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

TL;DR

This study explores the emergence of toroidal flux tubes in the solar atmosphere, showing that they can fully emerge and form stable sunspot pairs, addressing limitations of cylindrical models through 3D MHD simulations.

Contribution

It introduces a new initial condition using toroidal flux tubes and demonstrates their dynamic emergence, improving understanding of sunspot formation.

Findings

Toroidal flux tubes can fully emerge if initial field strength is sufficient.

Sunspot pairs formed do not drift apart indefinitely, but reach a maximum separation.

Emergence behavior varies with initial magnetic field strength and twist.

Abstract

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