Reorientation of global coronal magnetic fields due to differential rotation

Because of the progressive decrease in rotation rate of the solar plasma at increasing latitudes, the photospheric foot-points of large-scale closed magnetic structures in the corona, which are originally widely separated in longitude, may ultimately be brought into proximity. Magnetic mergers and reconnections between magnetic fields of opposite polarity are presumed to occur, producing major structural changes in the corona and in the locations of underlying filaments. Thus we believe that the differential rotation phenomenon is essential to understanding both gradual (evolutionary) and sudden (transient) changes in the corona, and that they can occur without any observable change in the photospheric magnetic flux. A process is suggested for the splitting or bifurcation of a high-latitude magnetic structure, producing two separate components at the same latitude, whose rotation rates are influenced by their respective magnetic linkages to other regions on the Sun.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Differential rotation of photospheric magnetic fields associated with coronal holes

An interesting aspect of solar rotation is the fact that coronal holes seem to exhibit little or no differential rotation. We set out to investigate the question of whether or not the photospheric magnetic fields underlying coronal holes also exhibit reduced differential rotation. In order to accomplish this we measured the daily positions of filaments and plages surrounding a large coronal hole that lasted for several disk passages. The resulting differential rotation curve was considerably flatter than the standard curve for long-lived filaments and was in remarkably good agreement with the curve found for the overlying coronal hole itself.     

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.     

Modelling coronal magnetic fields

The hairy ball model of coronal magnetic fields has a spherical source surface separating potential and radial magnetic fields. In the present model the source surface is chosen such that the wind speed equals the Alfvénic speed at selected points on the source surface. Results have been obtained for a dipole base field and an isothermal corona.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

The evolution of coronal magnetic fields

Slow photospheric motions can produce flow speeds in the corona which are fast enough to violate quasi-static evolution. Therefore, high-speed flows observed in the corona are not necessarily due to a loss of equilibrium or stability. In this letter we present an example where the flow speed increases indefinitely with, height, while the coronal magnetic energy increases quadratically with time.     

XUV observations of coronal magnetic fields

Spectroheliograms obtained with the Naval Research Laboratory's Extreme Ultraviolet Spectrograph (S082A) on Skylab are compared with Kitt Peak National Observatory magnetograms. A principal result is the characteristic reconnection of flux from an emerging bipolar magnetic region to previously existing flux in its vicinity. Examples of the disappearance of magnetic flux from the solar atmosphere are also shown. The results of a particularly simple, potential field calculation are shown for comparison with the Skylab observations.     

Thermal condensations in coronal magnetic fields

Conditions under which cool condensations can form in the solar corona are investigated using the powerful phase plane method to analyse the energy and hydrostatic balance equations. The importance of the phase plane approach is that the conclusions deduced are not sensitive to the actual choice of boundary conditions adopted which only determine the actual contour. The importance of heating variations and area divergence are studied as well as the influence of gravity for their effect on the formation of cool condensations. The cool temperature at which optically thin radiation and heating balance is important and the links with other cool solutions are mentioned.     

Electric fields in coronal magnetic loops

We analyze spectra taken with the 40 cm coronograph at Sacramento Peak Observatory, for evidence of Stark effect on Balmer lines formed in coronal magnetic structures. Several spectra taken near the apex of a bright post-flare loop prominence show significant broadening from H₁₀ to the limit of Balmer line visibility in these spectra, at about H₂₀ The most likely interpretation of the increasing width is Stark broadening, although unresolved blends of Balmer emissions with metallic lines could also contribute to the trend. Less significant broadening is seen in 3 other post-flare loops, and the data from 5 other active coronal condensations observed in this study show no broadening tendency at all, over this range of Balmer number. The trend clearly observed in one post-flare loop requires an ion density of n _i ? 2 × 10¹² cm^?3, if it is to be explained entirely as Stark effect caused by pressure broadening. But mean electron densities measured directly from the Thomson scattering at λ3875 in the same SPO spectra, yield n _e ? 3?7 × 10¹⁰ cm^?3 for the same condensations observed within that loop. Comparison of this evidence from electron scattering, with densities derived from emission measures and line-intensity ratios, argues against a volume filling factor small enough to reconcile the values of n _i and n _e derived in this study. This discrepancy leads us to suggest that the Stark effect observed in these loops, and possibly also in flares, could be caused by macroscopic electric fields, rather than by pressure broadening. The electric field required to explain the Stark broadening in the brightest post-flare loop observed here is approximately 170 V cm^?1. We suggest an origin for such an electric field and discuss its implications for coronal plasma dynamics.     

