An Implicit Lagrangean Code for Spherically Symmetric General Relativistic Hydrodynamics with an Approximate Riemann Solver

An implicit Lagrangian hydrodynamics code for general relativistic spherical collapse is presented. This scheme is based on an approximate linearized Riemann solver (Roe type scheme). This code is aimed especially at the calculation of the late phase of collapse-driven supernovae and the nascent neutron star, where there is a remarkable contrast between the dynamical time scale of the proto-neutron star and the diffusion time scale of neutrinos, without such severe limitation of the Courant condition at the center of the neutron star. Several standard test calculations have been done. Two other adiabatic simulations have also been done in order to test the performance of the code in the context of the collapse-driven supernovae. It is found that the time step can be extended far beyond the Courant limitation at the center of the neutron star. The details of the scheme and the results of these test calculations are discussed.Comment: AASTeX v4.0, 24 pages, 13 figures on request from [email protected], submitted to Ap

Aging in coherent noise models and natural time

Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling property discovered in the observed seismic data are well reproduced by the model. It is also found that the scaling function is given by the $q$-exponential function appearing in nonextensive statistical mechanics, showing power-law decay of event correlation in natural time.Comment: 4 pages and 5 figure

Numerical Study on Stellar Core Collapse and Neutrino Emission: Probe into the Spherically Symmetric Black Hole Progenitors with 3 - 30Msun Iron Cores

The existence of various anomalous stars, such as the first stars in the universe or stars produced by stellar mergers, has been recently proposed. Some of these stars will result in black hole formation. In this study, we investigate iron core collapse and black hole formation systematically for the iron-core mass range of 3 - 30Msun, which has not been studied well so far. Models used here are mostly isentropic iron cores that may be produced in merged stars in the present universe but we also employ a model that is meant for a Population III star and is obtained by evolutionary calculation. We solve numerically the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail under spherical symmetry. As a result, we find that massive iron cores with ~10Msun unexpectedly produce a bounce owing to the thermal pressure of nucleons before black hole formation. The features of neutrino signals emitted from such massive iron cores differ in time evolution and spectrum from those of ordinary supernovae. Firstly, the neutronization burst is less remarkable or disappears completely for more massive models because the density is lower at the bounce. Secondly, the spectra of neutrinos, except the electron type, are softer owing to the electron-positron pair creation before the bounce. We also study the effects of the initial density profile, finding that the larger the initial density gradient is, the more steeply the neutronization burst declines. Further more, we suggest a way to probe into the black hole progenitors from the neutrino emission and estimate the event number for the currently operating neutrino detectors.Comment: 33 pages, 13 figures, accepted by Ap

Alfven Wave-Driven Supernova Explosion

We investigate the role of Alfven waves in the core-collapse supernova (SN) explosion. We assume that Alfven waves are generated by convections inside a proto-neutron star (PNS) and emitted from its surface. Then these waves propagate outwards, dissipate via nonlinear processes, and heat up matter around a stalled prompt shock. To quantitatively assess the importance of this process for the revival of the stalled shock, we perform 1D time-dependent hydrodynamical simulations, taking into account the heating via the dissipation of Alfven waves that propagate radially outwards along open flux tubes. We show that the shock revival occurs if the surface field strength is larger than ~2e15 G and if the amplitude of velocity fluctuation at the PNS surface is larger than 20% of the local sound speed. Interestingly, the Alfven wave mechanism is self-regulating in the sense that the explosion energy is not very sensitive to the surface field strength and initial amplitude of Alfven waves as long as they are larger than the threshold values given above.Comment: 7 pages, 3 figures embedded, submitted to Ap

Nonextensive thermodynamic relations

The generalized zeroth law of thermodynamics indicates that the physical temperature in nonextensive statistical mechanics is different from the inverse of the Lagrange multiplier, beta. This leads to modifications of some of thermodynamic relations for nonextensive systems. Here, taking the first law of thermodynamics and the Legendre transform structure as the basic premises, it is found that Clausius definition of the thermodynamic entropy has to be appropriately modified, and accordingly the thermodynamic relations proposed by Tsallis, Mendes and Plastino [Physica A 261 (1998) 534] are also to be rectified. It is shown that the definition of specific heat and the equation of state remain form invariant. As an application, the classical gas model is reexamined and, in marked contrast with the previous result obtained by Abe [Phys. Lett. A 263 (1999) 424: Erratum A 267 (2000) 456] using the unphysical temperature and the unphysical pressure, the specific heat and the equation of state are found to be similar to those in ordinary extensive thermodynamics.Comment: 17 pages. The discussion about the Legendre transform structure is modified and some additional comments are mad

Entropy on the von Neumann lattice and its evaluation

Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the position and momentum observables in the discrete subset of the phase space. Evaluating for a class of the coherent states, it is shown that this entropy takes a stationary value for the ground state, modulo a unit cell of the lattice in such a class. This value for the ground state depends on the ratio of the position lattice spacing and the momentum lattice spacing. It is found that its minimum is realized for the perfect square lattice, i.e., absence of squeezing. Numerical evaluation of this minimum gives 1.386....Comment: 14 pages, no figures; J. Phys. A, in pres