Braiding Of Field Lines Research Articles

An Improved Magnetohydrodynamic Simulation of the 2006 December 13 Coronal Mass Ejection of NOAA Active Region 10930

We present a magnetohydrodynamic simulation of the coronal mass ejection on 2006 December 13 in the emerging δ-sunspot NOAA Active Region 10930, improving upon a previous simulation by Fan as follows. (1) Incorporate an ambient solar wind instead of using a static potential magnetic field extrapolation as the initial state. (2) In addition to imposing the emergence of a twisted flux rope, also impose at the lower boundary a random electric field that represents the effect of turbulent convection, which drives field-line braiding and produces resistive and viscous heating in the corona. With the inclusion of this heating, which depends on the magnetic field topology, we are able to model the synthetic soft X-ray images that would be observed by the X-Ray Telescope (XRT) of the Hinode satellite, produced by the simulated coronal magnetic field. We find that the simulated preeruption magnetic field with the buildup of a twisted magnetic flux rope produces synthetic soft X-ray emission that shows qualitatively similar morphology as that observed by the Hinode/XRT for both the ambient coronal loops of the active region and the central inverse S-shaped “sigmoid“ that sharpens just before the onset of the eruption. The synthetic postflare loop brightening also shows similar morphology to that seen in the Hinode/XRT image during the impulsive phase of the eruption. It is found that the kinematics of the erupting flux rope is significantly affected by the open magnetic fields and fast solar wind streams adjacent to the active region.

Parallel Plasma Loops and the Energization of the Solar Corona

The outer atmosphere of the Sun is composed of plasma heated to temperatures well in excess of the visible surface. We investigate short cool and warm (<1 MK) loops seen in the core of an active region to address the role of field-line braiding in energizing these structures. We report observations from the High-resolution Coronal imager (Hi-C) that have been acquired in a coordinated campaign with the Interface Region Imaging Spectrograph (IRIS). In the core of the active region, the 172 Å band of Hi-C and the 1400 Å channel of IRIS show plasma loops at different temperatures that run in parallel. There is a small but detectable spatial offset of less than 1″ between the loops seen in the two bands. Most importantly, we do not see observational signatures that these loops might be twisted around each other. Considering the scenario of magnetic braiding, our observations of parallel loops imply that the stresses put into the magnetic field have to relax while the braiding is applied: the magnetic field never reaches a highly braided state on these length scales comparable to the separation of the loops. This supports recent numerical 3D models of loop braiding in which the effective dissipation is sufficiently large that it keeps the magnetic field from getting highly twisted within a loop.

Stellar X-rays and magnetic activity in 3D MHD coronal models

Context. Observations suggest a power-law relation between the coronal emission in X-rays, LX, and the total (unsigned) magnetic flux at the stellar surface, Φ. The physics basis for this relation is poorly understood. Aims. We use three-dimensional (3D) magnetohydrodynamics (MHD) numerical models of the coronae above active regions, that is, strong concentrations of magnetic field, to investigate the LX versus Φ relation and illustrate this relation with an analytical model based on simple well-established scaling relations. Methods. In the 3D MHD model horizontal (convective) motions near the surface induce currents in the coronal magnetic field that are dissipated and heat the plasma. This self-consistently creates a corona with a temperature of 1 MK. We run a series of models that differ in terms of the (unsigned) magnetic flux at the surface by changing the (peak) magnetic field strength while keeping all other parameters fixed. Results. In the 3D MHD models we find that the energy input into the corona, characterized by either the Poynting flux or the total volumetric heating, scales roughly quadratically with the unsigned surface flux Φ. This is expected from heating through field-line braiding. Our central result is the nonlinear scaling of the X-ray emission as LX ∝ Φ3.44. This scaling is slightly steeper than found in recent observations that give power-law indices of up to only 2 or 3. Assuming that on a real star, not only the peak magnetic field strength in the active regions changes but also their number (or surface filling factor), our results are consistent with observations. Conclusions. Our model provides indications of what causes the steep increase in X-ray luminosity by four orders of magnitude from solar-type activity to fast rotating active stars.

