Modelling magnetic flux emergence in the solar convection zone

¹ School of Mathematics and Statistics, Newcastle University, Newcastle Upon Tyne, NE1 7RU UK
e-mail: paul.bushby@ncl.ac.uk
² School of Mathematics and Statistics, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, UK
e-mail: vasilis@mcs.st-and.ac.uk

Received: 13 September 2010
Accepted: 29 July 2012

Abstract

Context. Bipolar magnetic regions are formed when loops of magnetic flux emerge at the solar photosphere. Magnetic buoyancy plays a crucial role in this flux emergence process, particularly at larger scales. However it is not yet clear to what extent the local convective motions influence the evolution of rising loops of magnetic flux.

Aims. Our aim is to investigate the flux emergence process in a simulation of granular convection. In particular we aim to determine the circumstances under which magnetic buoyancy enhances the flux emergence rate (which is otherwise driven solely by the convective upflows).

Methods. We used three-dimensional numerical simulations, solving the equations of compressible magnetohydrodynamics in a horizontally-periodic Cartesian domain. A horizontal magnetic flux tube was inserted into fully developed hydrodynamic convection. We systematically varied the initial field strength, the tube thickness, the initial entropy distribution along the tube axis and the magnetic Reynolds number.

Results. Focusing upon the low magnetic Prandtl number regime (Pm < 1) at moderate magnetic Reynolds number, we find that the flux tube is always susceptible to convective disruption to some extent. However, stronger flux tubes tend to maintain their structure more effectively than weaker ones. Magnetic buoyancy does enhance the flux emergence rates in the strongest initial field cases, and this enhancement becomes more pronounced when we increase the width of the flux tube. This is also the case at higher magnetic Reynolds numbers, although the flux emergence rates are generally lower in these less dissipative simulations because the convective disruption of the flux tube is much more effective in these cases. These simulations seem to be relatively insensitive to the precise choice of initial conditions: for a given flow, the evolution of the flux tube is determined primarily by the initial magnetic field distribution and the magnetic Reynolds number.