  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.
