Viacheslav Titov

Magnetic reconnection at three-dimensional null points

The skeleton of an isolated null point in three dimensions consists of a ‘spine curve’ and a ‘fan surface’. Two isolated magnetic field lines approach (or recede from) the null point from both directions along the spine, and a continuum of field lines recedes from (or approaches) the null in the plane of the fan surface. Two bundles of field lines approach the null point around the spine (one from each direction) and spread out near the fan. The kinematics of steady reconnection at such a null point is considered, depending on the nature of the imposed boundary conditions on the surface that encloses the null, in particular on a cylindrical surface with its axis along the spine. Three kinds of reconnection are discovered. In ‘spine reconnection’ continuous footpoint motions are imposed on the curved cylindrical surface, crossing the fan and driving singular jetting flow along the spine. In ‘fan reconnection’ continuous footpoint motions are prescribed on the ends of the cylinder, crossing the spine and driving a singular swirling motion at the fan. An antireconnection theorem is proved, which states that steady MHD reconnection in three dimensions with plasma flow across the spine or fan is impossible in an inviscid plasma with a highly subAlfvenic flow and uniform magnetic diffusivity. One implication of this is that reconnection tends to be an inherently nonlinear phenomenon. A linear theory for slow steady reconnection is developed which demonstrates explicitly the nature of the spine singularity in spine reconnection. Finally, the properties of separator reconnection’ in complex configurations containing two null points are discussed by means of analytical examples.

A Model for the Sources of the Slow Solar Wind

Models for the origin of the slow solar wind must account for two seemingly contradictory observations: the slow wind has the composition of the closed-field corona, implying that it originates from the continuous opening and closing of flux at the boundary between open and closed field. On the other hand, the slow wind also has large angular width, up to ~60?, suggesting that its source extends far from the open-closed boundary. We propose a model that can explain both observations. The key idea is that the source of the slow wind at the Sun is a network of narrow (possibly singular) open-field corridors that map to a web of separatrices and quasi-separatrix layers in the heliosphere. We compute analytically the topology of an open-field corridor and show that it produces a quasi-separatrix layer in the heliosphere that extends to angles far from the heliospheric current sheet. We then use an MHD code and MDI/SOHO observations of the photospheric magnetic field to calculate numerically, with high spatial resolution, the quasi-steady solar wind, and magnetic field for a time period preceding the 2008 August 1 total solar eclipse. Our numerical results imply that, at least for this time period, a web of separatrices (which we term an S-web) forms with sufficient density and extent in the heliosphere to account for the observed properties of the slow wind. We discuss the implications of our S-web model for the structure and dynamics of the corona and heliosphere and propose further tests of the model.

A MODEL FOR MAGNETICALLY COUPLED SYMPATHETIC ERUPTIONS

Sympathetic eruptions on the Sun have been observed for several decades, but the mechanisms by which one eruption can trigger another remain poorly understood. We present a three-dimensional MHD simulation that suggests two possible magnetic trigger mechanisms for sympathetic eruptions. We consider a configuration that contains two coronal flux ropes located within a pseudo-streamer and one rope located next to it. A sequence of eruptions is initiated by triggering the eruption of the flux rope next to the streamer. The expansion of the rope leads to two consecutive reconnection events, each of which triggers the eruption of a flux rope by removing a sufficient amount of overlying flux. The simulation qualitatively reproduces important aspects of the global sympathetic event on 2010 August 1 and provides a scenario for the so-called twin filament eruptions. The suggested mechanisms are also applicable for sympathetic eruptions occurring in other magnetic configurations.

