Long-term variations in the rotation of the solar corona

The characteristic time scales for variations in the differential rotation of the solar corona are determined using measurements of the intensity of the FeXIV 5303 Å coronal line made from 1939–2004. Drift waves of the variations in the rotational speed with an 11-year periodicity can be distinguished. Moving averages with time intervals from two to five years are used to identify torsional waves. In addition, longer-period variations in the rotational speed can be distinguished when longer averaging intervals are used. When the interval used for the moving average is increased to 8–12 years, a quasi-22-year rotational period appears. The low-latitude corona rotates more slowly in odd cycles than in even cycles. Increasing the duration of the averaging interval further shows that rapid rotation at low latitudes was observed in 1940–1950 and 1990–2000, while slow rotation was observed in 1960–1980, possibly suggesting the presence of a 55-year period in the rotational variations. Long-term variations are found in the rotation of polar regions. The rotational variations for high-latitude corona are in antiphase with those for the low-latitude corona. The origins of zones of anomalous coronal rotation and their dynamics in the global activity cycle are discussed.     

The three-dimensional structure of the solar corona

The surface where the radial component of the solar magnetic field changes sign is computed for a minimum corona. It is shown that (1) the projection of the folds of this surface onto the plane of the sky is consistent with the helmet structures observed during the eclipse of June 30, 1954; (2) there are type 1 and type 2 helmets, according to the well-known classification of coronal structures; (3) some elements of this sign-change surface of the radial field can be classified as so-called envelopes. The results obtained suggest that more complex coronal structures can be described in a similar way. An MHD model of polar plumes is considered.     

Geometry of solar prominences and magnetic fields in the corona

The spatial location of the surface at which most of the prominence mass is concentrated is compared with the location of the “neutral surface” where B _r = 0 (B _r is the magnetic field) calculated in a potential approximation using photospheric data. More than fifty prominences (filaments) observed in 1999–2003 are studied. The vertical deviations of the prominences (predominantly toward the west) correspond well to the inclination of the neutral surface. The results provide evidence for the magnetic support of filaments of opposite polarities (the magnetic-rope model).     

Motion of an eruptive prominence in the solar corona

A model for the nonradial motion of an eruptive prominence in the solar corona is proposed. Such motions, which can sometimes be inaccessible to observation, result in an apparent break in the causal link between eruptive prominences and coronal mass ejections. The global magnetic field of the Sun governs coronal plasma motions. The complex structure of this field can form prominence trajectories that differ considerably from a simple vertical rise (i.e., radial motion). A solar filament is modeled as a current-carrying ring or twisted toroidal magnetic rope in equilibrium with the coronal magnetic field. The global field is described using two spherical harmonics. A catastrophic violation of the filament equilibrium followed by its rapid acceleration—eruption—is possible in this nonlinear system. The numerical solution of the equations of motion corresponds well to the eruption pattern observed on December 14, 1997.     

Cyclic variations in the differential rotation of the solar corona

The rotation of the solar corona is analyzed using the original database on the brightness of the FeXIV 530.3 nm coronal green line covering six recent activity cycles. The rate of the differential rotation of the corona depends on the cycle phase. In decay phases, there are only small differences in the rotation, which are similar to that of a rigid body. The differences are more significant (though less pronounced than in the photosphere) during rise phases, just before maxima, and sometimes at maxima. The total rate of the coronal rotation is represented as a superposition of two, i.e., fast and slow modes. The synodic period of the fast mode is approximately 27 days at the equator and varies slightly with time. This mode displays weak differences in rotation and is most pronounced in the middle of decay phases. The slow mode is manifested only at high latitudes during the rise phases of activity, and displays a mean period of 31 days. The relative contribution of each mode to the total rotational rate is determined as a function of time and heliographic latitude. These results indicate that the structure of the velocity field in the convective zone must also vary with time. This conclusion can be verified by helioseismology measurements in the near future.     

