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Three Dimensions of Core Collapse

TITLE: Dimensional Dependence of the Hydrodynamics of Core-Collapse Supernovae
AUTHORS: Joshua Dolence, Adam Burrows, Jeremiah Murphy, Jason Nordhaus
FIRST AUTHOR’S INSTITUTION: Princeton

Side-by-side comparison of 2D (left) and 3D (right) models with the same initial conditions and neutrino luminosity. The panels show, from top to bottom, entropy, radial velocity, magnitude of vorticity, and velocity divergence. The 3D models show more small-scale structure and don't have a preferred axis. (Image credit: Dolence et al 2012).

Astronomers studying supernovae have long pursued a challenging goal: an end-to-end simulation of a core-collapse supernova, from the beginnings of collapse to the explosion. Core-collapse supernovae (CCSN) occur when a massive star reaches the end of its life and its dense iron core can no longer support itself. The core collapses on itself (hence the name) and becomes a neutron star, while an outgoing shock wave explodes the rest of the star in a fiery display. The shock wave comes from the original collapse of the core; when the core becomes a neutron star, this inward-moving shock “bounces” off of it, turns around and begins to move outwards.

When the original model of CCSN was developed, it seemed like this shock would just keep moving outwards and explode the rest of the star. However, simulations showed that the pressure of the rest of the star trying to fall down would cause the shock to stall out. An extra injection of energy was necessary to revive this shock and send it on its way. This injection came in the form of neutrino reheating. Usually neutrinos barely interact with matter; but at the huge neutrino luminosities, temperatures, and densities in the collapsing pre-supernova star, neutrinos can in theory deposit enough energy to revive the stalled shock and touch off the explosion.

This mechanism works out both mathematically and in 1D simulations. However, we’ve had a lot of trouble getting it to work in more dimensions. Handling the neutrino transport properly requires very complex transport calculations, not to mention all the existing problems of modeling convection and turbulence on small scales in 3D. Because of the prohibitive computational expense of such models, the really accurate neutrino physics have thus far only been implemented in 2D. This paper seeks to investigate whether there are systematic differences in fluid behavior between 2D and 3D models in order to figure out whether a 2D model can really stand in for a 3D one.

Rather than model the complex neutrino physics, the authors use the “lightbulb” approximation, in which the neutrinos are modeled as an external energy source providing a certain amount of heating. They implement 6 simple models, 3 in 2D and 3 in 3D, with 3 different choices of neutrino luminosity, and look for systematic differences in the key parameters that measure how likely a simulated star is to explode.

The authors find that there are substantial differences between 2D and 3D models in the structure of the fluid flow around the core. The 2D models have higher integrated net heating rates and more mass being heated by neutrinos, while the 3D models have larger shock radii (the position of the stalled shock). All of these parameters influence when – and if – a CCSN will actually explode. They found that when their models did explode, the 3D models exploded earlier than their 2D models.

They also found that 2D models showed too much energy in long wavelength disturbances – sloshing motions from side to side. In 3 dimensions fluid dynamics theory predicts that energy moves from large scales (long wavelengths, or big motions) down to small scales (short wavelengths, or short motions like turbulence). In 2 dimensions, however, this energy cascade reverses, and energy will tend to move from small-scale disturbances up to large-scale ones – an unrealistic effect. The 2D models in this paper show that reversed energy flow, and imply that as much as 50% of the energy in the lowest mode in the 2D models may be an artifact of this process. This has serious implications for the study of the standing accretion shock instability (SASI). The SASI is a sloshing side-to-side motion that appears in many simulations of CCSN during the period where the shock has stalled out above the neutron star core, but matter is still flowing inwards. Gradually an instability builds up that causes the shock to move from side to side, bulging and distorting (you can watch a video of the SASI happening in shallow water here). The SASI has recently gained some credence as the phenomenon that finally triggers the actual explosion in a CCSN. However, if 2D simulations are artificially dumping energy into sloshing motions, the authors suggest that it may be impossible to disentangle the actual effect of the SASI from the effect of this inverse energy cascade.

In the end the authors come to the same conclusion that many papers before them have reached – we’re not going to know for sure until we can get 3D models with full neutrino transport physics and radiation hydrodynamics. Although such models are expensive now, supercomputers are only improving, and there’s hope that before long we may be able to tackle the full problem.

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I’m a graduate student at the University of California – Santa Cruz, working with Stan Woosley on simulations of supernovae. In the past I’ve tinkered with gamma-ray astronomy, galaxy evolution, exoplanet detection, and instrument design. I like supercomputers, aircraft, observing runs, loud techno, and videogames. I am on an unending quest to develop the nerdiest joke in the world. You can find me on Twitter at @GravityAndLight.

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