The structure and stability of coronal magnetic fields

Solar Physics - The high degree of symmetry often assumed in studies of the structure and stability of coronal magnetic field configurations is restrictive and can yield misleading results. We have...     

The structure and stability of coronal magnetic fields

The high degree of symmetry often assumed in studies of the structure and stability of coronal magnetic field configurations is restrictive and can yield misleading results. We have therefore developed fully three-dimensional numerical methods for constructing force-free equilibria and for examining their stability properties, which make no assumptions about symmetry. A test of the stability analysis has been performed by applying it to the Gold-Hoyle twisted flux tube, which is known to be kink-unstable if the helical field makes more than about one turn between the line-tying end-plates. Our preliminary result is that the critical number of turns is about 1.1, in good agreement with the previous best estimate. However, we find that the growth rate, which has not been discussed previously, is orders of magnitude smaller than expected, even when the flux tube is twisted far beyond the stability limit.     

A model of interplanetary and coronal magnetic fields

A model of the large-scale magnetic field structure above the photosphere uses a Green's function solution to Maxwell's equations. Sources for the magnetic field are related to the observed photospheric field and to the field computed at a source surface about 0.6 R above the photosphere. The large-scale interplanetary magnetic field sector pattern is related to the field pattern at this source surface. The model generates magnetic field patterns on the source surface that compare well with interplanetary observations. Comparisons are shown with observations of the interplanetary magnetic field obtained by the IMP-3 satellite.     

The orientation of pre-transient coronal magnetic fields

Loop-like white light coronal transients are generally believed to be nearly planar sheets which are thin compared to the loop extent; however, this picture may be questioned since virtually no observations (of the more than 100 transient events observed during 1973–74 Skylab period) show such loops edge-on. From the group of transient events studied by Munro etal. (1979) for which definite surface associations exist, we find loop transients are strongly correlated with filament regions where the filament axis was oriented north-south. From direct soft X-ray observations of an expanding arch, the possible identification of the soft X-ray signature of footpoints of transient loops, and monochramatic observations of low coronal loops, we infer that loop-like coronal transients have their origin in low-lying coronal loops nearly co-planar with the north-south aligned filament axis. The situation with respect to non-loop events is less clear; such events apparently often arise from more complex filament geometries. Possible reasons for the preference of transients to arise from north-south filament-oriented regions are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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....     

Penetration of coronal magnetic fields into solar-wind streams

The formation of solar-wind stream structure is investigated. Characteristic features of the solar and coronal magnetic-field structure, morphological features of the white-light corona, and radio maps of the solar-wind transition (transonic) region are compared. The solar-wind stream structure is detected and studied by using radio maps of the transition region, the raggedness of its boundaries, and their deviation from spherical symmetry. The radio maps have been constructed from radioastronomical observations in 1995–1997. It is shown that the structural changes in the transition region largely follow the changes occurring in regions closer to the Sun, in the circumsolar magnetic-field structure, and in the solar-corona structure. The correlations between the magnetic-field strength in the solar corona and the location of the inner (nearest the Sun) boundary of the transition region are analyzed. The distinct anticorrelation between the coronal magnetic-field strength and the distance of the transition region from the Sun is a crucial argument for the penetration of solar magnetic fields into plasma streams far from the Sun.     

Differential rotation of solar magnetic fields

The connection of the differential rotation of solar magnetic fields with the field sign and strength is studied. The synoptic maps of magnetic fields over the last three solar cycles taken at the Kitt Peak Observatory served as input data for the study. The algorithm of magnetic field filtering over 14 chosen strengt intervals and successive 5-degree latitude zones was applied to these data. The Fourier transform of the time series obtained was then used. Analysis of the power spectra led to the conclusion that there are two types of magnetic fields. These differ in strength (0–50 and 50–700 G) and rotation characteristics. The rotation differentiality for strong magnetic field is almost twice as large as that for weak magnetic fields.     