Current Accumulation at a Three-Dimensional Magnetic Null

The cold, linear, resistive, magnetohydrodynamic (MHD) equations are used to study the dynamics of current accumulation at a three-dimensional magnetic null. The particular null under study is axisymmetric about its so-called spine axis, allowing a decomposition into azimuthal modes labeled by mode number m. Analysis shows that the axisymmetric perturbations (m=0) can lead to a current parallel to the spine axis at the null, while the m=1 mode produces currents orthogonal to the spine axis at the null (in the so-called fan plane). For all the modes with m > 1, there is no current accumulation at the null. The dynamic processes involved in producing these currents are revealed using numerical simulations. In particular, it is found that the m=1 mode leads to motions across both the fan plane and the spine axis regardless of whether the initially imposed disturbances are restricted to be across either the fan plane or the spine axis. The m=1 mode efficiently focuses the excess magnetic energy in toward the null, and therefore we consider it to be the prime reconnective mode in three dimensions. In attempting to understand magnetic reconnection at a three-dimensional null, it is clearly important to detail the currents that can be produced. This we have done within the framework of the linear theory. We discuss the implications of these results for reconnection in the solar corona in the presence of finite-amplitude fields and flows.

Comparing eclipse observations of the 2008 August 1 solar corona with an MHD model prediction

Context. The structure of the white-light and emission solar coronas and their MHD modelling are the context of our work. Aims. A comparison is made between the structure of the solar corona as observed during the 2008 August 1 total eclipse from Mongolia and that predicted by an MHD model. Methods. The model has an improved energy formulation, including the effect of coronal heating, conduction of heat parallel to the magnetic field, radiative losses, and acceleration by Alfven waves. Results. The white-light corona, which was visible up to 20 solar radii, was of an intermediate type with well-pronounced helmet streamers situated above a chain of prominences at position angles of 48, 130, 241, and 322 degrees. Two polar coronal holes, filled with a plethora of thin polar plumes, were observed. High-quality pictures of the green (530.3 nm, Fe XIV) corona were obtained with the help of two narrow-passband filters (centered at the line itself and the vicinity of 529.1 nm background), with a FWHM of 0.15 nm. Conclusions. The large-scale shape of both the white-light and green corona was found to agree well with that predicted by the model. In this paper we describe the morphological properties of the observed corona, and how it compares with that predicted by the model. A more detailed analysis of the quantitative properties of the corona will be addressed in a future publication.

The Evolution of Open Magnetic Flux Driven by Photospheric Dynamics

The coronal magnetic field is of paramount importance in solar and heliospheric physics. Two profoundly different views of the coronal magnetic field have emerged. In quasi-steady models, the predominant source of open magnetic field is in coronal holes. In contrast, in the interchange model, the open magnetic flux is conserved, and the coronal magnetic field can only respond to the photospheric evolution via interchange reconnection. In this view, the open magnetic flux diffuses through the closed, streamer belt fields, and substantial open flux is present in the streamer belt during solar minimum. However, Antiochos and coworkers, in the form of a conjecture, argued that truly isolated open flux cannot exist in a configuration with one heliospheric current sheet—it will connect via narrow corridors to the polar coronal hole of the same polarity. This contradicts the requirements of the interchange model. We have performed an MHD simulation of the solar corona up to 20 R ☉ to test both the interchange model and the Antiochos conjecture. We use a synoptic map for Carrington rotation 1913 as the boundary condition for the model, with two small bipoles introduced into the region where a positive polarity extended coronal hole forms. We introduce flows at the photospheric boundary surface to see if open flux associated with the bipoles can be moved into the closed-field region. Interchange reconnection does occur in response to these motions. However, we find that the open magnetic flux cannot be simply injected into closed-field regions—the flux eventually closes down and disconnected flux is created. Flux either opens or closes, as required, to maintain topologically distinct open- and closed-field regions, with no indiscriminate mixing of the two. The early evolution conforms to the Antiochos conjecture in that a narrow corridor of open flux connects the portion of the coronal hole that is nearly detached by one of the bipoles. In the later evolution, a detached coronal hole forms, in apparent violation of the Antiochos conjecture. Further investigation reveals that this detached coronal hole is actually linked to the extended coronal hole by a separatrix footprint on the photosphere of zero width. Therefore, the essential idea of the conjecture is preserved, if we modify it to state that coronal holes in the same polarity region are always linked, either by finite width corridors or separatrix footprints. The implications of these results for interchange reconnection and the sources of the slow solar wind are briefly discussed.

