Dynamics and neutrino signal of black hole formation in non-rotating failed supernovae. I. EOS dependence

We study the black hole formation and the neutrino signal from the gravitational collapse of a non-rotating massive star of 40 Msun. Adopting two different sets of realistic equation of state (EOS) of dense matter, we perform the numerical simulations of general relativistic neutrino-radiation hydrodynamics under the spherical symmetry. We make comparisons of the core bounce, the shock propagation, the evolution of nascent proto-neutron star and the resulting re-collapse to black hole to reveal the influence of EOS. We also explore the influence of EOS on the neutrino emission during the evolution toward the black hole formation. We find that the speed of contraction of the nascent proto-neutron star, whose mass increases fast due to the intense accretion, is different depending on the EOS and the resulting profiles of density and temperature differ significantly. The black hole formation occurs at 0.6-1.3 sec after bounce when the proto-neutron star exceeds its maximum mass, which is crucially determined by the EOS. We find that the average energies of neutrinos increase after bounce because of rapid temperature increase, but at different speeds depending on the EOS. The duration of neutrino emission up to the black hole formation is found different according to the different timing of re-collapse. These characteristics of neutrino signatures are distinguishable from those for ordinary proto-neutron stars in successful core-collapse supernovae. We discuss that a future detection of neutrinos from black-hole-forming collapse will contribute to reveal the black hole formation and to constrain the EOS at high density and temperature.Comment: 32 pages, 33 figures, accepted for publication in Ap

Dynamics and neutrino signal of black hole formation in non-rotating failed supernovae. II. progenitor dependence

We study the progenitor dependence of the black hole formation and its associated neutrino signals from the gravitational collapse of non-rotating massive stars, following the preceding study on the single progenitor model in Sumiyoshi et al. (2007). We aim to clarify whether the dynamical evolution toward the black hole formation occurs in the same manner for different progenitors and to examine whether the characteristic of neutrino bursts is general having the short duration and the rapidly increasing average energies. We perform the numerical simulations by general relativistic neutrino-radiation hydrodynamics to follow the dynamical evolution from the collapse of pre-supernova models of 40Msun and 50Msun toward the black hole formation via contracting proto-neutron stars. For the three progenitor models studied in this paper, we found that the black hole formation occurs in ~0.4-1.5 s after core bounce through the increase of proto-neutron star mass together with the short and energetic neutrino burst. We found that density profile of progenitor is important to determine the accretion rate onto the proto-neutron star and, therefore, the duration of neutrino burst. We compare the neutrino bursts of black hole forming events from different progenitors and discuss whether we can probe clearly the progenitor and/or the dense matter.Comment: 30 pages, 11 figures, accepted for publication in Ap

The r-Process in Neutrino-Driven Winds from Nascent, "Compact" Neutron Stars of Core-Collapse Supernovae

We present calculations of r-process nucleosynthesis in neutrino-driven winds from the nascent neutron stars of core-collapse supernovae. A full dynamical reaction network for both the alpha-rich freezeout and the subsequent r-process is employed. The physical properties of the neutrino-heated ejecta are deduced from a general relativistic model in which spherical symmetry and steady flow are assumed. Our results suggest that proto-neutron stars with a large compaction ratio provide the most robust physical conditions for the r-process. The third peak of the r-process is well reproduced in the winds from these ``compact'' proto-neutron stars even for a moderate entropy, \sim 100-200 N_A k, and a neutrino luminosity as high as \sim 10^{52} ergs s^{-1}. This is due to the short dynamical timescale of material in the wind. As a result, the overproduction of nuclei with A \lesssim 120 is diminished (although some overproduction of nuclei with A \approx 90 is still evident). The abundances of the r-process elements per event is significantly higher than in previous studies. The total-integrated nucleosynthesis yields are in good agreement with the solar r-process abundance pattern. Our results have confirmed that the neutrino-driven wind scenario is still a promising site in which to form the solar r-process abundances. However, our best results seem to imply both a rather soft neutron-star equation of state and a massive proto-neutron star which is difficult to achieve with standard core-collapse models. We propose that the most favorable conditions perhaps require that a massive supernova progenitor forms a massive proto-neutron star by accretion after a failed initial neutrino burst.Comment: 12 pages, 6 figures, accepted for publication in the Astrophysical Journa

Tables of Hyperonic Matter Equation of State for Core-Collapse Supernovae

We present sets of equation of state (EOS) of nuclear matter including hyperons using an SU_f(3) extended relativistic mean field (RMF) model with a wide coverage of density, temperature, and charge fraction for numerical simulations of core collapse supernovae. Coupling constants of Sigma and Xi hyperons with the sigma meson are determined to fit the hyperon potential depths in nuclear matter, U_Sigma(rho_0) ~ +30 MeV and U_Xi(rho_0) ~ -15 MeV, which are suggested from recent analyses of hyperon production reactions. At low densities, the EOS of uniform matter is connected with the EOS by Shen et al., in which formation of finite nuclei is included in the Thomas-Fermi approximation. In the present EOS, the maximum mass of neutron stars decreases from 2.17 M_sun (Ne mu) to 1.63 M_sun (NYe mu) when hyperons are included. In a spherical, adiabatic collapse of a 15$M_\odot$ star by the hydrodynamics without neutrino transfer, hyperon effects are found to be small, since the temperature and density do not reach the region of hyperon mixture, where the hyperon fraction is above 1 % (T > 40 MeV or rho_B > 0.4 fm^{-3}).Comment: 23 pages, 6 figures (Fig.3 and related comments on pion potential are corrected in v3.