Two modes of the differential rotation of the solar corona

The differential rotation of the solar corona is studied using the brightness of the Fe XIV 530.3 nm green coronal line collected over 5.5 solar-activity cycles. The total observed velocity of the coronal rotation is analyzed as a superposition of two modes—fast and slow. A technique for separating two data series composing the initial data set and corresponding to the two differential-rotation modes of the solar corona is proposed. The first series is obtained by averaging the initial data set over six successive Carrington rotations; this series corresponds to long-lived, large-scale coronal regions. The second series is the difference between the initial data and the averaged series, and corresponds to relatively quickly varying coronal component. The coronal rotation derived from the first series coincides with the fast mode detected earlier using the initial data set; i.e., the synodic period of this mode is 27 days at the equator, then weakly increases with latitude, slightly exceeding 28 days at high latitudes. The second series describes a slow rotation displaying a synodic period of about 34 days. This coincides with the period of rotation of the high-latitude corona derived by M. Waldmeier for polar faculae. We expect that coronal objects corresponding to the fast mode are associated with magnetic fields on the scales typical for large activity complexes. The slow mode may be associated with weak fields on small scales.     

A charge-consistent model for the acceleration of iron in the solar corona: Nonisothermal injection

A charge-consistent numerical model for the joint (regular and stochastic) acceleration of iron by a spherical shock wave propagating in the solar corona is proposed. Large-scale irregularities of the plasma density and the nonisothermal injection of ions are taken into account. For the case of iron, the energy dependence of the mean charge q_Fe(E) is determined by the relationships between the characteristic acceleration time, the charge-variation time for the accelerated ions, and the time for their trapping in regions of high plasma density. Due to the global inhomogeneity of the medium, these relationships depend on the shock speed. Our calculations indicate that photoionization by soft X-rays from flare regions can substantially change the charge states of heavy ions only in the most powerful solar events (both impulsive and gradual).     

The magnetic-field geometry in polar ray structures of the solar corona

Variations in the positions of the intersection points of tangents to ray structures in the polar corona of the Sun during the solar cycle are considered. At first glance, the decrease in the distance q between the tangent intersection point and the center of the solar disk during activity maximum contradicts harmonic analyses that indicate that the relative weight of higher harmonics in the global field increases during this period. Indeed, the higher the harmonic number in an axisymmetric field, the closer the intersection point of the field-line tangents (the magnetic focus) to the solar surface. It is shown that q for a field composed of two harmonics with opposite polarities at the poles can be smaller than q for either of them taken alone. A simple model representing the global field using the third and seventh harmonics is analyzed; this model can reproduce quite satisfactorily the observed dynamics of magnetic foci of the polar field.     

Relationship between the brightness in the coronal green line and magnetic fields on various scales

The relationship between the brightness in the FeXIV 530.3 nm coronal green line and magnetic fields on various scales in the corona is studied quantitatively. The cross-correlations of the corresponding synoptic maps for 1977–2001 have been calculated. Maps of the brightness of the coronal green line are constructed using daily monitoring data. Maps of the magnetic field are constructed separately for fields on large and small spatial scales, based on computations in a potential approximation using photospheric observations for distances of 1.1R _⊙ carried out at the Wilcox Solar Observatory. The correlations between the brightness in the coronal green line and the magnetic-field strengths on various scales as a function of latitude have a cyclic character. The correlation coefficients in the spot-formation zone are positive. Here, the green-line brightness corresponds mainly to the strength of small-scale fields, corresponding to the sizes of large active regions and activity complexes. The correlation coefficients are sign-variable above 40° latitude, and reach their greatest positive and negative values at the cyclemaximum and minimum. Larger-scale fields influence the green-line brightness at higher latitudes and near the phase of the cycle minimum. The results obtained can be used to investigate mechanisms for heating the corona. The relationship between the results obtained and the subsurface and deep solar dynamos are also discussed.     

The total number of spicules on the solar surface and their role in heating and mass balanace in the solar corona

A critical review of determinations of the number of spicules is presented, and the role of both classical and Type 2 spicules in heating and mass balance in the corona is considered. The total number of Type 2 spicules is determined, together with the upward fluxes of energy and mass to which they give rise. The total number of Type 2 spicules on the solar surface is found to be ~10⁵, close to values obtained in other studies. The associated particle flux toward the corona is 2.5 × 10¹⁴ cm^?2 s^?1, an order of magnitude lower than the corresponding flux for classical spicules. The associated energy flux is 10⁴ erg cm^?2 s^?1, an order of magnaitude lower than estimates obtained in other studies. The results indicate that Type 2 spicules can supply the mass lost from the corona, but are not able to fully explain coronal energy losses.     