NON-NEUTRALIZED ELECTRIC CURRENT PATTERNS IN SOLAR ACTIVE REGIONS: ORIGIN OF THE SHEAR-GENERATING LORENTZ FORCE

Using solar vector magnetograms of the highest available spatial resolution and signal-to-noise ratio, we perform a detailed study of electric current patterns in two solar active regions (ARs): a flaring/eruptive and a flare-quiet one. We aim to determine whether ARs inject non-neutralized (net) electric currents in the solar atmosphere, responding to a debate initiated nearly two decades ago that remains inconclusive. We find that well-formed, intense magnetic polarity inversion lines (PILs) within ARs are the only photospheric magnetic structures that support significant net current. More intense PILs seem to imply stronger non-neutralized current patterns per polarity. This finding revises previous works that claim frequent injections of intense non-neutralized currents by most ARs appearing in the solar disk but also works that altogether rule out injection of non-neutralized currents. In agreement with previous studies, we also find that magnetically isolated ARs remain globally current-balanced. In addition, we confirm and quantify the preference of a given magnetic polarity to follow a given sense of electric currents, indicating a dominant sense of twist in ARs. This coherence effect is more pronounced in more compact ARs with stronger PILs and must be of sub-photospheric origin. Our results yield a natural explanation of the Lorentz force, invariably generating velocity and magnetic shear along strong PILs, thus setting a physical context for the observed pre-eruption evolution in solar ARs.

DISTRIBUTION OF ELECTRIC CURRENTS IN SOLAR ACTIVE REGIONS

There has been a long-standing debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a three-dimensional magnetohydrodynamic simulation of the emergence of a sub-photospheric, current-neutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active regions polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the regions center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ pre-eruption magnetic fields containing such currents.

The formation of magnetic singularities by time-dependent collapse of an X -type magnetic field

A self-consistent solution is presented for nonlinear time-dependent collapse of a two-dimensional X-type magnetic field to form a current sheet. A so-called ‘strong magnetic field approximation’ is adopted for highly sub-Alfvenic flow of an ideal low-beta plasma. To lowest order in the Alfven Mach number, the magnetic field evolves through a series of topologically accessible piece-wise potential states with the constraint that the acceleration be perpendicular to the magnetic field. A wide class of solutions is obtained using complex variable theory by assuming the magnetic potential is frozen to the plasma. The current sheet in the basic solution stretches along the x-axis from —/t to +/t, and regions of reversed current are found near the ends of the sheet. A current conservation theorem is proved, which states that the total current in the sheet is zero if it forms by collapse of an initially current-free X-point under the strong magnetic field approximation and with the magnetic potential frozen to the plasma. The basic solution is generalized to include other initial states and initial flows. A general numerical method for the evolution of magnetic fields under the strong magnetic field approximation is set up when the magnetic potential is not necessarily frozen to the plasma. This method is applied to an example of the formation of a current sheet with Y-type neutral points at its ends.

MHD simulation of the Bastille day event

We describe a time-dependent, thermodynamic, three-dimensional MHD simulation of the July 14, 2000 coronal mass ejection (CME) and flare. The simulation starts with a background corona developed using an MDI-derived magnetic map for the boundary condition. Flux ropes using the modified Titov-Demoulin (TDm) model are used to energize the pre-event active region, which is then destabilized by photospheric flows that cancel flux near the polarity inversion line. More than 1033 ergs are impulsively released in the simulated eruption, driving a CME at 1500 km/s, close to the observed speed of 1700km/s. The post-flare emission in the simulation is morphologically similar to the observed post-flare loops. The resulting flux rope that propagates to 1 AU is similar in character to the flux rope observed at 1 AU, but the simulated ICME center passes 15° north of Earth.