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.     

Magnetic fields and the structure of the solar corona

During the eclipse of 12 November 1966, the solar corona was photographed at an effective wavelength of 6500 Å with an f/16, 11.1 cm aperture camera. Reduction of the observations yields coronal radiances and polarizations from 1.4 to 3.5 solar radii. Standard techniques are used for the separation of F and K-coronas, determination of coronal electron densities and temperatures, and estimation of the orientation of the major streamers in space.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Magnetic fields and plasmas in the inner heliosphere: Helios results

The magnetic field of Mercury and the structure and dynamics of Mercury's magnetosphere, which will be studied by the spacecraft orbiting Mercury, are strongly influenced by the interaction of the solar wind with Mercury. In order to understand the internal magnetic field, it will be necessary to correct the observations of the external field for the distortions produced by the solar wind. Understanding of the solar wind interaction with Mercury is essential for understanding the structure and dynamics of the magnetosphere and phenomena such as magnetic storms. Helios 1 and 2 made a number of passes in the region traversed by the orbit of Mercury, and each pass provided a sample of the solar wind environment of Mercury. This paper reviews the plasma and magnetic field observations from Helios that provide a general basis for interpreting the observations of Mercury that will be made by orbiting spacecraft. The variables that govern the structure and dynamics of the magnetospheres of Mercury and Earth are approximately 5–10 times larger at Mercury than at Earth. Thus, the solar wind interaction with Mercury will be much stronger than the interaction with Earth. Moreover, the solar wind at Mercury is probably more variable than that at Earth. There is a clear need for measurements of the solar wind during the approach of spacecraft to Mercury and while they are in orbit around Mercury.     

Fine structure of solar magnetic fields

The problem of inequality of results of longitudinal magnetic fields measured in the magnotosensetive lines FeI 5250 and FeI 5247 is investigated. The observed ratio of longitudinal components of magnetic field H ₁₁(5250)/H ₁₁(5247) is compared to the calculated for different combinations of magnetic field elements. The calculations have been made with standard model photosphere for quiet regions. It was concluded that the underestimated value of magnetic field obtained with the FeI 5250 line is explained by the presence of unresolved elements with kilogauss magnetic fields.     

Fine structure of solar magnetic fields

The deduction of magnetic fields from chromospheric structure is extended to active regions and transverse fields. Fields independently predicted by these rules from a high resolution H filtergram are compared with a high resolution magnetogram. The H method has the advantage over conventional magnetograms that it shows transverse fields and relates the fields to the real Sun. It has the disadvantage that higher spatial resolution is required and that it is difficult and time consuming in very complicated regions.The response of the chromosphere to magnetic fields is most consistent. Vertical field is invariably marked by bright plage, with brightness roughly proportional to the field strength (except for sunspots). All dark fibrils mark transverse fields and are parallel to field lines. All polarity changes are marked by dark fibrils, which may be transverse fibrils perpendicular to the field boundary, or filaments (prominences) which connect more distant points, and in which the field lines run nearly parallel to the boundary. The asymmetry between preceding and following polarity found by Veeder and Zirin (1970) does not exist; it was due to the low resolution of the Mount Wilson magnetograms.The complexity of active region field structure depends on the history of the region; all flux erupts in simple bipolar form, and lines of force remain connected to sibling spots until reconnection takes place. Thus the complex structure only occurs after eruption of several dipoles which reconnect. The phenomenon of inverted polarity turns out to be due to the emergence of satellite bipolar fields, where the p spot merges with the rest of the p field and the f spot appears as an included f field. Flares usually occur when the field lines from f spot reconnect from its sibling to the main spot.     

Magnetic and thermal energies in the solar wind

Magnetic and thermal energy densities measured in the solar wind by the spacecraft Vela-3/IMP-3, Explorer-34 and HEOS-1 are compared. A linear relation seems to exist, on the average, between these parameters, suggesting a possible equipartition of energy between plasma and magnetic field.     

