Nonlinear Evolution of Thermal Structures. Numerical Approach

A numerical algorithm using a two stage, two level difference scheme has been developed to solve the heat transfer equation with nonlinear heat diffusion and bulk energy losses. The algorithm is an extension of the scheme developed by Meek and Norbury (1982). The first stage calculates an intermediate value which is used in a second stage to estimate a new value. The scheme is consistent, second-order convergent in space and almost second order in time. It has been applied to the nonlinear stability and time evolution of thermal structures constituted by optically thin plasmas with solar abundances. The configuration has been assumed to be heated at a rate T^m, cooled at a rate Tⁿ and a thermal conduction coefficient T^k. In particular, the second order analytical approximation considered in previous papers (Ibáñez and Rosenzweig, 1995; Steele and Ibáñez, 1997) has been worked out for arbitrary amplitude of the initial temperature disturbance. Particular cases of interest in Astrophysics are considered.     

On Rotation of the Solar Corona

We have studied the rotation of the solar corona using the images taken at a 9.4?nm wavelength by the AIA 094 instrument on board the Solar Dynamics Observatory (SDO) satellite. Our analysis implies that the solar corona rotates differentially. It appears that ??, the angular rotation velocity of the solar corona, does not only depend on heliographic latitude but is also a function of time, while the nature of the latter dependence remains unclear. Besides measurement errors, deviations ???? from the mean rotational speed are also caused by proper motion of the observed point source (the tracer) with respect to its surroundings. The spread in ?? values at a particular heliographic latitude is a real effect, not caused by measurement errors. Most of the observations carry relative error less than 1?% in???.     

A Model of the Thermal Expansion of the Solar Corona with Allowance for Radiation

The Parker model is modified to describe a rapid temperature increase from the region of temperature minimum to the coronal base and to relate the electron density in the region of the temperature minimum (～0.85×10¹¹ cm^?3 according to the modified model) to that at the orbit of the Earth (～7.42 cm^?3 according to the model). The coronal temperature reaches its maximum (1.8×10⁶ K) at the Parker critical point; physical processes at this point are left beyond the scope of the model. It is suggested to consider the expanding solar corona as a self-heating system in which heating of the solar corona is related to the transonic regime of its expansion, which is maintained by the high coronal temperature.     

On the Shape of Force-Free Field Lines in the Solar Corona

This paper studies the shape parameters of looped field lines in a linear force-free magnetic field. Loop structures with a sufficient amount of kinking are generally seen to form S or inverse S (Z) shapes in the corona (as viewed in projection). For a single field line, we can ask how much the field line is kinked (as measured by the writhe), and how much neighbouring flux twists about the line (as measured by the twist number). The magnetic helicity of a flux element surrounding the field line can be decomposed into these two quantities. We find that the twist helicity contribution dominates the writhe helicity contribution, for field lines of significant aspect ratio, even when their structure is highly kinked. These calculations shed light on some popular assumptions of the field. First, we show that the writhe of field lines of significant aspect ratio (the apex height divided by the footpoint width) can sometimes be of opposite sign to the helicity. Secondly, we demonstrate the possibility of field line structures which could be interpreted as Z-shaped, but which have a helicity value sign expected of an S-shaped structure. These results suggest that caution should be exercised in using two-dimensional images to draw conclusions on the helicity value of field lines and flux tubes.     

Mushrooms in the Solar Corona

In the solar atmosphere a new phenomenon is discovered, namely, the formation, growth, and disappearance of mushrooms as a consequence of eruptive processes. This phenomenon gives an insight into many geometric and physical properties of coronal mass ejections (CME).     

