We present a detailed, three-dimensional hydrodynamic study of the neutrino-driven winds that emerge from the remnant of a neutron star merger. Our simulations are performed with the Newtonian, Eulerian code FISH, augmented by a detailed, spectral neutrino leakage scheme that accounts for heating due to neutrino absorption in optically thin conditions. Consistent with the earlier, two-dimensional study of Dessart et al. (2009), we find that a strong baryonic wind is blown out along the original binary rotation axis within ≈100 milliseconds after the merger. We compute a lower limit on the expelled mass of 3.5 × 10 −3 M , large enough to be relevant for heavy element nucleosynthesis. The physical properties vary significantly between different wind regions. For example, due to stronger neutrino irradiation, the polar regions show substantially larger electron fractions than those at lower latitudes. This has its bearings on the nucleosynthesis: the polar ejecta produce interesting r-process contributions from A ≈ 80 to about 130, while the more neutron-rich, lower-latitude parts produce in addition also elements up to the third r-process peak near A ≈ 195. We also calculate the properties of electromagnetic transients that are powered by the radioactivity in the wind, in addition to the "macronova" transient that stems from the dynamic ejecta. The high-latitude (polar) regions produce UV/optical transients reaching luminosities up to 10 41 erg s −1 , which peak around 1 day in optical and 0.3 days in bolometric luminosity. The lower-latitude regions, due to their contamination with high-opacity heavy elements, produce dimmer and more red signals, peaking after ∼ 2 days in optical and infrared. Our numerical experiments indicate that it will be difficult to infer the collapse time-scale of the hypermassive neutron star to a black hole based on the wind electromagnetic transient, at least for collapse time-scales larger than the wind production time-scale.

We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae and compact binary mergers. Based on previous gray leakage schemes, the ASL scheme computes the neutrino cooling rates by interpolating local production and diffusion rates (relevant in optically thin and thick regimes, respectively), separately for discretized values of the neutrino energy. Neutrino trapped components are also modeled, based on equilibrium and timescale arguments. The better accuracy achieved by the spectral treatment allows a more reliable computation of neutrino heating rates in optically thin conditions. The scheme has been calibrated and tested against Boltzmann transport in the context of Newtonian spherically symmetric models of core-collapse supernovae. ASL shows a very good qualitative and a partial quantitative agreement, for key quantities from collapse to a few hundreds of milliseconds after core bounce. We have proved the adaptability and flexibility of our ASL scheme coupling it to an axisymmetric Eulerian and to a three-dimensional SPH code to simulate core-collapse. Therefore, the neutrino treatment presented here is ideal for large parameter-space explorations, parametric studies, high-resolution tests, code developments, and long-term modeling of asymmetric configurations, where more detailed neutrino treatments are not available or currently computationally too expensive.

Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulate the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations, which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics. These matrix formulations achieve better interpolations of the physical magnitudes but they are, in general, not fully conservative. The matrix approach to the Euler equations has never been used in astrophysics. Aims. We develop and test a fully conservative SPH scheme based on a tensor formulation that can be applied to simulate astrophysical systems. Methods. In the proposed scheme, derivatives are calculated from an integral expression that leads to a tensor (instead of a vectorial) estimation of gradients and reduces to the standard formulation in the continuum limit. The new formulation improves the interpolation of physical magnitudes, leading to a set of conservative equations that resembles those of standard SPH. The resulting scheme is verified using a variety of well-known tests, all of them simulated in two dimensions. We also discuss an application of the proposed tensor method to astrophysics by simulating the stability of a Sun-like polytrope calculated in three dimensions. Results. The proposed scheme is able to improve the results of standard SPH in the two-dimensional tests, especially in the simulation of subsonic hydrodynamic instabilities. Our results for the stability of the Sun-like polytrope suggest that the new method can be used in astrophysics to carry out three-dimensional calculations with a computational cost that is only slightly higher (i.e. ≤50% for a serial code) than that of a standard SPH formulation. Conclusions. A formalism based on a matrix approach to Euler SPH equations was developed and checked. The new scheme is more accurate because of the re-normalization imposed on the interpolations, which is fully conservative and probably less prone to undergo the tensile instability. The analysis of several test cases suggest that the method may improve the simulation of both subsonic and supersonic systems. An application of the tensor method to astrophysics is, for the first time, successfully carried out. These encouraging results indicates that more work should be invested in the applications of matrix SPH formulations to astrophysics.

