14,462 research outputs found
The Role of Turbulence in Neutrino-Driven Core-Collapse Supernova Explosions
The neutrino-heated "gain layer" immediately behind the stalled shock in a
core-collapse supernova is unstable to high-Reynolds-number turbulent
convection. We carry out and analyze a new set of 19 high-resolution
three-dimensional (3D) simulations with a three-species neutrino
leakage/heating scheme and compare with spherically-symmetric (1D) and
axisymmetric (2D) simulations carried out with the same methods. We study the
postbounce supernova evolution in a - progenitor star and vary the
local neutrino heating rate, the magnitude and spatial dependence of
asphericity from convective burning in the Si/O shell, and spatial resolution.
Our simulations suggest that there is a direct correlation between the strength
of turbulence in the gain layer and the susceptability to explosion. 2D and 3D
simulations explode at much lower neutrino heating rates than 1D simulations.
This is commonly explained by the fact that nonradial dynamics allows accreting
material to stay longer in the gain layer. We show that this explanation is
incomplete. Our results indicate that the effective turbulent ram pressure
exerted on the shock plays a crucial role by allowing multi-D models to explode
at a lower postshock thermal pressure and thus with less neutrino heating than
1D models. We connect the turbulent ram pressure with turbulent energy at large
scales and in this way explain why 2D simulations are erroneously exploding
more easily than 3D simulations.Comment: 13 pages, 8 figures, accepted by Ap
Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae
(Abridged) In the implicit large eddy simulation (ILES) paradigm, the
dissipative nature of high-resolution shock-capturing schemes is exploited to
provide an implicit model of turbulence. Recent 3D simulations suggest that
turbulence might play a crucial role in core-collapse supernova explosions,
however the fidelity with which turbulence is simulated in these studies is
unclear. Especially considering that the accuracy of ILES for the regime of
interest in CCSN, weakly compressible and strongly anisotropic, has not been
systematically assessed before. In this paper we assess the accuracy of ILES
using numerical methods most commonly employed in computational astrophysics by
means of a number of local simulations of driven, weakly compressible,
anisotropic turbulence. We report a detailed analysis of the way in which the
turbulent cascade is influenced by the numerics. Our results suggest that
anisotropy and compressibility in CCSN turbulence have little effect on the
turbulent kinetic energy spectrum and a Kolmogorov scaling is
obtained in the inertial range. We find that, on the one hand, the kinetic
energy dissipation rate at large scales is correctly captured even at
relatively low resolutions, suggesting that very high effective Reynolds number
can be achieved at the largest scales of the simulation. On the other hand, the
dynamics at intermediate scales appears to be completely dominated by the
so-called bottleneck effect, \ie the pile up of kinetic energy close to the
dissipation range due to the partial suppression of the energy cascade by
numerical viscosity. An inertial range is not recovered until the point where
relatively high resolution , which would be difficult to realize in
global simulations, is reached. We discuss the consequences for CCSN
simulations.Comment: 17 pages, 9 figures, matches published versio
Measuring the Angular Momentum Distribution in Core-Collapse Supernova Progenitors with Gravitational Waves
The late collapse, core bounce, and the early postbounce phase of rotating
core collapse leads to a characteristic gravitational wave (GW) signal. The
precise shape of the signal is governed by the interplay of gravity, rotation,
nuclear equation of state (EOS), and electron capture during collapse. We
explore the dependence of the signal on total angular momentum and its
distribution in the progenitor core by means of a large set of axisymmetric
general-relativistic core collapse simulations in which we vary the initial
angular momentum distribution in the core. Our simulations include a
microphysical finite-temperature EOS, an approximate electron capture treatment
during collapse, and a neutrino leakage scheme for the postbounce evolution. We
find that the precise distribution of angular momentum is relevant only for
very rapidly rotating cores with T/|W|>~8% at bounce. We construct a numerical
template bank from our baseline set of simulations, and carry out additional
simulations to generate trial waveforms for injection into simulated advanced
LIGO noise at a fiducial galactic distance of 10 kpc. Using matched filtering,
we show that for an optimally-oriented source and Gaussian noise, advanced
Advanced LIGO could measure the total angular momentum to within ~20%, for
rapidly rotating cores. For most waveforms, the nearest known degree of
precollapse differential rotation is correctly inferred by both our matched
filtering analysis and an alternative Bayesian model selection approach. We
test our results for robustness against systematic uncertainties by injecting
waveforms from simulations using a different EOS and and variations in the
electron fraction in the inner core. The results of these tests show that these
uncertainties significantly reduce the accuracy with which the total angular
momentum and its precollapse distribution can be inferred from observations.Comment: 22 pages, 16 figure
The Influence of Thermal Pressure on Equilibrium Models of Hypermassive Neutron Star Merger Remnants
The merger of two neutron stars leaves behind a rapidly spinning hypermassive
object whose survival is believed to depend on the maximum mass supported by
the nuclear equation of state, angular momentum redistribution by
(magneto-)rotational instabilities, and spindown by gravitational waves. The
high temperatures (~5-40 MeV) prevailing in the merger remnant may provide
thermal pressure support that could increase its maximum mass and, thus, its
life on a neutrino-cooling timescale. We investigate the role of thermal
pressure support in hypermassive merger remnants by computing sequences of
spherically-symmetric and axisymmetric uniformly and differentially rotating
equilibrium solutions to the general-relativistic stellar structure equations.