The origin of reconnection-mediated transient brightenings in the solar transition region

The ultraviolet emission from the solar transition region is dominated by dynamic, low-lying magnetic loops. The enhanced spatial and temporal resolution of the solar observation satellite Interface Region Imaging Spectrograph (IRIS) has made it possible to study these structures in fine detail. IRIS has observed ‘transient brightenings’ in these loops, associated with strong excess line broadenings1,2 providing important clues to the mechanisms that heat the solar atmosphere. However, the physical origin of the brightenings is debated. The line broadenings have been variously interpreted as signatures of nanoflares3, magneto-hydrodynamic turbulence4, plasmoid instabilities5 and magneto-acoustic shocks6. Here we use IRIS slit-jaw images and spectral data, and the Atmospheric Imaging Assembly of the Solar Dynamics Observatory spacecraft, to show that the brightenings are consistent with magnetic-reconnection-mediated impulsive heating at field-line braiding sites in multi-stranded transition-region loops. The spectroscopic observations present evidence for preferential heating of heavy ions from the transition region and we show that this is consistent with ion cyclotron turbulence caused by strong currents at the reconnection sites. Time-dependent differential emission measure distributions are used to determine the heating frequency7–9 and to identify pockets of faintly emitting ‘super-hot’ plasma. The observations we present and the techniques we demonstrate open up a new avenue of diagnostics for reconnection-mediated energy release in solar plasma. Solar imaging and spectral data indicate that impulsive heating through magnetic reconnection in transition region loops is responsible for observed transient brightenings, consistent with ion cyclotron turbulence due to strong currents at the reconnection sites.

Stellar coronal X-ray emission and surface magnetic flux

Context. Observations show that the coronal X-ray emission of the Sun and other stars depends on the surface magnetic field. Aims. Using power-law scaling relations between different physical parameters, we aim to build an analytical model to connect the observed X-ray emission to the surface magnetic flux. Methods. The basis for our model are the scaling laws of Rosner, Tucker &amp; Vaiana (RTV) that connect the temperature and pressure of a coronal loop to its length and energy input. To estimate the energy flux into the upper atmosphere, we used scalings derived for different heating mechanisms, such as field-line braiding or Alfvén wave heating. We supplemented this with observed relations between active region size and magnetic flux and derived scalings of how X-ray emissivity depends on temperature. Results. Based on our analytical model, we find a power-law dependence of the X-ray emission on the magnetic flux, LX ∝ Φm, with a power-law index m being in the range from about one to two. This finding is consistent with a wide range of observations, from individual features on the Sun, such as bright points or active regions, to stars of different types and varying levels of activity. The power-law index m depends on the choice of the heating mechanism, and our results slightly favor the braiding and nanoflare scenarios over Alfvén wave heating. In addition, the choice of instrument will have an impact on the power-law index m because of the sensitivity of the observed wavelength region to the temperature of the coronal plasma. Conclusions. Overall, our simple analytical model based on the RTV scaling laws gives a good representation of the observed X-ray emission. Therefore we might be able to understand stellar coronal activity though a collection of basic building blocks, like loops, which we can study in spatially resolved detail on the Sun.

Estimating the Rate of Field Line Braiding in the Solar Corona by Photospheric Flows

Abstract In this paper, we seek to understand the timescale in which the photospheric motions on the Sun braid coronal magnetic field lines. This is a crucial ingredient for determining the viability of the braiding mechanism for explaining the high temperatures observed in the corona. We study the topological complexity induced in the coronal magnetic field, primarily using plasma motions extracted from magneto-convection simulations. This topological complexity is quantified using the field line winding, finite time topological entropy (FTTE), and passive scalar mixing. With these measures, we contrast mixing efficiencies of the magneto-convection simulation, a benchmark flow known as a “blinking vortex”, and finally photospheric flows inferred from sequences of observed magnetograms using local correlation tracking. While the highly resolved magneto-convection simulations induce a strong degree of field line winding and FTTE, the values obtained from the observations from the plage region are around an order of magnitude smaller. This behavior is carried over to the FTTE. Nevertheless, the results suggest that the photospheric motions induce complex tangling of the coronal field on a timescale of hours.

