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The solar atmosphere is filled with clusters of hot small-scale loops commonly known as Coronal Bright Points (CBPs). These ubiquitous structures stand out in the Sun by their strong X-ray and/or extreme-ultraviolet (EUV) emission for hours to days, which makes them a crucial piece when solving the solar coronal heating puzzle. In addition, they can be the source of coronal jets and small-scale filament eruptions. Here we present a novel 3D numerical model using the Bifrost code that explains the sustained CBP heating for several hours. We find that stochastic photospheric convective motions alone significantly stress the CBP magnetic field topology, leading to important Joule and viscous heating concentrated around the CBP's inner spine at a few megameters above the solar surface. We also detect continuous upflows with faint EUV signal resembling observational dark coronal jets and small-scale eruptions when H$_{\alpha}$ fibrils interact with the reconnection site. We validate our model by comparing simultaneous CBP observations from SDO and SST with observable diagnostics calculated from the numerical results for EUV wavelengths as well as for the H$_{\alpha}$ line using the Multi3D synthesis code. Additionally, we provide synthetic observables to be compared with Hinode, Solar Orbiter, and IRIS. Our results constitute a step forward in the understanding of the many different facets of the solar coronal heating problem., Comment: Accepted in ApJL. 9 pages, 5 figures, 2 movies

{We report on the first of a series of studies on coronal bright points investigating the physical mechanism that generates these phenomena.} {The aim of this paper is to understand the magnetic-field structure that hosts the bright points.} {We use longitudinal magnetograms taken by the Solar Optical Telescope with the Narrowband Filter Imager. For a single case, magnetograms from the Helioseismic and Magnetic Imager were added to the analysis. The longitudinal magnetic field component is used to derive the potential magnetic fields of the large regions around the bright points. A magneto-static field extrapolation method is tested to verify the accuracy of the potential field modelling. The three dimensional magnetic fields are investigated for the presence of magnetic null points and their influence on the local magnetic domain.} {In 9 out of 10 cases the bright point resides in areas where the coronal magnetic field contains an opposite polarity intrusion defining a magnetic null point above it. It is found that X-ray bright points reside, in these 9 cases, in a limited part of the projected fan dome area, either fully inside the dome or expanding over a limited area below which typically a dominant flux concentration resides. The 10th bright point is located in a bipolar loop system without an overlying null point.} {All bright points in coronal holes and two out of tree bright points in quiet Sun regions are seen to reside in regions containing a magnetic null point. An yet unidentified process(es) generates the BPs in specific regions of the fan-dome structure. }, Comment: 14 pages, 9 figures, 10 movies located at http://comp.astro.ku.dk/kg/BP/movies/, Accepted for publication in A&A

Coronal magnetic null points exist in abundance as demonstrated by extrapolations of the coronal field, and have been inferred to be important for a broad range of energetic events. These null points and their associated separatrix and spine field lines represent discontinuities of the field line mapping, making them preferential locations for reconnection. This field line mapping also exhibits strong gradients adjacent to the separatrix (fan) and spine field lines, that can be analysed using the `squashing factor', $Q$. In this paper we make a detailed analysis of the distribution of $Q$ in the presence of magnetic nulls. While $Q$ is formally infinite on both the spine and fan of the null, the decay of $Q$ away from these structures is shown in general to depend strongly on the null-point structure. For the generic case of a non-radially-symmetric null, $Q$ decays most slowly away from the spine/fan in the direction in which $|{\bf B}|$ increases most slowly. In particular, this demonstrates that the extended, elliptical high-$Q$ halo around the spine footpoints observed by Masson et al. (Astrophys. J., 700, 559, 2009) is a generic feature. This extension of the $Q$ halos around the spine/fan footpoints is important for diagnosing the regions of the photosphere that are magnetically connected to any current layer that forms at the null. In light of this, we discuss how our results can be used to interpret the geometry of observed flare ribbons in `circular ribbon flares', in which typically a coronal null is implicated. We conclude that both the physics in the vicinity of the null and how this is related to the extension of $Q$ away from the spine/fan can be used in tandem to understand observational signatures of reconnection at coronal null points., Comment: Pre-print version of article accepted for publication in Solar Physics

