118984721
Gravitational radiation from rotational core collapse: Effects of magnetic fields and realistic equations of state
We perform a series of two-dimensional, axisymmetric, magnetohydrodynamic simulations of the rotational collapse of a supernova core. In order to calculate the waveforms of the gravitational wave, we derive the quadrupole formula including the contributions from the electromagnetic fields. Recent stellar evolution calculations imply that the magnetic fields of the toroidal components are much stronger than those of the poloidal ones at the presupernova stage. Thus, we systematically investigate the effects of the toroidal magnetic fields on the amplitudes and waveforms. Furthermore, we employ the two kinds of the realistic equation of states, which are often used in the supernova simulations. Then, we investigate the effects of the equation of states on the gravitational wave signals. With these computations, we find that the peak amplitudes are lowered by an order of 10% for the models with the strongest toroidal magnetic fields. However, the peak amplitudes are mostly within sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we point out that the amplitudes of second peaks are still within the detection limit of the first LIGO for the source, although the characteristics of second peaks are reduced by the magnetic fields. We stress the importance of the detection, since it will give us information about the angular momentum distribution of massive evolved stars. When we compare the gravitational waves from the two realistic equation of states, significant differences are not found, except that the typical frequencies of the gravitational wave become slightly higher for the softer equation of state.
122604041
NEUTRINOS FROM PROTONEUTRON STARS
We performed numerical simulations of the quasistatic evolution of protoneutron star with neutrino transfer using multigroup flux limited diffusion scheme. The second half of the supernova neutrinos are emitted in this stage. We found 1) the flux decays rapidly and its mean energy falls below j/e's mean energy at the late stage, 2) Pe's carry out energy of about 24% of the total energy emitted in this cooling phase, and 3) the time-integrated energy spectra of u^s and v^s can be roughly fitted by the Fermi-Dirac spectra with positive chemical potentials while those of the other neutrinos can be fitted by MaxwellBoltzmann spectra. These results suggest that the total energy of the neutrino burst from SN1987A was overestimated if one assumed that the Pe's spectrum is the Fermi-Dirac one with a vanishing chemical potential and that all species of neutrinos contribute equally.
122249200
Constraining neutrino oscillation parameters with future observations of supernova neutrinos by various types of detectors
We evaluate the potential for constraining neutrino oscillation parameters with future observations of supernova neutrinos. For some selected oscillation parameters, we calculate the expected energy spectra and angular distributions of neutrino events in various detectors (Super-Kamiokande, ICARUS, KamLAND and IceCube) for an assumed galactic core-collapse supernova. We investigate to what extent the oscillation parameters could be constrained using χ2 analysis when the expected events are really observed.
119251795
Global Simulations of Magnetorotational Instability in the Collapsed Core of a Massive Star
We performed the first global numerical simulations of magnetorotational instability from a sub-magnetar-class seed magnetic field in core-collapse supernovae. As a result of axisymmetric ideal MHD simulations, we found that the magnetic field is greatly amplified to magnetar-class strength. In the saturation phase, a substantial part of the core is dominated by turbulence, and the magnetic field possesses dominant large-scale components, comparable to the size of a proto-neutron star. A pattern of coherent channel flows, which generally appears during the exponential growth phase in previous local simulations, is not observed in our global simulations. While the approximate convergence in the exponential growth rate is attained by increasing spatial resolution, that of the saturation magnetic field is not achieved due to still large numerical diffusion. Although the effect of the magnetic field on the dynamics is found to be mild, a simulation with a high enough resolution might result in a larger impact.
118715119
EFFECTS OF RESISTIVITY ON MAGNETIZED CORE-COLLAPSE SUPERNOVAE
We studied the role of turbulent resistivity in the core-collapse of a strongly magnetized massive star, carrying out two-dimensional resistive-MHD simulations. Three cases with different initial strengths of magnetic field and rotation are investigated: (1) a strongly magnetized rotating core, (2) a moderately magnetized rotating core, and (3) a very strongly magnetized non-rotating core. In each case, one ideal-MHD model and two resistive-MHD models are computed. As a result of these computations, each model shows an eruption of matter assisted by magnetic acceleration (and also by centrifugal acceleration in the rotating cases). We found that resistivity attenuates the explosion in cases 1 and 2, while it enhances the explosion in case 3. We also found that in the rotating cases, the main mechanisms for the amplification of a magnetic field in the post-bounce phase are an outward advection of the magnetic field and a twisting of poloidal magnetic field lines by differential rotation, which are somewhat dampened down with the presence of resistivity. Although magnetorotational instability seems to occur in the rotating models, it plays only a minor role in magnetic field amplification. Another impact of resistivity is that on the aspect ratio. In the rotating cases, a large aspect ratio of the ejected matter, >2.5, attained in an ideal-MHD model is reduced to some extent in a resistive model. These results indicate that resistivity possibly plays an important role in the dynamics of strongly magnetized supernovae.