Observable Signatures of Energy Release in Braided Coronal Loops

Abstract We examine the turbulent relaxation of solar coronal loops containing non-trivial field line braiding. Such field line tangling in the corona has long been postulated in the context of coronal heating models. We focus on the observational signatures of energy release in such braided magnetic structures using MHD simulations and forward modeling tools. The aim is to answer the following question: if energy release occurs in a coronal loop containing braided magnetic flux, should we expect a clearly observable signature in emissions? We demonstrate that the presence of braided magnetic field lines does not guarantee a braided appearance to the observed intensities. Observed intensities may—but need not necessarily—reveal the underlying braided nature of the magnetic field, depending on the degree and pattern of the field line tangling within the loop. However, in all cases considered, the evolution of the braided loop is accompanied by localized heating regions as the loop relaxes. Factors that may influence the observational signatures are discussed. Recent high-resolution observations from Hi-C have claimed the first direct evidence of braided magnetic fields in the corona. Here we show that both the Hi-C data and some of our simulations give the appearance of braiding at a range of scales.

Magnetic field line braiding in the solar atmosphere

AbstractUsing a magnetic carpet as model for the near surface solar magnetic field we study its effects on the propagation of energy injectected by photospheric footpoint motions. Such a magnetic carpet structure is topologically highly non-trivial and with its magnetic nulls exhibits qualitatively different behavior than simpler magnetic fields. We show that the presence of magnetic fields connecting back to the photosphere inhibits the propagation of energy into higher layers of the solar atmosphere, like the solar corona. By applying certain types of footpoint motions the magnetic field topology is is greatly reduced through magnetic field reconnection which facilitates the propagation of energy and disturbances from the photosphere.

Braided magnetic fields: equilibria, relaxation and heating

We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling, in the context of testable predictions for the laboratory and their significance for solar coronal heating. We investigate the existence of braided force-free equilibria, and demonstrate that for a field anchored at perfectly-conducting plates, these equilibria exist and contain current sheets whose thickness scales inversely with the braid complexity—as measured for example by the topological entropy. By contrast, for a periodic domain braided exact equilibria typically do not exist, while approximate equilibria contain thin current sheets. In the presence of resistivity, reconnection is triggered at the current sheets and a turbulent relaxation ensues. We finish by discussing the properties of the turbulent relaxation and the existence of constraints that may mean that the final state is not the linear force-free field predicted by Taylor’s hypothesis.

Coronal energy input and dissipation in a solar active region 3D MHD model

Context. We have conducted a 3D MHD simulation of the solar corona above an active region (AR) in full scale and high resolution, which shows coronal loops, and plasma flows within them, similar to observations. Aims. We want to find the connection between the photospheric energy input by field-line braiding with the coronal energy conversion by Ohmic dissipation of induced currents. Methods. To this end we compare the coronal energy input and dissipation within our simulation domain above different fields of view, e.g. for a small loops system in the AR core. We also choose an ensemble of field lines to compare, e.g., the magnetic energy input to the heating per particle along these field lines. Results. We find an enhanced Ohmic dissipation of currents in the corona above areas that also have enhanced upwards-directed Poynting flux. These regions coincide with the regions where hot coronal loops within the AR core are observed. The coronal density plays a role in estimating the coronal temperature due to the generated heat input. A minimum flux density of about 200 Gauss is needed in the photosphere to heat a field line to coronal temperatures of about 1 MK. Conclusions. This suggests that the field-line braiding mechanism provides the coronal energy input and that the Ohmic dissipation of induced currents dominates the coronal heating mechanism.

What can large-scale magnetohydrodynamic numerical experiments tell us about coronal heating?

The upper atmosphere of the Sun is governed by the complex structure of the magnetic field. This controls the heating of the coronal plasma to over a million kelvin. Numerical experiments in the form of three-dimensional magnetohydrodynamic simulations are used to investigate the intimate interaction between magnetic field and plasma. These models allow one to synthesize the coronal emission just as it would be observed by real solar instrumentation. Large-scale models encompassing a whole active region form evolving coronal loops with properties similar to those seen in extreme ultraviolet light from the Sun, and reproduce a number of average observed quantities. This suggests that the spatial and temporal distributions of the heating as well as the energy distribution of individual heat deposition events in the model are a good representation of the real Sun. This provides evidence that the braiding of fieldlines through magneto-convective motions in the photosphere is a good concept to heat the upper atmosphere of the Sun.

