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We analyze the directional dependence of the gravitational wave (GW) emission from 15 3D neutrino radiation hydrodynamic simulations of core-collapse supernovae (CCSNe). Using spin weighted spherical harmonics, we develop a new analytic technique to quantify the evolution of the distribution of GW emission over all angles. We construct a physics-informed toy model that can be used to approximate GW distributions for general ellipsoid-like systems, and use it to provide closed form expressions for the distribution of GWs for different CCSN phases. Using these toy models, we approximate the protoneutron star (PNS) dynamics during multiple CCSN stages and obtain similar GW distributions to simulation outputs. When considering all viewing angles, we apply this new technique to quantify the evolution of preferred directions of GW emission. For nonrotating cases, this dominant viewing angle drifts isotropically throughout the supernova, set by the dynamical timescale of the PNS. For rotating cases, during core bounce and the following tens of milliseconds, the strongest GW signal is observed along the equator. During the accretion phase, comparable—if not stronger—GW amplitudes are generated along the axis of rotation, which can be enhanced by the lowT/∣W∣ instability. We show two dominant factors influencing the directionality of GW emission are the degree of initial rotation and explosion morphology. Lastly, looking forward, we note the sensitive interplay between GW detector site and supernova orientation, along with its effect on detecting individual polarization modes.

 

Abstract We present a discontinuous Galerkin (DG)–finite difference (FD) hybrid scheme that allows high-order shock capturing with the DG method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple. An unlimited DG candidate solution is computed for the next time step. If the candidate solution is inadmissible, the time step is retaken using robust FD methods. Because of its a posteriori nature, the hybrid scheme inherits the best properties of both methods. It is high-order with exponential convergence in smooth regions, while robustly handling discontinuities. We give a detailed description of how we transfer the solution between the DG and FD solvers, and the troubled-cell indicators necessary to robustly handle slow-moving discontinuities and simulate magnetized neutron stars. We demonstrate the efficacy of the proposed method using a suite of standard and very challenging 1D, 2D, and 3D relativistic magnetohydrodynamics test problems. The hybrid scheme is designed from the ground up to efficiently simulate astrophysical problems such as the inspiral, coalescence, and merger of two neutron stars.