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

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.

Multiple eruptions from magnetic flux emergence

“…The boundary conditions are closed on the top and base of the box and periodic on the sides. The background stratification is similar to that in MacTaggart & Hood (2009b). The non-magnetic stratification includes a solar interior that is marginally stable to convection (−20 < z < 0), a photosphere/chromosphere (0 < z < 10), a transition region (10 < z < 20) and a corona (20 < z < 85).…”

“…The second is that there are no imposed flows in the flux emergence model. The Lorentz force of the emerging arcade naturally shears the magnetic field (MacTaggart & Hood 2009b).…”

“…α is the initial twist and B 0 is the initial axial field strength. Varying these parameters can have a profound effect on the behaviour of toroidal emergence (MacTaggart & Hood 2009b). For this study, however, we shall only consider the values of B 0 = 5 and α = 0.4.…”

“…i.e. a density deficit relative to the background density is introduced (Hood et al 2009;MacTaggart & Hood 2009b). …”

“…This is a toroidal loop, placed in the solar interior, rather than a cylindrical one (Hood et al 2009). A comparison of these two models is discussed in MacTaggart & Hood (2009b). This paper will show that multiple large-scale eruptions are possible from the same emerging region and will discuss the physics of the trigger mechanisms.…”