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.     

Coronal magnetic structures associated with interplanetary clouds

Among all the signatures of solar ejecta in interplanetary space, magnetic clouds are particularly interesting. We have shown that they are associated with solar mass ejections that involve not only coronal heights, but also chromospheric heights and so, they are almost always associated with low-altitude solar activity such as H flares or filament eruptions. As a magnetic cloud is a very large structure, and not all the ejecta found in the interplanetary medium are clouds, it is interesting to investigate the characteristics of the large-scale coronal magnetic structures in the regions where the activity leading to a cloud takes place. In this paper we use Hoeksema's potential field model of the solar magnetosphere to obtain the magnetic structure of the site of the solar events associated with 35 interplanetary magnetic clouds. The position of the related solar activity was determined from the location of the near-surface solar explosive events (flares and filament eruptions) associated with each cloud, obtained in our previous study. We find that the solar activity associated with interplanetary magnetic clouds occurs in regions of low-altitude, magnetically closed structures lying between higher helmets, or between the highest helmets and coronal holes, where the magnetic field lines are longitudinally oriented.     

Magnetic fields of sunspots based on combined optical and radio observations

In the present paper we present the results of measurement of magnetic fields in some sunspots at different heights in the solar atmosphere, based on simultaneous optical and radio measurements. The optical measurements were made by traditional photographic spectral observations of Zeeman splitting in a number of spectral lines originating at different heights in the solar photosphere and chromosphere. Radio observations of the spectra and polarization of the sunspot - associated sources were made in the wavelength range of 2–4 cm using large reflector-type radio telescope RATAN-600. The magnetic field penetrating the hot regions of the solar atmosphere were found from the shortest wavelength of generation of thermal cyclotron emission (presumably in the third harmonic of electron gyrofrequency). For all the eight cases under consideration we have found that magnetic field first drops with height, increases from the photosphere to lower chromosphere, and then decreases again as we proceed to higher chromosphere and chromosphere-corona transition region. Radio measurements were found to be well correlated with optical measurements of magnetic fields for the same sunspot. An alternative interpretation implies that different lines used for magnetic field measurements refer to different locations on the solar surface. If this is the case, then the inversion in vertical gradients of magnetic fields may not exist above the sunspots. Possible sources of systematic and random errors are also discussed.     

The Evolution of Quasi-Separatrix Layer in Two Solar Eruptive Events

Quasi-separatrix layer, also called as QSL, is a region where magnetic connectivity changes drastically, and mostly well coincides with the location of flare ribbons in observations. The research on the relations of this topological structure with the 3-dimensional magnetic reconnection, and solar flares has attracted more and more attention. In this paper, using the theory of QSL we investigate a C5.7 classical two-ribbon solar flare (event 1) which occurred at AR11384 on 2011 December 26, and an M6.5 solar flare (event 2) which occurred at AR12371 on 2015 June 22, respectively. Combining the multi-wavelength data of AIA (Atmospheric Imaging Assembly) and vector magnetogrames of HMI (Helioseismic and Magnetic Imager) onboard SDO (Solar Dynamics Observatory), we extrapolate the coronal magnetic field using the PF (Potential Field) and NLFFF (Nonlinear Force Free Field) models, and calculate the evolution of the AR (Active Region) magnetic free energy. Then, we calculate the logarithmic distribution of Q-factors (magnetic squashing factor) at different heights above the solar photosphere with the results of the PF and NLFFF extrapolations, in order to determine the location of QSL. Afterward, we investigate the evolutionary relation between the QSLs at different heights above the solar photosphere and the flare ribbons observed at the corresponding heights. Finally, we study the multi-wavelength evolution features of the 2 flare events, and obtain by calculation the mean slip velocities of magnetic lines in the event 2 at 304 Å and 335 Å to be 4.6 km s^-1 and 6.3 km s^-1, respectively. We find that the calculated location of QSL in the chromosphere and corona is in good agreement with the location of flare ribbons at the same height, and the QSLs at different heights have almost the same evolutionary behavior in time as the flare ribbons of the corresponding heights, which highlights the role of QSL in the research of 3D magnetic reconnection and solar flare, and we suggest that the energy release in the flare of event 2 may be triggered by the magnetic reconnection at the place of QSL. We also suggest that the QSL is very important for us to study the essential relation between the 3D and 2D magnetic reconnections.     