Modelling the Global Solar Corona II: Coronal Evolution and Filament Chirality Comparison

This paper considers the hemispheric pattern of solar filaments using newly developed simulations of the real photospheric and 3D coronal magnetic fields over a six-month period, on a global scale. The magnetic field direction in the simulation is compared directly with the chirality of observed filaments, at their observed locations. In our model the coronal field evolves through a continuous sequence of nonlinear force-free equilibria, in response to the changing photospheric boundary conditions and the emergence of new magnetic flux. In total 119 magnetic bipoles with properties matching observed active regions are inserted. These bipoles emerge twisted and inject magnetic helicity into the solar atmosphere. When we choose the sign of this active-region helicity to match that observed in each hemisphere, the model produces the correct chirality for up to 96% of filaments, including exceptions to the hemispheric pattern. If the emerging bipoles have zero helicity, or helicity of the opposite sign, then this percentage is much reduced. In addition, the simulation produces a higher proportion of filaments with the correct chirality after longer times. This indicates that a key element in the evolution of the coronal field is its long-term memory, and the build-up and transport of helicity from low to high latitudes over many months. It highlights the importance of continuous evolution of the coronal field, rather than independent extrapolations at different times. This has significant consequences for future modelling such as that related to the origin and development of coronal mass ejections.     

Cyclotron Heating of the Solar Corona

A physical model of the solar transition region and corona is presented, in which plasma flows in rapidly-diverging coronal funnels and holes are described within the framework of a two-fluid model including wave-particle interactions. The ions are heated by wave dissipation and accelerated by the pressure gradient of high-frequency Alfvén waves, which are assumed to originate at the bottom of the magnetic network by small-scale reconnection. The heating is assumed to be due to cyclotron-resonant damping of the waves near the local ion gyrofrequency. The EUV emission lines observed by the SUMER spectrometer on SOHO show very strong broadenings, which seem to be ordered according to the ion charge-per-mass ratio and thus to indicate cyclotron-resonant heating by waves. Based on quasilinear theory, a closure scheme for anisotropic multi-component fluid equations is developed for the wave-particle interactions of the ions with Alfvén waves. The acceleration and heating rates are calculated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Flattening Index of the Solar Corona and the Solar Cycle

The photometrical flattening index of the solar corona a+b is defined according to Ludendorff. In this paper we have investigated how the flattening index varies with respect to the phase of solar activity and the sunspot number. We have compiled 170 values of the flattening index using the data on 60 total solar eclipses from 1851 to 2010. We have found that the flattening index takes values from 0 to 0.4, and is anticorrelated with solar activity. The value of the flattening index at the beginning of solar cycle 24 was used as a precursor to forecast the amplitude of the cycle. It was found that the amplitude of solar cycle 24 will be about 95 in terms of the smoothed monthly sunspot numbers.     

磁能和磁复杂性向日冕的传输

本文讨论了从太阳光球向日冕传输磁能和磁复杂性的过程。活动日冕，作为由电磁场和粒子组成的系统，其唯一的开场表面是太阳光球。光球层等离子体的运动和磁场的相互作用，是造成磁能和磁复杂性向日冕传播的主要根源；同时，光球上的耗散过程也对日冕磁能和磁复杂性的积累有不可忽视的贡献。     

Dynamic Three-Dimensional Tomography of the Solar Corona

Empirical, three-dimensional electron-density maps of the solar corona can be tomographically reconstructed using polarized-brightness images measured from ground- and space-based observatories. Current methods for computing these reconstructions require the assumption that the structure of the corona is unchanging with time. We present the first global reconstructions that do away with this static assumption and, as a result, allow for a more accurate empirical determination of the dynamic solar corona. We compare the new dynamic reconstructions of the coronal density during February 2008 to a sequence of static reconstructions. We find that the new dynamic reconstructions are less prone to certain computational artifacts that may plague the static reconstructions. In addition, these benefits come without a significant increase in computational cost.     

Nonlinear Evolution of Axisymmetric Twisted Flux Tubes in the Solar Tachocline

We study the periodicity of twisting motions in sunspot penumbral filaments, which were recently discovered from space (Hinode) and ground-based (SST) observations. A sunspot was well observed for 97 minutes by Hinode/SOT in the G-band (4305 Å) on 12 November 2006. By the use of the time?–?space gradient applied to intensity space?–?time plots, twisting structures can be identified in the penumbral filaments. Consistent with previous findings, we find that the twisting is oriented from the solar limb to disk center. Some of them show a periodicity. The typical period is about ≈?four minutes, and the twisting velocity is roughly 6 km s^?1. However, the penumbral filaments do not always show periodic twisting motions during the time interval of the observations. Such behavior seems to start and stop randomly with various penumbral filaments displaying periodic twisting during different intervals. The maximum number of periodic twists is 20 in our observations. Studying this periodicity can help us to understand the physical nature of the twisting motions. The present results enable us to determine observational constraints on the twisting mechanism.     

