On the emergence of toroidal flux tubes: general dynamics and comparisons with the cylinder model

School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland e-mail: dm428@st-andrews.ac.uk

Received: 20 July 2009
Accepted: 9 September 2009

Abstract

Aims. In this paper we study the dynamics of toroidal flux tubes emerging from the solar interior, through the photosphere and into the corona. Many previous theoretical studies of flux emergence use a twisted cylindrical tube in the solar interior as the initial condition. Important insights can be gained from this model, however, it does have shortcomings. The axis of the tube never fully emerges as dense plasma becomes trapped in magnetic dips and restrains its ascent. Also, since the entire tube is buoyant, the main photospheric footpoints (sunspots) continually drift apart. These problems make it difficult to produce a convincing sunspot pair. We aim to address these problems by considering a different initial condition, namely a toroidal flux tube.

Methods. We perform numerical experiments and solve the 3D MHD equations. The dynamics are investigated through a range of initial field strengths and twists.

Results. The experiments demonstrate that the emergence of toroidal flux tubes is highly dynamic and exhibits a rich variety of behaviour. In answer to the aims, however, if the initial field strength is strong enough, the axis of the tube can fully emerge. Also, the sunspot pair does not continually drift apart. Instead, its maximum separation is the diameter of the original toroidal tube.