Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Application to Discrete Data

We investigate how the divergence-free property of magnetic fields can be exploited to resolve the azimuthal ambiguity present in solar vector magnetogram data, by using line-of-sight and horizontal heliographic derivative information as approximated from discrete measurements. Using synthetic data we test several methods that each make different assumptions about how the divergence-free property can be used to resolve the ambiguity. We find that the most robust algorithm involves the minimisation of the absolute value of the divergence summed over the entire field of view. Away from disk centre this method requires the sign and magnitude of the line-of-sight derivatives of all three components of the magnetic field vector.     

Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: The Effects of Noise and Limited Spatial Resolution

We investigate how the azimuthal ambiguity in solar vector magnetogram data can be resolved by using the divergence-free property of magnetic fields. In a previous article, by Crouch, Barnes, and Leka?(Solar Phys. 260, 271, 2009), error-free synthetic data were used to test several methods that each make a different assumption about how the divergence-free property can be used to resolve the ambiguity. In this paper this testing is continued with an examination of the effects of Poisson photon noise and limited instrumental spatial resolution. We find that all currently available methods based on the divergence-free property can produce undesirable results when photon noise or unresolved structure is present in the data. We perform a series of experiments aimed at improving the performance of the global minimisation method, which is the most promising of the methods. We present a two-step approach that produces reasonable results in tests using synthetic data. The first step of this approach involves the global minimisation of a combination of the absolute value of the approximation for the divergence and a smoothness constraint, which is designed to minimise the difference between the magnetic field in neighbouring pixels. In the second step, pixels with measurements known to be strongly affected by photon noise are revisited with a smoothing algorithm that also seeks to minimise the difference between the magnetic field in neighbouring pixels.     

Calibration of Vector Magnetogram with the Nonlinear Least-squares Fitting Technique

To acquire Stokes profiles from observations of a simple sunspot with the Video Vector Magnetograph at Huairou Solar Observing Station (HSOS), we scanned the FeI λ5324.19A line over the wavelength interval from 150mA redward of the line center to 150 mA blueward, in steps of 10 mA. With the technique of analytic inversion of Stokes profiles via nonlinear least-squares, we present the calibration coefficients for the HSOS vector magnetic magnetogram. We obtained the theoretical calibration error with linear expressions derived from the Unno-Becker equation under weak-field approximation.     

利用双视角消除太阳矢量磁场观测中的180◦不确定性

随着"环日轨道器"(Solar Orbiter, SO)的在轨运行,太阳磁场观测进入了双视角遥测的时代.对利用太阳磁场的双视角观测改正矢量磁图中存在的横场(垂直于视线方向的磁场分量) 180°不确定性进行了模拟,首先模拟了对解析解得到磁图的双视角观测,然后利用"日震学和磁学成像仪"(Helioseismic and Magnetic Imager, HMI)在不同时间观测到的一个老化黑子的磁图模拟了双视角观测.发现要改正一个磁图中横场方向的180°不确定性,在观测上只需要另外一个平行于视线方向的磁场即纵向磁场观测的协助.利用HMI的磁场观测模拟,估算显示30°的张角能够改正50 Gs磁场中的180°不确定性.更大的张角虽然更有利于更弱磁场的改正,但是考虑到投影效应的不利影响, 30°左右的张角应该是未来空间设备进行多视角观测太阳磁场的最佳张角.     

Automatic Detection and Classification of Coronal Holes and Filaments Based on EUV and Magnetogram Observations of the Solar Disk