Context. Observations of many active regions show a slow systematic outflow/upflow from their edges lasting from hours to days. At present no physical explanation has been proven, while several suggestions have been put forward. Aims. This paper investigates one possible method for maintaining these upflows assuming that convective motions drive the magnetic field to initiate them through magnetic reconnection. Methods. We use Helioseismic and Magnetic Imager (HMI) data to provide an initial potential three dimensional magnetic field of the active region NOAA 11123 on 2010 November 13 where the characteristic upflow velocities are observed. A simple one-dimensional hydrostatic atmospheric model covering the region from the photosphere to the corona is derived. Local Correlation Tracking of the magnetic features in the HMI data is used to derive a proxy for the time dependent velocity field. The time dependent evolution of the system is solved using a resistive three-dimensional MagnetoHydro-Dynamic code. Results. The magnetic field contains several null points located well above the photosphere, with their fan planes dividing the magnetic field into independent open and closed flux domains. The stressing of the interfaces between the different flux domains is expected to provide locations where magnetic reconnection can take place and drive systematic flows. In this case, the region between the closed and open flux is identified as the region where observations find the systematic upflows. Conclusions. In the present experiment, the driving only initiates magneto-acoustic waves, without driving any systematic upflows at any of the flux interfaces., Comment: Accepted for publication in ApJ. Multi-instrument observations from where data for the current modelling is taken is presented in Vanninathan et al. 2015 (also accepted for publication in A&A and on arxiv)

Upflows at the edges of active regions (ARs) are studied by spatially and temporally combining multi-instrument observations obtained with EIS/Hinode, AIA and HMI/SDO and IBIS/NSO, to derive their plasma parameters. This information is used for benchmarking data-driven modelling of the upflows (Galsgaard et al., 2015). The studied AR upflow displays blueshifted emission of 5-20 km/s in Fe XII and Fe XIII and its average electron density is 1.8x10^9 cm^3 at 1 MK. The time variation of the density shows no significant change (in a 3sigma error). The plasma density along a single loop drops by 50% over a distance of 20000 km. We find a second velocity component in the blue wing of the Fe XII and Fe XIII lines at 105 km/s. This component is persistent during the whole observing period of 3.5 hours with variations of only 15 km/s. We also study the evolution of the photospheric magnetic field and find that magnetic flux diffusion is responsible for the formation of the upflow region. High cadence Halpha observations of the chromosphere at the footpoints of the upflow region show no significant jet-like (spicule/rapid blue excursion) activity to account for several hours/days of plasma upflow. Using an image enhancement technique, we show that the coronal structures seen in the AIA 193A channel is comparable to the EIS Fe XII images, while images in the AIA 171A channel reveals additional loops that are a result of contribution from cooler emission to this channel. Our results suggest that at chromospheric heights there are no signatures that support the possible contribution of spicules to AR upflows. We suggest that magnetic flux diffusion is responsible for the formation of the coronal upflows. The existence of two velocity components possibly indicate the presence of two different flows which are produced by two different physical mechanisms, e.g. magnetic reconnection and pressure-driven., Comment: Accepted for publication in A&A. Data driven modelling using observations from this paper is presented in Galsgaard et al. 2015 (also accepted for publication in A&A and on arxiv)

Three-dimensional magnetic null points are ubiquitous in the solar corona, and in any generic mixed-polarity magnetic field. We consider magnetic reconnection at an isolated coronal null point, whose fan field lines form a dome structure. We demonstrate using analytical and computational models several features of spine-fan reconnection at such a null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the null point during spine-fan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in quasi-separatrix layer or slip-running reconnection., Comment: Accepted for publication in the Astrophysical Journal

