Properties of the magnetic fields of coronal holes with active regions

We determine the structure of the magnetic fields of coronal holes (CHs) and investigate its change in connection with the emergence of active regions (ARs) in CHs. Based on our observations in the HeI 1083 nm line performed with the CrAO TST-2 telescope, we have selected CHs of two types: without (15 CHs) and with (28 CHs) ARs. Magnetograms obtained at the Kitt Peak National Solar Observatory have been used to calculate the magnetic fields of the same objects.     

Evidence for magnetic energy storage in coronal active regions

Examination of X-ray images obtained by the S-054 X-ray spectrographic telescope on Skylab shows the presence of some atypical X-ray emitting coronal structures in active regions which are not consistent with potential extrapolations of photospheric magnetic fields. Analysis of the observed temporal changes in the X-ray emitting active region structures demonstrates that the majority of these consist of brightness changes representing temperature (and perhaps, density) variations of the material in the loops.Harvard College Observatory / Smithsonian Astrophysical Observatory.     

Connection of coronal holes with active regions

We have determined two qualitative parameters for 643 coronal holes (CHs). Parameter A characterizes the magnetic-field variation in CHs depending on the height. Parameter B characterizes the connection between the magnetic field in a CH and the polar field at the photosphere level. A comparison of these parameters corresponding to CH with and without active regions (ARs) has led to the following conclusions: the formation of AR in CH is a frequent phenomenon, since the former exist in every other CH for at least 1 day; unlike the case of a CH without an AR, the configuration of the magnetic field above the CH with an AR often changes with the height: two out of three CHs have the opposite sign of the magnetic field in photosphere, as compared to the sign of the polar magnetic field; the areas of ARs in CHs do not differ from those for many other ARs outside of CHs.     

The coronal structure of active regions

A four-parameter model which assumes a Gaussian dependence of both temperature and pressure on distance from center is used to fit the compact part of coronal active regions as observed in X-ray photographs from a rocket experiment. The four parameters are the maximum temperature T _M, the maximum pressure P _M= 2N_MkT_M, the width of the pressure distribution σ _P, and the width of the temperature distribution σ _T = α^1/2σ_P. The maximum temperature T _M ranges from 2.2 to 2.8 × 10⁶K, and the maximum density N _M from 2 to 9 × 10⁹cm^?3. The range of σ _P is from 2 to 4 × 10⁹ cm and that of α from 2 to 7.     

Constraints on the solar coronal temperature in regions of open magnetic field

It is shown that the simultaneous consideration of observed values of the solar wind proton flux density at 1 AU and of the electron pressure at the base of the solar corona leads to relatively strong constraints on the coronal temperature in the region of subsonic solar wind flow. The extreme upper limit on the mean coronal temperature in the subsonic region is found to be about 2.6 × 10⁶ K, but this upper limit is reduced to about 2.0 × 10⁶ K if reasonable, rather than extreme, assumptions are made; the limit on the maximum temperature is about 0.5 × 10⁶ K greater than the limit on the mean. It is also found that the same two observations limit the rate of momentum addition possible in the region of subsonic solar wind flow.On leave from The Auroral Observatory, Institute of Mathematical and Physical Sciences, University of Troms0, N-9001 Tromsø, Norway.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A comparison of the temperature and emission measure of X-ray active regions with coronal magnetic fields

The distribution of temperature and of emission measure in X-ray active regions relative to the coronal magnetic fields has been investigated. The position of maximum temperature and the position of maximum emission measure were found to lie along the magnetic neutral line, with the maximum temperature tending to lie above the position of an abrupt change in direction of the neutral line. Several simple structural models of these regions are compared to the emission measure. The total magnetic energy and the total emission measure appear to be related by a power law in the regions studied by us.     

Measuring electron density in coronal active regions

In order to study the electron density at the scale of the most encountered structures in coronal active regions a new multichannel coronagraph associated with a photoelectric spectrograph is now used at the Pic-du-Midi Observatory. In its quasi-routine mode this instrument, which is described in this paper, works with a 30 field aperture in a parallel manner with aK-polarimeter. On each observed region it obtains maps of intensities of the 3388, 10747, and 10798 Å emission lines due to Fexiii ion. Each measurement point is associated with a quasi-simultaneous image of the emission corona structures viewed in the light of the5303 Å line of Fexiv. Three examples of observations are given and the capabilities are discussed.Measuring electron density in coronal active regions. II A multichannel photoelectric coronagraph with a photo-electric spectrograph and a reflex monitor at5303 Å.LA du CNRS No. 040285.     

