David MacTaggart

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

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.

3D MHD flux emergence experiments: idealised models and coronal interactions:

This paper reviews some of the many 3D numerical experiments of the emergence of magnetic fields from the solar interior and the subsequent interaction with the pre-existing coronal magnetic field. The models described here are idealised, in the sense that the internal energy equation only involves the adiabatic, Ohmic and viscous shock heating terms. However, provided the main aim is to investigate the dynamical evolution, this is adequate. Many interesting observational phenomena are explained by these models in a self-consistent manner.

Multiple eruptions from magnetic flux emergence

Aims. In this paper we study the effects of a toroidal magnetic flux tube emerging into a magnetiz ed corona, with an emphasis on large-scale eruptions. The orientation of the fields is such that the two flux systems are almost antiparallel when they me et. Methods. We follow the dynamic evolution of the system by solving the 3D MHD equations using a Lagrangian remap scheme. Results. Multiple eruptions are found to occur. The physics of the trigger mechanisms are discussed and related to well-known eruption models.

On the Periodicity of Oscillatory Reconnection

Context. Oscillatory reconnection is a time-dependent magnetic reconnection mechanism that naturally produces periodic outputs from aperiodic drivers. Aims. This paper aims to quantify and measure the periodic nature of oscillatory reconnection for the first time. Methods. We solve the compressible, resistive, nonlinear magnetohydrodynamics (MHD) equations using 2.5D numerical simulations. Results. We identify two distinct periodic regimes: the impulsive and stationary phases. In the impulsive phase, we find the greater the amplitude of the initial velocity driver, the longer the resultant current sheet and the earlier its formation. In the stationary phase, we find that the oscillations are exponentially decaying and for driving amplitudes 6.3−126. 2k ms −1 , we measure stationary-phase periods in the range 56.3−78.9 s, i.e. these are high frequency (0.01−0.02 Hz) oscillations. In both phases, we find that the greater the amplitude of the initial velocity driver, the shorter the resultant period, but note that different physical processes and periods are associated with both phases. Conclusions. We conclude that the oscillatory reconnection mechanism behaves akin to a damped harmonic oscillator.

On magnetic reconnection and flux rope topology in solar flux emergence

We present an analysis of the formation of atmospheric flux ropes in a magnetohydrodynamic solar flux emergence simulation. The simulation domain ranges from the top of the solar interior to the low corona. A twisted magnetic flux tube emerges from the solar interior and into the atmosphere where it interacts with the ambient magnetic field. By studying the connectivity of the evolving magnetic field, we are able to better understand the process of flux rope formation in the solar atmosphere. In the simulation, two flux ropes are produced as a result of flux emergence. Each has a different evolution resulting in different topological structures. These are determined by plasma flows and magnetic reconnection. As the flux rope is the basic structure of the coronal mass ejection, we discuss the implications of our findings for solar eruptions.

Flux emergence within mature solar active regions

Aims. Recent insterest in flux emergence within mature active regions has led to several observational studies. Our aim is to model such a scenario and investigate the evolution of the system. Methods. We solve the 3D MHD equations numerically with a Lagrangian-remap scheme. The mature active region is modelled, in the initial condition, with a potential field. The smaller emerging region is a twisted flux tube and is placed between the two polarities of the mature region. The polarities of the new flux are aligned the same way as those of the mature region. The new flux emerges closer to the main negative polarity than the main positive polarity. To investigate the effects of reconnection, the distribution of the parallel electric field is calculated throughout the simulation. The topology of the magnetic field is then studied in regions of interest indicated by the electric field distribution. Results. The expansion of the new negative polarity is restricted due to the curvature of the overlying field and also because it is of the same sign. Reconnection is found to be strongest at low heights (below the corona) and along the outer side of the new positive polarity and its magnetic tongue. The effect of reconnection, in combination with the pressure between the two flux systems, is to resist the expansion of the new flux. The system then relaxes. Large-scale eruptions, such as CMEs, are not expected from the setup considered. At the new negative polarity, the high magnetic pressure can generate strong parallel electric fields which may lead to localized reconnection. The results of the model are in qualitative agreement with observations.

