15 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
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
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
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