Coronal loops above an active region: Observation versus model

Abstract We conducted a high-resolution numerical simulation of the solar corona above a stable active region. The aim is to test the field line braiding mechanism for a sufficient coronal energy input. We also check the applicability of scaling laws for coronal loop properties like the temperature and density. Our 3D MHD model is driven from below by Hinode observations of the photosphere, in particular a high-cadence time series of line-of-sight magnetograms and horizontal velocities derived from the magnetograms. This driving applies stress to the magnetic field and thereby delivers magnetic energy into the corona, where currents are induced that heat the coronal plasma by Ohmic dissipation. We compute synthetic coronal emission that we directly compare to coronal observations of the same active region taken by Hinode. In the model, coronal loops form at the same places as they are found in coronal observations. Even the shapes of the synthetic loops in 3D space match those found from a stereoscopic reconstruction based on STEREO spacecraft data. Some loops turn out to be slightly over-dense in the model, as expected from observations. This shows that the spatial and temporal distribution of the Ohmic heating produces the structure and dynamics of a coronal loops system close to what is found in observations.

FORCE-FREE FIELD MODELING OF TWIST AND BRAIDING-INDUCED MAGNETIC ENERGY IN AN ACTIVE-REGION CORONA

The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region (AR) corona has only recently been substantiated by high-resolution observations. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We deliver estimates of the free magnetic energy associated with a braided coronal structure. Our model results suggest (∼100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the AR corona being heated by field line braiding. We were able to appropriately assess the coronal free energy by using vector field measurements and we attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase in the overall twist of a flare-related flux rope that was noted by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within 12 minutes. Unlike another method to which we compare our results, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal three-dimensional field line geometry. To our knowledge, this is done for the first time here.

Observationally driven 3D magnetohydrodynamics model of the solar corona above an active region

Aims. The goal is to employ a 3D magnetohydrodynamics (MHD) model including spectral synthesis to model the corona in an observed solar active region. This will allow us to judge the merits of the coronal heating mechanism built into the 3D model. Methods. Photospheric observations of the magnetic field and horizontal velocities in an active region are used to drive our coronal simulation from the bottom. The currents induced by this heat the corona through Ohmic dissipation. Heat conduction redistributes the energy that is lost in the end through optically thin radiation. Based on the MHD model, we synthesized profiles of coronal emission lines which can be directly compared to actual coronal observations of the very same active region. Results. In the synthesized model data we find hot coronal loops which host siphon flows or which expand and lose mass through draining. These synthesized loops are at the same location as and show similar dynamics in terms of Doppler shifts to the observed structures. This match is shown through a comparison with Hinode data as well as with 3D stereoscopic reconstructions of data from STEREO. Conclusions. The considerable match to the actual observations shows that the field-line braiding mechanism leading to the energy input in our corona provides the proper distribution of heat input in space and time. From this we conclude that in an active region the field-line braiding is the dominant heating process, at least at the spatial scales available to current observations.

Ejection of cool plasma into the hot corona

We investigate the processes that lead to the formation, ejection and fall of a confined plasma ejection that was observed in a numerical experiment of the solar corona. By quantifying physical parameters such as mass, velocity, and orientation of the plasma ejection relative to the magnetic field, we provide a description of the nature of this particular phenomenon. The time-dependent three-dimensional magnetohydrodynamic (3D MHD) equations are solved in a box extending from the chromosphere to the lower corona. The plasma is heated by currents that are induced through field line braiding as a consequence of photospheric motions. Spectra of optically thin emission lines in the extreme ultraviolet range are synthesized, and magnetic field lines are traced over time. Following strong heating just above the chromosphere, the pressure rapidly increases, leading to a hydrodynamic explosion above the upper chromosphere in the low transition region. The explosion drives the plasma, which needs to follow the magnetic field lines. The ejection is then moving more or less ballistically along the loop-like field lines and eventually drops down onto the surface of the Sun. The speed of the ejection is in the range of the sound speed, well below the Alfven velocity. The plasma ejection is basically a hydrodynamic phenomenon, whereas the rise of the heating rate is of magnetic nature. The granular motions in the photosphere lead (by chance) to a strong braiding of the magnetic field lines at the location of the explosion that in turn is causing strong currents which are dissipated. Future studies need to determine if this process is a ubiquitous phenomenon on the Sun on small scales. Data from the Atmospheric Imaging Assembly on the Solar Dynamics Observatory (AIA/SDO) might provide the relevant information.

