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

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

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

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

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

Core-Collapse Supernovae: Explosion Dynamics, Neutrinos and Gravitational Waves

The quest for the supernova explosion mechanism has been one of the outstanding challenges in computational astrophysics for several decades. Simulations have now progressed to a stage at which the solution appears close and neutrino and gravitational wave signals from self-consistent explosion models are becoming available. Here we focus one of the recent advances in supernova modeling, the inclusion of general relativity in multi-dimensional neutrino hydrodynamics simulations, and present the latest simulation results for an 11.2 and a 15 solar mass progenitor. We also mention 3D effects as another aspect in supernova physics awaiting further, more thorough investigation.Comment: Contribution to the Proceedings of HANSE 2011 workshop, 8 pages, 4 figure

Three-dimensional mixing and light curves: constraints on the progenitor of supernova 1987A

With the same method as used previously, we investigate neutrino-driven explosions of a larger sample of blue supergiant models. The larger sample includes three new presupernova stars. The results are compared with light-curve observations of the peculiar type IIP SN 1987A. The explosions were modeled in 3D with the neutrino-hydrodynamics code PROMETHEUS-HOTB, and light-curve calculations were performed in spherical symmetry with the radiation-hydrodynamics code CRAB. Our results confirm the basic findings of the previous work: 3D neutrino-driven explosions with SN 1987A-like energies synthesize an amount of Ni-56 that is consistent with the radioactive tail of the light curve. Moreover, the models mix hydrogen inward to minimum velocities below 400 km/s as required by spectral observations. Hydrodynamic simulations with the new progenitor models, which possess smaller radii than the older ones, show much better agreement between calculated and observed light curves in the initial luminosity peak and during the first 20 days. A set of explosions with similar energies demonstrated that a high growth factor of Rayleigh-Taylor instabilities at the (C+O)/He composition interface combined with a weak interaction of fast Rayleigh-Taylor plumes, where the reverse shock occurs below the He/H interface, provides a sufficient condition for efficient outward mixing of Ni-56 into the hydrogen envelope. This condition is realized to the required extent only in one of the older stellar models, which yielded a maximum velocity of around 3000 km/s for the bulk of ejected Ni-56, but failed to reproduce the helium-core mass of 6 Msun inferred from the absolute luminosity of the presupernova star. We conclude that none of the single-star progenitor models proposed for SN 1987A to date satisfies all constraints set by observations. (Abridged)Comment: 16 pages, 9 figures, 3 tables; accepted for publication in Astron. Astrophy

X-ray Absorption in Young Core-Collapse Supernova Remnants

The material expelled by core-collapse supernova (SN) explosions absorbs X-rays from the central regions. We use SN models based on three-dimensional neutrino-driven explosions to estimate optical depths to the center of the explosion, compare different progenitor models, and investigate the effects of explosion asymmetries. The optical depths below 2 keV for progenitors with a remaining hydrogen envelope are expected to be high during the first century after the explosion due to photoabsorption. A typical optical depth is $100 t_4^{-2} E^{-2}$, where $t_4$ is the time since the explosion in units of 10 000 days (${\sim}$27 years) and $E$ the energy in units of keV. Compton scattering dominates above 50 keV, but the scattering depth is lower and reaches unity already at ${\sim}$1000 days at 1 MeV. The optical depths are approximately an order of magnitude lower for hydrogen-stripped progenitors. The metallicity of the SN ejecta is much higher than in the interstellar medium, which enhances photoabsorption and makes absorption edges stronger. These results are applicable to young SN remnants in general, but we explore the effects on observations of SN 1987A and the compact object in Cas A in detail. For SN 1987A, the absorption is high and the X-ray upper limits of ${\sim}$100 Lsun on a compact object are approximately an order of magnitude less constraining than previous estimates using other absorption models. The details are presented in an accompanying paper. For the central compact object in Cas A, we find no significant effects of our more detailed absorption model on the inferred surface temperature.Comment: 21 pages, 7 figures. Accepted for publication in ApJ. Updated to match accepted version; added Section 2.5 on asymmetries and discussion on homologous expansion in preamble of Section