258 research outputs found
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
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
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
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
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