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.     

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.     

Force-free Magneitic Field Extrapolation for the Complex Sunspot Group of August 1972

Quantitative data on the magnetic field structure at all levels of the solar atmosphere are of basic importance for our understanding of physical processes in active regions in general and in flares in particular. Because photospheric longitudinal magnetograms are the most reliable data available, one has to look for a method of theoretical extrapolation of such data to higher levels. Such a method has been developed for force-free magnetic fields, i.e., ∇ X B = αB , with α = constant, satisfying more realistic boundary conditions as compared with earlier papers; e.g., the net magneitic flux through the magnetogram area is not required to be zero. The method has been used to calculate the magnetic field vector and lines of force in the flare-active region of August 1972. Calculated fields are compared with other observations such as structures in H α . Results of August 3rd show that the loop prominence systems observed during the flares of August 2nd and 4th are represented by a force-free field with positive α rather than by a current-free field ( α = 0) The extractable energy supply of this force-free field is of the order of magnitude of maximum flare demand (10³² erg); the height dependence of the magnetic field strengths agrees with that from radio and X-ray estimates. Similar results are obtained for the August 7th magnetic field structure.     

Magnetic fields,loop prominences and the great flares of August, 1972

Lines of magnetic force, computed under the assumption that the solar corona is free of electric currents, have been compared with loop prominence systems associated with three flares in August, 1972. The computed fields closely match the observations of loops at a height of 40000 km at times 3–4 h after onset of the associated flares. Inferred magnetic field intensities in the loops range from 1300 G where the loops converge into a sunspot to 50–80 G at 40 000 km above the photosphere. The first-seen and lowest-lying loops are sheared with respect to the calculated fields. Higher loops conform more closely to the current-free fieldlines. A model of Barnes and Sturrock is used to relate the degree of shear to the excess magnetic energy available during the flare of August 7. On various lines of evidence, it is suggested that magnetic energy was available to accelerate particles not only during the impulsive phase of the flare, but also during the following 2–3 h. The particle acceleration region seems to be in the magnetic fields just above the visible loops. The bright outer edges of the flare ribbons are identified as particle impact regions. The dense knots of loop prominence material fall to the ribbons' inner edges.On leave from Tel Aviv University, Tel Aviv, Israel.     

Representations of coronal magnetic fields including currents

Solar Physics - Coronal electric currents are superposed on the calculated large-scale current-free (potential) magnetic field of the solar corona and the new magnetic configurations are mapped....     

Numerical Simulations of Torsional Alfvén Waves in Axisymmetric Solar Magnetic Flux Tubes

We numerically investigate Alfvén waves propagating along an axisymmetric and non-isothermal solar flux tube embedded in the solar atmosphere. The tube magnetic field is current-free and diverges with height, and the waves are excited by a periodic driver along the tube magnetic field lines. The main results are that the two wave variables, the velocity and magnetic field perturbations in the azimuthal direction, behave differently as a result of gradients of the physical parameters along the tube. To explain these differences in the wave behavior, the time evolution of the wave variables and the resulting cutoff period for each wave variable are calculated and used to determine regions in the solar chromosphere where strong wave reflection may occur.     

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.     

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.     

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.     

Coronal holes

Coronal holes are extensive regions of extremely low density in the solar corona within 60° of latitude from the equator. (They are not to be confused with the well-known coronal cavities which surround quiescent prominences beneath helmet streamers.) We have superposed maps of the calculated current-free (potential) coronal magnetic field with maps of the coronal electron density for the period of November 1966, and find that coronal holes are generally characterized by weak and diverging magnetic field lines. The chromosphere underlying the holes is extremely quiet, being free of weak plages and filaments. The existence of coronal holes clearly has important implications for the energy balance in the transition region and the solar wind.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Destabilization of hydrodynamically stable rotation laws by azimuthal magnetic fields

We consider the effect of toroidal magnetic fields on hydrodynamically stable Taylor–Couette differential rotation flows. For current-free magnetic fields a non-axisymmetric   m = 1  magnetorotational instability arises when the magnetic Reynolds number exceeds   O (100)  . We then consider how this 'azimuthal magnetorotational instability' (AMRI) is modified if the magnetic field is not current-free, but also has an associated electric current throughout the fluid. This gives rise to current-driven Tayler instabilities (TIs) that exist even without any differential rotation at all. The interaction of the AMRI and the TI is then considered when both electric currents and differential rotation are present simultaneously. The magnetic Prandtl number Pm turns out to be crucial in this case. Large Pm have a destabilizing influence, and lead to a smooth transition between the AMRI and the TI. In contrast, small Pm have a stabilizing influence, with a broad stable zone separating the AMRI and the TI. In this region the differential rotation is acting to stabilize the TIs, with possible astrophysical applications (Ap stars). The growth rates of both the AMRI and the TI are largely independent of Pm , with the TI acting on the time-scale of a single rotation period, and the AMRI slightly slower, but still on the basic rotational time-scale. The azimuthal drift time-scale is ∼20 rotations, and may thus be a (flip-flop) time-scale of stellar activity between the rotation period and the diffusion time.     