General relativistic effects on neutrino-driven wind from young, hot neutron star and the r-process nucleosynthesis

Neutrino-driven wind from young hot neutron star, which is formed by supernova explosion, is the most promising candidate site for r-process nucleosynthesis. We study general relativistic effects on this wind in Schwarzschild geometry in order to look for suitable conditions for a successful r-process nucleosynthesis. It is quantitatively discussed that the general relativistic effects play a significant role in increasing entropy and decreasing dynamic time scale of the neutrino-driven wind. Exploring wide parameter region which determines the expansion dynamics of the wind, we find interesting physical conditions which lead to successful r-process nucleosynthesis. The conditions which we found realize in the neutrino-driven wind with very short dynamic time scale $\tau_{\rm dyn} \sim 6$ ms and relatively low entropy $S \sim 140$. We carry out the $\alpha$-process and r-process nucleosynthesis calculation on these conditions by the use of our single network code including over 3000 isotopes, and confirm quantitatively that the second and third r-process abundance peaks are produced in the neutrino-driven wind.Comment: Accepted for publication in Ap

Ledoux-Convection in Protoneutron Stars --- a Clue to Supernova Nucleosynthesis?

Two-dimensional hydrodynamical simulations of the deleptonization of a newly formed neutron star were performed. Driven by negative lepton fraction and entropy gradients, convection starts near the neutrinosphere about 20-30 ms after core bounce, but moves deeper into the protoneutron star, and after about one second the whole protoneutron star is convective. The deleptonization of the star proceeds much faster than in the corresponding spherically symmetrical model because the lepton flux and the neutrino luminosities increase by up to a factor of two. The convection below the neutrinosphere raises the neutrinospheric temperatures and mean energies of the emitted neutrinos by 10-20%. This can have important implications for the supernova explosion mechanism and changes the detectable neutrino signal from the Kelvin-Helmholtz cooling of the protoneutron star. In particular, the enhanced electron neutrino flux relative to the electron antineutrino flux during the early post-bounce evolution might solve the overproduction problem of certain elements in the neutrino-heated ejecta in models of type-II supernova explosions.Comment: 17 pages, LaTeX, 8 postscript figures, uses epsf.sty. To appear in ApJ 473 (Letters), 1996 December 1

Universal law for waiting internal time in seismicity and its implication to earthquake network

In their paper (Europhys. Lett., 71 (2005) 1036), Carbone, Sorriso-Valvo, Harabaglia and Guerra showed that "unified scaling law" for conventional waiting times of earthquakes claimed by Bak et al. (Phys. Rev. Lett., 88 (2002) 178501) is actually not universal. Here, instead of the conventional time, the concept of the internal time termed the event time is considered for seismicity. It is shown that, in contrast to the conventional waiting time, the waiting event time obeys a power law. This implies the existence of temporal long-range correlations in terms of the event time with no sharp decay of the crossover type. The discovered power-law waiting event-time distribution turns out to be universal in the sense that it takes the same form for seismicities in California, Japan and Iran. In particular, the parameters contained in the distribution take the common values in all these geographical regions. An implication of this result to the procedure of constructing earthquake networks is discussed.Comment: 21 pages, 5 figure

Semi-classical equation of state and specific heats for neutron-star inner crust with proton shell corrections

An approach to the equation of state for the inner crust of neutron stars based on Skyrme-type forces is presented. Working within the Wigner-Seitz picture, the energy is calculated by the TETF (temperature-dependent extended Thomas-Fermi) method, with proton shell corrections added self-consistently by the Strutinsky-integral method. Using a Skyrme force that has been fitted to both neutron matter and to essentially all the nuclear mass data, we find strong proton shell effects: proton numbers $Z$ = 50, 40 and 20 are the only values possible in the inner crust, assuming that nuclear equilibrium is maintained in the cooling neutron star right down to the ambient temperature. Convergence problems with the TETF expansion for the entropy, and our way of handling them, are discussed. Full TETF expressions for the specific heat of inhomogeneous nuclear matter are presented. Our treatment of the electron gas, including its specific heat, is essentially exact, and is described in detail.Comment: 41 pages, 6 figure

Microcanonical Foundation for Systems with Power-Law Distributions

Starting from microcanonical basis with the principle of equal a priori probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a theory describing systems with power-law distributions can also be derived.Comment: 9 page

Rates of convergence of nonextensive statistical distributions to Levy distributions in full and half spaces

The Levy-type distributions are derived using the principle of maximum Tsallis nonextensive entropy both in the full and half spaces. The rates of convergence to the exact Levy stable distributions are determined by taking the N-fold convolutions of these distributions. The marked difference between the problems in the full and half spaces is elucidated analytically. It is found that the rates of convergence depend on the ranges of the Levy indices. An important result emerging from the present analysis is deduced if interpreted in terms of random walks, implying the dependence of the asymptotic long-time behaviors of the walks on the ranges of the Levy indices if N is identified with the total time of the walks.Comment: 20 page