Magnetic field effect on the fine structure of convective motions in the solar atmosphere

Statistical properties of solar granulation in an active region on the solar surface from the photosphere to the lower chromosphere are studied. We use the values of the velocity, intensity, and magnetic field that were obtained at different heights in the solar atmosphere according to the observation data on the VTT telescope at Observatorio del Teide, Tenerife. The changes in the line??s parameters (central depth of the line, halfwidth, equivalent width, and central depth shift) and convective velocity are presented as functions of the value of the magnetic field. We propose a 16-column model of solar granulation depending on the direction of motion of convective elements and on the sign of contrast at two heights??in the continuous spectrum and in the highest layer (h = 650 km). We found that the magnetic field impedes the change in the sign and motion direction of convective elements.     

Relationship between coronal holes and boundaries of structures of the large-scale magnetic fields

By means of comparison of the positions of 665 observed coronal holes (CHs) and the structures of the magnetic field at different heights, it was shown that 43% of the observed CHs are not associated with unipolar regions of the background field at the photosphere. With height increasing from 1 to 2.5 solar radii, the structure of the magnetic field varies in 57% of all CHs. In 16% of the cases, variations of the structure can be observed at heights as small as 2500–10 000 km. Comparison of the positions of CHs with the longitudinal distribution of long-lived +/− and −/+ boundaries of the large-scale structure of the magnetic field at all the heights was carried out. It was shown that CHs adjoin or intersect with the Hale boundaries half as often as with those having the opposite distribution of the fields at both sides of the boundary. These results attest to a closer connection between the CHs and the photospheric and subphotospheric fields than with coronal fields. The magnetic fields of coronal structures can shield the coronal holes, thus creating “closed” CHs with a limited output of high-speed solar wind streams.     

Peculiarities of the mode of oscillations in a floccule and its neighborhoods at different chromospheric levels

The behavior of oscillations in the quite solar chromosphere under a coronal hole at several heights has been investigated. The properties of oscillations in cell, network, and weak-floccule areas have been analyzed. A time series of spectrograms in three ionized calcium lines, the Ca II K and H resonance doublet lines and the infrared Ca II 849.8-nm triplet line, was used. The observations were carried out at the horizontal solar telescope of the Sayan Observatory. The goal of this study was to compare the distributions of spectral power in various frequency ranges and their variations for selected spatial areas at different heights of the chromosphere. Particular attention was paid to the weak floccule due to a noticeable difference in the central intensity distribution between the K and H lines and the 849.8-nm line. A spectral Fourier analysis was used. The central intensities of the observed spectral lines, the K-index, and the equivalent width (the latter for the 849.8-nm line) were chosen as oscillation parameters. The studies have shown that the main intensity oscillation power at both atmospheric levels is concentrated at frequencies below 9 mHz. In the distribution of intensity oscillation power at different chromospheric levels, there are differences clearly distinguishable in the floccule. Powerful five-minute oscillations whose main peak frequency decreases with height, while the amplitude increases have been detected in the central part of the floccule. This result confirms the assumptions recently pointed out in the literature that vertical magnetic field concentrations can serve as a channel for the passage of low-frequency oscillations from the photosphere to the chromosphere in faculae. The intensity oscillation power in the frequency ranges under consideration has turned out to decrease with height, on average, for the entire observed spatial area. This may be related to the loss of part of the wave energy through the reflection, dissipation, and transformation of wave modes in the magnetic canopy layer. An area with a low brightness but powerful oscillations at about 3.3 mHz covering a considerable range of heights probably pertaining to “magnetic flashers” has been isolated in the telescope’s field of view.     

Sunspots and large-scale magnetic fields at various heights

Height variation of the magnetic field structure over groups of sunspots for heights ranging from the photosphere to the source surface (R = 2.5 Ro, where Ro is the radius of the Sun) is examined. For all heights, starting from the photospheric level, groups of sunspot are shown as being independent of long-lived boundaries of large-scale structures rotating with a period shorter than the Carrington period. At heights of 1–1.5 Ro, there is a clear relation between sunspot groups and boundaries separating the head and tail sunspots in the groups (the Hale boundaries). The rotation periods of these structures are close to the Carrington period, their lifespan being less than three to five rotations. The maximal intensity of the solar magnetic field drops by two orders when height increases from H = 1 to H = 1.1 Ro. Further decrease in intensity proceeds gradually (dropping by one order from H = 1.1 to 2.5 Ro). The results obtained can be considered as evidence that large-scale magnetic field structures and long-lived boundries between them (the lines dividing polarities of the magnetic field or zero lines) all exist irrespective of sunspot fields being generated by other sources than sunspots. At the photospheric level, active regions fields are superimposed on these structures.     

