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.     

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.     

Calculating the potential magnetic field of a local region on the Sun using the measured oblique component

We propose a method for solving the Neumann boundary-value problem using the known magnetic-field component at the boundary in a specified direction (the oblique-derivative problem). The method allows the normal field component at the boundary to be directly determined from the measured line-of-sight component. This makes it possible to calculate the potential magnetic field in the corona above a region far removed from the solar-disk center. A model potential magnetic field is used as an example to test our method.     

Scaling laws and coherent structures in the solar wind

The interplanetary medium is characterized by a very high Reynolds number and is pervaded by fluctuations providing information on a wide range of scales, from fractions of second up to the solar rotation period. In the past decade or so, turbulence in the solar wind has been used as a large wind tunnel to investigate scaling laws of turbulent fluctuations and multifractal models. Moreover, new interesting insights in the theory of turbulence have been derived from the point of view which considers a turbulent flow as a complex system, a sort of benchmark for the theory of dynamical systems. Important finding like the lack of a strict self-similarity of the fluctuations with the consequent nonapplicability of strict scale invariance, the strong anisotropy of velocity and magnetic field fluctuations, the clear lack of equipartition between magnetic and kinetic fluctuations all contributed to suggest the idea that interplanetary fluctuations could possibly be due to a mixture of propagating waves and static structures convected by the wind. In this paper we further discuss this point and bring new evidence about the fact that the presence of a background magnetic field introduces not only a symmetry breaking in interplanetary space but also organizes fluctuations about its large scale orientation.     

The charged particle distribution due to emission in a magnetic field

Charged particles emission in a magnetic field on the basis of Boltzman equation with source term is studied. The work develops the results of Narasimha (1962), where the neutral gas expansion into a vacuum is studied. The different specific cases of emission are given for moving sources. The results may be of use when we study phenomena which happen in plasma close to the Earth and in space, as well as for studies of phenomena which take place due to moving satellites in the ionosphere and in interplanetary or interstellar plasma.     

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.     

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.     

太阳表面磁场的分布与演化研究进展

太阳磁场、较差自转和内部对流使得日面磁场与磁活动在很大的时间尺度和空间尺度范围均表现得相当复杂.其中最有名的是太阳活动的11年周期,或22年磁周期.在较小时间尺度上,从几秒到几小时,有时太阳大气中会发生一些壮观的爆发事件,如耀斑、日珥爆发、日冕物质抛射等.所有这些形式的事件都与太阳磁场紧密关联.简单评述了太阳磁场起源与观测方法,重点论述了不同尺度太阳磁场的空间分布与演化,介绍了从太阳磁活动现象统计得到的有关太阳磁场的几个典型特征,同时讨论了进一步研究的方向.     

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)     

Small-scale magnetic helicity losses from a mean-field dynamo

Using mean-field models with a dynamical quenching formalism, we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong for both large- and small-scale fields. In the presence of shear, there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region, there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain.     

Small-scale magnetic field diagnostics outside sunspots: Comparison of different methods

We analyse different observational data related to the problem of intrinsic magnetic field strength in small-scale fluxtubes outside sunspots. We conclude that the kG range of fluxtube fields follows from not only classical line ratio method, but also from other old and new techniques. For the quiet regions on the Sun, the most probable mode of such fields has a magnetic field strength of 1.2–1.5 kG assuming the rectangular field profile. To best interpret the observations, a weak background field between fluxtubes should be assumed, and its magnetic field strength is expected to increase with the filling factor of fluxtubes. The alternative point of view about subkilogauss fluxtube fields is critically examined, and possible sources of different conclusions are presented.     

Electric charge and magnetic flux on rotating black holes in a force-free magnetosphere

The electric charge on rotating black holes is calculated to be ∼ BJ in the force-free configuration of Ghosh, with a horizon flux of ∼ BM ². This charge is gravitationally weak for B ∼10¹⁵ G , so that the Kerr metric applies. Being similar to the electric charge of a magnetar, both electric charge and magnetic flux should be, in sign and order of magnitude, continuous during stellar collapse into a black hole. Extraction of the rotational energy from newly formed black holes may proceed by interaction with the magnetic field.     

Speckle spectro‐polarimetry of magnetic structures

Two‐dimensional spectrograms were obtained with the Vacuum Tower Telescope, Tenerife, in order to study small‐scale structures and faculae on the Sun. Using the speckle reconstruction method, we obtain high‐resolution images and wavelength scans. Magnetic fields can be studied from Stokes V profiles, and velocity maps are gained by the Doppler shift of the center of gravity of Stokes I. Here some results about small‐scale structures and their magnetic fields are shown.     

Polarization line radiative transfer in the atmospheres of magnetic white dwarfs

Some physical mechanisms which can affect the Zeeman line profiles of magnetic white dwarfs are studied. The pure absorption polarization transfer equation is solved including these mechanisms. The broadening of lines in magnetic white dwarfs is briefly discussed.     

Non-axisymmetric solar magnetic fields

A simple non-linear, non-axisymmetric mean field dynamo model is applied to a differentially rotating spherical shell. Two approximations are used for the angular velocity, to represent what is now believed to be the solar rotation law. In each case, stable solutions are found which possess a small non-axisymmetric field component. Although the model has a number of obvious shortcomings, it may be relevant to the problem of the solar active longitudes.     

Fractal properties of solar magnetic fields

We study the spatial properties of solar magnetic fields using data from the Solar Vector Magnetograph of the Marshall Space Flight Center (MSFC) (FeI 5250.2 Å) and SOHO/MDI longitudinal magnetic field measurements (Ni 6767.8 Å) (96-min full-disk maps). Our study is focused on two objects: the fractal properties of sunspots and the fractal properties of the spatial magnetic field distribution of active and quiet regions considered as global structures. To study the spatial structure of sunspots, we use a well-known method of determining the fractal dimension based on an analysis of the perimeter—area relation. To analyze the fractal properties of the spatial magnetic field distribution over the solar surface, we use a technique developed by Higuchi. We have revealed the existence of three families of self-similar contours corresponding to the sunspot umbra, penumbra, and adjacent photosphere. The fractal coefficient has maxima near the umbra—penumbra and penumbra—photosphere boundaries. The fractal dependences of the longitudinal and transverse magnetic field distributions are similar, but the fractal numbers themselves for the transverse fields are larger than those for the longitudinal fields approximately by a factor of 1.5. The fractal numbers decrease with increasing mean magnetic field strength, implying that the magnetic field distribution is more regular in active regions.     

Night‐time science with large solar telescopes: The magnetic Sun through time

Today the Sun has a regular magnetic cycle driven by a dynamo action. But how did this regular cycle develop? How do basic parameters such as rotation rate, age, and differential rotation affect the generation of magnetic fields? Zeeman Doppler imaging (ZDI) is a technique that uses high‐resolution observations in circularly polarised light to map the surface magnetic topology on stars. Utilising the spectropolarimetric capabilities of future large solar telescopes it will be possible to study the evolution and morphology of the magnetic fields on a range of Sun‐like stars from solar twins through to rapidly‐rotating active young Suns and thus study the solar magnetic dynamo through time. In this article I discuss recent results from ZDI of Sun‐like stars and how we can use night‐time observations from future solar telescopes to solve unanswered questions about the origin and evolution of the Sun's magnetic dynamo (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.