Element Abundances in Solar Energetic Particles and the Solar Corona

This is a study of abundances of the elements He, C, N, O, Ne, Mg, Si, S, Ar, Ca, and Fe in solar energetic particles (SEPs) in the 2?–?15 MeV?amu^?1 region measured on the Wind spacecraft during 54 large SEP events occurring between November 1994 and June 2012. The origin of most of the temporal and spatial variations in abundances of the heavier elements lies in rigidity-dependent scattering during transport of the particles away from the site of acceleration at shock waves driven out from the Sun by coronal mass ejections (CMEs). Variation in the abundance of Fe is correlated with the Fe spectral index, as expected from scattering theory but not previously noted. Clustering of Fe abundances during the “reservoir” period, late in SEP events, is also newly reported. Transport-induced enhancements in one region are balanced by depletions in another, thus, averaging over these variations produces SEP abundances that are energy independent, confirms previous SEP abundances in this energy region, and provides a credible measure of element abundances in the solar corona. These SEP-determined coronal abundances differ from those in the solar photosphere by a well-known function that depends upon the first ionization potential (FIP) or ionization time of the element.     

Spectroscopic Studies of Solar Corona VIII. Temperature and Non-Thermal Variations in Steady Coronal Structures

With a view to investigate variations in parameters of coronal emission lines over a large range of radial distance from the limb, raster scans were made with sufficiently long exposure times on several days during September – October 2003. An analysis of the data shows that (i) in most of the coronal structures, the FWHM of the Fe xiv 5303 Å line decreases up to 300″±50″, (ii) the FWHM of the Fe x 6374 Å line increases up to about 200″ and then remains unchanged up to about 500″, and (iii) the FWHMs of the Fe xi 7892 Å and Fe xiii 10747 Å lines show an intermediate behaviour with height. The analysis of the data also shows that the ratio of FWHM of 6374 Å to that of 5303 Å increases from 0.93 at the limb to 1.18 at 200″ above the limb. From this and the ratio of intensities of the two lines we infer that the plasma in steady coronal structures at a height of about 200″ has a temperature of about 1.5 MK and a non-thermal velocity around 17 km s^?1. The observations also show that non-homogeneous temperatures and non-thermal velocities largely exist in the lower corona up to about 300″±100″ above the limb. Amplitudes of variations in FWHM of different emission lines with height in the coronal loops are similar to those in the diffuse plasma around the coronal loops.     

Heating the Solar Corona by Magnetic Reconnection

Here I review briefly the theory of magnetohydrodynamic reconnection and ask what observational evidence is there that it is heating the corona. In particular, the new directions in which three-dimensional theory for reconnection is heading are outlined. Part of the coronal heating problem has been solved with the identification of reconnection driven by converging flux motions as the key for x-ray bright points. Furthermore, it has been shown that the large-scale diffuse corona is heated rather uniformly, so that turbulent reconnection by braiding or ion-cyclotron waves driven by network micro-flares are prime candidates. Finally, reconnection is the natural explanation for a wide variety of phenomena discovered by SOHO including explosive events, blinkers, the magnetic carpet and even possibly tornadoes. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heating Events in the Quiet Solar Corona

Sensitive observations of the quiet Sun observed by EIT on the SOHO satellite in high-temperature iron-line emission originating in the corona are presented. The thermal radiation of the quiet corona is found to fluctutate significantly, even on the shortest time scale of 2 min and in the faintest pixels. The power spectrum of the emission measure time variations is approximately a power law with an exponent of 1.79±0.08 for the brightest pixels and 1.69±0.08 for the average and the faintest pixels. The more prominent enhancements are identified with previously reported X-ray network flares (Krucker et al., 1997) above the magnetic network of the quiet chromosphere. In coronal EUV iron lines they are amenable to detailed analysis suggesting that the brightenings are caused by additional plasma injected from below and heated to slightly higher temperature than the preexisting corona. Statistical investigations are consistent with the hypothesis that the weaker emission measure enhancements originate from the same parent population. The power input derived from the impulsive brightenings is linearly proportional to the radiative loss in the observed part of the corona. The absolute amount of impulsive input is model-dependent. It cannot be excluded that it can satisfy the total requirement for heating. These observations give strong evidence that a significant fraction of the heating in quiet coronal regions is impulsive.     

