Symmetries of Discrete Dynamical Systems Involving Two Species

The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to 10 dimensional. The equations can describe the interaction of two long molecular chains, each involving one type of atoms.Comment: 40 pages, no figures, typed in AMS-LaTe

Optical Emission from Aspherical Supernovae and the Hypernova SN 1998bw

A fully 3D Monte Carlo scheme is applied to compute optical bolometric light curves for aspherical (jet-like) supernova explosion models. Density and abundance distributions are taken from hydrodynamic explosion models, with the energy varied as a parameter to explore the dependence. Our models show initially a very large degree ($\sim 4$ depending on model parameters) of boosting luminosity toward the polar ($z$) direction relative to the equatorial ($r$) plane, which decreases as the time of peak is approached. After the peak, the factor of the luminosity boost remains almost constant ($\sim 1.2$) until the supernova enters the nebular phase. This behavior is due mostly to the aspherical $^{56}$Ni distribution in the earlier phase and to the disk-like inner low-velocity structure in the later phase. Also the aspherical models yield an earlier peak date than the spherical models, especially if viewed from near the z-axis. Aspherical models with ejecta mass \sim 10\Msun are examined, and one with the kinetic energy of the expansion $\sim 2 \pm 0.5 \times 10^{52}$ ergs and a mass of $^{56}$Ni \sim 0.4\Msun yields a light curve in agreement with the observed light curve of SN 1998bw (the prototypical hyper-energetic supernova). The aspherical model is also at least qualitatively consistent with evolution of photospheric velocities, showing large velocities near the z-axis, and with a late-phase nebular spectrum. The viewing angle is close to the z-axis, strengthening the case for the association of SN 1998bw with the gamma ray burst GRB980425.Comment: Accepted by the Astrophysical Journal. 28 pages, 14 figure

Subaru and Keck Observations of the Peculiar Type Ia Supernova 2006gz at Late Phases

Recently, a few peculiar Type Ia supernovae (SNe) that show exceptionally large peak luminosity have been discovered. Their luminosity requires more than 1 Msun of 56Ni ejected during the explosion, suggesting that they might have originated from super-Chandrasekhar mass white dwarfs. However, the nature of these objects is not yet well understood. In particular, no data have been taken at late phases, about one year after the explosion. We report on Subaru and Keck optical spectroscopic and photometric observations of the SN Ia 2006gz, which had been classified as being one of these "overluminous" SNe Ia. The late-time behavior is distinctly different from that of normal SNe Ia, reinforcing the argument that SN 2006gz belongs to a different subclass than normal SNe Ia. However, the peculiar features found at late times are not readily connected to a large amount of 56Ni; the SN is faint, and it lacks [Fe II] and [Fe III] emission. If the bulk of the radioactive energy escapes the SN ejecta as visual light, as is the case in normal SNe Ia, the mass of 56Ni does not exceed ~ 0.3 Msun. We discuss several possibilities to remedy the problem. With the limited observations, however, we are unable to conclusively identify which process is responsible. An interesting possibility is that the bulk of the emission might be shifted to longer wavelengths, unlike the case in other SNe Ia, which might be related to dense C-rich regions as indicated by the early-phase data. Alternatively, it might be the case that SN 2006gz, though peculiar, was actually not substantially overluminous at early times.Comment: 8 pages, 6 figures, 4 tables. Accepted for publication in The Astrophysical Journa

Phase ambiguity of the threshold amplitude in pp -> pp\pi^0

Measurements of spin observables in pp -> {\vec p}{\vec p}\pi^0 are suggested to remove the phase ambiguity of the threshold amplitude. The suggested measurements complement the IUCF data on {\vec p}{\vec p} -> pp\pi^0 to completely determine all the twelve partial wave amplitudes, taken into consideration by Mayer et.al. [15] and Deepak, Haidenbauer and Hanhart [20].Comment: 4 pages, 1 table

Nebular Spectra of SN 1998bw Revisited: Detailed Study by One and Two Dimensional Models

