Flare-produced coronal MHD-fast-mode wavefronts and Moreton's wave phenomenon

The propagation characteristics of MHD fast-mode disturbances, which can emanate from flare regions, are computed for realistic conditions of the solar corona at the times of particular flares. The path of a fast-mode disturbance is determined by the large-scale (global) coronal distributions of magnetic field and density, and can be computed by a general raytracing procedure (eikonal equation) adapted to MHD. We use the coronal (electron) density distribution calculated from daily K-coronameter data, and the coronal magnetic field calculated under the current-free approximation from magnetograph measurements of the photospheric magnetic field. We compare the path and time-development of an MHD fast-mode wavefront emitted from the flare region (as calculated from a realistic model corona for the day of the observed Moreton wave event) with actual observations of the Moreton wave event, and find that the Moreton wave can be identified with the rapidly moving intersection of the coronal fast-mode wavefront and the chromosphere (as hypothesized in our previous paper); the directivity (anisotropic propagation), as well as other characteristics of the propagation of the Moreton wave can be successfully explained.sponsored by the National Science Foundation.     

A sheet-current approach to coronal-interplanetary modeling

The most pertinent effect of the currents in the coronal-interplanetary space is their alteration of the magnetic topology to form configurations of open field lines. The important currents seem to be those in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines in the coronal helmet-streamer structures. Thus, the coronal-interplanetary space may be regarded as being partitioned by current-sheets into several piecewise current-free regions. These current sheets overlie the photospheric neutral lines, where the vertical component of the magnetic field reverses its polarity on the solar surface. But, their locations and strengths are determined by force balance between the magnetic field and the gas pressure in the coronal-interplanetary space. Since the pressure depends on the flow velocity of the solar wind and the solar wind channels along magnetic flux tubes, there is a strong magnetohydrodynamic coupling between the magnetic field and the solar wind. The sheetcurrent approach presented in this paper seems to be a reasonable way to account for this complicated interaction.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The Hall effect as the producer of current sheets in astrophysical plasmas

Our solution of the MHD equations with the Hall effect shows that this effect can produce thin current sheets in stellar atmospheres at heights where the plasma is tenuous and the Hall effect can profoundly influence the magnetic field variations. The current in the sheets is directed oppositely to the local plasma density gradient. In partiuclar, such a phenomenon is possible on the Sun near the base of the corona.     

A Comparison Between Nonlinear Force-Free Field and Potential Field Models Using Full-Disk SDO/HMI Magnetogram

Measurements of magnetic fields and electric currents in the pre-eruptive corona are crucial to the study of solar eruptive phenomena, like flares and coronal mass ejections (CMEs). However, spectro-polarimetric measurements of certain photospheric lines permit a determination of the vector magnetic field only at the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field above multiple active regions with the help of a potential field and a nonlinear force-free field (NLFFF) extrapolation code over the full solar disk using Helioseismic and Magnetic Imager (SDO/HMI) data as boundary conditions. We compare projections of the resulting magnetic field lines with full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for both models. This study has found that the NLFFF model reconstructs the magnetic configuration closer to observation than the potential field model for full-disk magnetic field extrapolation. We conclude that many of the trans-equatorial loops connecting the two solar hemispheres are current-free.     

An atlas of photospheric magnetic field observations and computed coronal magnetic fields: 1976–1985

Daily magnetogram observations of the large-scale photospheric magnetic field have been made at the John M. Wilcox Solar Observatory at Stanford since May of 1976. These measurements provide a homogeneous record of the changing solar field through most of solar cycle 21.Using the photospheric data, the configuration of the coronal and heliospheric fields can be calculated using a Potential Field - Source Surface model. This provides a three - dimensional picture of the heliospheric field evolution during the solar cycle.In this note we announce the publication of UAG Report No. 94, an Atlas containing the complete set of synoptic charts of the measured photospheric magnetic field, the computed field at the source surface, and the coefficients of the multipole expansion of the coronal field. The general underlying structures of the solar and heliospheric fields, which determine the environment for solar-terrestrial relations and provide the context within which solar activity related events occur, can be approximated from these data.     

Thermal instability of coronal neutral sheets and the formation of quiescent prominences

It is argued that the quiscent prominences are a natural consequence of the formation and thermal instability of current sheets in the corona. Thus observation and theory of prominences can give vital information on the presence of currents and the topology of magnetic fields in the corona. Conversely by developing the theory of the structure and evolution of current sheets under coronal conditions we can attempt to gain a comprehensive understanding of the structure, evolution, and mass and energy balance of quiescent prominences. A stability analysis for coronal material permeated by a vertical magnetic field rooted in the photosphere, indicates that a condensation will take the form of a thin vertical wedge of cool matter. The development of a finite condensation is followed and it is shown that photospheric line tying is only important in the initial stages. A perturbation analysis of vertical motions at the neutral sheet shows that thermal instability can lead to overstable oscillations. Cooling of coronal material can lead to both upward and downward mass motions, and gravitational energy release is important to the thermal balance of prominences. Relevant optical and radio observations are discussed. Synoptic observations of the development of active regions and magnetic fields are needed to test the basic hypothesis of the formation of prominences from neutral sheets.     

