Non-spherical core collapse supernovae

III. Evolution towards homology and dependence on the numerical resolution

¹ Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland
² Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA e-mail: tplewa@fsu.edu
³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, 85741 Garching, Germany

Received: 8 October 2009
Accepted: 24 June 2010

Abstract

Aims. We study the hydrodynamic evolution of a non-spherical core-collapse supernova in two spatial dimensions. We begin our study from the moment of shock revival – taking into account neutrino heating and cooling, nucleosynthesis, convection, and the standing accretion shock (SASI) instability of the supernova blast – and continue for the first week after the explosion when the expanding flow becomes homologous and the ejecta enter the early supernova remnant (SNR) phase. We observe the growth and interaction of Richtmyer-Meshkov, Rayleigh-Taylor, and Kelvin-Helmholtz instabilities resulting in an extensive mixing of the heavy elements throughout the ejecta. We obtain a series of models at progressively higher resolution and provide a discussion of numerical convergence.

Methods. Different from previous studies, our computations are performed in a single domain. Periodic mesh mapping is avoided. This is made possible by employing cylindrical coordinates, and an adaptive mesh refinement (AMR) strategy in which the computational workload (defined as the product of the total number of computational cells and the length of the time step) is monitored and, if necessary, reduced.

Results. Our results are in overall good agreement with the AMR simulations we have reported in the past. We show, however, that numerical convergence is difficult to achieve, due to the strongly non-linear nature of the problem. Even more importantly, we find that our model displays a strong tendency to expand laterally away from the equatorial plane and toward the poles. We demonstrate that this expansion is a physical property of the low-mode, SASI instability. Although the SASI operates only within about the first second of the explosion, it leaves behind a large lateral velocity gradient in the post shock layer which affects the evolution for minutes and hours later. This results in a prolate deformation of the ejecta and a fast advection of the highest-velocity ⁵⁶Ni-rich material from moderate latitudes to the polar regions of our grid within only 300 s after core bounce. This effect – if confirmed by 3D simulations – might actually be responsible for the global asymmetry of the nickel lines in SN 1987A. Yet, it also poses difficulties for the analysis of 2D SASI-dominated explosions in terms of the maximum nickel velocities, since discretization errors at the poles are considered non-negligible.

Conclusions. The simulations demonstrate that significant radial and lateral motions in the post-shock region, produced by convective overturn and the SASI during the early explosion phase, contribute to the evolution for minutes and hours after shock revival. They lead to both later clump formation, and a significant prolate deformation of the ejecta which are observed even as late as one week after the explosion. This ejecta deformation may be considered final, since the expansion has long become homologous by that time. As pointed out in the recent analysis by Kjaer et al., such an ejecta morphology is in good agreement with the observational data of SN 1987A. Systematic future studies are needed to investigate how the SASI-induced late-time lateral expansion that we find in this work depends on the dominant mode of the SASI when the early explosion phase ends, and to which extent it is affected by the dimensionality of the simulations. The impact on and importance of the SASI for the distribution of iron group nuclei and the morphology of the young SNR argues for future three-dimensional explosion and post-explosion studies on singularity-free grids that cover the entire sphere. Given the results of our 2D resolution study, present three-dimensional simulations must be regarded as underresolved, and their conclusions must be verified by a proper numerical convergence analysis in three dimensions.