Magnetic flux tubes and the dynamo problem
Abstract
The observed properties of the magnetic field in the solar photosphere and theoretical studies of magneto-convection in electrically well-conducting fluids suggest that the magnetic field in stellar convection zones is quite inhomogeneous: magnetic flux is concentrated into magnetic flux tubes embedded in significantly less magnetized plasma. Such a state of the magnetic field potentially has strong implications for stellar dynamo theory since the dynamics of an ensemble of flux tubes is rather different from that of a more uniform field and new phenomena like magnetic buoyancy appear.
If the diameter of a magnetic flux tube is much smaller than any other relevant length scale, the MHD equations governing its evolution can be considerably simplified in terms of the thin-flux-tube approximation. Studies of thin flux tubes in comparison with observed properties of sunspot groups have led to far-reaching conclusions about the nature of the dynamo-generated magnetic field in the solar interior. The storage of magnetic flux for periods comparable to the amplification time of the dynamo requires the compensation of magnetic buoyancy by a stably stratified medium, a situation realized in a layer of overshooting convection at the bottom of the convection zone. Flux tubes stored in mechanical force equilibrium in this layer become unstable with respect to an undular instability once a critical field strength is exceeded, flux loops rise through the convection zone and erupt as bipolar magnetic regions at the surface. For parameter values relevant for the solar case, the critical field strength is of the order of 105 G. A field of similar strength is also required to prevent the rising unstable flux loops from being strongly deflected poleward by the action of the Coriolis force and also from `exploding' in the middle of the convection zone. The latter process is caused by the superadiabatic stratification. The magnetic energy density of a field of 105 G is two orders of magnitude larger than the kinetic energy density of the convective motions in the lower solar convection zone. This raises serious doubts whether the conventional turbulent dynamo process based upon cyclonic convection can work on the basis of such a strong field. Moreover, it is unclear whether solar differential rotation is capable of generating a toroidal magnetic field of 105 G; it is conceivable that thermal processes like an entropy-driven outflow from exploded flux tubes leads to the large field strength required. The instability of magnetic flux tubes stored in the overshoot region suggests an alternative dynamo mechanism based upon growing helical waves propagating along the tubes. Since this process operates only for field strengths exceeding a critical value, such a dynamo can fall into a `grand minimum' once the field strength is globally driven below this value, for instance by magnetic flux pumped at random from the convection zone into the dynamo region in the overshoot layer. The same process may act as a (re-)starter of the dynamo operation. Other non-conventional dynamo mechanisms based upon the dynamics of magnetic flux tubes are also conceivable.- Publication:
-
Advances in Nonlinear Dynamics
- Pub Date:
- April 2003
- DOI:
- 10.1201/9780203493137.ch5
- Bibcode:
- 2003and..book..123S