On the Magnetic Correspondence between the Photosphere and the Heliosphere

The solar magnetic field maps every point in the corona to a corresponding place on the solar surface. Identifying the magnetic connection map is difficult at low latitudes near the heliospheric current sheet, but remarkably simple in coronal hole interiors. We present a simple analytic magnetic model (‘pseudocurrent extrapolation’) that reproduces the global structure of the corona, with significant physical advantages over other nearly analytic models such as source-surface potential field extrapolation. We use the model to demonstrate that local horizontal structure is preserved across altitude in the central portions of solar coronal holes, up to at least 30 R_s, in agreement with observations. We argue that the preserved horizontal structure may be used to track the magnetic footpoint associated with the location of a hypothetical spacecraft traveling through the solar corona, to relate in situ measurements of the young solar wind at ∼10–30 R_s to particular source regions at the solar surface. Further, we discuss the relationship between readily observable geometrical distortions and physical parameters of interest such as the field-aligned current density.     

A magnetic bald-patch flare in solar active region 11117

With SDO observations and a data-constrained magnetohydrodynamics(MHD)model,we identify a confined multi-ribbon flare that occurred on 2010 October 25 in solar active region 11117 as a magnetic bald patch(BP)flare with strong evidence.From the photospheric magnetic field observed by SDO/HMI,we find there are indeed magnetic BPs on the polarity inversion lines(PILs)which match parts of the flare ribbons.From the 3D coronal magnetic field derived from an MHD relaxation model constrained by the vector magnetograms,we find strikingly good agreement of the BP separatrix surface(BPSS)footpoints with the flare ribbons,and the BPSS itself with the hot flaring loop system.Moreover,the triggering of the BP flare can be attributed to a small flux emergence under the lobe of the BPSS,and the relevant change of coronal magnetic field through the flare is reproduced well by the pre-flare and post-flare MHD solutions,which match the corresponding pre-and post-flare AIA observations,respectively.Our work contributes to the study of non-typical flares that constitute the majority of solar flares but which cannot be explained by the standard flare model.     

SIGNATURES OF CORONAL CURRENTS IN MICROWAVE IMAGES

Microwave emission from solar active regions at frequencies above 4 GHz is dominated by gyroresonance opacity in strong coronal magnetic fields, which allows us to use radio observations to measure coronal magnetic field strengths. In this paper we demonstrate one powerful consequence of this fact: the ability to identify coronal currents from their signatures in microwave images. Specifically, we compare potential-field (i.e., current-free) extrapolations of photospheric magnetic fields with microwave images and are able to identify regions where the potential extrapolation fails to predict the magnetic field strength required to explain the microwave images. Comparison with photospheric vector magnetic field observations indicates that the location inferred for coronal currents agrees with that implied by the presence of vertical currents in the photosphere. The location, over a neutral line exhibiting strong shear, is also apparently associated with strong heating.     

A global numerical 3-D MHD model of the solar wind

A fully three-dimensional, steady-state global model of the solar corona and the solar wind is developed. A numerical, self-consistent solution for 3-D MHD equations is constructed for the region between the solar photosphere and the Earth's orbit. Boundary conditions are provided by the solar magnetic field observations. A steady-state solution is sought as a temporal relaxation to the dynamic equilibrium in the region of transonic flow near the Sun and then traced to the orbit of the Earth in supersonic flow region. The unique features of the proposed model are: (a) uniform coverage and self-consistent treatment of the regions of subsonic/sub-Alfvénic and supersonic/super-Alfvénic flows, (b) inferring the global structure of the interplanetary medium between the solar photosphere and 1 AU based on large-scale solar magnetic field data. As an experimental test for the proposed technique, photospheric magnetic field data for CR 1682 are used to prescribe boundary condition near the Sun and results of a simulation are compared with spacecraft measurements at 1 AU. The comparison demonstrates a qualitative agreement between computed and observed parameters. While the difference in densities is still significant, the 3-D model better reproduces variations of the solar wind velocity than does the 2-D model presented earlier (Usmanov, 1993).     