Catastrophe of coronal magnetic flux ropes in partially open magnetic fields

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, a numerical study is carried out to find equilibrium solutions associated with a magnetic flux rope in the corona. The ambient magnetic field is partially open, consisting of a closed arcade in the center and an open field at the flank. The coronal magnetic flux rope is characterized by its magnetic properties, including the axial and annular magnetic fluxes and the magnetic helicity, and its geometrical features, including the height of the rope axis, the halfwidth of the rope and the length of the vertical current sheet below the rope. It is shown that for a given partially open ambient magnetic field, the dependence of the geometrical features on the magnetic properties displays a catastrophic behavior, namely, there exists a certain critical point, across which an infinitesimal enhancement of the magnetic parameters causes a finite jump of the geometrical parameters for the rope. The amplitude of the jump depends on the extent to which the ambient magnetic field in open, and approaches to zero when the ambient magnetic field becomes completely closed. The implication of such a catastrophe in solar active phenomena is briefly discussed.     

Energy released by the interaction of coronal magnetic fields

Comparisons between coronal spectroheliograms and photospheric magnetograms are presented to support the idea that as coronal magnetic fields interact, a process of field line reconnection usually takes place as a natural way of preventing magnetic stresses from building up in the lower corona. This suggests that the energy which would have been stored in stressed fields is continuously released as kinetic energy of material being driven aside to make way for the reconnecting fields. However, this kinetic energy is negligible compared to the thermal energy of the coronal plasma. Therefore, it appears that these slow adjustments of coronal magnetic fields cannot account for even the normal heating of the corona, much less the energetic events associated with solar flares.Visiting Scientist, Kitt Peak National Observatory, Tucson Arizona.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

A new expression for cylindrically-symmetric magnetic fields in coronal magnetic loops

We present a set of cylindrically-symmetric force-free magnetic fields with non-constant scalar function scalar. We found that the kink instability of the fields can be suppressed by reducing the length of the flux tube. By using the pressure profile in coronal magnetic loops obtained on the basis of the observational data, and by neglecting the effect of gravity, these force-free fields ars modified to non-force-free ones. For the plasma of finite conductivity the time and space dependent magnetic fields are obtained, and the ohmic dissipation per unit volume per second is calculated. For the magnetic fields, presented in the investigation, it is also found that, due to the large electrical conductivity of the plasma, the ohmic dissipation is negligable in comparison to the conduction and the radiation loss. Hence, for the energy equilibrium in a coronal loop, the contribution of ohmic dissipation is insignificant.     

A class of force-free magnetic fields for modeling pre-flare coronal magnetic configurations

Three-dimensional, quasi-static evolutions of coronal magnetic fields driven by photospheric flux emergence are modeled by a class of analytic force-free magnetic fields. Our models relate commonly observed photospheric magnetic phenomena, such as the formation and growth of sunspots, the emergence of an X-type separator, and the collision and merging of sunspots, to the three-dimensional magnetic fields in the corona above. By tracking the evolution in terms of a continuous sequence of force-free states, we show that flux emergence and submergence along magnetic neutral lines in the photosphere are essential processes in all these photospheric phenomena. The analytic solutions we present have a parametric regime within which the magnetic energy attained by an evolving force-free field may be of the order of 10³⁰ ergs to several 10³¹ ergs, depending on the magnetic environment into which an emerging flux intrudes. The commonly used indicators of magnetic shear in magnetogram interpretation are discussed in terms of field connectivity in our models. It is demonstrated that the crossing angle of the photospheric transverse magnetic field with the neutral line may not be a reliable indicator of the magnetic shear in the coronal field above, due to the complexity of three-dimensionality. The poorly understood constraint of magnetic-helicity conservation on the availability of magnetic free energy for a flare is briefly discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Coronal magnetic fields from faraday rotation observations

In the first part of this communication we briefly summarize the results of the first observation of linear polarization in the microwave emission above a solar active region obtained with the Westerbork Synthesis Radio Telescope, taking advantage of the very narrow bandwidths of a multi-channel spectral line receiver. The intensity of the Stokes parameterU, measured at several points close to the line of zero circular polarization, showed a clear sinusoidal trend as a function of ², in accordance to what is expected from Faraday rotation (Alissandrakis and Chiuderi Drago, 1994). Combining the measured period of the Faraday rotation with the observed deplacement of the depolarization line with respect to the photospheric neutral line, the height above the photosphere of the depolarization point and the value of the electron density and the magnetic field at this point are computed. Although the calculations are done in the very simplified assumptions of a bipolar magnetic field and of a density following hydrostatic equilibrium, they represent the first estimate of the coronal magnetic field in an active region, far from sunspots.Presented at the CESRA-Workshop on Coronal Magnetic Energy Release at Caputh near Potsdam in May 1994.