Numerical MHD simulations of 3D reconnection events in the solar corona have improved enormously over the last few years, not only in resolution, but also in their complexity, enabling more and more realistic modeling. Various ways to obtain the initial magnetic field, different forms of solar atmospheric models as well as diverse driving speeds and patterns have been employed. This study considers differences between simulations with stratified and non-stratified solar atmospheres, addresses the influence of the driving speed on the plasma flow and energetics, and provides quantitative formulas for mapping electric fields and dissipation levels obtained in numerical simulations to the corresponding solar quantities. The simulations start out from a potential magnetic field containing a null-point, obtained from a Solar and Heliospheric Observatory (SOHO) magnetogram extrapolation approximately 8 hours before a C-class flare was observed. The magnetic field is stressed with a boundary motion pattern similar to - although simpler than - horizontal motions observed by SOHO during the period preceding the flare. The general behavior is nearly independent of the driving speed, and is also very similar in stratified and non-stratified models, provided only that the boundary motions are slow enough. The boundary motions cause a build-up of current sheets, mainly in the fan-plane of the magnetic null-point, but do not result in a flare-like energy release. The additional free energy required for the flare could have been partly present in non-potential form in the initial state, with subsequent additions from magnetic flux emergence or from components of the boundary motion that were not represented by the idealized driving pattern., Comment: 24 pages, 14 figures, published in Solar Physics (Springer)

Three-dimensional null points are present in abundance in the solar corona, and the same is likely to be true in other astrophysical environments. Recent studies suggest that reconnection at such 3D nulls may play an important role in the coronal dynamics. In this paper the properties of the torsional spine and torsional fan modes of magnetic reconnection at 3D nulls are investigated. New analytical models are developed, which for the first time include a current layer that is spatially localised around the null, extending along either the spine or the fan of the null. These are complemented with numerical simulations. The principal aim is to investigate the effect of varying the degree of asymmetry of the null point magnetic field on the resulting reconnection process - where previous studies always considered a non-generic radially symmetric null. The geometry of the current layers within which torsional spine and torsional fan reconnection occur is found to be strongly dependent on the symmetry of the magnetic field. Torsional spine reconnection still occurs in a narrow tube around the spine, but with elliptical cross-section when the fan eigenvalues are different, and with the short axis of the ellipse being along the strong field direction. The spatiotemporal peak current, and the peak reconnection rate attained, are found not to depend strongly on the degree of asymmetry. For torsional fan reconnection, the reconnection occurs in a planar disk in the fan surface, which is again elliptical when the symmetry of the magnetic field is broken. The short axis of the ellipse is along the weak field direction, with the current being peaked in these weak field regions. The peak current and peak reconnection rate in this case are clearly dependent on the asymmetry, with the peak current increasing but the reconnection rate decreasing as the degree of asymmetry is increased.

To systematically stress a rotationally symmetric 3D magnetic null point by advecting the opposite footpoints of the spine axis in opposite directions. This stress eventually concentrates in the vicinity of the null point forming a local current sheet through which magnetic reconnection takes place. The aim is to look for a steady state evolution of the current sheet dynamics which may provide scaling relations for various characteristic parameters of the system. The evolution is followed by solving numerically the non-ideal MHD equations in a Cartesian domain. The null point is embedded in an initially constant density and temperature plasma. It is shown that a quasi-steady reconnection process can be set up at a 3D null by continuous shear driving. It appears that a true steady state in unlikely to be realised as the current layer tends to grow until restricted by the geometry of the computational domain and imposed driving profile. However, ratios between characteristic quantities clearly settle after some time to stable values -- so that the evolution is quasi-steady. The experiments show a number of scaling relations, but they do not provide a clear consensus for extending to lower magnetic resistivity or faster driving velocities. More investigations are needed to fully clarify the properties of current sheets at magnetic null points., Comment: 9 pages, 11 figures, accepted for publication in A&A