Coronal Magnetic Field Context of Simple CMEs Inferred from Global Potential Field Models

Most work on coronal mass ejection (CME) interpretation focuses on the involved active region rather than on the large-scale coronal context. In this paper a global potential-field source-surface model of the coronal magnetic field is used to evaluate the sensitivity of the coronal field configuration to the location, orientation, and strength of a bipolar active region relative to a background polar field distribution. The results suggest that the introduction of antiparallel components between the field of the active region and the background field can cause significant topological changes in the large-scale coronal magnetic field resembling observations during some simple CMEs. Antiparallel components can be introduced in the real corona by the diffusion and convection of photospheric fields, flux emergence, or erupted or shear-induced twist of active-region fields. Global MHD models with time-dependent boundary conditions could easily test the stability of such configurations and the nature of any related transients.     

How To Use Magnetic Field Information For Coronal Loop Identification

The structure of the solar corona is dominated by the magnetic field because the magnetic pressure is about four orders of magnitude higher than the plasma pressure. Due to the high conductivity the emitting coronal plasma (visible, e.g., in SOHO/EIT) outlines the magnetic field lines. The gradient of the emitting plasma structures is significantly lower parallel to the magnetic field lines than in the perpendicular direction. Consequently information regarding the coronal magnetic field can be used for the interpretation of coronal plasma structures. We extrapolate the coronal magnetic field from photospheric magnetic field measurements into the corona. The extrapolation method depends on assumptions regarding coronal currents, e.g., potential fields (current-free) or force-free fields (current parallel to magnetic field). As a next step we project the reconstructed 3D magnetic field lines on an EIT-image and compare with the emitting plasma structures. Coronal loops are identified as closed magnetic field lines with a high emissivity in EIT and a small gradient of the emissivity along the magnetic field.     

3D Coronal Density Reconstruction and Retrieving the Magnetic Field Structure during Solar Minimum

Measurement of the coronal magnetic field is a crucial ingredient in understanding the nature of solar coronal phenomena at all scales. We employed STEREO/COR1 data obtained during a deep minimum of solar activity in February 2008 (Carrington Rotation CR 2066) to retrieve and analyze the three-dimensional (3D) coronal electron density in the range of heights from 1.5 to 4 R_⊙ using a tomography method. With this, we qualitatively deduced structures of the coronal magnetic field. The 3D electron-density analysis is complemented by the 3D STEREO/EUVI emissivity in the 195 Å band obtained by tomography for the same CR. A global 3D MHD model of the solar corona was used to relate the reconstructed 3D density and emissivity to open/closed magnetic-field structures. We show that the density-maximum locations can serve as an indicator of current-sheet position, while the locations of the density-gradient maximum can be a reliable indicator of coronal-hole boundaries. We find that the magnetic-field configuration during CR 2066 has a tendency to become radially open at heliocentric distances greater than 2.5 R_⊙. We also find that the potential-field model with a fixed source surface is inconsistent with the boundaries between the regions with open and closed magnetic-field structures. This indicates that the assumption of the potential nature of the coronal global magnetic field is not satisfied even during the deep solar minimum. Results of our 3D density reconstruction will help to constrain solar coronal-field models and test the accuracy of the magnetic-field approximations for coronal modeling.     

On the reality of potential magnetic fields in the solar corona

Global magnetic field calculations, using potential field theory, are performed for Carrington rotations 1601–1610 during the Skylab period. The purpose of these computations is to quantitatively test the spatial correspondence between calculated open and closed field distributions in the solar corona with observed brightness structures. The two types of observed structures chosen for this study are coronal holes representing open geometries and theK-coronal brightness distribution which presumably outlines the closed field regions in the corona. The magnetic field calculations were made using the Adams-Pneuman fixed-mesh potential field code based upon line-of-sight photospheric field data from the KPNO 40-channel magnetograph. Coronal hole data is obtained from AS&E's soft X-ray experiment and NRL's Heii observations and theK-coronal brightness distributions are from HAO'sK-coronameter experiment at Mauna Loa, Hawaii.The comparison between computed open field line locations and coronal holes shows a generally good correspondence in spatial location on the Sun. However, the areas occupied by the open field seem to be somewhat smaller than the corresponding areas of X-ray holes. Possible explanations for this discrepancy are discussed. It is noted that the locations of open field lines and coronal holes coincide with the locations ofmaximum field strength in the higher corona with the closed regions consisting of relatively weaker fields.The general correspondence between bright regions in theK-corona and computed closed field regions is also good with the computed neutral lines lying at the top of the closed loops following the same general warped path around the Sun as the maxima in the brightness. One curious feature emerging from this comparison is that the neutral lines at a given longitude tend systematically to lie somewhat closer to the poles than the brightness maxima for all rotations considered. This discrepancy in latitude increases as the poles are approached. Three possible explanations for this tendency are given: perspective effects in theK -coronal observations, MHD effects due electric currents not accounted for in the analysis, and reported photospheric field strengths near the poles which are too low. To test this latter hypothesis, we artificially increased the line-of-sight photospheric field strengths above 70° latitude as an input to the magnetic field calculations. We found that, as the polar fields were increased, the discrepancy correspondingly decreased. The best agreement between neutral line locations and brightness maxima is obtained for a polar field of about 30 G.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Connections Between the White-Light Eclipse Corona and Magnetic Fields over the Solar Cycle