Coronal magnetic fields from microwave polarization observations

The solar active region (AR) 7530 was observed at 6 cm on July 3 and 4, 1993 with the Westerbork Synthesis Radio Telescope, using a multi-channel receiver with very narrow bandwidth. We compare the radio data with Yohkoh SXT observations and with the magnetic field extrapolated from the Marshall vector magnetograms in the force-free and current-free approximations. The comparison with soft X-rays shows that, although a general agreement exists between the shape of the radio intensity map and the X-ray loops, the brightness temperature, T _b, obtained using the parameters derived from the SXT is much lower than that observed. The comparison with the extrapolated photospheric fields shows instead that they account very well for the observed T _b above the main sunspots, if gyroresonance emission is assumed. In the observation of July 4 an inversion and strong suppression of the circular polarization was clearly present above different portions of the AR, which indicates that particular relationships exist between the electron density and the magnetic field in the region where the corresponding lines of sight cross the field quasi-perpendicularly. The extrapolated magnetic field at a much higher level ( 10¹⁰ cm), satisfies the constraints required by the wave propagation theory all over the AR. However, a rather low electron density is derived.     

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.     

Computation of inner coronal magnetic fields from longitudinal field components on a spherical photosphere

A method is developed which for a certain day permits the approximate calculation of closed small and large scale magnetic field lines. From the photospheric longitudinal components of the magnetic field measured at this day normal components are derived taking into account the curvature of the solar surface. The magnetic fields are assumed to be potential or force-free fields.The method is applied to observations of September 5 and September 7, 1973. The projected magnetic field lines are compared with the loop structures which are visible in XUV pictures taken on these days. In the cases where no good agreement could be obtained for potential fields, force-free fields are calculated and fitted to the observed structures.     

Magnetic diffusion and flare energy buildup

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear two-dimensional force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field (B ₀ 10³ G) and photospheric velocity field (v _max 1 km s^–1) are used, it is found that 3–4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.     

Multi-Wavelength Analysis of High-Energy Electrons in Solar Flares: A Case Study of the August 20, 2002 Flare

A multi-wavelength spatial and temporal analysis of solar high-energy electrons is conducted using the August 20, 2002 flare of an unusually flat (γ₁ = 1.8) hard X-ray spectrum. The flare is studied using RHESSI, Hα, radio, TRACE, and MDI observations with advanced methods and techniques never previously applied in the solar flare context. A new method to account for X-ray Compton backscattering in the photosphere (photospheric albedo) has been used to deduce the primary X-ray flare spectra. The mean electron flux distribution has been analysed using both forward fitting and model-independent inversion methods of spectral analysis. We show that the contribution of the photospheric albedo to the photon spectrum modifies the calculated mean electron flux distribution, mainly at energies below ∼100 keV. The positions of the Hα emission and hard X-ray sources with respect to the current-free extrapolation of the MDI photospheric magnetic field and the characteristics of the radio emission provide evidence of the closed geometry of the magnetic field structure and the flare process in low altitude magnetic loops. In agreement with the predictions of some solar flare models, the hard X-ray sources are located on the external edges of the Hα emission and show chromospheric plasma heated by the non-thermal electrons. The fast changes of Hα intensities are located not only inside the hard X-ray sources, as expected if they are the signatures of the chromospheric response to the electron bombardment, but also away from them.     

ANALYSIS OF it YOHKOH SXT CORONAL LOOPS AND CALCULATED FORCE-FREE MAGNETIC FIELD LINES FROM VECTOR MAGNETOGRAMS

In this paper some soft X-ray loops observed by Yohkoh/SXT and extrapolated magnetic fields from the vector magnetogram data observed at the Mitaka Flare Telescope are compared and analyzed. The computed field lines generally agree with Yohkoh/SXT coronal loops. Typical examples of the magnetic field intensities, loop widths, and loop heights along field lines are presented.     

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.     

Coronal force-free magnetic field: Source-surface model

Models of the magnetic field in the solar chromosphere and corona are still mainly based on theoretical extrapolations of photospheric measurements. For the practical calculation of the global field, the so-called source-surface model has been introduced, in which the influence of the solar wind is described by the requirement that the field be radial at some exterior (source) surface. Then the assumption that the field is current-free in the volume between the photosphere and this surface allows for its determination from the photospheric measurement. In the present paper a generalization of the source-surface model to force-free fields is proposed. In the generalized model the parameter( = ×B·B/B ²)must be non-constant (or vanish identically) and currents are restricted to regions with closed field lines. A mathematical algorithm for computing the field from boundary data is devised.     

On the possibility of disk-fed formation in supergiant high-mass X-ray binaries

We consider the existence of a neutron star magnetic field by the detected cyclotron lines. We collected data on nine sources of high-mass X-ray binaries with supergiant companions as a test case for our model, to demonstrate their distribution and evolution. The wind velocity, spin period and magnetic field strength are studied under different mass loss rates. In our model, correlations between mass-loss rate and wind velocity are found and can be tested in further observations. We examine the parameter space where wind accretion is allowed, avoiding the barrier of rotating magnetic fields, with robust data on the magnetic field of neutron stars. Our model shows that most sources(six of nine systems) can be fed by the wind with relatively slow velocity, and this result is consistent with previous predictions. In a few sources,our model cannot fit the standard wind accretion scenario. In these peculiar cases, other scenarios(disk formation, partial Roche lobe overflow) should be considered. This would provide information about the evolutionary tracks of various types of binaries, and thus exhibit a clear dichotomy behavior in wind-fed X-ray binary systems.