A new method for the automated detection of coronal holes and filaments on the solar disk is presented. The starting point is coronal images taken by the Extreme Ultraviolet Telescope on the Solar and Heliospheric Observatory (SOHO/EIT) in the Fe ix/x 171 Å, Fe xii 195 Å, and He ii 304 Å extreme ultraviolet (EUV) lines and the corresponding full-disk magnetograms from the Michelson Doppler Imager (SOHO/MDI) from different phases of the solar cycle. The images are processed to enhance their contrast and to enable the automatic detection of the two candidate features, which are visually indistinguishable in these images. Comparisons are made with existing databases, such as the He i 10830 Å NSO/Kitt Peak coronal-hole maps and the Solar Feature Catalog (SFC) from the European Grid of Solar Observations (EGSO), to discriminate between the two features. By mapping the features onto the corresponding magnetograms, distinct magnetic signatures are then derived. Coronal holes are found to have a skewed distribution of magnetic-field intensities, with values often reaching 100?–?200 gauss, and a relative magnetic-flux imbalance. Filaments, in contrast, have a symmetric distribution of field intensity values around zero, have smaller magnetic-field intensity than coronal holes, and lie along a magnetic-field reversal line. The identification of candidate features from the processed images and the determination of their distinct magnetic signatures are then combined to achieve the automated detection of coronal holes and filaments from EUV images of the solar disk. Application of this technique to all three wavelengths does not yield identical results. Furthermore, the best agreement among all three wavelengths and NSO/Kitt Peak coronal-hole maps occurs during the declining phase of solar activity. The He ii data mostly fail to yield the location of filaments at solar minimum and provide only a subset at the declining phase or peak of the solar cycle. However, the Fe ix/x 171 Å and Fe xii 195 Å data yield a larger number of filaments than the Hα data of the SFC.     

Simulating Solar Cycles in Northern and Southern Hemispheres by Assimilating Magnetic Data into a Calibrated Flux-Transport Dynamo

We use the flux-transport dynamo prediction scheme introduced by Dikpati, de Toma, and Gilman (Geophys. Res. Lett. 33, L05102, 2006) to make separate simulations and predictions of sunspot cycle peaks for northern and southern hemispheres. Despite the division of the data, the skill level achieved is only slightly lower than that achieved for the sum of both hemispheres. The model shows skill at simulating and predicting the difference in peaks between North and South, provided that difference is more than a few percent. The simulation and prediction skill is achieved without adjustment to any parameters of the model that were used when peaks for the sum of North and South sunspot areas was simulated. The results are also very insensitive to the averaging length applied to the input data, provided the simulations and predictions are for peaks defined by averaging the observations over at least 13 rotations. However, in its present form, the model is not capable of skillfully simulating or predicting short-time-scale features of individual solar cycles.     

解决太阳横向磁场方向测定中180°不确定性的一个方法

本文提出了一种解决太阳横向磁场方向测定中１８０°不确定性的方法。该方法首先将Ｇａｒｙ等提出的方法定量化，客观地确定每一点的横场方向；然后由独立的Ｈ＿α观测或磁场演化历史，分析和确定磁力线的拓扑联接性，对客观确定的横场方向做经验修正。对活动区的应用表明，该方法是一个可供选择的解决横场方向不确定性的有效方法。     

The Butterfly Diagram in the Eighteenth Century

Digitized images of the drawings by J.C. Staudacher were used to determine sunspot positions for the period 1749 – 1796. From the entire set of drawings, 6285 sunspot positions were obtained for a total of 999 days. Various methods have been applied to find the orientation of the solar disk, which is not given for the vast majority of the drawings by Staudacher. Heliographic latitudes and longitudes in the Carrington rotation frame were determined. The resulting butterfly diagram shows a highly-populated Equator during the first two cycles (cycles 0 and 1 in the usual counting since 1749). An intermediate period is cycle 2, whereas cycles 3 and 4 show a typical butterfly shape. A tentative explanation may be the transient dominance of a quadrupolar magnetic field during the first two cycles.     

Principal Components and Independent Component Analysis of Solar and Space Data

Principal components analysis (PCA) and independent component analysis (ICA) are used to identify global patterns in solar and space data. PCA seeks orthogonal modes of the two-point correlation matrix constructed from a data set. It permits the identification of structures that remain coherent and correlated or that recur throughout a time series. ICA seeks for maximally independent modes and takes into account all order correlations of the data. We apply PCA to the interplanetary magnetic field polarity near 1 AU and to the 3.25R _⊙ source-surface fields in the solar corona. The rotations of the two-sector structures of these systems vary together to high accuracy during the active interval of solar cycle 23. We then use PCA and ICA to hunt for preferred longitudes in northern hemisphere Carrington maps of magnetic fields.     

