Nonlinear Force-Free Reconstruction of the Global Solar Magnetic Field: Methodology

We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields that, via Faraday’s equation, give rise to a respective normal-field distribution approaching asymptotically the target distribution. At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic field above the boundary surface, modeled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal-field distribution on the boundary. This is different from existing methods relying on a fixed boundary condition – the boundary evolves toward the a priori given one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time that a nonlinear force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but it depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge, this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts, is applied to the global solar magnetic field.     

Transport Effects in the Evolution of the Global Solar Magnetic Field

The axisymmetric component of the large-scale solar magnetic fields has a pronounced poleward branch at higher latitudes. In order to clarify the origin of this branch we construct an axisymmetric model of the passive transport of the mean poloidal magnetic field in the convective zone, including meridional circulation, anisotropic diffusivity, turbulent pumping and density pumping. For realistic values of the transport coefficients we find that diffusivity is prevalent, and the latitudinal distribution of the field at the surface simply reflects the conditions at the bottom of the convective zone. Pumping effects concentrate the field to the bottom of the convective zone; a significant part of this pumping occurs in a shallow subsurface layer, normally not resolved in dynamo models. The phase delay of the surface poloidal field relative to the bottom poloidal field is found to be small. These results support the double dynamo wave models, may be compatible with some form of a mixed transport scenario, and exclude the passive transport theory for the origin of the polar branch.     

On the Power in the Legendre Modes of the Solar Radial Magnetic Field

The power in the different modes of an expansion of the solar radial magnetic field at the surface in terms of Legendre polynomials,P , is calculated with the help of a solar dynamo model studied earlier. The model is of the Babcock–Leighton type, i.e., the surface eruptions of the toroidal magnetic field – through the tilt angle, , formed by the magnetic axis of a bipolar magnetic region with the east-west line – are the sources for the poloidal field. In this paper it is assumed that the tilt angle is subject to fluctuations of the form, = ()+ <> where <> is the average value and () is a random normal fluctuation with standard deviation which is taken from Howard's observations of the distribution of tilt angles. For numerical considerations, negative values of were not allowed. If this occurred, was recalculated. The numerical integrations were started with a toroidal magnetic field antisymmetric across the equator, large enough to generate eruptions, and a negligible poloidal field. The fluctuations in the tilt angle destroy the antisymmetry as time increases. The power of the antisymmetric modes across the equator (i.e., odd values of ) is concentrated in frequencies, _p, corresponding to the cycle period. The maximum power lies in the =3 mode with considerable power in the =5 mode, in broad agreement with Stenflo's results who finds a maximum power at =5. For the symmetric modes, there is considerable power in frequencies larger than _p, again in broad agreement with Stenflo's power spectrum.     

太阳磁场的观测

分析了太阳的观测磁图所涉及的磁场位形 ,以及磁场观测研究中的一些问题。     

Intermittency of the Solar Magnetic Field and Solar Magnetic Activity Cycle

Small-scale solar magnetic fields demonstrate features of fractal intermittent behavior, which requires quantification. For this purpose we investigate how the observational estimate of the solar magnetic flux density \(B\) depends on resolution \(D\) in order to obtain the scaling \(\ln B_{D} = - k \ln D +a\) in a reasonably wide range. The quantity \(k\) demonstrates cyclic variations typical of a solar activity cycle. In addition, \(k\) depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity \(a\) demonstrates some cyclic variation, but it is much weaker than in the case of \(k\). The scaling obtained generalizes previous scalings found for the particular cycle phases. The scaling is typical of fractal structures. In our opinion, the results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection.     

Fluctuations of the Solar Dynamo Observed in the Solar Wind and Interplanetary Magnetic Field at 1 AU and in the Outer Heliosphere

