A Generalized Solution Method for Parallelized Computation of the Three-dimensional Gravitational Potential on a Multi-patch grid in Spherical Geometry

We present a generalized algorithm based on a spherical harmonics expansion method for efficient computation of the three-dimensional gravitational potential on a multi-patch grid in spherical geometry. Instead of solving for the gravitational potential by superposition of separate contributions from the mass density distribution on individual grid patch our new algorithm computes directly the gravitational potential due to contributions from all grid patches in one computation step, thereby reducing the computational cost of the gravity solver. This is possible by considering a set of angular weights which are derived from rotations of spherical harmonics functions defined in a global coordinate system that is common for all grid patches. Additionally, our algorithm minimizes data communication between parallel compute tasks by eliminating its proportionality to the number of subdomains in the grid configuration, making it suitable for parallelized computation on a multi-patch grid configuration with any number of subdomains. Test calculations of the gravitational potential of a tri-axial ellipsoidal body with constant mass density on the Yin-Yang two-patch overset grid demonstrate that our method delivers the same level of accuracy as a previous method developed for the Yin-Yang grid, while offering improved computation efficiency and parallel scaling behaviour.Comment: 12 pages, 5 figures; accepted for publication in Ap

Three-Dimensional Simulations of Core-Collapse Supernovae: From Shock Revival to Shock Breakout

We present 3D simulations of core-collapse supernovae from blast-wave initiation by the neutrino-driven mechanism to shock breakout from the stellar surface, considering two 15 Msun red supergiants (RSG) and two blue supergiants (BSG) of 15 Msun and 20 Msun. We demonstrate that the metal-rich ejecta in homologous expansion still carry fingerprints of asymmetries at the beginning of the explosion, but the final metal distribution is massively affected by the detailed progenitor structure. The most extended and fastest metal fingers and clumps are correlated with the biggest and fastest-rising plumes of neutrino-heated matter, because these plumes most effectively seed the growth of Rayleigh-Taylor (RT) instabilities at the C+O/He and He/H composition-shell interfaces after the passage of the SN shock. The extent of radial mixing, global asymmetry of the metal-rich ejecta, RT-induced fragmentation of initial plumes to smaller-scale fingers, and maximal Ni and minimal H velocities do not only depend on the initial asphericity and explosion energy (which determine the shock and initial Ni velocities) but also on the density profiles and widths of C+O core and He shell and on the density gradient at the He/H transition, which lead to unsteady shock propagation and the formation of reverse shocks. Both RSG explosions retain a great global metal asymmetry with pronounced clumpiness and substructure, deep penetration of Ni fingers into the H-envelope (with maximum velocities of 4000-5000 km/s for an explosion energy around 1.5 bethe) and efficient inward H-mixing. While the 15 Msun BSG shares these properties (maximum Ni speeds up to ~3500 km/s), the 20 Msun BSG develops a much more roundish geometry without pronounced metal fingers (maximum Ni velocities only ~2200 km/s) because of reverse-shock deceleration and insufficient time for strong RT growth and fragmentation at the He/H interface.Comment: 21 pages, 15 figures; revised version with minor changes in Sect.1; accepted by Astron. Astrophy

Spatial distribution of radionuclides in 3D models of SN 1987A and Cas A

Fostered by the possibilities of multi-dimensional computational modeling, in particular the advent of three-dimensional (3D) simulations, our understanding of the neutrino-driven explosion mechanism of core-collapse supernovae (SNe) has experienced remarkable progress over the past decade. First self-consistent, first-principle models have shown successful explosions in 3D, and even failed cases may be cured by moderate changes of the microphysics inside the neutron star (NS), better grid resolution, or more detailed progenitor conditions at the onset of core collapse, in particular large-scale perturbations in the convective Si and O burning shells. 3D simulations have also achieved to follow neutrino-driven explosions continuously from the initiation of the blast wave, through the shock breakout from the progenitor surface, into the radioactively powered evolution of the SN, and towards the free expansion phase of the emerging remnant. Here we present results from such simulations, which form the basis for direct comparisons with observations of SNe and SN remnants in order to derive constraints on the still disputed explosion mechanism. It is shown that predictions based on hydrodynamic instabilities and mixing processes associated with neutrino-driven explosions yield good agreement with measured NS kicks, light-curve properties of SN 1987A, and asymmetries of iron and 44Ti distributions observed in SN 1987A and Cassiopeia A.Comment: 9 pages, 6 figures; submitted to: "SN 1987A, 30 years later", Proceedings IAU Symposium No. 331, 2017; eds. M. Renaud et a

Light curve analysis of ordinary type IIP supernovae based on neutrino-driven explosion simulations in three dimensions

