G. W. Pneuman

Magnetic reconnection in the corona and the loop prominence phenomenon

Many classes of transient solar phenomena, such as flares, flare sprays, and eruptive prominences, cause major disruptions in the magnetic geometry of the overlying corona. Typically, the results from Skylab indicate that pre-existing closed magnetic loops in the corona are torn open by the force of the disruption. We examine here some of the theoretical consequences to be expected during the extended relaxation phase which must follow such events. This phase is characterized by a gradual reconnection of the outward-distended field lines. In particular, the enhanced coronal expansion which occurs on open field lines just before they reconnect appears adequate to supply the large downward mass fluxes observed in Ha loop prominence systems that form during the post-transient relaxation. In addition, this enhanced flow may produce nonrecurrent high speed streams in the solar wind after such events. Calculations of the relaxation phase for representative field geometries and the resulting flow configurations are described.

GAS--MAGNETIC FIELD INTERACTIONS IN THE SOLAR CORONA.

It is evident from eclipse photographs that gas-magnetic field interactions are important in determining the structure and dynamical properties of the solar corona and interplanetary medium. Close to the Sun in regions of strong field, the coronal gas can be contained within closed loop structures. However, since the field in these regions decreases outward rapidly, the pressure and inertial forces of the solar wind eventually dominate and distend the field outward into interplanetary space. The complete geometrical and dynamical state is determined by a complex interplay of inertial, pressure, gravitational, and magnetic forces. The present paper is oriented toward the understanding of this interaction. The ‘helmet’ streamer type configuration with its associated neutral point and sheet currents is of central importance in this problem and is, therefore, considered in some detail.Integration of the relevant partial differential equations is made tractable by an iterative technique consisting of three basic stages, which are described at length. A sample solution obtained by this method is presented and its physical properties discussed.

Magnetic reconnection and coronal transients

Every two-ribbon flare observed during the Skylab period produced an observable coronal transient, provided the flare occurred close enough to the limb. The model presented here treats these two events as a combined process. Transients that occur without flares are believed to involve magnetic fields that are too weak to produce significant chromospheric emission. Adopting the hypothesis that the rising flare loop systems observed during two-ribbon flares are exhibiting magnetic reconnection, a model of a coronal transient is proposed which incorporates this reconnection process as the driving force. When two oppositely directed field lines reconnect a lower loop is created rooted to the solar surface (the flare loop) and an upper disconnected loop is produced which is free to rise. The magnetic flux of these upper loops is proposed as the driver for the transient. The force is produced by the increase in magnetic pressure under the filament and transient.A quantitative model is developed which treats the transient configuration in terms of four distinct parts- the transient itself with its magnetic field and material, the region just below the transient but above the filament, the filament with its magnetic field, and the reconnected flux beneath the filament. Two cases are considered - one in which all the prominence material rises with the transient and one in which the material is allowed to fall out of the transient. The rate of rise of the neutral line during the reconnection process is taken from the observations of the rising X-ray flare loop system during the 29 July, 1973 flare. The MHD equations for the system are reduced to four non-linear ordinary coupled differential equations which are solved using parameters believed to be realistic for solar conditions. The calculated velocity profiles, widths, etc., agree quite well with the observed properties of coronal transients as seen in white light. Since major flares are usually associated with a filament eruption about 10–15 min before the flare and since this model associates the transient with the filament eruption, we suspect that the transient is actually initiated some time before the actual flare itself.