Magnetic and thermal pressures in the solar wind

Explorer 34 solar wind data for the period June to December, 1967 show that(a) The magnetic pressure, P _BB ²/8, and thermal pressure,P _kn _p kTp+n kT+n _e kTe,are variable and positively correlated on a scale of 2 days, but (b) changes in P _b and P _k are anticorrelated on a scale 1 hr (0.01 AU). Thus, dynamical hydromagnetic processes (dv/dto) must occur on the mesoscale, but the solar wind tends to be in equilibrium(P _B+P _Kconstant) on a smaller scale, the microscale. The 3-hr averages show that the most probable value of P _{k/P B} is =1.0±0.1, which implies that the most probable state of the solar wind at 1 AU is not one of equipartition between the thermal energy and magnetic energy. The average total pressure for a given bulk speed(P(V)=P ^k+P _k+P _B) is essentially independent of V, implying that P is not determined by the heating or acceleration mechanisms of the solar wind; the average pressure is P=(2.9±1.5)×10^-10dyne/cm².     

Magnetic and boundary effects on thermal instabilities in solar magnetic fields: Localized modes in a slab geometry

The coupling of thermal and ideal MHD effects in a sheared magnetic field is investigated. A slab geometry is considered so that the Alfvén mode can be decoupled from the system. With the total perturbed pressure approximately zero, the fast mode is eliminated and a system of linearized equations describing magnetic effects on the slow mode and thermal mode is derived. These modes evolve independently on individual fieldlines. One of the main features of this approach is that the influence of the dense photosphere can be included. A variety of different conditions that simulate the photospheric boundary are presented and the different results are discussed. A choice of field geometry and boundary conditions is made which removes mode rational surfaces so that there are no regions in which parallel thermal conduction can be neglected. This provides a stabilizing mechanism for the thermal mode. Growth rates are reduced by 30–40% and there is complete stabilization for sufficiently short fieldlines. The influence of dynamic and thermal boundary conditions on the formation of prominences is discussed.     

Differential rotation and sector structure of solar magnetic fields

The differential rotation and sector structure of solar magnetic fields has been studied using digitized data on photospheric magnetic fields recorded at the Mount Wilson Observatory during the period August 1959–May 1970. The power spectra show considerable power in high-frequency peaks, corresponding to harmonic components with wavelengths less than 1/10 solar rotation. Calculations for a series of shorter time intervals show how the distribution of power over the various harmonic components in the sector pattern varies strongly with the solar cycle. The equatorial rotation rate of solar magnetic fields is about 0.1 km s^-1 faster than that of the photospheric plasma determined from Doppler shifts. It is shown that the Doppler measurements mainly refer to the non-network regions. The differential flow of 0.1 km s^-1 forms streamlines around the magnetic fine structures. The different rotation rates of various solar features can be explained in terms of the rotation rates of magnetic and non-magnetic regions. The rotation rates of the magnetic fields in active and quiet regions agree at the equator. At higher latitudes, however, the background fields deviate less from solid-body rotation, indicating that their source is below the deepest layers to which the sunspot magnetic fields penetrate. This suggests that turbulent diffusion of the field in old active regions may not be the main source for the background magnetic field, but that the source is located close to a rigidly rotating solar core with a synodic rotation period of 26.87 days.     

Magnetic and microwave structure in solar active regions

The structure of six active regions observed at 2.8 cm with the Stanford interferometer is compared with the configuration of the underlying photospheric magnetic fields, as given by the Kitt Peak magnetograph.The similar resolution and accuracy on the measured positions of both instruments allowed us to establish a more detailed spatial correspondence between radio and magnetic features than previously reached.The radio features which correspond to the cores of the active sources are always found to overlay regions of enhanced magnetic fields. Different spatial associations have been found depending on the brightness temperature of the sources. The possibility that this effect might be due to the development of the active region is also considered.     

On the small-scale structure of solar magnetic fields

The small-scale structure of solar magnetic fields has been studied using simultaneous recordings in the spectral lines Fe i 5250 Å and Fe i 5233 Å, obtained with the Kitt Peak multi-channel magnetograph. We find that more than 90% of the magnetic flux in active regions (excluding the sunspots), observed with a 2.4 by 2.4 aperture, is channelled through narrow filaments. This percentage is even higher in quiet areas. The field lines in a magnetic filament diverge rapidly with height, and part of the flux returns back to the neighbouring photosphere. Therefore the strong fields within a magnetic filament are surrounded by weak fields of the order of a few gauss of the opposite polarity. The field-strength distribution within a filament, including the surrounding opposite-polarity fields, seems to be almost the same for all filaments within a given active or quiet region.The analysis of a scan made during an imp. 2 flare showed that observations during and after the flare would give a fictitious decrease of the magnetic energy in the region by a factor of 2–3 due to line-profile changes during the flare.Visiting Astronomer, Kitt Peak National Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Zonal structure and meridional drift of large-scale solar magnetic fields