Type II-plateau supernovae (SNe IIP) are the most numerous subclass of core-collapse SNe originating from massive stars. In the framework of the neutrino-driven explosion mechanism, we study the SN outburst properties for a red supergiant progenitor model and compare the corresponding light curves with observations of the ordinary Type IIP SN 1999em. Three-dimensional (3D) simulations of (parametrically triggered) neutrino-driven explosions are performed with the (explicit, finite-volume, Eulerian, multifluid hydrodynamics) code PROMETHEUS, using a presupernova model of a 15 Msun star as initial data. At approaching homologous expansion, the hydrodynamical and composition variables of the 3D models are mapped to a spherically symmetric configuration, and the simulations are continued with the (implicit, Lagrangian radiation-hydrodynamics) code CRAB to follow the blast-wave evolution during the SN outburst. Our 3D neutrino-driven explosion model with an explosion energy of about 0.5x10^51 erg produces Ni-56 in rough agreement with the amount deduced from fitting the radioactively powered light-curve tail of SN 1999em. The considered presupernova model, 3D explosion simulations, and light-curve calculations can explain the basic observational features of SN 1999em, except for those connected to the presupernova structure of the outer stellar layers. Our 3D simulations show that the distribution of Ni-rich matter in velocity space is asymmetric with a strong dipole component that is consistent with the observations of SN 1999em. The monotonic luminosity decline from the plateau to the radioactive tail in ordinary SNe IIP is a manifestation of the intense turbulent mixing at the He/H composition interface.Comment: 16 pages, 13 figures, 2 tables; added figure, discussions, and references; accepted for publication in Ap

The infancy of core-collapse supernova remnants

We present 3D hydrodynamic simulations of neutrino-driven supernovae (SNe) with the PROMETHEUS-HOTB code, evolving the asymmetrically expanding ejecta from shock breakout until they reach the homologous expansion phase after roughly one year. Our calculations continue the simulations for two red supergiant (RSG) and two blue supergiant (BSG) progenitors by Wongwathanarat et al., who investigated the growth of explosion asymmetries produced by hydrodynamic instabilities during the first second of the explosion and their later fragmentation by Rayleigh-Taylor instabilities. We focus on the late time acceleration and inflation of the ejecta caused by the heating due to the radioactive decay of $^{56}$Ni to $^{56}$Fe and by a new outward-moving shock, which forms when the reverse shock from the He/H-shell interface compresses the central part of the ejecta. The mean velocities of the iron-rich ejecta increase between 100 km/s and 350 km/s ($\sim$8-30\%), and the fastest one percent of the iron accelerates by up to $\sim$1000 km/s ($\sim$20-25\%). This 'Ni-bubble effect', known from 1D models, accelerates the bulk of the nickel in our 3D models and causes an inflation of the initially overdense Ni-rich clumps, which leads to underdense, extended fingers, enveloped by overdense skins of compressed surrounding matter. We also provide volume and surface filling factors as well as a spherical harmonics analysis to characterize the spectrum of Ni-clump sizes quantitatively. Three of our four models give volume filling factors larger than 0.3, consistent with what is suggested for SN 1987A by observations.Comment: 30 pages, 22 figures, 6 tables, extended discussion of correlation of late and initial explosion asymmetries, accepted by MNRA

Supernova 1987A: neutrino-driven explosions in three dimensions and light curves

The well-studied type IIP SN 1987A, produced by the explosion of a blue supergiant (BSG) star, is a touchstone for massive-star evolution, simulations of neutrino-driven explosions, and modeling of light curves and spectra. In the framework of the neutrino-driven mechanism, we study the dependence of explosion properties on the structure of four different BSGs and compare the corresponding light curves with observations of SN 1987A. We perform 3D simulations with the PROMETHEUS code until about one day and map the results to the 1D code CRAB for the light curve calculations. All of our 3D models with explosion energies compatible with SN 1987A produce 56Ni in rough agreement with the amount deduced from fitting the radioactively powered light-curve tail. One of the progenitors yields maximum velocities of ~3000 km/s for the bulk of ejected 56Ni, consistent with observations. In all of our models inward mixing of hydrogen during the 3D evolution leads to minimum H-velocities below 100 km/s, in good agreement with spectral observations. The considered BSG models, 3D explosion simulations, and light-curve calculations can thus explain basic observational features of SN 1987A. However, all progenitors have too large pre-SN radii to reproduce the narrow initial luminosity peak, and the structure of their outer layers is not suitable to match the observed light curve during the first 30-40 days. Only one stellar model has a structure of the He core and the He/H composition interface that enables sufficient outward mixing of 56Ni and inward mixing of hydrogen to produce a good match of the dome-like shape of the observed light-curve maximum. But this model falls short of the He-core mass of 6 Msun inferred from the absolute luminosity of the pre-SN star. The lack of an adequate pre-SN model for SN 1987A is a pressing challenge for the theory of massive-star evolution. (Abridged)Comment: 18 pages, 11 figures, 4 tables; revised version, accepted by Astron. Astrophy