On Signatures of Twisted Magnetic Flux Tube Emergence

Recent studies of NOAA active region 10953, by Okamoto et al. (Astrophys. J. Lett.673, 215, 2008; Astrophys. J.697, 913, 2009), have interpreted photospheric observations of changing widths of the polarities and reversal of the horizontal magnetic field component as signatures of the emergence of a twisted flux tube within the active region and along its internal polarity inversion line (PIL). A filament is observed along the PIL and the active region is assumed to have an arcade structure. To investigate this scenario, MacTaggart and Hood (Astrophys. J. Lett.716, 219, 2010) constructed a dynamic flux emergence model of a twisted cylinder emerging into an overlying arcade. The photospheric signatures observed by Okamoto et al. (2008, 2009) are present in the model although their underlying physical mechanisms differ. The model also produces two additional signatures that can be verified by the observations. The first is an increase in the unsigned magnetic flux in the photosphere at either side of the PIL. The second is the behaviour of characteristic photospheric flow profiles associated with twisted flux tube emergence. We look for these two signatures in AR 10953 and find negative results for the emergence of a twisted flux tube along the PIL. Instead, we interpret the photospheric behaviour along the PIL to be indicative of photospheric magnetic cancellation driven by flows from the dominant sunspot. Although we argue against flux emergence within this particular region, the work demonstrates the important relationship between theory and observations for the successful discovery and interpretation of signatures of flux emergence.

Can magnetic breakout be achieved from multiple flux emergence

Aims. We study the breakout model using multiple flux emergence to produce the magnetic configuration and the trigger. We do not impose any artificial motions on the boundaries. Once the original flux tube configuration is chosen the system is left to evolve itself. Methods. We perform non-linear simulations in 2.5D by solving the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Lare2D). To produce a quadrupolar configuration from flux emergence we build on previous work where the interaction of two flux tubes forms the required quadrupole. Instead of imposing a shearing flow, a third flux tube is then allowed to emerge up through the central arcade. Results. Breakout is not achieved in any of the experiments. This is due to the interaction of the third tube with the quadrupole and the effect of the plasma β being O(1) at the photosphere and β > O(1) in the solar interior. When β is of these orders, flows generated in the plasma can influence the magnetic field and so photospheric footpoints do not remain fixed.

The magnetic structure of surges in small-scale emerging flux regions

Aims. To investigate the relationship between surges and magnetic reconnection during the emergence of small-scale active regions. In particular, to examine how the large-scale geometry of the magnetic field, shaped by di erent phases of reconnection, guides the flowing of surges. Methods. We present three flux emergence models. The first model, and the simplest, consists of a region emerging into a horizontal ambient field that is initially parallel to the top of the emerging region. The second model is the same as the first but with an extra smaller emerging region which perturbs the main region. This is added to create a more complex magnetic topology and to test how this complicates the development of surges compared to the first model. The last model has a non-uniform ambient magnetic field to model the e ects of emergence near a sunspot field and impose asymmetry on the system through the ambient magnetic field. At each stage, we trace the magnetic topology to identify the locations of reconnection. This allows for field lines to be plotted from di erent topological regions, highlighting how their geometry a ects the development of surges. Results. In the first model, we identify distinct phases of reconnection. Each phase is associated with a particular geometry for the magnetic field and this determines the paths of the surges. The second model follows a similar pattern to the first but with a more complex magnetic topology and extra eruptions. The third model highlights how an asymmetric ambient field can result in preferred locations for reconnection, subsequently guiding the direction of surges. Conclusions. Each of the identified phases highlights the close connection between magnetic field geometry, reconnection and the flow of surges. These phases can now be detected observationally and may prove to be key signatures in determining whether or not an emerging region will produce a large-scale (CME-type) eruption.

Optimal Energy Growth in Current Sheets

In this article, we investigate the possibility of transient growth in the linear perturbation of current sheets. The resistive magnetohydrodynamics operator for a background field consisting of a current sheet is non-normal, meaning that associated eigenvalues and eigenmodes can be very sensitive to perturbation. In a linear stability analysis of a tearing current sheet, we show that modes that are damped as t→∞