According to Einstein's General Theory of Relativity, binary systems of two neutron stars emit some of their orbital kinetic energy and angular momentum in the form of gravitational waves. Therefore, the stars spiral in towards each other until they finally merge. A black hole forms, swallowing most of the matter immediately. For a short period of time, however, a small fraction of the gas forms a torus, which is rotating rapidly about the black hole. In less than a second, this remnant falls onto the black hole, liberating ultrafast jets of plasma (akin to a huge and extremely powerful geyser), which are later an intense source of gamma radiation, a so-called short gamma-ray burst (GRB).

Most neutron stars possess a magnetic field which can be directly detected in pulsars. This, in principle, could affect the merger. Dramatic effects occur only at field strengths largely exceeding all observed values - even the 100 trillion Gauss observed for so-called magnetars, the most strongly magnetised neutron stars. Somewhat weaker effects, however, can occur for smaller field strengths if the field is amplified during the merger.

As soon as the neutron stars touch each other, a thin layer forms where the gas is flowing in opposite directions. This contact layer is unstable against the so-called shear instability (see Fig. 1). After some time, roughly circular vortices develop. Magnetic field lines embedded in the gas are stretched by the vortex flow, leading to an amplification of the field -- similar to the increasing tension of a rubber band when it is stretched. In previous studies, D. Price and S. Rosswog estimated that the magnetic field could reach values in excess of a thousand trillion Gauss by this mechanism; if this holds, merging neutron stars would be by far the most powerful magnets in the universe.

For a simulation of the interaction between the gas and the magnetic field, the model of these fine structures has to be very accurate, which comes at a high computational cost. On the other hand, to follow the motion of the two neutron stars one needs to simulate a large domain that is covering both stars. Even though the extremely high accuracy is needed only in a small part of this large domain, simulations of the entire merger that are able to describe in detail the magnetised turbulence in the contact layer are currently not feasible.

Large scale models of the merger, which include the final phase of approach before the neutron stars touch each other, cannot determine an accurate value of the expected field strength, although they give an adequate description of the merger process in many other respects. Scientists at the Max Planck Institute for Astrophysics and the University of Valencia have therefore performed simulations of magnetised shear flows resembling those in merging neutron stars. They considered only regions of a few hundred metres next to the contact layer, thus simulating only a small part of the entire merger that encomasses a few tens of kilometres.

The flow is unstable. Initially, the magnetic field grows very rapidly along with the shear instability. After a short time, however, a vortex forms and terminates the growth of the shear instability, while the magnetic field continues to grow as the vortex flow stretches the field lines (see Fig.2).

The magnetic field affects the gas flow noticeably only if its energy is comparable to the kinetic energy of the gas. In this case, the magnetic field is sufficiently strong to resist further stretching and exerts forces onto the matter. This decelerates the rotation of the vortex, which means that the field is no longer amplified. In extreme cases, the vortex can be disrupted completely (see Fig. 3). At this stage, the magnetic field decreases, partly because its energy is used to decelerate the flow, partly because of dissipation in secondary hydro-magnetic instabilities.

The maximum field attainable depends only on the shear flow and not on the initial field strength. However, the growth of the magnetic field is not uniform across the whole unstable, turbulent shearing layer. A huge magnetic field may be built up in only small and localised parts of the layer, while the rest of the layer retains the initial (weak) field (see Fig. 4). On average, the mean value of the field is smaller the weaker the initial field is, and the back-reaction of the field onto the flow is significantly slower.

In merging neutron stars, these results show that we can indeed expect extremely strong magnetic fields in the shear flows, even if both neutron stars are only weakly magnetised. The impact of the field, however, is limited as only a small fraction of the gas is threaded by a strong field.

Martin Obergaulinger, Miguel Angel Aloy, Ewald Müller

The computations were performed at the Rechenzentrum Garching (RZG) and the Barcelona Supercomputing Center - Centro Nacional de Supercomputación.

Publication

M. Obergaulinger, M.A. Aloy, E. Müller, "Local simulations of the magnetized Kelvin-Helmholtz instability in neutron-star mergers", Astronomy & Astrophysics 515 (2010), id.A30