Aims: Our aim is to investigate the resistive relaxation of a magnetic loop that contains braided magnetic flux but no net current or helicity. The loop is subject to line-tied boundary conditions. We investigate the dynamical processes that occur during this relaxation, in particular the magnetic reconnection that occurs, and discuss the nature of the final equilibrium. Methods: The three-dimensional evolution of a braided magnetic field is followed in a series of resistive MHD simulations. Results: It is found that, following an instability within the loop, a myriad of thin current layers forms, via a cascade-like process. This cascade becomes more developed and continues for a longer period of time for higher magnetic Reynolds number. During the cascade, magnetic flux is reconnected multiple times, with the level of this `multiple reconnection' positively correlated with the magnetic Reynolds number. Eventually the system evolves into a state with no more small-scale current layers. This final state is found to approximate a non-linear force-free field consisting of two flux tubes of oppositely-signed twist embedded in a uniform background field., Comment: To be published in A&A

The role of null-point reconnection in a 3D numerical MHD model of solar emerging flux is investigated. The model consists of a twisted magnetic flux tube rising through a stratified convection zone and atmosphere to interact and reconnect with a horizontal overlying magnetic field in the atmosphere. Null points appear as the reconnection begins and persist throughout the rest of the emergence, where they can be found mostly in the model photosphere and transition region, forming two loose clusters on either side of the emerging flux tube. Up to 26 nulls are present at any one time, and tracking in time shows that there is a total of 305 overall, despite the initial simplicity of the magnetic field configuration. We find evidence for the reality of the nulls in terms of their methods of creation and destruction, their balance of signs, their long lifetimes, and their geometrical stability. We then show that due to the low parallel electric fields associated with the nulls, null-point reconnection is not the main type of magnetic reconnection involved in the interaction of the newly emerged flux with the overlying field. However, the large number of nulls implies that the topological structure of the magnetic field must be very complex and the importance of reconnection along separators or separatrix surfaces for flux emergence cannot be ruled out., Comment: 26 pages, 12 figures. Added one reference

Recent observations of coronal hole areas with the XRT and EIS instruments onboard the Hinode satellite have shown with unprecedented detail the launching of fast, hot jets away from the solar surface. In some cases these events coincide with episodes of flux emergence from beneath the photosphere. In this letter we show results of a 3D numerical experiment of flux emergence from the solar interior into a coronal hole and compare them with simultaneous XRT and EIS observations of a jet-launching event that accompanied the appearance of a bipolar region in MDI magnetograms. The magnetic skeleton and topology that result in the experiment bear a strong resemblance to linear force-fee extrapolations of the SOHO/MDI magnetograms. A thin current sheet is formed at the boundary of the emerging plasma. A jet is launched upward along the open reconnected field lines with values of temperature, density and velocity in agreement with the XRT and EIS observations. Below the jet, a split-vault structure results with two chambers: a shrinking one containing the emerged field loops and a growing one with loops produced by the reconnection. The ongoing reconnection leads to a horizontal drift of the vault-and-jet structure. The timescales, velocities, and other plasma properties in the experiment are consistent with recent statistical studies of this type of events made with Hinode data., Comment: 10 pages, 4 figures. Revised version submitted to ApJ Letters

The emergence of magnetic flux from the convection zone into the corona is an important process for the dynamical evolution of the coronal magnetic field. In this paper we extend our previous numerical investigations, by looking at the process of flux interaction as an initially twisted flux tube emerges into a plane parallel, coronal magnetic field. Significant differences are found in the dynamical appearance and evolution of the emergence process depending on the relative orientation between the rising flux system and any preexisting coronal field. When the flux systems are nearly anti-parallel, the experiments show substantial reconnection and demonstrate clear signatures of a high temperature plasma located in the high velocity outflow regions extending from the reconnection region. However, the cases that have a more parallel orientation of the flux systems show very limited reconnection and none of the associated features. Despite the very different amount of reconnection between the two flux systems, it is found that the emerging flux that is still connected to the original tube, reaches the same height as a function of time. As a compensation for the loss of tube flux, a clear difference is found in the extent of the emerging loop in the direction perpendicular to the main axis of the initial flux tube. Increasing amounts of magnetic reconnection decrease the volume, which confines the remaining tube flux., Comment: 21 pages, 16 figures Accepted for ApJ