Diagnostics with the Hanle effect

The Hanle effect has been extensively used for the determination of the magnetic field strength and direction in solar prominences. Here we address the problem of the diagnostics of weak magnetic fields in the solar photosphere and chromosphere by means of their Hanle effect in some selected absorption lines. As this is a relatively new area we will focus on the diagnostic methods and summarize some results that relate to the presence of a weak, turbulent magnetic field in the photosphere and to the chromospheric magnetic canopy. Finally we will outline some directions for future work.     

Magnetograph response to canopy-type fields

The response of longitudinal-field magnetographs to magnetic fields which are semi-infinite or confined to a horizontal layer is discussed with respect to the interpretation of solar diffuse fields, observed towards the limb, in terms of magnetic canopy models. Numerical results are presented for several reference solar models and typical calibration curves are shown for the C I 9111 Å, Fe I 8688 Å, and Ca II 8542 Å lines in magnetostatic atmospheres derived from a mean model. A procedure is developed for determining the base heights of magnetic canopies from observations with an uncertainty not exceeding the order of a pressure scale height. Until definitive information regarding atmospheric structure inside flux tubes can be developed from theory or observation, reliable field strengths cannot be derived from the data.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

On the origin of the prolate solar chromosphere

A simple geometric model is proposed to explain the recently reported effect of the prolateness of the solar chromosphere. We assume that a specific dynamical part of the solar atmosphere above the 2 Mm level, being a mixture of moving up and down jets of chromospheric matter with the coronal plasma between them, is responsible for the solar prolateness. Due to the dynamic nature of this layer, the magnetic field is considered to play a very important role in the density distribution with the height, guiding the mass flows along the field lines. The difference of the magnetic field topology in the polar and the equatorial regions leads to different heights of the chromospheric limb. Calculations show a satisfactory coincidence with observations when the mean separation between opposite polarity concentrations is about 9 Mm. The possible observational signature of this network in low photospheric and chromospheric layers is discussed.     

Microwave Mode Coupling Above Active Regions as a Coronal Density Diagnostic

It is well recognized that the phenomenon of depolarization (the conversion of polarized radio emission into unpolarized emission) of microwaves over solar active regions can be used to infer the coronal electron density once the coronal magnetic field is known. In this paper we explore this technique using an active region for which we have excellent radio data showing depolarization at two frequencies, and for which we have an excellent magnetic field model which has been tested against observations. We show that this technique for obtaining coronal densities is very sensitive to a number of factors. When Cohen's (1960) theory where depolarization is due to magnetic field rotation alone is used, the result is particularly sensitive to the location of the surface on which the magnetic field is orthogonal to the line of sight. Depending on whether we take into account the presence of electric currents in the photosphere or not, their extrapolation into the corona can result in very different heights being deduced for the location of the depolarization strip, and this changes the density which is then deduced from the depolarization condition. Such extreme sensitivity to the magnetic field model requires that field extrapolations be able to accurately predict the polarity of magnetic fields up to coronal heights as high as 10⁵ km in order to exploit depolarization as a density diagnostic.     

The height stratification of solar magnetic fields in cycles 21–23

The radial component of the solar magnetic field, Br, was calculated in the potential approximation in the height range from 1 to 2.5 solar radii, Ro. According to these data, synoptic maps of the magnetic field for solar cycles 21–23 were constructed. For each 10-degree latitudinal zone, the proportion of its area, S _+field, that was occupied by the “+” field in each rotation was found. In the entire latitudinal zone, the radial component of the field is assumed to be positive if S_+field ≥ 80% and negative if S _+field ≤ 20%. The field proved to be virtually unipolar at the level of the photosphere (R = Ro) during most of the cycle, from the poles to the north and south latitude ≈60°. In the vicinity of minimums between cycles 21 and 22, as well as cycles 22 and 23, for a few rotations of the Sun, the field was almost unipolar within the range of latitudes (?40°)-90°. At R = 2.5 Ro, for most of each cycle, the field was unipolar in the range of latitudes (?20°-(-90°)) and (20°–90°). According to our interpretation, the shift of the polar-field boundary to the equator with height reflects superradial expansion of open magnetic flux tubes from the polar coronal holes. It was found that the reversal of the polar fields began with 1–2 rotations and ended from 2 to 14 solar rotations earlier at great heights than at the surface of the Sun. This indicates that the reversal of the large-scale field occurs first and then that of the small-scale one. In the study of the sectoral structure of the magnetic field at different heights it was found that the boundaries that rotate with a period of less than the Carrington revolution extend to greater heights than the boundaries with a Carrington or longer period. We assume that the boundaries of the first type are formed by the large-scale structures of the magnetic field and the boundaries of the second type are determined by the active regions.     

