Post-Newtonian hydrodynamics and post-Newtonian gravitational wave generation for numerical relativity

Blanchet, Luc; Damour, Thibault; Schaêfer, G.

doi:10.1093/mnras/242.3.289

Cited by 197 publications

(204 citation statements)

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“…Following Nakamura & Oohara (1989) and Blanchet et al (1990), the second-order time derivatives read in a Cartesian orthonormal basis (the spatial indices i and j run from 1 to 3)…”

Section: Non-radial Mass Flowmentioning

confidence: 99%

Parametrized 3D models of neutrino-driven supernova explosions

Müller

Janka

Wongwathanarat

2012

A&A

119

144

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Time-dependent and direction-dependent neutrino and gravitational-wave (GW) signatures are presented for a set of three-dimensional (3D) hydrodynamic models of parametrized, neutrino-driven supernova explosions of non-rotating 15 and 20 M stars. We employed an approximate treatment of neutrino transport based on a gray spectral description and a ray-by-ray treatment of multi-dimensional effects. Owing to the excision of the high-density core of the proto-neutron star (PNS) and the use of an axis-free (Yin-Yang) overset grid, the models can be followed from the post-bounce accretion phase through the onset of the explosion into more than one second of the early cooling evolution of the PNS without imposing any symmetry restrictions and covering a full sphere. Gravitational waves and neutrino emission exhibit the generic time-dependent features already known from 2D (axi-symmetric) models. Violent non-radial hydrodynamic mass motions in the accretion layer and their interaction with the outer layers of the proto-neutron star together with anisotropic neutrino emission give rise to a GW signal with an amplitude of ∼5−20 cm in the frequency range of 100−500 Hz. The GW emission from mass motions usually reaches a maximum before the explosion sets in. After the onset of the explosion the GW signal exhibits a low-frequency modulation, in some cases describing a quasi-monotonic growth, associated with the non-spherical expansion of the explosion shock wave and the large-scale anisotropy of the escaping neutrino flow. Variations of the mass-quadrupole moment caused by convective activity inside the nascent neutron star add a high-frequency component to the GW signal during the post-explosion phase. The GW signals exhibit strong variability between the two polarizations, different explosion simulations and different observer directions, and besides common basic features do not possess any template character. The neutrino emission properties (fluxes and effective spectral temperatures) show fluctuations over the neutron star surface on spatial and temporal scales that reflect the different types of non-spherical mass motions in the supernova core, i.e., post-shock overturn flows and proto-neutron star convection. However, because very prominent, quasi-periodic sloshing motions of the shock caused by the standing accretion-shock instability are absent and the emission from different surface areas facing an observer adds up incoherently, the modulation amplitudes of the measurable neutrino luminosities and mean energies are significantly lower than predicted by 2D simulations.

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“…Following Nakamura & Oohara (1989) and Blanchet et al (1990), the second-order time derivatives read in a Cartesian orthonormal basis (the spatial indices i and j run from 1 to 3)…”

Section: Non-radial Mass Flowmentioning

confidence: 99%

Parametrized 3D models of neutrino-driven supernova explosions

Müller

Janka

Wongwathanarat

2012

A&A

119

144

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“…The (quadrupole) gravitational-wave amplitudes, energy spectra, and spectrograms resulting from anisotropic mass motion can be computed for axisymmetric models as described in Müller & Janka (1997;Eqs. (10)- (12)), using the Einstein quadrupole formula in the numerically convenient form derived by Blanchet et al (1990), and by standard FFT techniques. Assuming an observer that is located at an angle θ with respect to the symmetry axis of the source, the dimensionless gravitational wave amplitude h(t) is related to the quadrupole wave amplitude A E2 20 (measured in units of cm), the lowest-order nonvanishing term of a multipole expansion of the radiation field into pure-spin tensor harmonics (see Eq.…”

Section: Gravitational Wavesmentioning

confidence: 99%

Equation-of-state dependent features in shock-oscillation modulated neutrino and gravitational-wave signals from supernovae

Marek

Janka

Müller

2009

A&A

189

272

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We present two-dimensional (axisymmetric) neutrino-hydrodynamic simulations of the long-time accretion phase of a 15 M progenitor star after core bounce and before the launch of a supernova explosion, when non-radial hydrodynamic instabilities like convection occur in different regions of the collapsing stellar core and the standing accretion shock instability (SASI) leads to large-amplitude oscillations of the stalled shock with a period of tens of milliseconds. Our simulations were performed with the Prometheus-Vertex code, which includes a multi-flavor, energy-dependent neutrino transport scheme and employs an effective relativistic gravitational potential. Testing the influence of a stiff and a soft equation of state for hot neutron star matter, we find that the non-radial mass motions in the supernova core impose a time variability on the neutrino and gravitational-wave signals with larger amplitudes, as well as higher frequencies in the case of a more compact nascent neutron star. After the prompt shock-breakout burst of electron neutrinos, a more compact accreting remnant produces higher neutrino luminosities and higher mean neutrino energies. The observable neutrino emission in the SASI sloshing direction exhibits a modulation of several ten percent in the luminosities and around 1 MeV in the mean energies with most power at typical SASI frequencies between roughly 20 and 100 Hz. The modulation is caused by quasi-periodic variations in the mass accretion rate of the neutron star in each hemisphere. At times later than ∼50-100 ms after bounce, the gravitational-wave amplitude is dominated by the growing low-frequency ( < ∼ 200 Hz) signal associated with anisotropic neutrino emission. A high-frequency wave signal results from nonradial gas flows in the outer layers of the anisotropically accreting neutron star. Right after bounce such nonradial mass motions occur due to prompt post-shock convection in both considered cases and contribute mostly to the early wave production around 100 Hz. Later they are instigated by the SASI and by convective overturn that vigorously stir the neutrino-heating and cooling layers, and also by convective activity developing below the neutrinosphere. The gravitational-wave power then peaks at about 300-800 Hz, connected to changes in the mass quadrupole moment on a timescale of milliseconds. Distinctively higher spectral frequencies originate from the more compact and more rapidly contracting neutron star. Both the neutrino and gravitational-wave emission therefore carry information that is characteristic of the properties of the nuclear equation of state in the hot remnant. The detectability of the SASI effects in the neutrino and gravitational-wave signals is briefly discussed.

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“…In this way the retarded character of the gravitational field is taken into account in the linear approximation. This is in contrast to the post-Newtonian approximation scheme [20] - [23], which assumes that velocities of light-deflecting bodies must be small with respect to the speed of light. Such a treatment destroys the causal character of a gravitational null cone and makes the gravitational interaction appear to propagate instantaneously at each step of the iteration procedure.…”

Section: Introductionmentioning

confidence: 98%