Recent helioseismic observations have found strong fluctuations at a period of about 1.3 years in the rotation speed around the tachocline in the deep solar convection layer. Similar mid-term quasi-periodicities (MTQP; periods between 1–2 years) are known to occur in various solar atmospheric and heliospheric parameters for centuries. Since the deep convection layer is the expected location of the solar magnetic dynamo, its fluctuations could modulate magnetic flux generation and cause related MTQP fluctuations at the solar surface and beyond. Accordingly, it is likely that the heliospheric MTQP periodicities reflect similar changes in solar dynamo activity. Here we study the occurrence of the MTQP periodicities in the near and distant heliosphere in the solar wind speed and interplanetary magnetic field observed by several satellites at 1 AU and by four interplanetary probes (Pioneer 10 and 11 and Voyager 1 and 2) in the outer heliosphere. The overall structure of MTQP fluctuations in the different locations of the heliosphere is very consistent, verifying the solar (not heliospheric) origin of these periodicities. We find that the mid-term periodicities were particularly strong during solar cycle 22 and were observed at two different periods of 1.3 and 1.7 years simultaneously. These periodicities were latitudinally organized so that the 1.3-year periodicity was found in solar wind speed at low latitudes and the 1.7-year periodicity in IMF intensity at mid-latitudes. While all heliospheric results on the 1.3-year periodicity are in a good agreement with helioseismic observations, the 1.7-year periodicity has so far not been detected in helioseismic observations. This may be due to temporal changes or due to the helioseismic method where hemispherically antisymmetric fluctuations would so far have remained hidden. In fact, there is evidence that MTQP fluctuations may occur antisymmetrically in the northern and southern solar hemisphere. Moreover, we note that the MTQP pattern was quite different during solar cycles 21 and 22, implying fundamental differences in solar dynamo action between the two halves of the magnetic cycle.     

太阳磁场理论外推研究进展

太阳磁场是研究太阳物理的关键。目前对太阳磁场的精确测量只限于光球层。对日冕磁场结构的了解,则多是以观测的光球磁场作为边界条件,在某种理论模型下进行外推。势场模型、线性无力场模型和非线性无力场模型是无力场假设下的三种理论外推模型。文章介绍了太阳磁场理论外推的基本方法和最新进展,和对三种模型中使用较多的外推方法,列举了它们在天文研究中的一些应用,同时也简略讨论了外推方法中存在的一些问题。     

Magnetic Field Properties of Solar X-Ray Jets

From a list of X-ray jets made by Shimojo et al. (1996), we selected events for which there were magnetic field data from NSO/Kitt Peak. Using co-aligned SXT and magnetograms, we examined the magnetic field properties of X-ray jets. We found that 8% of the jets studied occurred at a single pole (SP), 12% at a bipole (BP), 24% in a mixed polarity (MP) and 48% in a satellite polarity (ST). If the satellite polarity region is the same as the mixed polarity region, 72% of the jets occurred at the (general) mixed polarity region.We also investigated the magnetic evolution of jet-producing areas in active regions NOAA 7067, NOAA 7270, and NOAA 7858. It is found that X-ray jets favored regions of evolving magnetic flux (increasing or decreasing).     

Interpretation of Solar Magnetic Field Strength Observations

This study based on longitudinal Zeeman effect magnetograms and spectral line scans investigates the dependence of solar surface magnetic fields on the spectral line used and the way the line is sampled to estimate the magnetic flux emerging above the solar atmosphere and penetrating to the corona from magnetograms of the Mt. Wilson 150-foot tower synoptic program (MWO). We have compared the synoptic program λ5250 Å line of Fe?i to the line of Fe?i at λ5233 Å since this latter line has a broad shape with a profile that is nearly linear over a large portion of its wings. The present study uses five pairs of sampling points on the λ5233 Å line. Line profile observations show that the determination of the field strength from the Stokes V parameter or from line bisectors in the circularly polarized line profiles lead to similar dependencies on the spectral sampling of the lines, with the bisector method being the less sensitive. We recommend adoption of the field determined with the line bisector method as the best estimate of the emergent photospheric flux and further recommend the use of a sampling point as close to the line core as is practical. The combination of the line profile measurements and the cross-correlation of fields measured simultaneously with λ5250 Å and λ5233 Å yields a formula for the scale factor δ ^?1 that multiplies the MWO synoptic magnetic fields. By using ρ as the center-to-limb angle (CLA), a fit to this scale factor is δ ^?1=4.15?2.82sin?²(ρ). Previously δ ^?1=4.5?2.5sin?²(ρ) had been used. The new calibration shows that magnetic fields measured by the MDI system on the SOHO spacecraft are equal to 0.619±0.018 times the true value at a center-to-limb position 30°. Berger and Lites (2003, Solar Phys. 213, 213) found this factor to be 0.64±0.013 based on a comparison using the Advanced Stokes Polarimeter.     

