20 research outputs found
Exploring the relativistic regime with Newtonian hydrodynamics: II. An effective gravitational potential for rapid rotation
We present the generalization of a recently introduced modified gravitational
potential for self-gravitating fluids. The use of this potential allows for an
accurate approximation of general relativistic effects in an otherwise
Newtonian hydrodynamics code also in cases of rapid rotation. We test this
approach in numerical simulations of astrophysical scenarios related to compact
stars, like supernova core collapse with both a simplified and detailed
microphysical description of matter, and rotating neutron stars in equilibrium.
We assess the quality of the new potential, and demonstrate that it provides a
significant improvement compared to previous formulations for such potentials.
Newtonian simulations of compact objects employing such an effective
relativistic potential predict inaccurate pulsation frequencies despite the
excellent agreement of the collapse dynamics and structure of the compact
objects with general relativistic results. We analyze and discuss the reason
for this behavior.Comment: 15 pages, 12 figures, minor modification
"Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations
We present a new 3D general relativistic hydrodynamics code for simulations
of stellar core collapse to a neutron star, as well as pulsations and
instabilities of rotating relativistic stars. It uses spectral methods for
solving the metric equations, assuming the conformal flatness approximation for
the three-metric. The matter equations are solved by high-resolution
shock-capturing schemes. We demonstrate that the combination of a finite
difference grid and a spectral grid can be successfully accomplished. This
"Mariage des Maillages" (French for grid wedding) approach results in high
accuracy of the metric solver and allows for fully 3D applications using
computationally affordable resources, and ensures long term numerical stability
of the evolution. We compare our new approach to two other, finite difference
based, methods to solve the metric equations. A variety of tests in 2D and 3D
is presented, involving highly perturbed neutron star spacetimes and
(axisymmetric) stellar core collapse, demonstrating the ability to handle
spacetimes with and without symmetries in strong gravity. These tests are also
employed to assess gravitational waveform extraction, which is based on the
quadrupole formula.Comment: 29 pages, 16 figures; added more information about convergence tests
and grid setu
Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
Uniqueness problems in the elliptic sector of constrained formulations of
Einstein equations have a dramatic effect on the physical validity of some
numerical solutions, for instance when calculating the spacetime of very
compact stars or nascent black holes. The fully constrained formulation (FCF)
proposed by Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak is one of these
formulations. It contains, as a particular case, the approximation of the
conformal flatness condition (CFC) which, in the last ten years, has been used
in many astrophysical applications. The elliptic part of the FCF basically
shares the same differential operators as the elliptic equations in CFC scheme.
We present here a reformulation of the elliptic sector of CFC that has the
fundamental property of overcoming the local uniqueness problems. The correct
behavior of our new formulation is confirmed by means of a battery of numerical
simulations. Finally, we extend these ideas to FCF, complementing the
mathematical analysis carried out in previous studies.Comment: 17 pages, 5 figures. Minor changes to be consistent with published
versio
Dynamic migration of rotating neutron stars due to a phase transition instability
Using numerical simulations based on solving the general relativistic
hydrodynamic equations, we study the dynamics of a phase transition in the
dense core of isolated rotating neutron stars, triggered by the back bending
instability reached via angular momentum loss. In particular, we investigate
the dynamics of a migration from an unstable configuration into a stable one,
which leads to a mini-collapse of the neutron star and excites sizeable
pulsations in its bulk until it acquires a new stable equilibrium state. We
consider equations of state with softening at high densities, a simple analytic
one with a mixed hadron-quark phase in an intermediate pressure interval and
pure quark matter at very high densities, and a microphysical one that has a
first-order phase transition, originating from kaon condensation. Although the
marginally stable initial models are rigidly rotating, we observe that during
the collapse (albeit little) differential rotation is created. We analyze the
emission of gravitational radiation, which in some models is amplified by mode
resonance effects, and assess its prospective detectability by interferometric
detectors. We expect that the most favorable conditions for dynamic migration
exist in very young magnetars. We find that the damping of the post-migration
pulsations strongly depends on the character of the equation of state
softening. The damping of pulsations in the models with the microphysical
equation of state is caused by dissipation associated with matter flowing
through the density jump at the edge of the dense core. If at work, this
mechanism dominates over all other types of dissipation, like bulk viscosity in
the exotic-phase core, gravitational radiation damping, or numerical viscosity.Comment: 23 pages, 18 figures, minor modification
Gravitational waves from relativistic rotational core collapse
We present results from simulations of axisymmetric relativistic rotational
core collapse. The general relativistic hydrodynamic equations are formulated
in flux-conservative form and solved using a high-resolution shock-capturing
scheme. The Einstein equations are approximated with a conformally flat
3-metric. We use the quadrupole formula to extract waveforms of the
gravitational radiation emitted during the collapse. A comparison of our
results with those of Newtonian simulations shows that the wave amplitudes
agree within 30%. Surprisingly, in some cases, relativistic effects actually
diminish the amplitude of the gravitational wave signal. We further find that
the parameter range of models suffering multiple coherent bounces due to
centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure
Bayesian reconstruction of gravitational wave burst signals from simulations of rotating stellar core collapse and bounce
Presented in this paper is a technique that we propose for extracting the
physical parameters of a rotating stellar core collapse from the observation of
the associated gravitational wave signal from the collapse and core bounce.