THE EFFECT OF LARGE-SCALE MAGNETIC TURBULENCE ON THE ACCELERATION OF ELECTRONS BY PERPENDICULAR COLLISIONLESS SHOCKS

We study the physics of electron acceleration at collisionless shocks that move through a plasma containing large-scale magnetic fluctuations. We numerically integrate the trajectories of a large number of electrons, which are treated as test particles moving in the time dependent electric and magnetic fields determined from 2-D hybrid simulations (kinetic ions, fluid electron). The large-scale magnetic fluctuations effect the electrons in a number of ways and lead to efficient and rapid energization at the shock front. Since the electrons mainly follow along magnetic lines of force, the large-scale braiding of field lines in space allows the fast-moving electrons to cross the shock front several times, leading to efficient acceleration. Ripples in the shock front occuring at various scales will also contribute to the acceleration by mirroring the electrons. Our calculation shows that this process favors electron acceleration at perpendicular shocks. The current study is also helpful in understanding the injection problem for electron acceleration by collisionless shocks. It is also shown that the spatial distribution of energetic electrons is similar to in-situ observations (e.g., Bale et al. 1999; Simnett et al. 2005). The process may be important to our understanding of energetic electrons in planetary bow shocks and interplanetary shocks, and explaining herringbone structures seen in some type II solar radio bursts.

Mean Field Model for the Formation of Filament Channels on the Sun

The coronal magnetic field is subject to random footpoint motions that cause small-scale twisting and braiding of field lines. We present a mean field theory describing the effects of such small-scale twists on the large-scale coronal field. This theory assumes that the coronal field is force free, with electric currents flowing parallel or antiparallel to magnetic field lines. Random footpoint motions are described in terms of diffusion of the mean magnetic field at the photosphere. The appropriate mean field equations are derived, and a numerical method for solving these equations in three dimensions is presented. Preliminary results obtained with this method are also presented. In particular the formation of filament channels is studied. Filament channels are regions where the coronal magnetic field is strongly aligned with the underlying polarity inversion line in the photosphere. It is found that magnetic flux cancellation plays an important role in the formation of such channels. Various models of the coronal field are presented, including some in which the axial field is assumed to originate from below the photosphere. The models reproduce many of the observed features of filament channels, but the observed hemisphere pattern of dextral and sinistral channels remains a mystery.

The Implications of 3D for Solar MHD Modelling

The effects of three-dimensionality on the modelling of solar magnetic fields are described. We focus on two processes that are believed to play an important role in coronal heating – the braiding of field lines by photospheric motions and the reconnection of colliding flux tubes. First, it is shown that a proper treatment of boundary conditions at the photosphere in 3D entails qualitatively new physical processes that are not present in 2D. The numerical resolution of even simple boundary velocity patterns in 3D leads to obstacles which have no counterpart in the 2D case. We conclude that adaptive mesh refinement is necessary for capturing the essential 3D physics of a braiding motion at the photosphere. Next, the effects of 3D on magnetic reconnection are discussed. Reconnection in 3D can lead to an evolution of interacting flux tubes, magnetic tunneling, that is not only impossible in lower dimensionality, but is strikingly counterintuitive. The implications of these results for the structure of the solar magnetic field and for coronal heating are described.

Structure and Equilibrium of Coronal Magnetic Fields

In “closed” magnetic structures (i.e., coronal loops) the random shuffling of magnetic footpoints in the photosphere causes twisting and braiding of field lines in the corona. If the motions are sufficiently slow, the coronal field evolves through a sequence of force-free equilibrium states. Numerical simulations are presented for a simplified model in which the overall curvature of the coronal loop is neglected. It is shown that magnetic fine structures develop on spatial scales significantly smaller than those of the imposed “photospheric” velocity field.