The Global Solar Magnetic Field Through a Full Sunspot Cycle: Observations and Model Results

Based on 11 years of SOHO/MDI observations from the cycle minimum in 1997 to the next minimum around 2008, we compare observed and modeled axial dipole moments to better understand the large-scale transport properties of magnetic flux in the solar photosphere. The absolute value of the axial dipole moment in 2008 is less than half that in the corresponding cycle-minimum phase in early 1997, both as measured from synoptic maps and as computed from an assimilation model based only on magnetogram data equatorward of 60° in latitude. This is incompatible with the statistical fluctuations expected from flux-dispersal modeling developed in earlier work at the level of 7 – 10 σ. We show how this decreased axial dipole moment can result from an increased strength of the diverging meridional flow near the Equator, which more effectively separates the two hemispheres for dispersing magnetic flux. Based on the combination of this work with earlier long-term simulations of the solar surface field, we conclude that the flux-transport properties across the solar surface have changed from preceding cycles to the most recent one. A plausible candidate for such a change is an increase of the gradient of the meridional-flow pattern near the Equator so that the two hemispheres are more effectively separated. The required profile as a function of latitude is consistent with helioseismic and cross-correlation measurements made over the past decade.     

太阳磁场观测研究

简要回顾了近几年国际上太阳磁场研究的一些重要进展，包括耀斑与磁切和电流的关系，电流螺度和磁螺度，磁场拓扑性，三维磁场外推，色球磁场研究，日冕磁场研究，内网络磁元，磁流和振荡，极区磁场观测以及色球磁元观测等方面内容，同时也介绍了怀柔太阳观测站最近所取得的主要成果，自20世纪90年代以来，YOHKOH高分辨率的太阳X射线数据，SOHO的多波段大尺度观测，TRACE的高分辨太阳过渡区资料，为研究太阳磁场从内部到距离几十太阳半径处的大范围演化提供了依据，高效的空间资料结合长期的地面资料，将是正派推动太阳磁场研究的重要手段和必然趋势。     

Contribution to the Solar Mean Magnetic Field from Different Solar Regions

Seven-year-long seeing-free observations of solar magnetic fields with the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) were used to study the sources of the solar mean magnetic field, SMMF, defined as the net line-of-sight magnetic flux divided over the solar disk area. To evaluate the contribution of different regions to the SMMF, we separated all the pixels of each SDO/HMI magnetogram into three subsets: weak (\(B^{\mathrm{W}}\)), intermediate (\(B^{\mathrm{I}}\)), and strong (\(B^{\mathrm{S}}\)) fields. The \(B^{\mathrm{W}}\) component represents areas with magnetic flux densities below the chosen threshold; the \(B^{\mathrm{I}}\) component is mainly represented by network fields, remains of decayed active regions (ARs), and ephemeral regions. The \(B^{\mathrm{S}}\) component consists of magnetic elements in ARs. To derive the contribution of a subset to the total SMMF, the linear regression coefficients between the corresponding component and the SMMF were calculated. We found that i) when the threshold level of 30 Mx?cm^?2 is applied, the \(B^{\mathrm{I}}\) and \(B^{\mathrm{S}}\) components together contribute from 65% to 95% of the SMMF, while the fraction of the occupied area varies in a range of 2?–?6% of the disk area; ii) as the threshold magnitude is lowered to 6 Mx?cm^?2, the contribution from \(B^{\mathrm{I}}+B^{\mathrm{S}}\) grows to 98%, and the fraction of the occupied area reaches a value of about 40% of the solar disk. In summary, we found that regardless of the threshold level, only a small part of the solar disk area contributes to the SMMF. This means that the photospheric magnetic structure is an intermittent inherently porous medium, resembling a percolation cluster. These findings suggest that the long-standing concept that continuous vast unipolar areas on the solar surface are the source of the SMMF may need to be reconsidered.     

日冕磁场重建方法在研究太阳爆发活动中的应用

太阳是与地球关系最为密切的天体.发生在日面上的剧烈爆发性活动可能对人类的生存环境产生巨大影响甚至是灾难性后果.包含太阳耀斑、暗条爆发和日冕物质抛射在内的太阳爆发活动是同一物理过程的不同表现形式,其能量来源于爆发前储存在日冕中的磁场自由能.因此,了解日冕磁场的3维结构是理解太阳爆发的触发机制以及活动区的稳定性等现象的前提.由于观测技术限制,目前尚无法对日冕磁场进行常规观测,因此发展了多种利用可常规观测的光球磁场来重建日冕磁场的方法.主要评述近10 yr来各种日冕磁场重建方法在研究太阳爆发活动中的应用.     