Data from interferometric gravitational wave detectors can be used to provide
information on the mass of the progenitor model, precollapse rotation and the
nuclear equation of state. We use waveform libraries provided by the latest
numerical simulations of rotating stellar core collapse models in general
relativity, and from them create an orthogonal set of eigenvectors using
principal component analysis. Bayesian inference techniques are then used to
reconstruct the associated gravitational wave signal that is assumed to be
detected by an interferometric detector. Posterior probability distribution
functions are derived for the amplitudes of the principal component analysis
eigenvectors, and the pulse arrival time. We show how the reconstructed signal
and the principal component analysis eigenvector amplitude estimates may
provide information on the physical parameters associated with the core
collapse event.Comment: 17 pages, 9 figure
Gravitational wave burst signal from core collapse of rotating stars
We present results from detailed general relativistic simulations of stellar core collapse to a proto-neutron star, using two different microphysical nonzero-temperature nuclear equations of state as well as an approximate description of deleptonization during the collapse phase. Investigating a wide variety of rotation rates and profiles as well as masses of the progenitor stars and both equations of state, we confirm in this very general setup the recent finding that a generic gravitational wave burst signal is associated with core bounce, already known as type I in the literature. The previously suggested type II (or “multiple-bounce”) waveform morphology does not occur. Despite this reduction to a single waveform type, we demonstrate that it is still possible to constrain the progenitor and postbounce rotation based on a combination of the maximum signal amplitude and the peak frequency of the emitted gravitational wave burst. Our models include to sufficient accuracy the currently known necessary physics for the collapse and bounce phase of core-collapse supernovae, yielding accurate and reliable gravitational wave signal templates for gravitational wave data analysis. In addition, we assess the possibility of nonaxisymmetric instabilities in rotating nascent proto-neutron stars. We find strong evidence that in an iron core-collapse event the postbounce core cannot reach sufficiently rapid rotation to become subject to a classical bar-mode instability. However, many of our postbounce core models exhibit sufficiently rapid and differential rotation to become subject to the recently discovered dynamical instability at low rotation rates
A new multi-dimensional general relativistic neutrino hydrodynamics code for core-collapse supernovae. I. Method and code tests in spherical symmetry
We present a new general relativistic (GR) code for hydrodynamic supernova
simulations with neutrino transport in spherical and azimuthal symmetry
(1D/2D). The code is a combination of the CoCoNuT hydro module, which is a
Riemann-solver based, high-resolution shock-capturing method, and the
three-flavor, energy-dependent neutrino transport scheme VERTEX. VERTEX
integrates the neutrino moment equations with a variable Eddington factor
closure computed from a model Boltzmann equation and uses the ray-by-ray plus
approximation in 2D, assuming the neutrino distribution to be axially symmetric
around the radial direction, and thus the neutrino flux to be radial. Our
spacetime treatment employs the ADM 3+1 formalism with the conformal flatness
condition for the spatial three-metric. This approach is exact in 1D and has
been shown to yield very accurate results also for rotational stellar collapse.
We introduce new formulations of the energy equation to improve total energy
conservation in relativistic and Newtonian hydro simulations with Eulerian
finite-volume codes. Moreover, a modified version of the VERTEX scheme is
developed that simultaneously conserves energy and lepton number with better
accuracy and higher numerical stability. To verify our code, we conduct a
series of tests, including a detailed comparison with published 1D results for
stellar core collapse. Long-time simulations of proto-neutron star cooling over
several seconds both demonstrate the robustness of the new CoCoNuT-VERTEX code
and show the approximate treatment of GR effects by means of an effective
gravitational potential as in PROMETHEUS-VERTEX to be remarkably accurate in
1D. (abridged)Comment: 36 pages, 19 eps figures; submitted to ApJS (minor revisions; some
typos corrected
The gravitational wave burst signal from core collapse of rotating stars
We present results from detailed general relativistic simulations of stellar
core collapse to a proto-neutron star, using two different microphysical
nonzero-temperature nuclear equations of state as well as an approximate
description of deleptonization during the collapse phase. Investigating a wide
variety of rotation rates and profiles as well as masses of the progenitor
stars and both equations of state, we confirm in this very general setup the
recent finding that a generic gravitational wave burst signal is associated
with core bounce, already known as type I in the literature. The previously
suggested type II (or "multiple-bounce") waveform morphology does not occur.
Despite this reduction to a single waveform type, we demonstrate that it is
still possible to constrain the progenitor and postbounce rotation based on a
combination of the maximum signal amplitude and the peak frequency of the
emitted gravitational wave burst. Our models include to sufficient accuracy the
currently known necessary physics for the collapse and bounce phase of
core-collapse supernovae, yielding accurate and reliable gravitational wave
signal templates for gravitational wave data analysis. In addition, we assess
the possiblity of nonaxisymmetric instabilities in rotating nascent
proto-neutron stars. We find strong evidence that in an iron core-collapse
event the postbounce core cannot reach sufficiently rapid rotation to become
subject to a classical bar-mode instability. However, many of our postbounce
core models exhibit sufficiently rapid and differential rotation to become
subject to the recently discovered dynamical instability at low rotation rates.Comment: 28 pages, 23 figures, minor change