Using a set of finite-temperature nuclear equations of state, we find that hot
maximum-mass critically spinning configurations generally do not support larger
baryonic masses than their cold counterparts. However, subcritically spinning
configurations with mean density of less than a few times nuclear saturation
density yield a significantly thermally enhanced mass. Even without decreasing
the maximum mass, cooling and other forms of energy loss can drive the remnant
to an unstable state. We infer secular instability by identifying approximate
energy turning points in equilibrium sequences of constant baryonic mass
parametrized by maximum density. Energy loss carries the remnant along the
direction of decreasing gravitational mass and higher density until instability
triggers collapse. Since configurations with more thermal pressure support are
less compact and thus begin their evolution at a lower maximum density, they
remain stable for longer periods after merger.Comment: 20 pages, 12 figures. Accepted for publication in Ap
Quantifying Spatiotemporal Chaos in Rayleigh-B\'enard Convection
Using large-scale parallel numerical simulations we explore spatiotemporal
chaos in Rayleigh-B\'enard convection in a cylindrical domain with
experimentally relevant boundary conditions. We use the variation of the
spectrum of Lyapunov exponents and the leading order Lyapunov vector with
system parameters to quantify states of high-dimensional chaos in fluid
convection. We explore the relationship between the time dynamics of the
spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics
we find that all of the Lyapunov exponents are positively correlated with the
leading order Lyapunov exponent and we quantify the details of their response
to the dynamics of defects. The leading order Lyapunov vector is used to
identify topological features of the fluid patterns that contribute
significantly to the chaotic dynamics. Our results show a transition from
boundary dominated dynamics to bulk dominated dynamics as the system size is
increased. The spectrum of Lyapunov exponents is used to compute the variation
of the fractal dimension with system parameters to quantify how the underlying
high-dimensional strange attractor accommodates a range of different chaotic
dynamics
Influence of carbon substitution on the heat transport in single crystalline MgB2
We report data on the thermal conductivity \kappa(T,H) in the basal plane of
hexagonal single-crystalline and superconducting Mg(B_{1-x}C_x)_2 (x= 0.03,
0.06) at temperatures between 0.5 and 50 K, and in external magnetic fields H
between 0 and 50 kOe. The substitution of carbon for boron leads to a
considerable reduction of the electronic heat transport, while the phonon
thermal conductivity seems to be much less sensitive to impurities. The
introduction of carbon enhances mostly the intraband scattering in the
\sigma-band. In contrast to the previously observed anomalous behavior of pure
MgB, the Wiedemann-Franz law is valid for Mg(B_0.94 C_0.06)_2 at low
temperatures.Comment: 4 pages, 4 figures. Final version to appear in Phys. Rev.
A New Open-Source Code for Spherically-Symmetric Stellar Collapse to Neutron Stars and Black Holes
We present the new open-source spherically-symmetric general-relativistic
(GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR
hydrodynamics (GRHD) put forth by Romero-Ibanez-Gourgoulhon and employs
radial-gauge, polar-slicing coordinates in which the 3+1 equations simplify
substantially. We discretize the GRHD equations with a finite-volume scheme,
employing piecewise-parabolic reconstruction and an approximate Riemann solver.
GR1D is intended for the simulation of stellar collapse to neutron stars and
black holes and will also serve as a testbed for modeling technology to be
incorporated in multi-D GR codes. Its GRHD part is coupled to various
finite-temperature microphysical equations of state in tabulated form that we
make available with GR1D. An approximate deleptonization scheme for the
collapse phase and a neutrino-leakage/heating scheme for the postbounce epoch
are included and described. We also derive the equations for effective rotation
in 1D and implement them in GR1D. We present an array of standard test
calculations and also show how simple analytic equations of state in
combination with presupernova models from stellar evolutionary calculations can
be used to study qualitative aspects of black hole formation in failing
rotating core-collapse supernovae. In addition, we present a simulation with
microphysical EOS and neutrino leakage/heating of a failing core-collapse
supernova and black hole formation in a presupernova model of a 40 solar mass
zero-age main-sequence star. We find good agreement on the time of black hole
formation (within 20%) and last stable protoneutron star mass (within 10%) with
predictions from simulations with full Boltzmann neutrino radiation
hydrodynamics.Comment: 25 pages, 6 figures, 2 appendices. Accepted for publication to the
Classical and Quantum Gravity special issue for MICRA2009. Code may be
downloaded from http://www.stellarcollapse.org Update: corrected title, small
modifications suggested by the referees, added source term derivation in
appendix
Natural clustering: the modularity approach
We show that modularity, a quantity introduced in the study of networked
systems, can be generalized and used in the clustering problem as an indicator
for the quality of the solution. The introduction of this measure arises very
naturally in the case of clustering algorithms that are rooted in Statistical
Mechanics and use the analogy with a physical system.Comment: 11 pages, 5 figure enlarged versio
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