The magnetic fields of A-stars and white dwarfs explained

How can a star be magnetic? In his PhD thesis, Jonathan Braithwaite from the Max-Planck-Institute for Astrophysics has found out how, by discovering stable magnetic field configurations which can survive inside a star for the whole of its lifetime.

Fig. 1 (click to magnify): Stereo pairs showing the three-dimensional structure of the magnetic field configurations found by numerical MHD evolution. Blue lines show the twisted field lines that make up the stable torus inside the star, red are the field lines that cross the stellar surface. Black loop outlines the core of this torus. The field is static on human time scales, but over millions of years evolves slowly by magnetic diffusion (see Fig. 2). Top pair shows the field as it would appear in an Ap-star or magnetic white dwarf, lower pair the configuration in the final unstable phase before it disappears from the star. The torus has then deformed into a shape like the seam on a tennis ball.

Fig. 2: Long-term evolution of the field configuration. Figures show the axisymmetric average of the 3-D field of Fig. 1, projected onto a plane through the magnetic axis. Red lines show the `poloidal' field lines, the stable torus defined by the toroidal (azimuthal) field component is indicated by blue shading. Surface field strength increases by magnetic diffusion of the torus to the surface. When the azimuthal flux in the torus becomes too small, the field becomes unstable and decays quickly (last frame).

This discovery is important for three groups of stars on which strong magnetic fields are observed: the so-called magnetic `Ap' stars, the magnetic white dwarfs, and the `magnetars'. Unlike the magnetic field observed on the surface of the Sun, which is weak, small-scale and continuously fluctuating, the field observed on these stars is large-scale, strong, and static.

Since the discovery of magnetic stars over half a century ago, there have been two competing ideas to explain their magnetism: one theory proposes that the magnetic field is generated by a convective dynamo process operating in the core of the star. The other, the so-called fossil-field theory, claims that the field is simply left over from the formation of the star, having been present in the gas cloud out of which the star condensed. There is circumstantial evidence in favour of the fossil-field theory, but the main problem has been the lack of a known magnetic field configuration which is able to survive for a sufficiently long time. All configurations considered so far (by analytic means) are unstable and would decay in a matter of years, (i.e. very quickly compared to the lifetime of a star). There has to be a stable configuration, and the field has to have a way to find it. This special configuration has now been found, using numerical simulations to follow the evolution of an arbitrary initial field as it relaxes into a stable state.

The stable field has the shape of a twisted torus, not unlike the fields used in fusion reactors. It is roughly axisymmetric and the field on the surface of the star is approximately dipolar, but not exactly, in agreement with the observations. Its shape and existence appears to be closely linked to a global property called magnetic helicity.

With these results there is now a reliable basis for the theory of the magnetic fields in A-stars, white dwarfs and neutron stars.

J. Braithwaite, H. Spruit


J. Braithwaite, PhD thesis, University of Amsterdam, 8. April 2004.