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We present numerical results from a parameter study of the standing accretion shock instability (SASI), investigating the impact of general relativity (GR) on the dynamics. Using GR hydrodynamics with GR gravity, and nonrelativistic (NR) hydrodynamics with Newtonian gravity, in an idealized model setting, we vary the initial radius of the shock, and by varying its mass and radius in concert, the proto-neutron star compactness. We investigate four compactnesses expected in a post-bounce core-collapse supernova (CCSN). We find that GR leads to a longer SASI oscillation period, with ratios between the GR and NR cases as large as 1.29 for the highest- compactness suite. We also find that GR leads to a slower SASI growth rate, with ratios between the GR and NR cases as low as 0.47 for the highest-compactness suite. We discuss implications of our results for CCSN simulations. 

We present numerical results from a parameter study of the standing accretion shock instability (SASI), investigating the impact of general relativity (GR) on the dynamics. Using GR hydrodynamics with GR gravity, and nonrelativistic (NR) hydrodynamics with Newtonian gravity, in an idealized model setting, we vary the initial radius of the shock, and by varying its mass and radius in concert, the proto-neutron star compactness. We investigate four compactnesses expected in a post-bounce core-collapse supernova (CCSN). We find that GR leads to a longer SASI oscillation period, with ratios between the GR and NR cases as large as 1.29 for the highest- compactness suite. We also find that GR leads to a slower SASI growth rate, with ratios between the GR and NR cases as low as 0.47 for the highest-compactness suite. We discuss implications of our results for CCSN simulations. 

We present a methodology based on the implementation of a fully connected neural network algorithm to estimate the temporal evolution of the high-frequency gravitational wave emission for a core collapse supernova (CCSN). For this study, we selected a fully connected deep neural network (DNN) regression model because it can learn both linear and nonlinear relationships between the input and output data, it is more appropriate for handling large-dimensional input data, and it offers high performance at a low computational cost. To train the Machine Learning (ML) algorithm, we construct a training dataset using synthetic waveforms, and several CCSN waveforms are used to test the algorithm. We performed a first-order estimation of the high-frequency gravitational wave emission on real interferometric LIGO data from the second half of the third observing run (O3b) with a two detector network (L1 and H1). The relative error associated with the estimate of the slope of the resonant frequency versus time for the GW from CCSN signals is within 13% for the tested candidates included in this study up to different Galactic distances (1.0, 2.3, 3.1, 4.3, 5.4, 7.3, and 10 kpc). This method is, to date, the best estimate of the temporal evolution of the high-frequency emission in real interferometric data. Our methodology of estimation can be used in future studies focused on physical properties of the progenitor. The distances where comparable performances could be achieved for Einstein Telescope and Cosmic Explorer roughly rescale with the noise floor improvements. 

We present a methodology based on the implementation of a fully connected neural network algorithm to estimate the temporal evolution of the high-frequency gravitational wave emission for a core collapse supernova (CCSN). For this study, we selected a fully connected deep neural network (DNN) regression model because it can learn both linear and nonlinear relationships between the input and output data, it is more appropriate for handling large-dimensional input data, and it offers high performance at a low computational cost. To train the Machine Learning (ML) algorithm, we construct a training dataset using synthetic waveforms, and several CCSN waveforms are used to test the algorithm. We performed a first-order estimation of the high-frequency gravitational wave emission on real interferometric LIGO data from the second half of the third observing run (O3b) with a two detector network (L1 and H1). The relative error associated with the estimate of the slope of the resonant frequency versus time for the GW from CCSN signals is within 13% for the tested candidates included in this study up to different Galactic distances (1.0, 2.3, 3.1, 4.3, 5.4, 7.3, and 10 kpc). This method is, to date, the best estimate of the temporal evolution of the high-frequency emission in real interferometric data. Our methodology of estimation can be used in future studies focused on physical properties of the progenitor. The distances where comparable performances could be achieved for Einstein Telescope and Cosmic Explorer roughly rescale with the noise floor improvements. 

We compare the core-collapse evolution of a pair of 15.8 M☉ stars with significantly different internal structures, a consequence of the bimodal variability exhibited by massive stars during their late evolutionary stages. The 15.78 and 15.79 M☉ progenitors have core masses (masses interior to an entropy of 4 kB baryon−1) of 1.47 and 1.78 M☉ and compactness parameters ξ1.75 of 0.302 and 0.604, respectively. The core-collapse simulations are carried out in 2D to nearly 3 s postbounce and show substantial differences in the times of shock revival and explosion energies. The 15.78 M☉ model begins exploding promptly at 120 ms postbounce when a strong density decrement at the Si– Si/O shell interface, not present in the 15.79 M☉ progenitor, encounters the stalled shock. The 15.79 M☉ model takes 100 ms longer to explode but ultimately produces a more powerful explosion. Both the larger mass accretion rate and the more massive core of the 15.79 M☉ model during the first 0.8 s postbounce time result in larger νe/n ̄e luminosities and RMS energies along with a flatter and higher-density heating region. The more-energetic explosion of the 15.79 M☉ model resulted in the ejection of twice as much 56Ni. Most of the ejecta in both models are moderately proton rich, though counterintuitively the highest electron fraction (Ye = 0.61) ejecta in either model are in the less-energetic 15.78 M☉ model, while the lowest electron fraction (Ye = 0.45) ejecta in either model are in the 15.79 M☉ model. 

