Inequivalent Quantizations of the N = 3 Calogero model with Scale and Mirror-S_3 Symmetry

We study the inequivalent quantizations of the N = 3 Calogero model by separation of variables, in which the model decomposes into the angular and the radial parts. Our inequivalent quantizations respect the ` mirror-S_3\rq\ invariance (which realizes the symmetry under the cyclic permutations of the particles) and the scale invariance in the limit of vanishing harmonic potential. We find a two-parameter family of novel quantizations in the angular part and classify the eigenstates in terms of the irreducible representations of the S_3 group. The scale invariance restricts the quantization in the radial part uniquely, except for the eigenstates coupled to the lowest two angular levels for which two types of boundary conditions are allowed independently from all upper levels. It is also found that the eigenvalues corresponding to the singlet representations of the S_3 are universal (parameter-independent) in the family, whereas those corresponding to the doublets of the S_3 are dependent on one of the parameters. These properties are shown to be a consequence of the spectral preserving SU(2) (or its subrgoup U(1)) transformations allowed in the family of inequivalent quantizations.Comment: 24 pages, LaTe

A New Estimation of Mass Accumulation Efficiency in Helium Shell Flashes toward Type Ia Supernova Explosions

We have calculated the mass accumulation efficiency during helium shell flashes to examine whether or not a carbon-oxygen white dwarf (C+O WD) grows up to the Chandrasekhar mass limit to ignite a Type Ia supernova explosion. It has been frequently argued that luminous super-soft X-ray sources and symbiotic stars are progenitors of SNe Ia. In such systems, a C+O WD accretes hydrogen-rich matter from a companion and burns hydrogen steadily on its surface. The WD develops a helium layer underneath the hydrogen-rich envelope and undergoes periodic helium shell flashes. Using OPAL opacity, we have reanalyzed a full cycle of helium shell flashes on a 1.3 M_\odot C+O WD and confirmed that the helium envelope of the WD expands to blow a strong wind. A part of the accumulated matter is lost by the wind. The mass accumulation efficiency is estimated as \eta_{He} = -0.175 (\log \dot M + 5.35)^2 + 1.05, for -7.3 < \log \dot M < -5.9, where the mass accretion rate \dot M is in units of M_\odot yr^{-1}. In relatively high mass accretion rates as expected in recent SN Ia progenitor models, the mass accumulation efficiency is large enough for C+O WDs to grow to the Chandrasekhar mass, i.e., \eta_{He} = 0.9 for \log \dot M = -6.3, and \eta_{He}=0.57 for \log \dot M = -7.0. The wind velocity (\sim 1000 km/s) is much faster than the orbital velocity of the binary (< 300 km/s) and therefore, the wind cannot be accelerated further by the companion's motion.Comment: 11 pages including 4 eps-files, accepted for publication in ApJ Letter

A Modeling of the Super-Eddington Luminosity in Nova Outbursts: V1974 Cygni

We have modeled nova light curves exceeding the Eddington luminosity. It has been suggested that a porous structure develops in nova envelopes during the super Eddington phase and the effective opacity is much reduced for such a porous atmosphere. Based on this reduced opacity model, we have calculated envelope structures and light curves of novae. The optically thick wind model is used to simulate nova winds. We find that the photospheric luminosity and the wind mass-loss rate increase inversely proportional to the reducing factor of opacities, but the wind velocity hardly changes. We also reproduce the optical light curve of V1974 Cygni (Nova Cygni 1992) in the super-Eddington phase, which lasts 13 days from the optical peak 1.7 mag above the Eddington luminosity.Comment: 8 pages, 4 figures, to appear in ApJ

Evolution of Rotating Accreting White Dwarfs and the Diversity of Type Ia Supernovae

Type Ia supernovae (SNe Ia) have relatively uniform light curves and spectral evolution, which make SNe Ia useful standard candles to determine cosmological parameters. However, the peak brightness is not completely uniform, and the origin of the diversity has not been clear. We examine whether the rotation of progenitor white dwarfs (WDs) can be the important source of the diversity of the brightness of SNe Ia. We calculate the structure of rotating WDs with an axisymmetric hydrostatic code. The diversity of the mass induced by the rotation is ~0.08 Msun and is not enough to explain the diversity of luminosity. However, we found the following relation between the initial mass of the WDs and their final state; i.e., a WD of smaller initial mass will rotate more rapidly before the supernova explosion than that of larger initial mass. This result might explain the dependence of SNe Ia on their host galaxies.Comment: 7 pages, 6 figure

Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete

A planar calculus for infinite index subfactors

We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.Comment: 56 pages, many figure

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction

A Theoretical Light-Curve Model for the Recurrent Nova V394 Coronae Austrinae

A theoretical light curve for the 1987 outburst of V394 Coronae Austrinae (V394 CrA) is modeled to obtain various physical parameters of this recurrent nova. We then apply the same set of parametersto a quiescent phase and confirm that these parameters give a unified picture of the binary. The early visual light curve (1-10 days after the optical maximum) is well reproduced by a thermonuclear runaway model on a very massive WD close to the Chandrasekhar limit (1.37 +- 0.01 M_sun). The ensuing plateau phase (10-30 days) is also reproduced by the combination of a slightly irradiated MS and a fully irradiated flaring-up disk with a radius ~1.4 times the Roche lobe size. The best fit parameters are the WD mass 1.37 M_sun, the companion mass 1.5 M_sun (0.8-2.0 M_sun is acceptable), the inclination angle of the orbit i~65-68 degree, and the flaring-up rim ~0.30 times the disk radius. The envelope mass at the optical peak is estimated to be ~6 x 10^{-6} M_sun, which indicates an average mass accretion rate of 1.5 x 10^{-7} M_sun yr^{-1} during the quiescent phase between the 1949 and 1987 outbursts. In the quiescent phase, the observed light curve can be reproduced with a disk size of 0.7 times the Roche lobe size and a rather slim thickness of 0.05 times the accretion disk size at the rim. About 0.5 mag sinusoidal variation of the light curve requires the mass accretion rate higher than ~1.0 x 10^{-7} M_sun yr^{-1}, which is consistent with the above estimation from the 1987 outburst. These newly obtained quantities are exactly the same as those predicted in a new progenitor model of Type Ia supernovae.Comment: 9 pages including 4 figures, to appear in the Astrophysical Journal, Part