The Varying Multipolar Structure of the Sun's Magnetic Field and the Evolution of the Solar Magnetosphere Through the Solar Cycle

The Sun's magnetic field extends far from the photosphere, into the corona, defining a magnetically dominated region before being drawn out radially by the solar wind flow. This region, where the internal sources of the solar field dominate the plasma structures and the energetic particle movement, can be properly considered the solar magnetosphere. The magnetic field in this region can be approximately described by models that extrapolate photospheric magnetic field observations under some simplifying assumptions. In this paper we use a potential field model which describes the solar field up to a source surface at 3.25 R_s, where the field is constrained to become radial. We present the variation of the magnitude and inclination of the various multipolar components throughout the solar magnetic cycle that characterise the changes in the structure of the solar magnetosphere over a period of 22 years. We also present some 3-D images of the coronal magnetic structure to show the global evolution of the solar magnetosphere throughout the solar cycle and discuss the importance of taking this structure into account in order to relate interplanetary and solar features.     

On the comparison of radio-astronomical measurements of the height structure of magnetic field with results of model approximations

The results of microwave observations of the polarized emission of active regionsmade with the RATAN-600 radio telescope are used to develop the method for determining the structure of the magnetic field of these regions at coronal heights. About 1000-G-strong magnetic fields are observed in the solar atmosphere at rather high altitudes (from 10 to 25 Mm). This result is confirmed fairly well by the ultraviolet observations of magnetic loops, it is consistent with earlier radio-astronomical observations of the magnetic field at the height of the transition region, and it corresponds as well, if interpreted in terms of the dipole magnetic field model, to the vertical gradients of the photospheric magnetic field.     

Magnetic field lines for a flux tube

Equations for the magnetic field components in a two dimensional cylindrically symmetric flux tube equilibrium have been derived and, in a simple case, solved. The resulting magnetic configuration possesses a strong magnetic field in a thin tube below a reference level (solar photosphere). Above this reference level the field lines spread out in all directions.     

Radiative transfer across a magnetic flux tube

In the coming years, some solar telescopes will be able to yield the Stokes' parameters of polarized light with a resolution better than 1 arc sec (0.3 arc sec for THEMIS). We have simulated the Stokes' parameters of a solar magnetic flux tube as seen with such a resolution. We have shown that, observing with a line-of-sight not parallel to the axis of the flux tube (assumed vertical and axisymmetric), it is possible to see differences between different configurations of the magnetic field inside the flux tube (presence, and in what direction, of an azimuthal component of the field). Furthermore, along such a line-of-sight, the polarization profiles of any atomic line are strongly absorbed at the line center. We then suggest a strategy to infer the structure of the magnetic field from observations at high spatial resolution.     

Height stratification of solar magnetic fields in cycle 23

The radial component Br of magnetic field was calculated in the potential approximation and the synoptic maps of Br for several heights in the Solar atmosphere were constructed based on observations of the photospheric magnetic field made on the old magnetograph at the US Kitt Peak National Observatory and on the new SOLIS magnetograph at the US National Solar Observatory for cycle 23 (the years 1997–2009). Parameters of large-scale structures of magnetic field with positive and negative polarities were determined at seven heights in the Sun’s atmosphere—from the photosphere (H = Ro) to H = 2.5 Ro (Ro is the Solar radius). The processes of polar reversal for polar fields and changing of the sector structure of the field at middle latitudes were observed. Characteristic lifespans and rotations were ascertained. The general picture of variations of the large-scale solar magnetic field during cycle 23 was put forward. Two types of boundaries of large magnetic structures at various heights were identified.     

Basic properties of magnetic flux tubes and restrictions on theories of solar activity

It is shown that the mean longitudinal field in a magnetic flux tube is reduced, rather than enhanced, by twisting the tube to form a rope. It is shown that there is no magnetohydrostatic equilibrium when one twisted rope is wound around another. Instead there is rapid line cutting (neutral point annihilation). It is shown that the twisting increases, and the field strength decreases, along a flux tube extending upward through a stratified atmosphere.These facts are at variance with Piddington's recent suggestion that solar activity is to be understood as the result of flux tubes which are enormously concentrated by twisting, which consist of several twisted ropes wound around each other, and which came untwisted where they emerge through the photosphere.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001.