Aims. Hydrodynamical instabilities and shocks are ubiquitous in astrophysical scenarios. Therefore, an accurate numerical simulation of these phenomena is mandatory to correctly model and understand many astrophysical events, such as supernovas, stellar collisions, or planetary formation. In this work, we attempt to address many of the problems that a commonly used technique, smoothed particle hydrodynamics (SPH), has when dealing with subsonic hydrodynamical instabilities or shocks. To that aim we built a new SPH code named SPHYNX, that includes many of the recent advances in the SPH technique and some other new ones, which we present here. Methods. SPHYNX is of Newtonian type and grounded in the Euler-Lagrange formulation of the smoothed-particle hydrodynamics technique. Its distinctive features are: the use of an integral approach to estimating the gradients; the use of a flexible family of interpolators called sinc kernels, which suppress pairing instability; and the incorporation of a new type of volume element which provides a better partition of the unity. Unlike other modern formulations, which consider volume elements linked to pressure, our volume element choice relies on density. SPHYNX is, therefore, a density-based SPH code. Results. A novel computational hydrodynamic code oriented to Astrophysical applications is described, discussed, and validated in the following pages. The ensuing code conserves mass, linear and angular momentum, energy, entropy, and preserves kernel normalization even in strong shocks. In our proposal, the estimation of gradients is enhanced using an integral approach. Additionally, we introduce a new family of volume elements which reduce the so-called tensile instability. Both features help to suppress the damp which often prevents the growth of hydrodynamic instabilities in regular SPH codes. Conclusions. On the whole, SPHYNX has passed the verification tests described below. For identical particle setting and initial conditions the results were similar (or better in some particular cases) than those obtained with other SPH schemes such as GADGET-2, PSPH or with the recent density-independent formulation (DISPH) and conservative reproducing kernel (CRKSPH) techniques.

a b s t r a c tA set of interpolating functions of the type f ðvÞ ¼ fsinÀ Á g n is analyzed in the context of the smoothed-particle hydrodynamics (SPH) technique. The behaviour of these kernels for several values of the parameter n has been studied either analytically as well as numerically in connection with several tests carried out in two-dimensions. The main advantage of this kernel relies in its flexibility because for n ¼ 3 it is similar to the standard widely used cubic-spline, whereas for n > 3 the interpolating function becomes more centrally condensed, being well suited to track discontinuities such as shock fronts and thermal waves.

Abstract. Core-collapse supernovae are the first polluters of heavy elements in the galactic history. As such, it is important to study the nuclear compositions of their ejecta, and understand their dependence on the progenitor structure (e.g., mass, compactness, metallicity). Here, we present a detailed nucleosynthesis study based on two long-term, two-dimensional core-collapse supernova simulations of a 11.2 M and a 17.0 M star. We find that in both models nuclei well beyond the iron group (up to Z ≈ 44) can be produced, and discuss in detail also the nucleosynthesis of the p-nuclei 92,94 Mo and 96,98 Ru. While we observe the production of 92 Mo and 94 Mo in slightly neutron-rich conditions in both simulations, 96,98 Ru can only be produced efficiently via the νp-process. Furthermore, the production of Ru in the νp-process heavily depends on the presence of very proton-rich material in the ejecta. This disentanglement of production mechanisms has interesting consequences when comparing to the abundance ratios between these isotopes in the solar system and in presolar grains.

The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a Sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ablative implosion of a small capsule). New material concerning the standard SPH formalism is given. That includes the numerical handling of those mass points which move close to the singularity axis, more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self-gravity in the simulations. The algorithm developed to compute gravity does not rely in any sort of grid, leading to a numerical scheme totally compatible with the Lagrangian nature of the SPH equations.Peer ReviewedPostprint (published version

Context. Modeling core-collapse supernovae (SNe) with neutrino transport in three dimensions (3D) requires tremendous computing resources and some level of approximation. We present a first comparison study of core-collapse SNe in 3D with different physics approximations and hydrodynamics codes. Aims. The objective of this work is to assess the impact of the hydrodynamics code, approximations for the neutrino, gravity treatments, and rotation on the simulation of core-collapse SNe in 3D. Methods. We use four different hydrodynamics codes in this work (ELEPHANT, FLASH, fGR1, and SPHYNX) in combination with two different neutrino treatments, the isotropic diffusion source approximation (IDSA) and two-moment M1, and three different gravity treatments (Newtonian, 1D General Relativity correction, and full General Relativity). Additional parameters discussed in this study are the inclusion of neutrino-electron scattering via a parametrized deleptonization and the influence of rotation. Results. The four codes compared in this work include Eulerian and fully Lagrangian (smoothed particle hydrodynamics) codes for the first time. They show agreement in the overall evolution of the collapse phase and early post-bounce within the range of 10% (20% in some cases). The comparison of the different neutrino treatments highlights the need to further investigate the antineutrino luminosities in IDSA, which tend to be relatively high. We also demonstrate the requirement for a more detailed heavy-lepton neutrino leakage. When comparing with a full General Relativity code, including an M1 transport method, we confirm the influence of neutrino-electron scattering during the collapse phase, which is adequately captured by the parametrized deleptonization scheme. Also, the effective general relativistic potential reproduces the overall dynamic evolution correctly in all Newtonian codes. Additionally, we verify that rotation aids the shock expansion and estimate the overall angular momentum losses for each code in rotating scenarios.