Refined one- and two-dimensional models for the nebular spectra of the hyper-energetic Type Ic supernova (SN) 1998bw, associated with the gamma-ray burst GRB980425, from 125 to 376 days after B-band maximum are presented. One dimensional, spherically symmetric spectrum synthesis calculations show that reproducing features in the observed spectra, i.e., the sharply peaked [OI] 6300\AA doublet and MgI] 4570\AA emission, and the broad [FeII] blend around 5200\AA, requires the existence of a high-density O-rich core expanding at low velocities (\lsim 8,000 km s$^{-1}$) and of Fe-rich material moving faster than the O-rich material. Synthetic spectra at late phases from aspherical (bipolar) explosion models are also computed with a two-dimensional spectrum synthesis code. The above features are naturally explained by the aspherical model if the explosion is viewed from a direction close to the axis of symmetry ($\sim 30^{\rm o}$), since the aspherical model yields a high-density O-rich region confined along the equatorial axis. By examining a large parameter space (in energy and mass), our best model gives following physical quantities: the kinetic energy $E_{51} \equiv E_{\rm K}/10^{51}$ ergs \gsim 8 - 12 and the main-sequence mass of the progenitor star M_{\rm ms} \gsim 30 - 35 \Msun. The temporal spectral evolution of SN 1998bw also indicates mixing among Fe-, O-, and C-rich regions, and highly clumpy structure.Comment: 38 pages, 22 figures. ApJ, 640 (01 April 2006 issue), in pres

The final fate of instability of Reissner-Nordstr\"om-anti-de Sitter black holes by charged complex scalar fields

We investigate instability of 4-dimensional Reissner-Nordstr\"om-anti-de Sitter (RN-AdS$_4$) black holes with various topologies by charged scalar field perturbations. We numerically find that the RN-AdS$_4$ black holes become unstable against the linear perturbations below a critical temperature. It is analytically shown that charge extraction from the black holes occurs during the unstable evolution. To explore the end state of the instability, we perturbatively construct static black hole solutions with the scalar hair near the critical temperature. It is numerically found that the entropy of the hairly black hole is always larger than the one of the unstable RN-AdS$_4$ black hole in the microcanonical ensemble. Our results support the speculation that the black hole with charged scalar hair always appears as the final fate of the instability of the RN-AdS$_4$ black hole.Comment: 9 pages, 4 figures. To appear in PR

Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere

In the previous papers, we studied the 't Hooft-Polyakov (TP) monopole configurations in the U(2) gauge theory on the fuzzy 2-sphere,and showed that they have nonzero topological charge in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provide a meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that the configuration space can be classified into the topological sectors. We further calculate the spectrum of the GW Dirac operator in the TP monopole backgrounds, and consider the index theorem in these cases.Comment: Latex2e, 37 pages, 3 figure

Domain Wall Dynamics in Brane World and Non-singular Cosmological Models

We study brane cosmology as 4D (4-dimensional) domain wall dynamics in 5D bulk spacetime. For a generic 5D bulk with 3D maximal symmetry, we derive the equation of motion of a domain wall and find that it depends on mass function of the bulk spacetime and the energy-momentum conservation in a domain wall is affected by a lapse function in the bulk. Especially, for a bulk spacetime with non-trivial lapse function, energy of matter field on the domain wall goes out or comes in from the bulk spacetime. Applying our result to the case with SU(2) gauge bulk field, we obtain a singularity-free universe in brane world scenario, that is, not only a big bang initial singularity of the brane is avoided but also a singularity in a 5D bulk does not exist.Comment: 12 pages, 11 figures, submitted to PRD. One reference is added. (v2

Mass of perfect fluid black shells

The spherically symmetric singular perfect fluid shells are considered for the case of their radii being equal to the event horizon (the black shells). We study their observable masses, depending at least on the three parameters, viz., the square speed of sound in the shell, instantaneous radial velocity of the shell at a moment when it reaches the horizon, and integration constant related to surface mass density. We discuss the features of black shells depending on an equation of state.Comment: 1 figure, LaTeX; final version + FA