Magnetic Fields and Solar Activities

We discuss the study of solar magnetic fields based on the photospheric vector magnetograms of solar active regions which were obtained at Huairou Solar Observing Station near Beijing in the period of 22nd and 23th solar cycles. The measurements of the chromospheric magnetic field and the spatial configuration of the field at the lower solar atmosphere inferred by the distribution of the solar photospheric and chromospheric magnetic field. After the analysis on the formation process of delta configuration in some super active regions based on the photospheric vector magnetogram observations, some results are obtained: (1) The analysis of magnetic writhe of whole active regions cannot be limited in the strong field of sunspots, because the contribution of the fraction of decayed magnetic field is non-negligible. (2) The magnetic model of kink magnetic ropes, proposed to be generated in the subatmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and the relationship with magnetic shear in some delta active regions completely. (3) The proposition is that the large-scale delta active regions are formed from contribution by highly sheared non-potential magnetic flux bundles generated in the subatmosphere. We present some results of a study of the magnetic helicity. We also compare these results with other data sets obtained by magnetographs (or Stokes polarimeters) at different observatories, and analyze the basic chirality of the magnetic field in the solar atmosphere.     

Modulation of the Solar Magnetic Cycle

The modulation model of the solar magnetic cycle for the time interval from 1650 to 1996 A.D. describes an harmonic oscillator with a basic (22.13 ± 0.05)-yr period, which is subjected to amplitude and phase variations that can be represented by a sum of trigonometric series. The simulated sunspot data explain 97.9% of cycle peak height variance and the residual standard deviation is 8.6 mean annual sunspots. A peak height of 139 for cycle 23 occurring in 2001 is predicted, whereas cycle 24 would have a maximum around 132 in 2014. Simulation of the sunspot numbers from 1000 until 2400 A.D. shows that the model recreates recurring minima (Maunder and Spörer Minimum). The prediction also expects a high level of amplitude modulation in the interval 1950–2010 with a rapid decrease afterwards. A greatly reduced cycle activity is reproduced by the simulation from about 2065 to 2100 A.D. No direct explanation of the long-term periodicities of the model can be advanced. The high-frequency contribution of the phase modulation, which accounts for the skewness of the solar cycle, shows coincidences with the orbital periods of Jupiter and Saturn, but no physical basis for the matching periodicities can be conceived.     

Rotation Characteristics of Large-Scale Solar Magnetic Fields

The rotation characteristics of large-scale (global) magnetic fields (GMF) and their relation to the activity of local fields (LMF) are studied over a long time interval (1915–1996). The main results are as follows. The GMF rotation rates and LMF activity vary in anticorrelation. Both variations have similar periods (11 years and a quasi-secular period of about 55–60 years), but are shifted relative to each other by half an 11-year cycle. Therefore, (1) the GMF rotation rate increases at the minimum of the 11-year cycle of LMF activity. (2) The GMF rotation rate is faster in the less active hemisphere. (3) The GMF rotation period slows down at the maximum of the secular LMF activity (cycles 18 and 19).     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .     

Distribution of Helical Properties of Solar Magnetic Fields

We summarize studies of helical properties of solar magnetic fields such as current helicity and twist of magnetic fields in solar active regions (ARs), that are observational tracers of the alpha-effect in the solar convective zone (SCZ). Information on their spatial distribution is obtained by analysis of systematic mag-netographic observations of active regions taken at Huairou Solar Observing Station of National Astronomical Observatories of Chinese Academy of Sciences. The main property is that the tracers of the alpha-effect are antisymmetric about the solar equator. Identifying longitudinal migration of active regions with their individual rotation rates and taking into account the internal differential rotation law within the SCZ known from helioseismology, we deduce the distribution of the effect over depth. We have found evidence that the alpha-effect changes its value and sign near the bottom of the SCZ, and this is in accord with the theoretical studies and numerical simulations. We discuss     

