Computer simulation confirms supernova mechanism in three dimensions

During their lifetimes, stars "burn" light elements such as hydrogen into heavier ones by nuclear fusion. This process produces energy until, at the end, an iron core is formed. Since iron has the largest binding energy of all nuclei, no heavier elements can be produced in fusion reactions and nuclear burning ceases. However, the iron core continues to grow by fusion processes at its surface. At this stage, gravity is balanced by the quantum mechanical pressure of the electrons. Similar to a white dwarf star, there is a critical mass above which the iron core can no longer resist the pull of gravity and collapses. Under appropriate conditions, this results in a powerful stellar explosion: a supernova.

Fig. 1: History of the explosion in the stellar interior: within fractions of a second, the core inflates to many times its volume. The snapshots impressively show that the explosion is far from symmetric and that convective buoyancy and turbulence play an important role. The colour code indicates the speed of the ejected material. The thin bluish line shows the position of the shock front.

Already in the middle of the past century, first theories proposed the origin of the supernova energy: Because of the extreme gravitational force, the core collapses within fractions of a second to produce a neutron star. Gravitational binding energy is released and transported outwards by a shock front, but gets quickly absorbed by the outer layers of the iron core. To actually trigger the explosion, an additional effect is required: heating by neutrinos (see Highlight 2001). These elementary particles are generated in vast numbers in the new-born neutron star and propagate outwards relatively freely, once they are outside the neutron star's surface. Therefore they can extract energy from the so-called "cooling layer" and deposit this energy at greater distances from the neutron star where they are re-absorbed and thus heat the plasma in the so-called "heating layer" behind the shock wave. If the amount of deposited energy is large enough, the shock is pushed outwards, which eventually disrupts the star in a supernova. At least that is how the theory goes.

The process to confirm this paradigm in detailed physical models, however, has been long: In the 1980s, the first star "exploded" in a computer, but only in spherically symmetric (i.e. one-dimensional) models and with some special assumptions to simplify the description of the physics involved. But the observation of supernova 1987A showed that multi-dimensional effects play an important role during the explosion. The shells surrounding the neutron star are mixed by convection, which further supports neutrino heating. After a few decades, scientists could confirm the basic functioning of the neutrino mechanism with two-dimensional models (see Press Release 2009). Still, the forced rotational symmetry about an arbitrary axis severely restricts motions of the stellar plasma. In addition, turbulent flows behave differently under these symmetry assumptions compared to three dimensions. It is therefore necessary to perform three-dimensional calculations to model all processes during the supernova correctly.

So far, simulations have not yielded successful explosions in three dimensions (Press Release 2013 und Highlight 2014). But now, the scientists obtained their long desired result: the first successful, neutrino-driven explosion of a star with an initial mass of 9.6 solar masses in a three-dimensional, self-consistent simulation (see Fig. 1). The challenge was to describe the neutrinos as correctly as possible, so that the resulting complex calculation kept even supercomputers busy for a few months. The new method provides the currently most complete description of how neutrinos interact with matter in a supernova calculation. In particular, there is an open, controversial question whether three-dimensional turbulence in the neutrino heated plasma helps or hinders the explosion.

In this case, the answer is definitely yes: three-dimensional turbulence leads to about 10% higher explosion energy. Turbulent effects in the heating layer change the flow of stellar material into the cooling layer, which means that the temperature in this region remains lower. As the cooling by neutrinos strongly depends on temperature, the energy loss by neutrino emission decreases at lower temperature and the explosion gets stronger. However, it is difficult to predict whether this phenomenon could play an equally important role for even more massive stars. To answer this question, the scientists need further simulations. They also plan to calculate the explosion with even higher resolution to better resolve turbulence and investigate it on smaller scales. Another important question is whether the star might have been asymmetric before collapse and how this would affect the explosion. So even with this significant milestone, the astrophysicists still have some way to go.

Tobias Melson, Hans-Thomas Janka
Public outreach: Hannelore Hämmerle