118908804
Multigroup simulation of protoneutron star cooling and neutrino spectra
15095584
A local formulation of lattice Wess-Zumino model with exact U(1)R symmetry
A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson fermions. In perturbation theory, our formulation is equivalent to the formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is, however, free from a singular nature of the latter formulation due to an additional auxiliary chiral supermultiplet on a lattice. The model posssesses an exact U(1)R symmetry as a supersymmetric counterpart of the L?scher lattice chiral U(1) symmetry. A restration of the supersymmetric Ward-Takahashi identity in the continuum limit is analyzed in renormalized perturbation theory. In the one-loop level, a supersymmetric continuum limit is ensured by suitably adjusting a coefficient of a single local term *. The non-renormalization theorem holds to this order of perturbation theory. In higher orders, on the other hand, coefficents of local terms with dimension ? 4 that are consistent with the U(1)R symmetry have to be adjusted for a supersymmetric continuum limit. The origin of this complexicity in higher-order loops is clarified on the basis of the Reisz power counting theorem. Therefore, from a view point of supersymmetry, the present formulation is not quite better than a lattice Wess-Zumino model formulated by using Wilson fermions, although a number of coefficients which require adjustment is much less due to the exact U(1)R symmetry. We also comment on an exact non-linear fermionic symmetry which corresponds to the one studied by Bonini and Feo; an existence of this exact symmetry itself does not imply a restoration of supersymmetry in the continuum limit without any adjustment of parameters.
492141
Manifestly Gauge Covariant Treatment of Lattice Chiral Fermion
We propose a lattice formulation of the chiral fermion which maximally respects the gauge symmetry and simultaneously is free of the unwanted species doublers. This is achieved by directly dealing with the lattice fermion propagator and the composite operators, rather than the lattice action and the fermionic determinant. The latter is defined as a functional integral of the expectation value of the gauge current operator with respect to the background gauge field. The gauge anomaly is characterized as a non-integrability of this integration process and, the determinant is defined only for anomaly free cases. Gauge singlet operators on the other hand are always regularized gauge invariantly. Some perturbative check is performed to confirm the gauge covariance and the absence of the doublers. This formulation can be applied rather straightforwardly to numerical simulations in the quenched approximation. ⋆ e-mail: hsuzuki@mito.ipc.ibaraki.ac.jp The chiral fermion on the lattice has refused the manifestly gauge invariant formulation [1]. There even exists the no-go theorem [2] for such an endeavor. In the continuum counterpart, the chiral fermion exhibits a curious phenomenon called the quantum anomaly [3], or more definitely the gauge anomaly [4]. The difficulty in the lattice chiral gauge theory seems to be a rather natural consequence of the gauge anomaly. Suppose that we start from a well regularized partition function or a fermionic determinant defined by a manifestly gauge invariant lattice fermion action. In the continuum limit, the gauge anomaly is realized as a gauge variation of the partition function. Therefore if the fermion content is not free of the gauge anomaly, the partition function is not gauge invariant. But this contradicts with the very gauge invariance of the formulation. There are mainly two possible ways out: One is the appearance of the species doublers which cancels the gauge anomaly [5]. Another is some pathology in the continuum limit such as the non-Lorentz covariance [6]. The trouble of the lattice regularization is that it always regularizes the ultraviolet divergence, even when a gauge invariant regularization is impossible due to the gauge anomaly. From the above reasoning, the appearance of the unwanted doublers are quite natural. But the problem in the conventional approach is of course that the doublers appear even in the anomaly free cases. Presumably, the ideal lattice formulation of the chiral fermion will be the one which distinguishes the anomaly free gauge representations from the anomalous ones. † That unknown lattice action should have a structure that can be written down, for example, for the spinor rep. of SO(4) but not for the fundamental rep. of SU(3), because the latter is anomalous. Such an ideal formulation seems to require a deeper understanding on the origin of the quantum anomaly, which is not available at present. In this article, we simply abandon a direct gauge invariant definition of the † Besides the perturbative anomaly, it should also explain the topological global anomaly [7] because the partition function is ill-defined with this anomaly.
17171161
Observing dynamical supersymmetry breaking with euclidean lattice simulations
A strict positivity of the ground-state energy is a necessary and sufficient condition for spontaneous supersymmetry breaking. This ground-state energy may be directly determined from the expectation value of the Hamiltonian in the functional integral, defined with an antiperiodic temporal boundary condition for all fermionic variables. We propose to use this fact to observe the dynamical spontaneous supersymmetry breaking in Euclidean lattice simulations. If a lattice formulation possesses a manifestly preserved fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological nature of the Witten index. We numerically confirm the validity of our idea in models of supersymmetric quantum mechanics. We further examine the possibility of dynamical supersymmetry breaking in the two-dimensional N =( 2, 2) super Yang-Mills theory with the gauge group SU(2), for which the Witten index is unknown. Although statistical errors are still large, we do not observe positive ground-state energy, at least within one standard deviation. This prompts us to draw a different conclusion from a recent conjectural claim that supersymmetry is dynamically broken in this system.
118158501
Path integrals and quantum anomalies
1. Genesis of quantum anomalies 2. The Feynman path integral and Schwinger's action principle 3. Quantum theory of photons and the phase operator 4. Regularization of field theory and chiral anomalies 5. The Jacobian in path integrals and quantum anomalies 6. Quantum breaking of gauge symmetry 7. The Weyl anomaly and renormalization group 8. Two-dimensional field theory and bosonization 9. Index theorem on the lattice and chiral anomalies 10. Gravitational anomalies 11. Concluding remarks A. Basics of quantum electrodynamics B. Field theory in curved space-time C. References with brief comments
17537098
Supersymmetric gauge anomaly with general homotopic paths
Abstract We use the method of Banerjee, Banerjee and Mitra and minimal homotopy paths to compute the consistent gauge anomaly for several superspace models of SSYM coupled to matter. We review the derivation of the anomaly for N=1 in four dimensions and then discuss the anomaly for two-dimensional models with (2,0) supersymmetry.