Numerical {3 + 1} General Relativistic Hydrodynamics: A Local Characteristic Approach

We present results from detailed general relativistic simulations of stellar core collapse to a protoneutron 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.

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“…The local conservation laws (2) are written as a first-order, flux-conservative system of hyperbolic equations [46],…”

Section: A General Relativistic Hydrodynamicsmentioning

confidence: 99%

Gravitational wave burst signal from core collapse of rotating stars

et al. 2008

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“…1 As we derived in [21], the resulting equations are very similar to those of the original Valencia formulation above, except that all appearances of √γ have to replaced with γ/γ (which immediately solves the problem discussed above), and all partial derivatives ∂ have to be replaced with covariant derivatives with respect to the reference metric,D. The continuity equation (28), for example, becomes…”

Section: A Reference-metric Formulation Of Relativistic Hydrodynamicsmentioning

confidence: 90%

“…In the process, a new set of hydrodynamical variables, namely the conserved variables, are introduced. A particularly common such formulation is the so-called "Valencia" form [28] (see also [29,30] for reviews).…”

Section: A Reference-metric Formulation Of Relativistic Hydrodynamicsmentioning

confidence: 99%

Numerical relativity in spherical polar coordinates: Off-center simulations

Baumgarte¹,

Montero

Müller

2015

Phys. Rev. D

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We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system. 04.25.dg, 95.30.Lz, 97.60.Lf

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“…We use so called "Valencia formulation" to numerically solve the relativistic hydrodynamic equation (Banyuls et al 1997). This formulation gives flux conservative form of the system of hydrodynamics equation in the framework of 3+1 formalism.…”

Section: Numerical Simulation Proceduresmentioning

confidence: 99%

General relativistic numerical simulation of sub-Keplerian transonic accretion flows on to black holes: Schwarzschild space–time

Kim

Garain

Balsara

et al. 2017

Monthly Notices of the Royal Astronomical Society

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We study time evolution of sub-Keplerian transonic accretion flows onto black holes using a general relativistic numerical simulation code. We perform simulations in Schwarzschild spacetime. We first compare one-dimensional simulation results with theoretical results and validate the performance of our code. Next, we present results of axisymmetric, two-dimensional simulation of advective flows. We find that even in this case, for which no complete theoretical analysis is present in the literature, steady state shock formation is possible.

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Numerical {3 + 1} General Relativistic Hydrodynamics: A Local Characteristic Approach

Cited by 320 publications

References 42 publications

Gravitational wave burst signal from core collapse of rotating stars

Gravitational wave burst signal from core collapse of rotating stars

Numerical relativity in spherical polar coordinates: Off-center simulations

General relativistic numerical simulation of sub-Keplerian transonic accretion flows on to black holes: Schwarzschild space–time

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