Evolution of the magnetic field imbalance on the Sun

The time and latitude change of the flux and rotation of magnetic-field imbalance structures with various strengths has been determined from observations at the Kitt-Peak observatory for 26 years. The regularities revealed during the work allow this change to be explained as follows. The structure of the imbalance of the magnetic field of a particular strength emerges at the photosphere surface while possessing a rotation typical for the area of this structure formation. After this, the structure begins to drift along the meridian (toward the pole or toward the equator) while rotating at the same velocity and occupying several interval of latitudes. Having displaced to the poles from the emerging latitude by about 20° (or more, depending on the rotation period), structures that have a certain significant period cease to exist as a whole, giving rise to other structures with other significant rotation periods. From here it follows that the differential rotation of the layers responsible for forming the imbalance structures of fields with various strengths can be determined from the dependence of the rotation period on the latitude of the emergence of the imbalance structure.     

Small-scale stochastic structure of the solar magnetic field

The small-scale (～10″) stochastic properties of the solar magnetic field B are analyzed in terms of the two-dimensional model of a fractal Brownian process (the mean square of the difference between the field strengths at two points separated by a distance D is proportional to D ^2H ). Digitized solar magnetograms with a 2″ resolution are used to determine the standard deviation s of the magnetic field and the exponents H at various levels of |B|. It has been established that the transition from the background magnetic field to the fields of an active region occurs near 25–50 G. A dependence of the exponent H on the magnetic field amplitude has been derived. The exponent H for the background magnetic field has been found to be much smaller than that for the fields of an active region. The relationship of the results obtained to certain fundamental properties of plasma in a magnetic field is discussed.     

Imbalance of magnetic fields on the Sun

Differences of magnetic field flows of “+” and “?” polarities, i.e. the imbalance of magnetic fields for 26 years—from January 1, 1977, to September 30, 2003—are investigated,. The synoptic maps of the longitudinal vector of Sun’s magnetic field strength obtained at the Kitt Peak National Observatory (United States) and kindly given to us by Dr. J. Harvey have served as the initial material. The imbalance of magnetic fields’ cyclicity features and the deviations from the dipole structure of Sun’s magnetic field are determined. The contribution of latitude zones and fields of various strength into the general magnetic flux from the Sun is found. The latter characteristic was compared with the Sun’s mean magnetic field (MMF) obtained from the observations of the Sun as a star (Kotov et al., 2002; Kotov, 2008). The obtained results testify that the imbalance is one of physical characteristics of the Sun. The confirmations of this conclusion are the strict regularities of the Sun’s dipole structure changing; the complicated character of the imbalance cyclicity, i.e., the multiplicity of cycles; the solar nature of MMF changing; and the distinction between two classes of magnetic fields in the imbalance characteristics.     

Rotation of the magnetic elements in polar regions on the Sun

Using the Michelson Doppler Imager (MDI) data from Solar and Heliospheric Observatory (SOHO), the rotation rate of the unipolar magnetic regions in North high-latitude regions of the Sun is estimated by tracking individual magnetic elements. The analysis reveals a strong spin down near the pole, which is greater than the Doppler and magnetic rotation rates estimated by Snodgrass & Ulrich (1990), and rotation rate inferred from helioseismology (Birch & Kosovichev 1998), and is probably related to variation of velocity gradient in the subsurface shear layer. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Temporal and spatial distribution of the magnetic field and density of nonthermal electrons in the source of solar microwave bursts

The temporal and spatial distribution of the magnetic field and density of non-thermal electrons in the source of solar microwave bursts are studied by the gyrosynchrotron model, using the observations of the high-resolution spectrometer at the Owens Valley solar interferometer. The general results are consistent with the previous knowledge about these parameters. For example, the magnetic field decreases with increasing radio flux, and the distribution gradually flattens, so that the non-uniformity of the magnetic field decreases gradually, meanwhile the density increases, and the nonthermal electrons propagate from lower to higher levels. It is interesting that the oscillation of the density is detected at lower frequencies, and there is a correlation between the density and the energy index. The main purpose of this paper is to develop a diagnostic method for the basic plasma parameters in solar flares.     

Determination of the Topology Skeleton of Magnetic Fields in a Solar Active Region

Magnetic topology has been a key to the understanding of magnetic energy re-lease mechanism. Based on observed vector magnetograms, we have determined the three-dimensional (3D) topology skeleton of the magnetic fields in the active region NOAA 10720.The skeleton consists of six 3D magnetic nulls and a network of corresponding spines, fans,and null-null lines. For the first time, we have identified a spiral magnetic null in Sun's corona.The magnetic lines of force twisted around the spine of the null, forming a 'magnetic wreath'with excess of free magnetic energy and resembling observed brightening structures at extra-ultraviolet (EUV) wavebands. We found clear evidence of topology eruptions which are re-ferred to as catastrophic changes of topology skeleton associated with a coronal mass ejection(CME) and an explosive X-ray flare. These results shed new lights on the structural complex-ity and its role in explosive magnetic activity. The concept of flux rope has been widely used in modelling explosive magnetic activity, although their observational identity is rather ob-scure or, at least, lacking of necessary details up to date. We suggest that the magnetic wreath associated with the 3D spiral null is likely an important class of the physical entity of flux ropes.     