We compare the core-collapse evolution of a pair of 15.8 M☉ stars with significantly different internal structures, a consequence of the bimodal variability exhibited by massive stars during their late evolutionary stages. The 15.78 and 15.79 M☉ progenitors have core masses (masses interior to an entropy of 4 kB baryon−1) of 1.47 and 1.78 M☉ and compactness parameters ξ1.75 of 0.302 and 0.604, respectively. The core-collapse simulations are carried out in 2D to nearly 3 s postbounce and show substantial differences in the times of shock revival and explosion energies. The 15.78 M☉ model begins exploding promptly at 120 ms postbounce when a strong density decrement at the Si– Si/O shell interface, not present in the 15.79 M☉ progenitor, encounters the stalled shock. The 15.79 M☉ model takes 100 ms longer to explode but ultimately produces a more powerful explosion. Both the larger mass accretion rate and the more massive core of the 15.79 M☉ model during the first 0.8 s postbounce time result in larger νe/n ̄e luminosities and RMS energies along with a flatter and higher-density heating region. The more-energetic explosion of the 15.79 M☉ model resulted in the ejection of twice as much 56Ni. Most of the ejecta in both models are moderately proton rich, though counterintuitively the highest electron fraction (Ye = 0.61) ejecta in either model are in the less-energetic 15.78 M☉ model, while the lowest electron fraction (Ye = 0.45) ejecta in either model are in the 15.79 M☉ model. 

We develop implicit-explicit (IMEX) schemes for neutrino transport in a background material in the context of a two-moment model that evolves the angular moments of a neutrino phase-space distribution function. Considering the upper and lower bounds that are introduced by Pauli’s exclusion principle on the moments, an algebraic moment closure based on Fermi-Dirac statistics and a convex-invariant time integrator both are demanded. A finite-volume/first-order discontinuous Galerkin(DG) method is used to illustrate how an algebraic moment closure based on Fermi-Dirac statistics is needed to satisfy the bounds. Several algebraic closures are compared with these bounds in mind, and the Cernohorsky and Bludman closure, which satisfies the bounds, is chosen for our IMEX schemes. For the convex-invariant time integrator, two IMEX schemes named PD-ARS have been proposed. PD-ARS denotes a convex-invariant IMEX Runge-Kutta scheme that is high-order accurate in the streaming limit, and works well in the diffusion limit. Our two PD-ARS schemes use second- and third-order, explicit, strong-stability-preserving Runge-Kutta methods as their explicit part, respectively, and therefore are second- and third-order accurate in the streaming limit, respectively. The accuracy and convex-invariance of our PD-ARS schemes are demonstrated in the numerical tests with a third-order DG method for spatial discretization and a simple Lax-Friedrichs flux. The method has been implemented in our high-order neutrino-radiation hydrodynamics (thornado) toolkit. We show preliminary results employing tabulated neutrino opacities. 

Building on the framework of Zhang & Shu [1,2], we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function f. The two-moment model is closed using algebraic moment closures; e.g., as proposed by Cernohorsky & Bludman [3] and Banach & Larecki [4]. Variations of this model have recently been used to simulate neutrino transport in nuclear astrophysics applications, including core-collapse supernovae and compact binary mergers. We employ the discontinuous Galerkin (DG) method for spatial discretization (in part to capture the asymptotic diffusion limit of the model) combined with implicit-explicit (IMEX) time integration to stably bypass short timescales induced by frequent interactions between particles and the background. Appropriate care is taken to ensure the method preserves strict algebraic bounds on the evolved moments (particle density and flux) as dictated by Pauli’s exclusion principle, which demands a bounded distribution function (i.e., f ∈ [0, 1]). This realizability-preserving scheme combines a suitable CFL condition, a realizability- enforcing limiter, a closure procedure based on Fermi-Dirac statistics, and an IMEX scheme whose stages can be written as a convex combination of forward Euler steps combined with a backward Euler step. The IMEX scheme is formally only first-order accurate, but works well in the diffusion limit, and — without interactions with the background — reduces to the optimal second-order strong stability-preserving explicit Runge-Kutta scheme of Shu & Osher [5]. Numerical results demonstrate the realizability-preserving properties of the scheme. We also demonstrate that the use of algebraic moment closures not based on Fermi-Dirac statistics can lead to unphysical moments in the context of fermion transport. 

The toolkit for high-order neutrino-radiation hydrodynamics (thornado) is being developed for simulations of core-collapse supernovae (CCSNe) and related problems. Current capabilities in thornado include solvers for the Euler equations — in non-relativistic and special relativistic limits — and the two-moment model of neutrino transport. The spatial discretization in thornado is based on the discontinuous Galerkin (DG) method, which is receiving increased attention from the computational astrophysics community. In this paper, we provide an overview of the numerical methods for the Euler equations in thornado, and present some encouraging preliminary numerical results from a set of basic tests in one and two spatial dimensions.