Observations of ten solar eclipses (1973–1999) enabled us to reveal and describe mutual relations between the white-light corona structures (e.g., global coronal forms and most conspicuous coronal features, such as helmet streamers and coronal holes) and the coronal magnetic field strength and topology. The magnetic field strength and topology were extrapolated from the photospheric data under the current-free assumption. In spite of this simplification the found correspondence between the white-light corona structure and magnetic field organization strongly suggests a governing role of the field in the appearance and evolution of local and global structures. Our analysis shows that the study of white-light corona structures over a long period of time can provide valuable information on the magnetic field cyclic variations. This is particularly important for the epoch when the corresponding measurements of the photospheric magnetic field are absent.     

Solar coronal heating by magnetosonic waves

Solar coronal heating by magnetohydrodynamic (MHD) waves is investigated. ultraviolet (UV) and X-ray emission lines of the corona show non-thermal broadenings. The wave rms velocities inferred from these observations are of the order of 25–60 km s⁻¹ . Assuming that these values are not negligible, we solved MHD equations in a quasi-linear approximation, by retaining the lowest order non-linear term in rms velocity. Plasma density distribution in the solar corona is assumed to be inhomogeneous. This plasma is also assumed to be permeated by dipole-like magnetic loops. Wave propagation is considered along the magnetic field lines. As dissipative processes, only the viscosity and parallel (to the local magnetic field lines) heat conduction are assumed to be important. Two wave modes emerged from the solution of the dispersion relation. The fast mode magneto-acoustic wave, if originated from the coronal base can propagate upwards into the corona and dissipate its mechanical energy as heat. The damping length-scale of the fast mode is of the order of 500 km. The wave energy flux associated with these waves turned out to be of the order of 2.5×10⁵ ergs cm⁻² s⁻¹ which is high enough to replace the energy lost by thermal conduction to the transition region and by optically thin coronal emission. The fast magneto-acoustic waves prove to be a likely candidate to heat the solar corona. The slow mode is absent, in other words cannot propagate in the solar corona.     

Differential rotation and the structure and energy content of coronal magnetic fields

It is argued that differential rotation of the photospheric magnetic fields will induce currents in the corona. The work done against surface magnetic stresses will increase the energy content of the coronal magnetic field. The electrical conductivities are high and the foot points of field lines move with the differential rotation. The force-free field equations are solved with this constraint to obtain a minimum estimate of the energy increase for a quadrupole field. During a solar rotation the magnetic energy increases by 25%. Local release of this energy in the corona would have a significant effect. The expansion of field lines as a result of the differential rotation should increase the amount of flux and the field strength in the solar wind region.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Magnetic fields and the structure of the solar corona

Several different mathematical methods are described which use the observed line-of-sight component of the photospheric magnetic field to determine the magnetic field of the solar corona in the current-free (or potential-field) approximation. Discussed are (1) a monopole method, (2) a Legendre polynomial expansion assuming knowledge of the radial photospheric magnetic field, (3) a Legendre polynomial expansion obtained from the line-of-sight photospheric field by a least-meansquare technique, (4) solar wind simulation by zero-potential surfaces in the corona, (5) corrections for the missing flux due to magnetograph saturation. We conclude (1) that the field obtained from the monopole method is not consistent with the given magnetic data because of non-local effects produced by monopoles on a curved surface, (2) that the field given by a Legendre polynomial (which is fitted to the measured line-of-sight magnetic field) is a rigorous and self-consistent solution with respect to the available data, (3) that it is necessary to correct for the saturation of the magnetograph (at about 80 G) because fields exceeding 80 G provide significant flux to the coronal field, and (4) that a zero-potential surface at 2.5 solar radii can simulate the effect of the solar wind on the coronal magnetic field.     

Current convection in solar active regions

Current carrying magnetic fields which penetrate sunspots can be unstable to current convective modes caused by the large gradient of electrical conductivity. The linear growth rates and wavelengths of the unstable modes are found. The unstable modes produce fine-scale vortices perpendicular to the magnetic field, which overshoot well into the solar corona. The modes provide a turbulent vorticity source at the photospheric footpoints of the field. This can cause braiding and reconnection of the coronal magnetic field. The modes twist the coronal magnetic field into loops with a typical radius of 200 km, consistent with recent X-ray observations.