The polarization of the solar corona on March 29, 2006

The effect of the auroral ring on the polarization of the solar corona during the solar eclipse of March 29, 2006 is studied. The angle and degree of polarization for emission arising from the combination of two partially polarized components is calculated. The emission of each component is described in terms of the Stokes parameters, and the corresponding parameters added. The position angle and degree of polarization are found for all cases realized in observations of the polarized corona with polarizing filter positions of 0°, 60°, 120° and 0°, 45°, and 90°. These calculations indicate that singular polarization points (saddles with index ?1/2) arise at a distance of about 1R_⊙ from the limb. A model for the total emission of the corona is constructed, which is used to calculate deviations of the polarization plane from the tangential direction (with respect to the limb).     

Evidence for shock generation in the solar corona in the absence of coronal mass ejections

The solar event SOL2012–10–23T03:13, which was associated with a X1.8 flare without an accompanying coronal mass ejection (CME) and with a Type II radio burst, is analyzed. A method for constructing the spatial and temporal profiles of the difference brightness detected in the AIA/SDOUVand EUV channels is used together with the analysis of the Type II radio burst. The formation and propagation of a region of compression preceded by a collisional shock detected at distances R < 1.3R _⊙ from the center of the Sun is observed in this event (R _⊙ is the solar radius). Comparison with a similar event studied earlier, SOL2011–02–28T07:34 [1], suggests that the region of compression and shock could be due to a transient (impulsive) action exerted on the surrounding plasma by an eruptive, high-temperature magnetic rope. The initial instability and eruption of this rope could be initiated by emerging magnetic flux, and its heating from magnetic reconnection. The cessation of the eruption of the rope could result from its interaction with surrounding magnetic structures (coronal loops).     

Some features of the streamer belt in the solar corona and at the Earth’s orbit

The rays of enhanced brightness making up the structure of the coronal-streamer belt can be traced to the lowest atmospheric layers in the Sun, with the angular size remaining nearly constant, d ≈ 2.5° ± 0.5°. This suggests that the physical mechanism generating the slow solar wind in the rays of the streamer belt differs from the mechanism giving rise to the fast solar wind from coronal holes. At distances of R < (4–5) R _⊙, the rays of the streamer belt are not radial in the plane of the sky and show deviations toward the corresponding pole. They then become essentially radial at R > (4–5) R _⊙. A transverse cross section of streamers in the corona and its continuation into the heliosphere—a plasma sheet—can be represented as two radially oriented, closely spaced rays (d ≈ 2.0°–2.5°) with enhanced density and an angular size of d. We also show that the ray structure of the streamer belt is involved in the development of coronal mass ejections (CMEs). The motion of a small-scale CME occurs within a magnetic flux tube (ray of enhanced brightness) and leads to an explosive increase in its angular size (rapid expansion of the tube). It seems likely that large-scale CMEs are the result of the simultaneous expansion of several magnetic tubes. We suggest that a small-scale CME corresponds to a “plasmoid” (clump of plasma of limited size with its own magnetic field) ejected into the base of a magnetic tube, which subsequently moves away from the Sun along the tube.     

Fine structure of convective motions in the solar photosphere: Observations and theory