Stability of Current Sheets in the Solar Corona

This work aims at investigating unstable modes of oscillation of quasi-vertical two-dimensional current sheets with sheared magnetic fields under physical conditions typical for the solar corona. We use linear magnetohydrodynamic equations to obtain sets of unstable modes related to the longitudinal inhomogeneity of the current sheet. It is shown that these modes of current sheet oscillations can modulate the current sheet thickness along the polarity inversion line. Based on the obtained results, we propose a scenario which can naturally explain both the quasi-periodic pulsations of hard X-ray emission and the parallel movement of their double footpoint-like sources along the polarity inversion line observed in some eruptive two-ribbon solar flares.     

A Study of the Rotation of the Solar Corona

Synoptic photoelectric observations of the coronal Fexiv and Fex emission lines at 530.3 nm and 637.4 nm, respectively, are analyzed to study the rotational behavior of the solar corona as a function of latitude, height, time and temperature between 1976 (1983 for Fex) and 2001. An earlier similar analysis of the Fexiv data at 1.15 R over only one 11-year solar activity cycle (Sime, Fisher, and Altrock, 1989, Astrophys. J. 336, 454) found suggestions of solar-cycle variations in the differential (latitude-dependent) rotation. These results are tested over the longer epoch now available. In addition, the new Fexiv 1.15 R results are compared with those at 1.25 R and with results from the Fex line. I find that for long-term averages, both ions show a weakly-differential rotation period that may peak near 80° latitude and then decrease to the poles. However, this high-latitude peak may be due to sensing low-latitude streamers at higher latitudes. There is an indication that the Fexiv rotation period may increase with height between 40° and 70° latitude. There is also some indication that Fex may be rotating slower than Fexiv in the mid-latitude range. This could indicate that structures with lower temperatures rotate at a slower rate. As found in the earlier study, there is very good evidence for solar-cycle-related variation in the rotation of Fexiv. At latitudes up to about 60°, the rotation varies from essentially rigid (latitude-independent) near solar minimum to differential in the rising phase of the cycle at both 1.15 R and 1.25 R . At latitudes above 60°, the rotation at 1.15 R appears to be nearly rigid in the rising phase and strongly differential near solar minimum, almost exactly out of phase with the low-latitude variation.     

Evolution of CME Mass in the Corona

The idea that coronal mass ejections (CMEs) pile up mass in their transport through the corona and heliosphere is widely accepted. However, it has not been shown that this is the case. We perform an initial study of the volume electron density of the fronts of 13 three-part CMEs with well-defined frontal boundaries observed with the Solar and Heliospheric Observatory/Large Angle and Spectrometric COronagraph (SOHO/LASCO) white-light coronagraphs. We find that, in all cases, the volume electron density decreases as the CMEs travel through the LASCO-C2 and -C3 fields of view, from \(2.6\,\mbox{--}\,30~\mbox{R}_{\odot}\). The density decrease follows closely a power law with an exponent of ?3, which is consistent with a simple radial expansion. This indicates that in this height regime there is no observed pile-up.     

Probing the Fundamental Physics of the Solar Corona with Lunar Solar Occultation Observations

Imaging and spectroscopy of the solar corona, coupled with polarimetry, are the only tools available at present to capture signatures of physical processes responsible for coronal heating and solar wind acceleration within the first few solar radii above the solar limb. With the recent advent of improved detector technology and image processing techniques, broad-band white light and narrow-band multi-wavelength observations of coronal forbidden lines, made during total solar eclipses, have started to yield new views about the thermodynamic and magnetic properties of coronal structures. This paper outlines these unique capabilities, which until present, have been feasible primarily with observations during natural total solar eclipses. This work also draws attention to the exciting possibility of greatly increasing the frequency and duration of solar eclipse observations with Moon orbiting observatories utilizing lunar limb occultation of the solar disk for coronal measurements.