We present a gravitational wave (GW) analysis of an extensive series of three-dimensional magnetohydrodynamical core-collapse simulations. Our 25 models are based on a 15 M progenitor stemming from (i) stellar evolution calculations; (ii) a spherically symmetric effective general relativistic potential, either the Lattimer-Swesty (with three possible compressibilities) or the Shen equation of state for hot, dense matter; and (iii) a neutrino parametrisation scheme that is accurate until about 5 ms postbounce. For three representative models, we also included long-term neutrino physics by means of a leakage scheme, which is based on partial implementation of the isotropic diffusion source approximation (IDSA). We systematically investigated the effects of the equation of state, the initial rotation rate, and both the toroidal and the poloidal magnetic fields on the GW signature. We stress the importance of including of postbounce neutrino physics, since it quantitatively alters the GW signature. Slowly rotating models, or those that do not rotate at all, show GW emission caused by prompt and proto-neutron star (PNS) convection. Moreover, the signal stemming from prompt convection allows for the distinction between the two different nuclear equations of state indirectly by different properties of the fluid instabilities. For simulations with moderate or even fast rotation rates, we only find the axisymmetric type I wave signature at core bounce. In line with recent results, we could confirm that the maximum GW amplitude scales roughly linearly with the ratio of rotational to gravitational energy at core bounce below a threshold value of about 10%. We point out that models set up with an initial central angular velocity of 2π rad s −1 or faster show nonaxisymmetric narrow-band GW radiation during the postbounce phase. This emission process is caused by a low T/|W| dynamical instability. Apart from these two points, we show that it is generally very difficult to discern the effects of the individual features of the input physics in a GW signal from a rotating core-collapse supernova that can be attributed unambiguously to a specific model. Weak magnetic fields do not notably influence the dynamical evolution of the core and thus the GW emission. However, for strong initial poloidal magnetic fields ( 10 12 G), the combined action of flux-freezing and field winding leads to conditions where the ratio of magnetic field pressure to matter pressure reaches about unity which leads to the onset of a jet-like supernova explosion. The collimated bipolar out-stream of matter is then reflected in the emission of a type IV GW signal. In contradiction to axisymmetric simulations, we find evidence that nonaxisymmetric fluid modes can counteract or even suppress jet formation for models with strong initial toroidal magnetic fields. The results of models with continued neutrino emission show that including of the deleptonisation during the postbounce phase is an indispensable issue for the quantitative prediction of GWs fro...
We present the gravitational wave analyses from rotating (model s15g) and nearly non-rotating (model s15h) 3D MHD core collapse supernova simulations at bounce and during the first couple of ten milliseconds afterwards. The simulations are launched from 15 M progenitor models stemming from stellar-evolution calculations. Gravity is implemented by a spherically symmetric effective general relativistic potential. The input physics uses the Lattimer-Swesty equation of state for hot, dense matter and a neutrino parametrisation scheme that is accurate until the first few ms after bounce. The 3D simulations allow us to study features already known from 2D simulations, as well as nonaxisymmetric effects. In agreement with recent results, we find only type I gravitational wave signals at core bounce. In the later stage of the simulations, one of our models (s15g) shows nonaxisymmetric gravitational wave emission caused by a low T/|W| dynamical instability, while the other model radiates gravitational waves due to a convective instability in the protoneutron star. The total energy released in gravitational waves within the considered time intervals is 1.52 × 10 −7 M (s15g) and 4.72 × 10 −10 M (s15h). Both core collapse simulations indicate that corresponding events in our Galaxy would be detectable either by the LIGO or Advanced LIGO detector.
We present a flexible and scalable method to compute global solutions of high-dimensional stochastic dynamic models. Within a time-iteration setup, we interpolate policy functions using an adaptive sparse grid algorithm with piecewise multi-linear (hierarchical) basis functions. As the dimensionality increases, sparse grids grow considerably slower than standard tensor product grids. In addition, the grid scheme we use is automatically refined locally and can thus capture steep gradients or even non-differentiabilities. To further increase the maximum problem size we can handle, our implementation is fully hybrid parallel, i.e. using a combination of distributed and shared memory parallelization schemes. This parallelization enables us to efficiently use high-performance computing architectures. Our algorithm scales up nicely to more than one thousand parallel processes. To demonstrate the performance of our method, we apply it to high-dimensional international real business cycle models with capital adjustment costs and irreversible investment.Keywords: Adaptive Sparse Grids, High-Performance Computing, International Real Business Cycles, Occasionally Binding Constraints JEL Classification: C63, C68, F41 * We are very grateful to Felix Kübler for helpful discussions and support. We thank Ken Judd, Karl Schmedders and seminar participants at University of Zürich, Stanford University, University of Chicago, Argonne National Laboratory, and CEF 2013 in Vancouver for valuable comments. Moreover, we thank Xiang Ma for very instructive email discussions regarding the workings of adaptive sparse grids. We are grateful for the support of Olaf Schenk, Antonio Messina and Riccardo Murri concerning HPC related issues. We acknowledge CPU time granted on the University of Zürich's 'Schrödinger' HPC cluster. Johannes Brumm gratefully acknowledges financial support from the ERC.
We have performed a set of 11 three-dimensional magnetohydrodynamical core-collapse supernova simulations in order to investigate the dependencies of the gravitational wave signal on the progenitor's initial conditions. We study the effects of the initial central angular velocity and different variants of neutrino transport. Our models are started up from a 15M ⊙ progenitor and incorporate an effective general relativistic gravitational potential and a finite temperature nuclear equation of state. Furthermore, the electron flavour neutrino transport is tracked by efficient algorithms for the radiative transfer of massless fermions. We find that non-and slowly rotating models show gravitational wave emission due to prompt-and lepton driven convection that reveals details about the hydrodynamical state of the fluid inside the protoneutron stars. Furthermore we show that protoneutron stars can become dynamically unstable to rotational instabilities at T/|W| values as low as ∼ 2% at core bounce. We point out that the inclusion of deleptonization during the postbounce phase is very important for the quantitative GW prediction, as it enhances the absolute values of the gravitational wave trains up to a factor of ten with respect to a lepton-conserving treatment.PACS numbers: 04.30. Db, 95.30.Qd, 97.60.Bw
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