Flow instabilities of magnetic flux tubes^*

IV. Flux storage in the solar overshoot region

¹ Department of Mathematics and Computer Science, İstanbul Kültür University, Ataköy Campus, Bakırköy 34156, İstanbul, Turkey e-mail: e.isik@iku.edu.tr
² Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Straße 2, 37191 Katlenburg-Lindau, Germany
³ Fraunhofer-Institut für Kurzzeitdynamik, Ernst-Mach-Institut, Eckerstraße 4, 79104 Freiburg im Breisgau, Germany e-mail: volkmar.holzwarth@emi.fraunhofer.de

Received: 3 July 2009
Accepted: 22 September 2009

Abstract

Context. Flow-induced instabilities of magnetic flux tubes are relevant to the storage of magnetic flux in the interiors of stars with outer convection zones. The stability of magnetic fields in stellar interiors is of importance to the generation and transport of solar and stellar magnetic fields.

Aims. We consider the effects of material flows on the dynamics of toroidal magnetic flux tubes located close to the base of the solar convection zone, initially within the overshoot region. The problem is to find the physical conditions in which magnetic flux can be stored for periods comparable to the dynamo amplification time, which is of the order of a few years.

Methods. We carry out nonlinear numerical simulations to investigate the stability and dynamics of thin flux tubes subject to perpendicular and longitudinal flows. We compare the simulations with the results of simplified analytical approximations.

Results. The longitudinal flow instability induced by the aerodynamic drag force is nonlinear in the sense that the growth rate depends on the perturbation amplitude. This result is consistent with the predictions of linear theory. Numerical simulations without friction show that nonlinear Parker instability can be triggered below the linear threshold of the field strength, when the difference in superadiabaticity along the tube is sufficiently large. A localised downflow acting on a toroidal tube in the overshoot region leads to instability depending on the parameters describing the flow, as well as the magnetic field strength. We determined ranges of the flow parameters for which a linearly Parker-stable magnetic flux tube is stored in the middle of the overshoot region for a period comparable to the dynamo amplification time.

Conclusions. The longitudinal flow instability driven by frictional interaction of a flux tube with its surroundings is relevant to determining the storage time of magnetic flux in the solar overshoot region. The residence time for magnetic flux tubes with 2 10²¹ Mx in the convective overshoot layer can be comparable to the dynamo amplification time, provided that the average speed and the duration of an external downflow do not exceed about 50 m s ^-1 and 100 days, respectively, and that the lateral extension of the flow is smaller than about 10°.