The granulation brightnesses and convective velocities in the solar photosphere between the levels of formation of the continuum radiation and the temperature minimum are examined. Spectral images of the granulation observed in lines of neutral and ionized iron with high spatial (0.5″) and temporal (9 s) resolutions were obtained using the German Vacuum Tower Telescope in Izana (Tenerife, Spain). A correlation analysis shows that the granules and intergranules change their relative brightness at a height near 250 km, and a general reversal of the velocity occurs near a height of 490 km, where the material above granules begins to predominantly descend, and the material above intergranules, to ascend. The maximum correlation coefficient between the velocity and the line brightnesdoesnot exceed 0.75. The properties of the brightness and velocity are analyzed in a sixteen-column model. Four sorts of motions are most typical and efficient. In the first two, only the sign of the relative contrast of the material changes (an efficiency of 46%). This occurs, on average, at a height of 270 km. In the last two motions, both the sign of the contrast and the direction of the motion are reversed near a height of 350 km (an efficiency of 28%). All the observed dependences are compared with theoretical relations obtained in a three-dimensional hydrodynamical model, with deviations from local thermodynamic equilibrium included in the calculation of the spectral-line profiles. This model can satisfactorily reproduce all the basic features of the convective velocities and intensities. It is concluded that the convective motions maintain their column structure throughout the photosphere, right to the level of the temperature minimum. This makes a separation of the photosphere into two regions with different granulation brightnesses and convective motions unjustified.     

Fine structure of wave motions in the solar photosphere: Observations and theory

Spectral observations of the 639.361-nm FeI line at the center of the quiet solar disk with high spatial (0.4″) and temporal (10 s) resolution are used to investigate the behavior of local 5-min oscillations over granules and intergranular lanes. The power of the 5-min oscillations in the upper photosphere (at heights of H ≈ 490 km) is higher the faster the convective motions in the lower photosphere (H ≈ 10 km). This suggests that turbulent convection is responsible for the excitation of local solar oscillations. A statistical analysis of the oscillations shows that, on average, both the intensity and velocity of the oscillation amplitudes are greater over intergranular lanes. This difference in amplitudes is present throughout the studied heights in the photosphere (H = 0?490 km). The period at which the power spectrum of velocity oscillations reaches its maximum is longer over intergranules than over granules. Simulations of the propagation of acoustic-gravity waves in an atmosphere taking into account the convection pattern give a satisfactory explanation for the above observed effects. It is concluded that the atmospheric modulation of the 5-min oscillations is an additional or alternative mechanism responsible for differences between these oscillations over granules and intergranules.     

The structure of solar filaments. Prominences in the corona free from external magnetic field

The new approach to the modeling of quiescent solar prominences is proposed. We solve the inverse magnetohydrostatic problem, when the pressure, density and temperature of plasma in the filament are calculated from the equilibrium equations using the given magnetic structure (magnetic flux function is proposed to be known). The new exact nonlinear solutions for dense (n ≈ (2?3) × 10¹¹ cm^?3) and cold (T ≈ (5?10) × 10³ K) filaments, embedded in the plan, vertically stratified atmosphere (hot solar corona) free of magnetic field, are derived. The filaments are stretched along the horizontal axisy(the translational symmetry is assumed: ?/?y = 0) and located parallel to and above a photospheric, magnetic polarity reversal line. The magnetic field lines have a structure of magnetic flux rope with helical field lines in three-dimensional space; the strength of magnetic field falls rapidly with distance from a rope axis. No external longitudinal magnetic field is needed to equilibrate the prominence. The net electric current along the filament is equal to zero. The model of magnetic arcade with the deflection (sag) on the top, proposed by Pikelner (1971) as a basic form of normal prominence, is calculated also using the method proposed. It is shown that such magnetic arcade, having the magnetic field strength of few gauss only, can effectively maintain the equilibrium of cool dense filament at the heights about 50–60 Mm.     

Apparent angular sizes of the sources of microwave subsecond pulses and electron-density fluctuations in the lower solar corona

Data on the visible angular sizes of sources of microwave subsecond pulses (MSPs) obtained using the Siberian Solar Radio Telescope are analyzed assuming a dominant role for scattering on small-scale electron-density inhomogeneities in the solar corona. The observed dependence of the angular sizes of MSPs on the distance from the solar-disk center confirms that the MSP sources are localized in low layers of the solar corona. Both absolute and fractional levels of small-scale electron-density fluctuations have been estimated. These estimates suggest that flicker-noise-type turbulence power spectra are formed in the lower corona, and are preserved in the solar-wind acceleration region. A composite dependence of the scattering angle of a sounding radio wave on distance from the Sun is presented.