A comparison of coronal X-ray structures of active regions with magnetic fields computed from photospheric observations

The appearances of several X-ray active regions observed on March 7, 1970 and June 15, 1973 are compared with the corresponding coronal magnetic field topology. Coronal fields have been computed from measurements of the longitudinal component of the underlying magnetic fields, under the current-free hypothesis. An overall correspondence between X-ray structures and calculated field lines is established, and the magnetic counterpart of different X-ray features is also examined. A correspondence between enhanced X-ray emission and the location of compact closed field lines is suggested by this study. Representative magnetic field values calculated under the assumption of current-free fields are given for heights up to 200″.     

Measuring electron density in coronal active regions

The new coronameter described in this paper, now in service at Pic du Midi Observatory, has been designed for the study of coronal condensations with a 30 spatial resolution. The instrument associates measurements of the K-corona polarized light with simultaneous pictures of the coronal structures as seen in the light of the green emission line of Fe xiv (5303 Å). It has allowed us to engage in an extensive program of observation devoted to the study of electron density in active coronal regions. As an example we present results concerning a coronal condensation observed on 1980 February 15, which is some hours before the time of the India-Kenya total eclipse.L. A. du C.N.R.S. No. 040285.     

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.     

Predicting the evolution of photospheric magnetic field in solar active regions using deep learning

The continuous observation of the magnetic field by the Solar Dynamics Observatory(SDO)/Helioseismic and Magnetic Imager(HMI) produces numerous image sequences in time and space.These sequences provide data support for predicting the evolution of photospheric magnetic field. Based on the spatiotemporal long short-term memory(LSTM) network, we use the preprocessed data of photospheric magnetic field in active regions to build a prediction model for magnetic field evolution. Because of the elaborate learning and memory mechanism, the trained model can characterize the inherent relationships contained in spatiotemporal features. The testing results of the prediction model indicate that(1) the prediction pattern learned by the model can be applied to predict the evolution of new magnetic field in the next 6 hours that have not been trained, and predicted results are roughly consistent with real observed magnetic field evolution in terms of large-scale structure and movement speed;(2) the performance of the model is related to the prediction time; the shorter the prediction time, the higher the accuracy of the predicted results;(3) the performance of the model is stable not only for active regions in the north and south but also for data in positive and negative regions. Detailed experimental results and discussions on magnetic flux emergence and magnetic neutral lines finally show that the proposed model could effectively predict the large-scale and short-term evolution of the photospheric magnetic field in active regions. Moreover, our study may provide a reference for the spatiotemporal prediction of other solar activities.     

On the magnetic field line topology in solar active regions

The field lines of closed magnetic structures above the photosphere define a mapping from the photosphere to itself. This mapping is discontinuous, and the field line connectivity to the boundary can change discontinuously in response to continuous changes of field strength and direction, if field lines either end in a singular point of the field or are tangential to the photosphere at one end. Whereas the general existence of singular points is questionable, the field has typically a cell structure due to the presence of segments of the zero line of the photospheric longitudinal field on which the transversal field is directed from negative (pointing into the Sun) to positive fields. The cell boundaries are made up of field lines which all touch the photosphere on one of these line segments. Within each of the cells the field line mapping is continuous. When during a slow evolution a substantial part of a coronal loop or of an arcade has passed from one cell into another a fast dynamic instability may set in which was previously prevented by the anchoring of field lines in the dense photosphere.     

Comment on coronal magnetic field models

A long-standing misconception about the mathematical validity of utilizing Green's function solutions to coronal magnetic fields is discussed. Although this type of solution does not fit the observed line-of-sight component of the photospheric magnetic field, but rather the net flux in a region, the solution does obey Laplace's equation in the inner corona.     

An investigation of the structure of coronal active regions

The temperature and density structure of a typical coronal active region is deduced from X-ray observations of several active regions. Observations of the limb transits of three regions from OSO-5 indicate that the X-ray emission originates between 2 × 10⁴ km and 1.5 × 10⁵ km. An emission measure-temperature distribution is deduced from high resolution X-ray spectra obtained with a rocket observation of two similar regions. These observations are combined to give a model of a typical active region, the temperature varying from 2 to 6 × 10⁶ K with corresponding densities between 2 × 10⁹ and 10¹⁰ cms^–3.     