The behaviour of magnetic perturbations of an initially potential three-dimensional equilibrium magnetic null point are investigated. The basic components which constitute a typical disturbance are taken to be rotations and shears, in line with previous work. The spine and fan of the null point (the field lines which asymptotically approach or recede from the null) are subjected to such rotational and shear perturbations, using three-dimensional magnetohydrodynamic simulations. It is found that rotations of the fan plane and about the spine lead to current sheets which are spatially diffuse in at least one direction, and form in the locations of the spine and fan. However, shearing perturbations lead to 3D-localised current sheets focused at the null point itself. In addition, rotations are associated with a growth of current parallel to the spine, driving rotational flows and a type of rotational reconnection. Shears, on the other hand, cause a current through the null which is parallel to the fan plane, and are associated with stagnation-type flows and field line reconnection across both the spine and fan. The importance of the parallel electric field, and its meaning as a reconnection rate, are discussed., Comment: Accepted for publication in JGR (Space Physics)

The nature of current sheet formation in the vicinity of three-dimensional (3D) magnetic null points is investigated. The particular focus is upon the effect of the compressibility of the plasma on the qualitative and quantitative properties of the current sheet. An initially potential 3D null is subjected to shearing perturbations, as in a previous paper [Pontin et al., Phys. Plasmas, in press (2007)]. It is found that as the incompressible limit is approached, the collapse of the null point is suppressed, and an approximately planar current sheet aligned to the fan plane is present instead. This is the case regardless of whether the spine or fan of the null is sheared. Both the peak current and peak reconnection rate are reduced. The results have a bearing on previous analytical solutions for steady-state reconnection in incompressible plasmas, implying that fan current sheet solutions are dynamically accessible, while spine current sheet solutions are not., Comment: to appear in Physics of Plasmas. This version contains updated figures and references, additional discussion, and typos are fixed. This is the second in a series of papers - the first of which (by the same authors) is located at astro-ph/0701462. A version with higher quality figures can be found at http://www.maths.dundee.ac.uk/~dpontin/

The nature of the evolution of the magnetic field, and of current sheet formation, at three-dimensional (3D) magnetic null points is investigated. A kinematic example is presented which demonstrates that for certain evolutions of a 3D null (specifically those for which the ratios of the null point eigenvalues are time-dependent) there is no possible choice of boundary conditions which renders the evolution of the field at the null ideal. Resistive MHD simulations are described which demonstrate that such evolutions are generic. A 3D null is subjected to boundary driving by shearing motions, and it is shown that a current sheet localised at the null is formed. The qualitative and quantitative properties of the current sheet are discussed. Accompanying the sheet development is the growth of a localised parallel electric field, one of the signatures of magnetic reconnection. Finally, the relevance of the results to a recent theory of turbulent reconnection is discussed., Comment: to appear in Phys. Plasmas. A version with higher quality figures can be found at http://www.maths.dundee.ac.uk/~dpontin/ In this replacement version, typos have been corrected, and in addition references and some further discussion added

The magnetic field plays a crucial role in heating the solar corona, but the exact energy release mechanism(s) is(are) still unknown. Here, we investigate in detail, the process of magnetic energy release in a situation where two initially independent flux systems are forced into each other. Work done by the foot point motions goes in to building a current sheet in which magnetic reconnection takes place. The scaling relations of the energy input and output are determined as functions of the driving velocity and the strength of fluxes in the independent flux systems. In particular, it is found that the energy injected into the system is proportional to the distance travelled not the rate of travel. Similarly, the rate of Joule dissipation is related to the distance travelled. Hence, rapidly driven foot points lead to bright, intense, but short-lived events, whilst slowly driven foot points produce weaker, but longer-lived brightenings. Integrated over the lifetime of the events both would produce the same heating if all other factors were the same. A strong overlying field has the affect of creating compact flux lobes from the sources. These appear to lead to a more rapid injection of energy, as well as a more rapid release of energy. Thus, the stronger the overlying field the more compact and more intense the heating. This means observers must know the rate of movement of the magnetic fragments involved in an events, as well as determine the strength and orientation of the surrounding field to be able to predict anything about the energy dissipated., Comment: A&A accepted, 24 pages, 11 figures