High-Resolution Studies of the Solar Polar Magnetic Fields

We present high-resolution studies of the solar polar magnetic fields near sunspot maximum in 1989 and towards sunspot minimum in 1995. We show that, in 1989, the polar latitudes were covered by several unipolar regions of both polarities. In 1995, however, after the polar field reversal was complete, each pole exhibited only one dominant polarity region.Each unipolar region contains magnetic knots of both polarities but the number count of the knots of the dominant polarity exceeds that of the opposite polarity by a ratio of order 4:1, and it is rare to find opposite polarity pairs, i.e., magnetic bipoles.These knots have lifetimes greater than 7 hours but less than 24 hours. We interpret the longitudinal displacement of the knots over a 7-hour period as a measure of the local rotation rate. This rotation rate is found to be generally consistent with Snodgrass' (1983) magnetic rotation law.In an attempt to obtain some insight into the operation of the solar dynamo, sketches of postulated subsurface field configurations corresponding to the observed surface fields at these two epochs of the solar cycle are presented.     

Solar Magnetic Carpet II: Coronal Interactions of Small-Scale Magnetic Fields

This paper is the second in a series of studies working towards constructing a realistic, evolving, non-potential coronal model for the solar magnetic carpet. In the present study, the interaction of two magnetic elements is considered. Our objectives are to study magnetic energy build-up, storage and dissipation as a result of emergence, cancellation, and flyby of these magnetic elements. In the future these interactions will be the basic building blocks of more complicated simulations involving hundreds of elements. Each interaction is simulated in the presence of an overlying uniform magnetic field, which lies at various orientations with respect to the evolving magnetic elements. For these three small-scale interactions, the free energy stored in the field at the end of the simulation ranges from 0.2 – 2.1×10²⁶ ergs, whilst the total energy dissipated ranges from 1.3 – 6.3×10²⁶ ergs. For all cases, a stronger overlying field results in higher energy storage and dissipation. For the cancellation and emergence simulations, motion perpendicular to the overlying field results in the highest values. For the flyby simulations, motion parallel to the overlying field gives the highest values. In all cases, the free energy built up is sufficient to explain small-scale phenomena such as X-ray bright points or nanoflares. In addition, if scaled for the correct number of magnetic elements for the volume considered, the energy continually dissipated provides a significant fraction of the quiet Sun coronal heating budget.     

Effect of Large-Scale Magnetic Fields on Total Solar Irradiance

The effect of large-scale magnetic fields on total solar irradiance (TSI) was studied both in time–frequency and in time–longitude aspects. A continuous wavelet analysis revealed that the energy of thermomagnetic disturbances due to sunspots and faculae cascades into the magnetic network and facular macrostructure. A numerical technique of time–longitude analysis was developed to study the fine structure of temporal changes in the TSI caused by longitudinal brightness inhomogeneities and rotation of the Sun. The analysis facilitates mapping large-scale thermal inhomogeneities of the Sun and reveals patterns of radiative excesses and deficits relative to the undisturbed solar photosphere. These patterns are organized into 2- and 4-sector structures that exhibit the effects of both activity complexes and magnetically active longitudes. Large-scale patterns with radiative excess display a facular macrostructure and bright patterns in the magnetic network caused by the dissipation of large-scale thermomagnetic disturbances. Similar global-scale temperature patterns were found in the upper solar atmosphere. These temperature patterns are also causally related to long-lived magnetic fields of the Sun. During activity cycles 21–23 the patterns with radiative excess tend to be concentrated around the active longitudes which are centered at about 60° and 230° in the Carrington system.     

The Topology of Background Magnetic Fields and Solar Flare Activity

We investigate the topological properties and evolution of background magnetic fields on synoptic maps from Wilcox Solar Observatory using mathematical morphology methods in terms of the Minkowski functionals. The total length of the neutral line, the total areas occupied by positive and negative polarities, and the Euler characteristics of background magnetic fields vary over an eleven-year cycle. Changes in the length of the neutral line that separates the polarities of the background magnetic field correlate well with flare activity. A time–longitude analysis of solar flare activity revealed a complicated organization and rotation of the entire flare ensemble. On the time–longitude diagram, flare activity is organized into the patterns which follow the rearrangements in background magnetic field and exhibit coexisting and alternating modes of rigid rotation. The character of rotation of the entire flare ensemble is similar to the rotation of background magnetic fields. The emergence of background magnetic fields and changes in their topology and rotation are often accompanied by enhancements in flare activity. A comparative analysis of the topological changes in background magnetic fields and flare activity reveals their causal relation.     