Stereoscopic determination of the three-dimensional geometry of coronal magnetic loops

The three-dimensional shape of coronal magnetic loops is restored from extreme ultraviolet (XUV) images of the Sun (Skylab mission 3, 1973) by using the perspective effect due to the solar rotation. An original method is developed which only depends on the assumption that the magnetic structures under consideration are (at least geometrically) stable within the time interval used for restoration. Large scale loops interconnecting different active regions are studied by applying this method. They are found to lie approximately in planes inclined from the local vertical. Generally these loops are asymmetric, i.e. their apices are shifted toward one of the footpoints. This tendency is also confirmed by the computation of coronal magnetic fields based on the photospheric magnetic data.On leave from Observatoire de Paris-Meudon, 91190 Meudon, France.     

A simple method to compute spherical harmonic coefficients for the potential model of the coronal magnetic field

It is impossible to make a direct measurement of the coronal magnetic field from the ground. The coronal magnetic field is, then, usually inferred by extrapolation of the observed photospheric magnetic field. The so-called potential model has been used for this extrapolation. We have to solve the Laplacian equation of the magnetic scalar potential. This magnetic scalar potential can be expanded into a spherical harmonic series. In this paper, new simple recursion formulae are proposed to solve the Laplacian equation; that is, to determine the spherical harmonic coefficients.     

A new technique of observing the magnetic field of solar active regions

By fitting a new type of polarization detector after the entrance slit of a solar spectrograph, the two dimensional magnetic field of solar active regions can be obtained. Not only the field intensity, but also the longitudinal map is obtained quickly. The simultaneous observation of a few lines will also provide data on the structure of the magnetic tubes etc.     

Skinning process stability of the magnetic field in the solar active regions

Skinning process stability of the magnetic field in homogeneous plasma is studied. A set of magnetohydrodynamic equations is used. Dependence of electrical conductivity on the plasma parameters and radiation intensity in grey-body approximation are taken into account. The investigation is carried out on the model problems in linear approximation and by means of numerical solution of MHD equations. Threshold of stability and critical gradient of magnetic field in skin-layer are obtained. The model of the phenomenon proposed in the paper indicates on overheating instability of plasma with electric current in large gradient magnetic field zones as a possible trigger mechanism of solar flare origin.     

Diagnosis of coronal magnetic field with data of Nobeyama Radio Heliograph

The expression is derived for the coronal magnetic field strength from the observations of brightness, temperature, peak frequency, spectral index, and polarization degree of solar microwave bursts. One example of solar burst on November 28, 1998 is given for the calculation of coronal magnetic field from the data of Nobeyama Radio Heliograph (NoRH). The results are comparable with the SOHO/MDI magnetogram and the calculation from the Nobeyama Radio Polarimeters (NoRP), as well as the coronal loops in SOHO/EIT and YOHKOH/SXT images. Therefore, it may be the first time that the two-dimensional diagnosis of coronal magnetic field in a microwave burst source from the radio observations has been made.     

A coronal magnetic field model with horizontal volume and sheet currents

When globally mapping the observed photospheric magnetic field into the corona, the interaction of the solar wind and magnetic field has been treated either by imposing source surface boundary conditions that tacitly require volume currents outside the source surface (Schatten, Wilcox, and Ness, 1969) or by limiting the interaction to thin current sheets between oppositely directed field regions (Wolfson, 1985). Yet observations and numerical MHD calculations suggest the presence of non-force-free volume currents throughout the corona as well as thin current sheets in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines surrounding coronal helmet-streamer structures. This work presents a model including both horizontal volume currents and streamer sheet currents. The present model builds on the magnetostatic equilibria developed by Bogdan and Low (1986) and the current-sheet modeling technique developed by Schatten (1971). The calculation uses synoptic charts of the line-of-sight component of the photospheric magnetic field measured at the Wilcox Solar Observatory. Comparison of an MHD model with the calculated model results for the case of a dipole field and comparison of eclipse observations with calculations for CR 1647 (near solar minimum) show that this horizontal current-current-sheet model reproduces polar plumes and axes of corona streamers better than the source-surface model and reproduces coronal helmet structures better than the current-sheet model.