin kernel of the complement of the hyperplane for the symmetric α-stable Lévy processes. Some extensions for the relativistic α-stable processes are discussed

Hardy spaces for the Laplacian with lower order perturbations

We consider Hardy spaces of functions harmonic on smooth domains in Euclidean spaces of dimension greater than two with respect to the Laplacian perturbed by lower order terms. We deal with the gradient and Schrödinger perturbations under appropriate Kato conditions. In this context we show the usual correspondence between the harmonic Hardy spaces and the Lp spaces (or the space of finite measures if p=1) on the boundary. To this end we prove the uniform comparability of the respective harmonic measures for a class of approximating domains and the relative Fatou theorem for harmonic functions of the perturbed operator

Law of corresponding state for the transport properties of molten salts

Corresponding state theory for transport properties of ionic fused alkali salt

Re-examination of the possible tidal stream in front of the LMC

It has recently been suggested that the stars in a vertical extension of the red clump feature seen in LMC color-magnitude diagrams could belong to a tidal stream of material located in front of that galaxy. If this claim is correct, this foreground concentration of stars could contribute significantly to the rate of gravitational microlensing events observed in the LMC microlensing experiments. Here we present radial velocity measurements of stars in this so-called ``vertical red clump'' (VRC) population. The observed stellar sample, it transpires, has typical LMC kinematics. It is shown that it is improbable that an intervening tidal stream should have the same distribution of radial velocities as the LMC, which is consistent with an earlier study that showed that the VRC feature is more likely a young stellar population in the main body of that galaxy. However, the kinematic data do not discriminate against the possibility that the VRC is an LMC halo population.Comment: 10 pages, 3 figures, 1 table. Accepted for publication in ApJ

A comparison between Pa alpha and H alpha emission: The relation between HII region mean reddening, local gas density and metallicity

We measure reddenings to HII regions in NGC 2903, NGC 1512, M51, NGC 4449 and NGC 6946 from Hubble Space Telescope Pa alpha and H alpha images. Extinctions range from A_V ~ 5 - 0 depending upon the galaxy. For the galaxies with HST images in both lines, NGC 2903, NGC 1512 and M51, the Pa alpha and H alpha emission are almost identical in morphology which implies that little emission from bright HII regions is hidden from view by regions of comparatively high extinction. The scatter in the measured extinctions is only +- 0.5 mag. We compare the reddenings we measure in five galaxies using the Pa alpha to H alpha ratios to those measured previously from the Balmer decrement in the LMC and as a function of radius in M101 and M51. We find that luminosity weighted mean extinctions of these ensembles of HI regions are correlated with gas surface density and metallicity. The correlation is consistent with the mean extinction depending on dust density where the dust to gas mass ratio scales with the metallicity. This trend is expected if HII regions tend to be located near the mid-plane of a gas disk and emerge from their parent molecular clouds soon after birth. In environments with gas densities below a few hundred Msol/pc^2 star formation rates estimated from integrated line fluxes and mean extinctions are likely to be fairly accurate.Comment: accepted for publication in A

ASCA Observation of the New Transient X-ray Pulsar XTE J0111.2-7317 in the Small Magellanic Cloud

The new transient X-ray pulsar XTE J0111.2-7317 was observed with Advanced Satellite for Cosmology and Astrophysics (ASCA) on 1998 November 18, a few days after its discovery with the Proportional Counter Array onboard the Rossi X-ray Timing Explorer. The source was detected at a flux level of 3.6x10^-10 erg cm^-2 s^-1 in the 0.7--10.0 keV band, which corresponds to the X-ray luminosity of 1.8x10^38 erg s^-1, if a distance of 65 kpc for this pulsar in the Small Magellanic Cloud is assumed. Nearly sinusoidal pulsations with a period of 30.9497 +/- 0.0004 s were unambiguously detected during the ASCA observation. The pulsed fraction is low and slightly energy dependent with average value of \~27%. The energy spectrum shows a large soft excess below ~2 keV when fitted to a simple power-law type model. The soft excess is eliminated if the spectrum is fitted to an ``inversely broken power-law'' model, in which photon indices below and above a break energy of 1.5 keV are 2.3 and 0.8, respectively. The soft excess can also be described by a blackbody or a thermal bremsstrahlung when the spectrum above ~2 keV is modeled by a power-law. In these models, however, the thermal soft component requires a very large emission zone, and hence it is difficult to explain the observed pulsations at energies below 2 keV. A bright state of the source enables us to identify a weak iron line feature at 6.4 keV with an equivalent width of 50 +/- 14 eV. Pulse phase resolved spectroscopy revealed a slight hardening of the spectrum and marginal indication of an increase in the iron line strength during the pulse maximum.Comment: 8 pages, 5 Figures, to be published in ApJ. Also available at http://www-cr.scphys.kyoto-u.ac.jp/member/jun/job

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

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