Magnetic Power Spectra Derived from Ground and Space Measurements of the Solar Magnetic Fields

We study magnetic power spectra of active and quiet regions by using Big Bear Solar Observatory and SOHO/MDI measurements of longitudinal magnetic fields. The MDI power spectra were corrected with Gaussian Modulation Transfer Function. We obtained reliable magnetic power spectra in the high wave numbers range, up to k=4.6 Mm⁻¹, which corresponds to a spatial scale l=1.4 Mm. We find that the occurrence of the spectral discontinuity at high wave numbers, k≥3 Mm⁻¹, largely depends on the spatial resolution of the data and it appears at progressively higher wave numbers as the resolution of the data improves. The spectral discontinuity in the raw spectra is located at wave numbers about 3 times smaller than wave numbers, corresponding to the resolution of the data, and about 1.5–2.0 times smaller in the case of the noise- and-resolution corrected spectra. The magnetic power spectra for active and quiet regions are different: active-region power spectra are described as ∼k ^−1.7, while in a quiet region the spectrum behaves as ∼k ^−1.3. We suggest that the difference can be due to small-scale dynamo action in the quiet-Sun photosphere. Our estimations show that the dynamo can generate more than 6% of the observed magnetic power.     

Numerical MHD Simulations of Solar Magnetoconvection and Oscillations in Inclined Magnetic Field Regions

The sunspot penumbra is a transition zone between the strong vertical magnetic field area (sunspot umbra) and the quiet Sun. The penumbra has a fine filamentary structure that is characterized by magnetic field lines inclined toward the surface. Numerical simulations of solar convection in inclined magnetic field regions have provided an explanation of the filamentary structure and the Evershed outflow in the penumbra. In this article, we use radiative MHD simulations to investigate the influence of the magnetic field inclination on the power spectrum of vertical velocity oscillations. The results reveal a strong shift of the resonance mode peaks to higher frequencies in the case of a highly inclined magnetic field. The frequency shift for the inclined field is significantly greater than that in vertical-field regions of similar strength. This is consistent with the behavior of fast MHD waves.     

The Evolution of Sunspot Magnetic Fields Associated with a Solar Flare

Solar flares occur due to the sudden release of energy stored in active-region magnetic fields. To date, the precursors to flaring are still not fully understood, although there is evidence that flaring is related to changes in the topology or complexity of an active-region’s magnetic field. Here, the evolution of the magnetic field in active region NOAA 10953 was examined using Hinode/SOT-SP data over a period of 12 hours leading up to and after a GOES B1.0 flare. A number of magnetic-field properties and low-order aspects of magnetic-field topology were extracted from two flux regions that exhibited increased Ca ii H emission during the flare. Pre-flare increases in vertical field strength, vertical current density, and inclination angle of ≈ 8° toward the vertical were observed in flux elements surrounding the primary sunspot. The vertical field strength and current density subsequently decreased in the post-flare state, with the inclination becoming more horizontal by ≈ 7°. This behavior of the field vector may provide a physical basis for future flare-forecasting efforts.     

Resolving Azimuth Ambiguity Using Vertical Nature of Solar Quiet-Sun Magnetic Fields

The measurement of solar magnetic fields using the Zeeman effect diagnostics has a fundamental 180° ambiguity in the determination of the azimuth angle of the transverse field component. There are several methods that are used in the community and each one has its merits and demerits. Here we present a disambiguation idea that is based on the assumption that most of the magnetic field on the sun is predominantly vertical. While the method is not applicable to penumbra or other features harboring predominantly horizontal fields like the sheared neutral lines, it is useful for regions where fields are predominantly vertical like network and plage areas. The method is tested with the full-disk solar vector magnetograms observed by the SOLIS/VSM instrument. We find that statistically about 60?–?85 % of the pixels in a typical full-disk magnetogram has a field inclination in the range of 0?–?30° with respect to the local solar normal, and thus can be successfully disambiguated by the proposed method. Due to its non-iterative nature, the present method is extremely fast and therefore can be used as a good initial guess for iterative schemes like the non-potential field computation (NPFC) method. Furthermore, the method is insensitive to noisy pixels as it does not depend upon the neighboring pixels or derivatives.     