Digitized synoptic charts of photospheric magnetic fields were analyzed for the past 4 incomplete solar activity cycles (1969–2000). The zonal structure and cyclic evolution of large-scale solar magnetic fields were investigated using the calculated values of the radial B _r, |B _r|, meridional B _θ, |B _θ|, and azimuthal B _φ, |B _φ| components of the solar magnetic field averaged over a Carrington rotation (CR). The time–latitude diagrams of all 6 parameters and their correlation analysis clearly reveal a zonal structure and two types of the meridional poleward drift of magnetic fields with the characteristic times of travel from the equator to the poles equal to ∼16–18 and ∼2–3 years. A conclusion is made that we observe two different processes of reorganization of magnetic fields in the Sun that are related to generation of magnetic fields and their subsequent redistribution in the process of emergence from the field generation region to the solar surface. Redistribution is supposed to be caused by some external forces (presumably, by sub-surface plasma flows in the convection zone).     

Cooling of solar flare plasmas

A simple model for the cooling of solar flare plasmas is considered. This model predicts that an increase in emission measure with decreasing temperature is a general feature of a cooling flare. The results are compared to solar flare data.     

Magnetic reconnection in plasmas

A review of the present status of the theory of magnetic reconnection is given. In strongly collisional plasmas reconnection proceeds via resistive current sheets, i.e. quasi-stationary macroscopic Sweet-Parker sheets at intermediate values of the magnetic Reynolds numberR _m , or mirco-current sheets in MHD turbulence, which develops at highR _m . In hot, dilute plasmas the reconnection dynamics is dominated by nondissipative effects, mainly the Hall term and electron inertia. Reconnection rates are found to depend only on the ion mass, being independent of the electron inertia and the residual dissipation coefficients. Small-scale whistler turbulence is readily excited giving rise to an anomalous electron viscosity. Hence reconnection may be much more rapid than predicted by conventional resistive theory.     

Magnetic fields and the temperature structure of the chromosphere-corona interface

The temperature structure of the transition region between the chromosphere and corona is discussed in the context of current ideas about magnetic fields in these layers. Magnetic channeling of the downward conductive heat flow from the corona into the regions of enhanced field at the supergranulation boundaries is proposed as a mechanism for explaining the measured intensities of solar ultraviolet emission lines which originate in layers with temperatures below 10⁵ °K. It is shown that nearly all of the observed ultraviolet line emission originates in interspicule regions, and that this emission plays an important part in the energy balance of the cooler layers of the transition region. It is suggested that certain motions observed in the upper chromosphere may represent the earliest visual evidence for conversion of inflowing conduction energy into kinetic motions.On leave from the Observatory Sonnenborgh at Utrecht, The Netherlands.     

The thermal structure of the magnetized solar transition region

The detailed thermal structure of the magnetized solar transition region, as measured by itsdifferential emission measure [DEM(T)], is unknown. Proposals have been made that envision a significant lower-temperature contribution to the energy balance from cross-field (ion) heat flux. In this paper, we describe a self-consistent, 2-D, MHD simulation (including the full effects of anisotropic thermal conduction) of a conceptual model due to Athay (1990). We display the detailed, irregular, thermal and magnetic structure of the transition region, and demonstrate that the predicted DEM agrees with observations, particularly in theT < 10⁵ K regime where previous theories had difficulty.     

Interactions between solar neutrinos and solar magnetic fields

We attempt to correlate all of the available solar-neutrino data with the strong magnetic fields these neutrinos encounter in the solar interior along their Earth-bound path. We approximate these fields using the photospheric, magnetograph-measured flux from central latitude bands, time delayed to proxy the magnetic fields in the solar interior. Our strongest evidence for anticorrelation is for magnetic fields within the central ±5° solar-latitude band that have been delayed by 0.85 ± 0.55 yr. Assuming a neutrino-magnetic interaction, this might indicate that interior fields travel to the solar surface in this period of time. As more solar-neutrino flux information is gathered, the question of whether this result arises from a physical process or is merely a statistical fluke should be resolved, providing that new data are obtained spanning additional solar cycles and that correlation studies focus on these same regions of the solar magnetic field.