The formation of solar prominences by magnetic reconnection and condensation

A model for solar quiescent prominences nested in a ‘Figure 8’ magnetic field topology is developed. This topology is argued to be the natural consequence of the distention of bipolar regions upward into the corona. If this distention is slow enough so that hydrostatic equilibrium holds approximately along the field lines, the transverse gas pressure forces fall exponentially with height whereas the inward Lorentz forces fall as a power law. At a low height in the corona, the pressure forces cannot balance the Lorentz forces provided the field lines remain tied to the photosphere and an inward collapse with subsequent reconnection at the point of closest approach should occur. Because of initial shear in the magnetic field, the reconnection would produce isolated helices above the point of reconnection since field lines would not interact with themselves but with their neighbors. This resulting topology produces a field above the elevated neutral line which is opposite in polarity to that of the photospheric field as in the current sheet models of Kuperus and Tandberg-Hanssen (1967). Raadu and Kuperus (1973), Kuperus and Raadu (1974), and Raadu (1979) and in agreement with recent observations of Leroy (1982), and Leroy et al. (1983).Assuming the isolated helices formed by reconnection are insulated from coronal thermal conduction and heating, the radiative cooling process and condensation is considered for the temperature range of 104-6000 K. This condensation results in a steady downflow to the bottom of the helices as the temperature scale-height falls, thus forming a dense, cool, prominence at the bottom of the helical configuration resting on the elevated neutral line with the remainder of the helix being essentially evacuated of material. We identify this neutral line at the bottom of the prominence with the sharp lower edge often seen when viewing quiescent prominences side-on and the evacuated helix with the coronal cavity observed around prominences when seen during total eclipses.Downflow speeds associated with the condensation process are calculated for prominence temperatures and yield velocities in the range of the observed downflows of about 1 km s−1.

Downflow in the supergranulation network and its implications for transition region models

Three independent observations by rocket, Skylab, and OSO-8 have all indicated the presence of steady downflows of the order of a few kilometers per second in the solar transition region overlying the chromospheric network. Using density estimates at these heights from traditional transition region models, we find that the downward mass fluxes associated with these velocities are comparable with the estimated upward mass flux in spicules, originating in the same regions. Since both observations and theoretical calculations show that the solar wind can accept only a small fraction of the upward spicule flux, we suggest that the downflow represents spicular material returning to the chromosphere after being heated to coronal temperatures. In this context, the differential velocity measurement of Cushman and Rense is interpreted as indicating a difference in downflow speeds rather than a difference in expansion speeds.Moreover, the enthalpy flux associated with the downflow of coronal material into these regions is shown by various estimates to exceed the inward heat flow expected by thermal conduction and it may constitute the dominant energy source for the transition region. Simplified analytical models are used to explore the nature of the transition region overlying the supergranulation boundaries, under the assumption that the thermal structure results from a balance of the downward convection of enthalpy and radiative losses. Models based upon these considerations are shown to be consistent with the observed emission measures.

Solar-interplanetary modeling: 3-D solar wind solutions in prescribed non-radial magnetic field geometries

A model is presented which describes the 3-dimensional non-radial solar wind expansion between the Sun and the Earth in a specified magnetic field configuration subject to synoptically observed plasma properties at the coronal base. In this paper, the field is taken to be potential in the inner corona based upon the Mt. Wilson magnetograph observations and radial beyond a certain chosen surface. For plasma boundary conditions at the Sun, we use deconvoluted density profiles obtained from synopticK-coronameter brightness observations. The temperature is taken to be 2 × 106 K at the base of closed field lines and 1.6 x 106K at the base of open field lines.For a sample calculation, we employ data taken during the period of the 12 November 1966 eclipse. Although qualitative agreement with observations at 1 AU is obtained, important discrepancies emerge which are not apparent from spherically symmetric models or those models which do not incorporate actual observations in the lower corona. These discrepancies appear to be due to two primary difficulties - the rapid geometric divergence of the open field lines in the inner corona as well as the breakdown in the validity of the Spitzer heat conduction formula even closer to the Sun than predicted by radial flow models. These two effects combine to produce conductively dominated solutions and lower velocities, densities, and field strengths at the Earth than those observed. The traditional difficulty in solar wind theory in that unrealistically small densities must be assumed at the coronal base in order to obtain observed densities at 1 AU is more than compensated for here by the rapid divergence of field lines in the inner corona.For these base conditions, the value ofβ(ratio of gas pressure to magnetic pressure) is shown to be significantly greater than one over most of the lower corona - suggesting that, for the coronal boundary conditions used here, the use of a potential or force-free magnetic field configuration may not be justified.The calculations of this paper point to the directions where future research on solar-interplanetary modelling should receive priority:(a)better models for the coronal magnetic field structure(b)improved understanding of the thermal conductivity relevant for the solar wind plasma.