Penetration of coronal magnetic fields into solar-wind streams

The formation of solar-wind stream structure is investigated. Characteristic features of the solar and coronal magnetic-field structure, morphological features of the white-light corona, and radio maps of the solar-wind transition (transonic) region are compared. The solar-wind stream structure is detected and studied by using radio maps of the transition region, the raggedness of its boundaries, and their deviation from spherical symmetry. The radio maps have been constructed from radioastronomical observations in 1995–1997. It is shown that the structural changes in the transition region largely follow the changes occurring in regions closer to the Sun, in the circumsolar magnetic-field structure, and in the solar-corona structure. The correlations between the magnetic-field strength in the solar corona and the location of the inner (nearest the Sun) boundary of the transition region are analyzed. The distinct anticorrelation between the coronal magnetic-field strength and the distance of the transition region from the Sun is a crucial argument for the penetration of solar magnetic fields into plasma streams far from the Sun.     

Evidence for interchange reconnection between a coronal hole and an adjacent emerging flux region

Coronal holes are regions of dominantly monopolar magnetic field on the Sun where the field is considered to be ‘open’ towards interplanetary space. Magnetic bipoles emerging in proximity to a coronal hole boundary naturally interact with this surrounding open magnetic field. In the case of oppositely aligned polarities between the active region and the coronal hole, we expect interchange reconnection to take place, driven by the coronal expansion of the emerging bipole as well as occasional eruptive events. Using SOHO/EIT and SOHO/MDI data, we present observational evidence of such interchange reconnection by studying AR 10869 which emerged close to a coronal hole. We find closed loops forming between the active region and the coronal hole leading to the retreat of the hole. At the same time, on the far side of the active region, we see dimming of the corona which we interpret as a signature of field line ‘opening’ there, as a consequence of a topological displacement of the ‘open’ field lines of the coronal hole. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling helioseismic modes in the magnetic atmosphere of the Sun

The pulsation of the solar surface is caused by acoustic waves traveling in the solar interior. Thorough analyses of observational data indicate that these f and p helioseismic oscillation modes are not bounced back completely at the surface but they partially penetrate into the atmosphere. Atmospheric effects and their possible observational application are investigated in one‐dimensional magnetohydrodynamic models. It is found that f and p mode frequencies are shifted of the order of μHz due to the presence of an atmospheric magnetic field. This shift varies with the direction of the wave propagation.Resonant coupling of global helioseismic modes to local Alfvén and slow waves reduce the life time of the global modes. The resulting line width of the frequency line is of the order of nHz, and it also varies with propagation angle. These features enable us to use helioseismic observations in magnetic diagnostics of the lower atmosphere. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of noise on sunspot magnetic field parameters

Using a perturbated (noised) dipole model of a sunspot magnetic field structure we simulated the influence of background noise or apparent noise (unresolved small-scale magnetic field structure) on sunspot magnetic field parameters. We evaluated mean values of the vertical and horizontal electric current densities |j|_∥ and |j|_⊥, respectively, of the force-free parameter α and of the Lorentz force |F|. For comparison we estimated |j_⊥| and |F| of a standard sunspot magnetic field model (return-flux model, OSHEROVICH 1982). Furthermore, we compared our results with those from observations resulting in estimated values of |j|_∥ for quiet sunspots. Our investigation led to the following results: the estimated values of 〈|F|〉 show clearly that due to the noise the axisymmetric magnetic dipole model is clustered into several subsystems of fluxbundles. The latter are connected with a system of electric current densities of the order of |j|_∥ ∼ 10⁻³ Am⁻² and |j|_⊥ = 10⁻¹ Am⁻², i.e., this system is a noise-generated nonaxisymmetric magnetohydrostatic model.     

Small-scale background magnetic field on the sun in solar cycle 23

Based on SOHO/MDI data (an archive of magnetic maps with a resolution of ～2″), we have investigated the dynamics of the small-scale background magnetic field on the Sun in solar cycle 23. The cyclic variations and surface structure of the background magnetic field have been analyzed using the mean estimates of 〈B〉 and 〈B ²〉 of the observed magnetic field strength B for various solar surface areas and at various B levels. We have established that the cyclic variations of 〈2〉 at latitudes below 30° are essentially similar to those of the total radio flux F _10.7. A significant difference between the background magnetic fields in the northern and southern solar hemispheres persisting throughout the solar cycle has been detected. We have found the effect of background magnetic field growth toward the solar limb and concluded that the transversal component in the background magnetic field is significant. The relatively weak small-scale background magnetic fields are shown to form a special population with its own special laws of cyclic variation.     