We present the results of a set of three-dimensional numerical simulations of magnetic flux emergence from below the photosphere into the corona that include a uniform and horizontal coronal magnetic field mimicking a pre-existing large-scale coronal magnetic system. Cases with different relative orientations of the upcoming and coronal fields are studied. Upon contact, a concentrated current sheet with the shape of an arch or bridge is formed at the interface which marks the positions of maximum jump in the field vector between the two systems. Relative angles above 90 degrees yield abundant magnetic reconnection and plasma heating. The reconnection is seen to be intrisincally three-dimensional in nature, except at singular positions along the current sheet. It drives collimated high-speed and high-temperature outflows only a short distance from the reconnection site that propagate along the ambient magnetic field lines as jets. Due to the low plasma density in the corona, these jets may propagate over large distances and, therefore help distribute high-density and high-temperature plasma along these newly reconnected field lines. The experiments permit to discern and visualize the three-dimensional shape and relative position of the upcoming plasma hill, high-speed jets and subphotospheric flux system. As a result of the reconnection, magnetic field lines from the magnetized plasma below the surface end up as coronal field lines, thus causing a profound change in the connectivity of the magnetic regions in the corona. The experiments presented here thus yield a number of features repeatedly observed with the TRACE satellite and the YOHKOH-SXT detector, like the establishment of connectivity between emergent and pre-existing active regions, local heating and high-velocity outflows., Comment: 13 pages, 7 figures, inpress ApJL

In this paper, we investigate a simple model where two, initially unconnected, flux systems are forced to interact in response to the imposed boundary driving by solving the non-ideal 3D MHD equations numerically. The reconnection rate of the dynamical process is determined and compared with the corresponding rate for the potential evolution of the magnetic field. This shows that the dynamic reconnection rate is about a factor of two smaller than the potential (perfect, instantaneous) rate for realistic solar driving velocities demonstrating that this three-dimensional magnetic reconnection process is fast. The energy input for a fixed advection distance is found to be independent of the driving velocity. The Joule dissipation associated with the reconnection process is also found to be basically dependent on the advection distance rather than driving velocity. This implies that the timescale for the event determines the effect the heating has on the temperature increase. Finally, the numerical experiments indicate that the observational structure of the reconnection site changes dramatically depending on the phase of the evolution of the passage of the two flux sources. In the initial phase, where the sources become connected, the heating is confined to a compact region. For the disconnecting phase the energy gets distributed over a larger area due to the reconnected field line connectivity., Comment: 6 pages, 8 figures. Procedings of SOHO 15 Coronal Heating, ESA publication

The concept of hyperbolic flux tubes (HFTs) is a generalization of the concept of separator field lines for coronal magnetic fields with a trivial magnetic topology. An effective mechanism of a current layer formation in HFTs is proposed. This mechanism is called magnetic pinching and it is caused by large-scale shearing motions applied to the photospheric feet of HFTs in a way as if trying to twist the HFT. It is shown that in the middle of an HFT such motions produce a hyperbolic flow that causes an exponentially fast growth of the current density in a thin force-free current layer. The magnetic energy associated with the current layer that is built up over a few hours is sufficient for a large flare. Other implications of HFT pinching for solar flares are discussed as well., Comment: 31 pages, 12 figures, accepted to Astrophysical Journal, added typos in Eq. (A9) and new comments to Sections 2 and 7, references updated