太阳宁静区磁场的功率谱分析

利用１９９８年１０月３日北京天文台怀柔太阳观测站的高质量磁图,对给定的太阳宁静区两种不同极性的磁场进行了功率谱分析．结果表明,空间功率谱在超米粒和中米粒尺度具有明显的尖峰结构,这对应于空间周期性分布的网络和内网络磁结构．结果也显示出,超米粒边缘所包含的两种极性场中,其中的一种极性占优势．通过瞬态功率谱的分析,得出网络和内网络场寿命之间的比例关系,这一结果和其他学者得出的超米粒和中米粒对流寿命之间的关系相符．     

Helioseismic Constraints on Rotation and Magnetic Fields in the Solar Core

In recent years, more and more precise measurements have been made of solar oscillation frequencies and line widths. From space, the Solar and Heliospheric Observatory/Michelson Doppler Imager (MDI) data has led to much progress. From the ground, networks, like Global Oscillation Network Group (GONG), Taiwanese Oscillation Network (TON), and Birmingham Solar Oscillations Network (BiSON) have also led to much progress. The sharpened and enriched oscillation spectrum of data have been critically complemented by advances in the treatments of the opacities and the equation of state. All of this has led to a significantly more precise probing of the solar core. Here we discuss the progress made and suggest how the core may be better probed with seismic data on-hand. In particular, we review our knowledge of the rotation and structure of the core. We further argue that much may be learned about the core by exploiting the line width data from the aforementioned sources. Line-width data can be used to place sharper constraints on core properties, like the degree to which the Sun rotates on a single axis and the upper limit on magnetic fields that may be buried in the core.     

On a Reliable Representation of a Class of Force-free Solar Magnetic Fields

It is shown that for a class of force-free magnetic fields, i.e., ∇ × B = α B with α = constant, the magnetic field cannot be determined uniquely from the observed vertical component of the photospheric magnetic field given in an area of limited extent. Then it is proposed how some functions, the additional knowledge of which permits the magnetic field to be determined uniquely, could be chosen as a first approximation.     

Turbulence and Solar p-Mode Oscillations

The discrepancy between observed and theoretical mode frequencies can be used to examine the reliability of the standard solar model as a faithful representation of solar real situation. With the help of an improved time-dependent convective model that takes into account contribution of the full spatial and temporal turbulent energy spectrum, we study the influence of turbulent pressure on structure and solar p-mode frequencies. For the radial modes we find that the Reynolds stress produces signification modifications in structure and p-mode spectrum. Compared with an adiabatic approximation, the discrepancy is largely removed by the turbulent correction. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Study of the Periodic Variations of Solar Magnetic Fields During Maxima and Minima of Solar Activity

By using the solar magnetic ?eld data of Wilcox Observatory from 1975 to 2010, the short-time periodicities of solar mean magnetic ?elds during solar maximum and minimum years are analyzed. The results reveal that the solar magnetic ?elds mainly exhibit the approximate periods of 9 d, 13 d, and 27 d. During maximal solar activity the period about 27 d is most conspicuous, while during minimal solar activity the most evident period is approximately 13.5 d (except the solar minimum in the years 1984-1986). These results imply that solar active regions exhibit evidently different distributions in the periods of maxima and minima of solar activity.     

行星摄动力对太阳活动的调制

本文采用天体力学方法，考虑太阳系九大行星对太阳表面局部区域的摄动力，建立了太阳表面受行星起潮力的数值计算模型．利用此模型，针对历史上发生的100个大太阳耀斑事件，计算各耀斑区耀斑发生前后所受行星起潮力的变化．从耀斑发生的时间分布统计得到：在100个耀斑中，有75个耀斑发生在行星综合起潮力合力极大前后三天内．证明行星摄动对太阳活动有调制作用．最后，本文还对太阳活动起源、活动周期等问题进行了简要的讨论．