Critical fields and growth rates of the Tayler instability as probed by a columnar gallium experiment

TL;DR

This study experimentally and theoretically investigates the Tayler instability in a liquid-metal setup, confirming critical magnetic fields and growth rates relevant to astrophysical phenomena like stellar core rotation.

Contribution

It provides the first laboratory measurements of the critical fields and growth rates of the Tayler instability, validating theoretical predictions with experiments.

Findings

Critical Hartmann number matches theoretical predictions

Measured growth rates of nonaxisymmetric modes are on the order of minutes

Instability characteristics are independent of the experiment size

Abstract

Many astrophysical phenomena (such as the slow rotation of neutron stars or the rigid rotation of the solar core) can be explained by the action of the Tayler instability of toroidal magnetic fields in the radiative zones of stars. In order to place the theory of this instability on a safe fundament it has been realized in a laboratory experiment measuring the critical field strength, the growth rates as well as the shape of the supercritical modes. A strong electrical current flows through a liquid-metal confined in a resting columnar container with an insulating outer cylinder. As the very small magnetic Prandtl number of the gallium-indium-tin alloy does not influence the critical Hartmann number of the field amplitudes, the electric currents for marginal instability can also be computed with direct numerical simulations. The results of this theoretical concept are confirmed by the experiment. Also the predicted growth rates of the order of minutes for the nonaxisymmetric perturbations are certified by the measurements. That they do not directly depend on the size of the experiment is shown as a consequence of the weakness of the applied fields and the absence of rotation.