The solar wind and the temperature-density structure of the solar corona

The influence of the solar wind on large-scale temperature and density distributions in the lower corona is studied. This influence is most profoundly felt through its effect upon the geometry of coronal magnetic fields since the presence of expansion divides the corona into magnetically ‘open’ and ‘closed’ regions. Each of these regions is governed by entirely different energy transport processes. This results in significant temperature differences since only the open field regions suffer outward conductive heat losses. Because the temperature influences the density in an exponential manner, large density inhomogeneities are to be expected.An approximate method for calculating the temperature and density distribution in a known magnetic field geometry is outlined and numerical estimates are carried out for representative coronal conditions. These estimates show that temperature differences of a factor of about two and density differences of ten can be expected in the lower corona even for uniform base conditions. As a result, we do not regard the so-called ‘coronal holes’ necessairly as locations of reduced mechanical heating. Alternatively, we suggest that they are regions of open magnetic field lines being continuously drained of energy contert by the solar wind expansion and outward thermal conduction.

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&Es soft X-ray experiment and NRLs Heii observations and theK-coronal brightness distributions are from HAOsK-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.

CORONAL STREAMERS. III. ENERGY TRANSPORT IN STREAMER AND INTERSTREAMER REGIONS.

The geometrical and dynamical structure of a corona consisting of streamer and interstreamer regions is examined. The present paper is an extension of previous works of this series in that energy transport processes are included in the theoretical framework of the model. Under specified conditions at some reference level above the coronal base, the structure at larger distances is determined by simultaneous integration of the continuity, momentum, and energy equations for each region subject to the condition for a lateral balance of magnetic and gas pressure at all levels. Outward thermal conduction and convection by the solar wind are assumed to be the processes contributing to the energy balance of each region, the magnetic field effectively thermally insulating one region from the other.Numerical results are presented for situations representative of the solar corona. Regions occupied by streamers are found to have higher densities than their surroundings at all distances from the sun. For a given density at the coronal base, the density at the orbit of earth is lower in both the streamer and interstreamer region than that predicted for radial flow. The density enhancement increases outward to a maximum value at a distance of several solar radii. In addition, beyond a distance of a few radii streamers are characterized by higher expansion velocities and lower temperatures than their immediate surroundings. Similar to the case of radial flow, supersonic solutions exist only for base densities below a certain value, which depends upon the specified base temperature and magnetic field distribution. The general features illustrated by these models are expected to persist in the advent of more sophisticated multi-region models.

A NEW TECHNIQUE FOR THE DETERMINATION OF CORONAL MAGNETIC FIELDS: A FIXED MESH SOLUTION TO LAPLACE'S EQUATION USING LINE-OF-SIGHT BOUNDARY CONDITIONS

AbstractA new method for computing potential magnetic field configurations in the solar atmosphere is described. A discrete approximation to Laplaces equation is solved in the domain R⊙ ≤ r ≤R1, 0 ≤ θ ≤ π, 0 ≤ φ ≤ 2π (R1being an arbitrary radial distance from the solar center). The method utilizes the measured line-of-sight magnetic fields directly as the boundary condition at the solar surface and constrains the field to become radial at the outer boundary, R1. First the differential equation and boundary conditions are reduced to a set of two-dimensional equations in r, θ by Fourier transforming out the periodic φ dependence. Next each transformed boundary condition is converted to a Dirichlet surface condition. Then each two-dimensional equation with standard Dirichlet-Dirichlet boundary conditions is solved for the Fourier coefficient it determines. Finally, the solution of the original three dimensional equation is obtained through inverse Fourier transformation. The primary numerical tools in this technique are the use of a finite fast Fourier transform technique and also a generalized cyclic reduction algorithm developed at NCAR. Any extraneous monopole component present in the data can be removed if so desired.The code was developed for the HAO solar-interplanetary modeling effort in response to the following specific requirements:(1)High resolution.(2)Speed in computation.(3)Sufficiently accurate solutions of Laplaces equation at all heights. The spatial resolution of the present code is such that measured surface line-of-sight magnetic fields to a resolution of 2.8° in both latitude and longitude can be adequately treated.Comparisons with the Altschuler-Newkirk code shows that the two methods are more-or-less equivalent for computing large-scale fields at ≈2R⊙but that the fixed mesh method is capable of much greater accuracy close to the Sun.