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

Finite deformation in ideal magnetohydrodynamics

Aims: In this paper we investigate the finite deformation of magnetic fields that can enable one to find complex analytical magnetohydrostatic (MHS) equilibria. These can be used as input to non-linear simulations. Methods: In order to find analytical equilibria, one normally has to consider simplifications or exploit a particular symmetry. Even with these measures, however, the desired equilibrium is often out of analytical reach. Here we describe a method that can work when traditional methods fail. It is based on the smooth deformation of simple magnetic fields into complex ones. Results: Examples are given, to demonstrate the method, that are of practical importance in coronal physics. This technique will prove useful in setting up the initial conditions of non-linear magnetohydrodynamic simulations

Optimal Energy Growth in Current Sheets

In this paper, we investigate the possibility of transient growth in the linear perturbation of current sheets. The resistive magnetohydrodynamic (MHD) 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 $t\rightarrow\infty$ can produce transient energy growth, contributing faster growth rates and higher energy attainment (within a fixed finite time) than the unstable tearing mode found from normal-mode analysis. We determine the transient growth for tearing-stable and tearing-unstable regimes and discuss the consequences of our results for processes in the solar atmosphere, such as flares and coronal heating. Our results have significant potential impact on how fast current sheets can be disrupted. In particular, transient energy growth due to (asymptotically) damped modes may lead to accelerated current sheet thinning and, hence, a faster onset of the plasmoid instability, compared to the rate determined by the tearing mode alone.Comment: Accepted for Solar Physic

Simulating the "Sliding Doors" Effect Through Magnetic Flux Emergence

D.M. acknowledges financial assistance from STFC. The computational work for this Letter was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St. Andrews. D.M. and A.W.H. acknowledge financial support form the European Commission through the SOLAIRE Network (MTRN-CT-2006-035484).Recent Hinode photospheric vector magnetogram observations have shown that the opposite polarities of a long arcade structure move apart and then come together. In addition to this "sliding doors" effect, orientations of horizontal magnetic fields along the polarity inversion line on the photosphere evolve from a normal-polarity configuration to an inverse one. To explain this behavior, a simple model by Okamoto et al. suggested that it is the result of the emergence of a twisted flux rope. Here, we model this scenario using a three-dimensional megnatohydrodynamic simulation of a twisted flux rope emerging into a pre-existing overlying arcade. We construct magnetograms from the simulation and compare them with the observations. The model produces the two signatures mentioned above. However, the cause of the "sliding doors" effect differs from the previous model.Publisher PDFPeer reviewe

The non-modal onset of the tearing instability

We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number $S$ increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the $L_2$-norm, for the classical setup of current sheets unstable to the TI, scales as $O(S^{1/4})$ on time scales of $O(S^{1/4})$ for $S\gg 1$. This behaviour is much faster than the time scale $O(S^{1/2})$ when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.Comment: Accepted for Journal of Plasma Physic

The pre-penumbral magnetic canopy in the solar atmosphere

Penumbrae are the manifestation of magnetoconvection in highly inclined (to the vertical direction) magnetic field. The penumbra of a sunspot tends to form, initially, along the arc of the umbra antipodal to the main region of flux emergence. The question of how highly inclined magnetic field can concentrate along the antipodal curves of umbrae, at least initially, remains to be answered. Previous observational studies have suggested the existence of some form of overlying magnetic canopy which acts as the progenitor for penumbrae. We propose that such overlying magnetic canopies are a consequence of how the magnetic field emerges into the atmosphere and are, therefore, part of the emerging region. We show, through simulations of twisted flux tube emergence, that canopies of highly inclined magnetic field form preferentially at the required locations above the photosphere

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 6.3−126.2 kms−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

The plasmoid instability in a confined solar flare

Eruptive flares (EFs) are associated with erupting filaments and, in some models, filament eruption drives flare reconnection. Recently, however, observations of a confined flare (CF) have revealed all the hallmarks of an EF (impulsive phase, flare ribbons, etc.) without the filament eruption itself. Therefore, if the filament is not primarily responsible for impulsive flare reconnection, what is? In this Letter, we argue, based on mimimal requirements, that the plasmoid instability is a strong candidate for explaining the impulsive phase in the observed CF. We present magnetohydrodynamic simulation results of the non-linear development of the plasmoid instability, in a model active region magnetic field geometry, to strengthen our claim. We also discuss how the ideas described in this Letter can be generalized to other situations, including EFs