Studying Solar Eruptions from Reconstructed Coronal Magnetic Field

The Sun is the celestial body in the sky with the closest relationship with the Earth. The violent eruptive activities happening on the Sun can greatly impact the human living environment and lead to disastrous consequences. It is well accepted that solar eruptions including the solar flare, prominence eruption and coronal mass ejection are the different manifestations of a single physical process powered by the magnetic free energy gradually stored in the corona prior to eruptions. Therefore, mapping the three-dimensional structure of coronal magnetic field is a prerequisite to understand the initiation mechanism of solar eruptions. Due to the technological and methodological difficulties, routine observations of the coronal magnetic field are still unavailable. Therefore, a number of methods have been developed to reconstruct the coronal magnetic field. This paper mainly reviews the applications of various reconstruction methods to the studies of the solar eruptions in the recent ten years.     

太阳耀斑的光球磁场和色球速度场观测

太阳磁场望远镜安装了CCD图象接收处理系统后,得到许多精细结构的两维、实时磁场、速度场图。本文对其中观测的两群黑子,做耀斑磁场、速度场分析。在此基础上指出,异极性磁区相互渗透是普遍存在的,耀斑亮核均发生在异极性磁区相互挤压的前锋。这就为挤压无力场耀斑模式提供了有力的证据。同时发现,在耀斑发生的区域,流场的方向是向下的。     

Fine Structures of Magnetic Field in Solar Quiet Region

In this paper, we present a time series of Fei 5250.2 Å photospheric filtergrams and corresponding magnetograms in a quiet region. The relationship between fine structures of granulation and magnetic fields is analyzed. It is found that although most bright filigree features in photospheric filtergrams are related to corresponding magnetic features, they are generally not cospatial. It is also found that some bright features and their corresponding photospheric magnetic fields show fast changes within several minutes.     

Plasma and Magnetic Field Inside Magnetic Clouds: a Global Study

Data observed during spacecraft encounters with magnetic clouds have been extensively analyzed in the literature. Moreover, several models have been proposed for the magnetic topology of these events, and fitted to the observations. Although these interplanetary events present well-defined plasma features, none of those models have included a simultaneous analysis of magnetic field and plasma data. Using as a starting point a non-force-free model that we have developed previously, we present a global study of MCs that include both the magnetic field topology and the plasma pressure. In this paper we obtain the governing equations for both magnitudes inside a MC. The expressions deduced are fitted simultaneously to the measurements of plasma pressure and magnetic field vector. We perform an analysis of magnetic field and plasma WIND observations within several MCs from 1995 to 1998. The analysis is confined to four of these events that have high-quality data. Only in one fitting procedure we obtain the orientation of the magnetic cloud relative to the ecliptic plane and the current density of the plasma inside the cloud. We find that the equations proposed reproduce the experimental data quite well.     

The Floor in the Solar Wind Magnetic Field Revisited

Svalgaard and Cliver (Astrophys. J. Lett. 661, L203, 2007) proposed that the solar-wind magnetic-field strength [B] at Earth has a ??floor?? value of ??4.6 nT in yearly averages, which is approached but not broached at solar minima. They attributed the floor to a constant baseline solar open flux. In both 2008 and 2009, the notion of such a floor was undercut by annual B averages of ??4 nT. Here we present a revised view of both the level and the concept of the floor. Two independent correlations indicate that B has a floor of ??2.8 nT in yearly averages. These are i) a relationship between solar polar-field strength and yearly averages of B for the last four 11-year minima (B _MIN), and ii) a precursor relationship between peak sunspot number for cycles 14??C?23 and B _MIN at their preceding minima. These correlations suggest that at 11-year minima, B consists of i) a floor of ??2.8 nT, and ii) a component primarily due to the solar polar fields that varies from ??0 nT to ??3 nT. The solar polar fields provide the ??seed?? for the subsequent sunspot maximum. Removing the ??2.8 nT floor from B _MIN brings the percentage decrease in B between the 1996 and 2009 minima into agreement with the corresponding decrease in solar polar-field strength. Based on a decomposition of the solar wind (from 1972??C?2009) into high-speed streams, coronal mass ejections, and slow solar wind, we suggest that the source of the floor in B is the slow solar wind. During 2009, Earth was in slow solar-wind flows ??70% of the time. We propose that the floor corresponds to a baseline (non-cyclic or ground state) open solar flux of ??8×10¹³ Wb, which originates in persistent small-scale (supergranular and granular) field.