SASI Activity in Three-Dimensional Neutrino-Hydrodynamics Simulations of Supernova Cores

The relevance of the standing accretion shock instability (SASI) compared to neutrino-driven convection in three-dimensional (3D) supernova-core environments is still highly controversial. Studying a 27 Msun progenitor, we demonstrate, for the first time, that violent SASI activity can develop in 3D simulations with detailed neutrino transport despite the presence of convection. This result was obtained with the Prometheus-Vertex code with the same sophisticated neutrino treatment so far used only in 1D and 2D models. While buoyant plumes initially determine the nonradial mass motions in the postshock layer, bipolar shock sloshing with growing amplitude sets in during a phase of shock retraction and turns into a violent spiral mode whose growth is only quenched when the infall of the Si/SiO interface leads to strong shock expansion in response to a dramatic decrease of the mass accretion rate. In the phase of large-amplitude SASI sloshing and spiral motions, the postshock layer exhibits nonradial deformation dominated by the lowest-order spherical harmonics (l=1, m=0,-1,+1) in distinct contrast to the higher multipole structures associated with neutrino-driven convection. We find that the SASI amplitudes, shock asymmetry, and nonradial kinetic energy in 3D can exceed those of the corresponding 2D case during extended periods of the evolution. We also perform parametrized 3D simulations of a 25 Msun progenitor, using a simplified, gray neutrino transport scheme, an axis-free Yin-Yang grid, and different amplitudes of random seed perturbations. They confirm the importance of the SASI for another progenitor, its independence of the choice of spherical grid, and its preferred growth for fast accretion flows connected to small shock radii and compact proto-neutron stars as previously found in 2D setups.Comment: 17 pages, 10 figures, accepted by The Astrophysical Journa

Induced Rotation in 3D Simulations of Core Collapse Supernovae: Implications for Pulsar Spins

It has been suggested that the observed rotation periods of radio pulsars might be induced by a non-axisymmetric spiral-mode instability in the turbulent region behind the stalled supernova bounce shock, even if the progenitor core was not initially rotating. In this paper, using the three-dimensional AMR code CASTRO with a realistic progenitor and equation of state and a simple neutrino heating and cooling scheme, we present a numerical study of the evolution in 3D of the rotational profile of a supernova core from collapse, through bounce and shock stagnation, to delayed explosion. By the end of our simulation ($\sim$420 ms after core bounce), we do not witness significant spin up of the proto-neutron star core left behind. However, we do see the development before explosion of strong differential rotation in the turbulent gain region between the core and stalled shock. Shells in this region acquire high spin rates that reach $\sim$$150\,$ Hz, but this region contains too little mass and angular momentum to translate, even if left behind, into rapid rotation for the full neutron star. We find also that much of the induced angular momentum is likely to be ejected in the explosion, and moreover that even if the optimal amount of induced angular momentum is retained in the core, the resulting spin period is likely to be quite modest. Nevertheless, induced periods of seconds are possible.Comment: Accepted to the Astrophysical Journa

Modelling supernova nebular lines in 3D with ExTraSS\texttt{ExTraSS}

We present $\texttt{ExTraSS}$ (EXplosive TRAnsient Spectral Simulator), a newly developed code aimed at generating 3D spectra for supernovae in the nebular phase by using modern multi-dimensional explosion models as input. It is well established that supernovae are asymmetric by nature, and that the morphology is encoded in the line profiles during the nebular phase, months after the explosion. In this work, we use $\texttt{ExTraSS}$ to study one such simulation of a $3.3\,M_\odot$ He-core explosion ($M_\text{ejecta}=1.3\,M_\odot$, $E_\text{kin}=1.05\times10^{51}\,$erg) modelled with the $\texttt{Prometheus-HotB}$ code and evolved to the homologous phase. Our code calculates the energy deposition from the radioactive decay of $^{56}$Ni $\rightarrow$ $^{56}$Co $\rightarrow$ $^{56}$Fe and uses this to determine the Non-Local-Thermodynamic-Equilibrium temperature, excitation and ionization structure across the nebula. From the physical condition solutions we generate the emissivities to construct spectra depending on viewing angles. Our results show large variations in the line profiles with viewing angles, as diagnosed by the first three moments of the line profiles; shifts, widths, and skewness. We compare line profiles from different elements, and study the morphology of line-of-sight slices that determine the flux at each part of a line profile. We find that excitation conditions can sometimes make the momentum vector of the ejecta emitting in the excited states significantly different from that of the bulk of the ejecta of the respective element, thus giving blueshifted lines for bulk receding material, and vice versa. We compare the 3.3 $M_\odot$ He-core model to observations of the Type Ib supernova SN 2007Y.Comment: 20 pages, 15 Figures 2 Tables. Accepted for publication in MNRA