Convective intensification of magnetic fields in the quiet Sun

Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field B _e, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field B _p that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealized numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and characterized by a pattern of vigorous, time-dependent, 'granular' motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localized concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than B _e and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contains ultraintense magnetic fields that are significantly greater than B _p. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultraintense fields develop owing to non-linear interactions between magnetic fields and convection; they cannot be explained in terms of 'convective collapse' within a thin flux tube that remains in overall pressure equilibrium with its surroundings.     

Solar coronal heating by magnetic cancellation – III. Thermodynamics

We present two-dimensional numerical magnetohydrodynamics simulations of a coronal X-ray bright point (XBP) caused by a cancelling magnetic feature (CMF). Cancellation is driven by converging motions of two magnetic bipolar sources. These sources are initially disconnected from each other so that both, the CMF and the associated reconnection/heating event (i.e. the XBP), are modelled in a self-consistent way. In the initial state, there is no X-point but two separatrices are present. Hence, the reconnection/heating and the cancellation phases have not yet started. Our numerical experiments end shortly after the converging magnetic bipole has fully cancelled. By this time, reconnection in the inner domain has ceased and occurs only at the base. Solving the energy equation with various heating and cooling terms included, and considering different bottom boundary conditions, reveals that the unrealistically high temperatures produced by Ohmic heating are reduced to more moderate temperatures of 1.5–2 MK consistent with observations of XBPs, if thermal conduction is included and density and temperature are fixed at the base.     

Small-scale magnetic structures on the Sun

Summary The Sun provides us with a unique astrophysics laboratory for exploring the fundamental processes of interaction between a turbulent, gravitationally stratified plasma and magnetic fields. Although the magnetic structures and their evolution can be observed in considerable detail through the use of the Zeeman effect in photospheric spectral lines, a major obstacle has been that all magnetic structures on the Sun, excluding sunspots, are smaller than what can be resolved by present-day instruments. This has led to the development of indirect, spectral techniques (combinations of two or more polarized spectral lines), which overcome the resolution obstacle and have revealed unexpected properties of the small-scale magnetic structures. Indirect empirical and theoretical estimates of the sizes of the flux elements indicate that they may be within reach of planned new telescopes, and that we are on the verge of a unified understanding of the diverse phenomena of solar and stellar activity.In the present review we describe the observational properties of the smallscale field structures (while indicating the diagnostic methods used), and relate these properties to the theoretical concepts of formation, equilibrium structure, and origin of the surface magnetic flux.On leave from Institute of Astronomy, ETH-Zentrum, CH-8092 Zürich, SwitzerlandThe National Center for Atmospheric Research is sponsored by the National Science Foundation     

Solar coronal heating by magnetic cancellation – II. Disconnected and unequal bipoles

Two-dimensional numerical magnetohydrodynamic simulations of a cancelling magnetic feature (CMF) and the associated coronal X-ray bright point (XBP) are presented. Coronal magnetic reconnection is found to produce the Ohmic heating required for a coronal XBP. During the BP phase where reconnection occurs above the base, about 90–95 per cent of the magnetic flux of the converging magnetic bipole cancels at the base. The last ≈5 to 10 per cent of the base magnetic flux is cancelled when reconnection occurs at the base. Reconnection happens in a time-dependent way in response to the imposed converging footpoint motions. A potential field model gives a good first approximation to the qualitative behaviour of the system, but the magnetohydrodynamics (MHD) experiments reveal several quantitative differences: for example, the effects of plasma inertia and a pressure build-up in-between the converging bipole are to delay the onset of coronal reconnection above the base and to lower the maximum X -point height.     

Search for nonpotential features in the magnetic field of the solar active region SD 135 on 1984 June 4

Wir untersuchten die Struktur des Magnetfeldes in der relativ kleinen und einfachen solaren aktiven Region SD 135/1984 in der frühen, relativ ruhigen Phase am 24. Juni. Für diese Arbeit nutzten wir die Daten des Vektormagnetografen des SibIZMIR und Resultate von Modellrechnungen in der stromfreien Näherung. Wir haben das gemessene Magnetfeld mit dem Transversal-Feld der Modellrechnung verglichen. Wir konnten keinen signifikanten Nonpotential-Effekt größer als im Niveau der Sensitivität des Transversal-Magnetfeldes B_T 200 G finden. Wir schluß-folgern daher, daß die globale Magnetfeldstruktur in der untersuchten solaren aktiven Region nahezu eine Potentialstruktur besaß. Die Effekte der Entwicklung der aktiven Region auf die Magnetfeldstruktur scheinen vernachlässigbar zu sein.