Modelling the Global Solar Corona: Filament Chirality Observations and Surface Simulations

The hemispheric pattern of solar filaments is considered in the context of the global magnetic field of the solar corona. In recent work Mackay and van Ballegooijen have shown how, for a pair of interacting magnetic bipoles, the observed chirality pattern could be explained by the dominant range of bipole tilt angles and helicity in each hemisphere. This study aims to test this earlier result through a direct comparison between theory and observations, using newly developed simulations of the actual surface and 3D coronal magnetic fields over a 6-month period, on a global scale. We consider two key components: (1) observations of filament chirality for the sample of 255 filaments and (2) our new simulations of the large-scale surface magnetic field. Based on a flux-transport model, these will be used as the lower boundary condition for the future 3D coronal simulations. Our technique differs significantly from those of other authors, where the coronal field is either assumed to be purely potential or has to be reset back to potential every 27 days for the photospheric field to remain accurate. In our case we ensure accuracy by the insertion of newly emerging bipolar active regions, based on observed photospheric synoptic magnetograms. The large-scale surface field is shown to remain accurate over the 6-month period, without any resetting. This new technique will enable future simulations to consider the long-term buildup and transport of helicity and shear in the coronal magnetic field over many months or years.     

Multiresolution Analysis of Active Region Magnetic Structure and its Correlation with the Mount Wilson Classification and Flaring Activity

Two different multiresolution analyses are used to decompose the structure of active-region magnetic flux into concentrations of different size scales. Lines separating these opposite polarity regions of flux at each size scale are found. These lines are used as a mask on a map of the magnetic field gradient to sample the local gradient between opposite polarity regions of given scale sizes. It is shown that the maximum, average, and standard deviation of the magnetic flux gradient for α,β,β γ, and β γ δ active-regions increase in the order listed, and that the order is maintained over all length scales. Since magnetic flux gradient is strongly linked to active-region activity, such as flares, this study demonstrates that, on average, the Mt. Wilson classification encodes the notion of activity over all length scales in the active-region, and not just those length scales at which the strongest flux gradients are found. Further, it is also shown that the average gradients in the field, and the average length-scale at which they occur, also increase in the same order. Finally, there are significant differences in the gradient distribution, between flaring and non-flaring active regions, which are maintained over all length scales. It is also shown that the average gradient content of active-regions that have large flares (GOES class “M” and above) is larger than that for active regions containing flares of all flare sizes; this difference is also maintained at all length scales. All of the reported results are independent of the multiresolution transform used. The implications for the Mt. Wilson classification of active-regions in relation to the multiresolution gradient content and flaring activity are discussed.     

Solar activity I: aspects of magnetic activity

It is now accepted that the solar activity has direct impact on the Earth climate, but is also responsible for the geomagnetic storms. It is thus fundamental to understand the mechanisms responsible for this activity. We present here first some aspects of the solar activity at the different atmospheric layers of the sun: active region at photospheric levels, filaments (prominences) and flares at chromospheric level and CME's at coronal level. A quick sum‐up of the principal characteristics of each is given as well as the key questions still under investigation. In the second part, two principal parameters are presented to describe these features: helicity and topology. Finally, we sum‐up the observational challenges for new solar telescopes.     

A Pair of Conjugate Current Ribbons Coinciding with the Double-ribbon Flare

Using the vector magnetograms observed by SDO (Solar Dynamics Observatory)/HMI (Helioseismic and Magnetic Imager), the current distribution and evolution associated with an X9.3 flare occurred in the active region AR12673 on Sept. 6, 2017 are studied in detail. The results show that there is a pair of electric current ribbons with opposite directions and the magnitude of 0.4 A/m${}^2$, which can be called a pair of conjugate electric current ribbons. This pair of conjugate electric current ribbons exist before, during, and after the flare; their positions are almost coincident with the two bright ribbons of the flare, and their shapes are also extremely similar with them. The light curve of the total electric current intensity on Sept. 6 shows that the electric current intensity enhanced sharply during the strong X9.3 flare eruption, and this phenomenon persisted for several hours. The results of this study strongly support the model of QSL (Quasi-Separatrix Layer) 3D magnetic reconnection.     

与耀斑双带重合的一对共轭电流带

利用SDO (Solar Dynamics Observatory)/HMI (Helioseismic and Magnetic Imager)观测到的矢量磁图,研究了与活动区AR12673上爆发的一个X9.3级耀斑(2017年9月6日)的相关电流分布和演化.结果显示,在该活动区的磁中性线两边存在一对方向相反的电流密度约为0.4 A/m~2的长电流带,可称其为一对共轭电流带.这对共轭电流带在耀斑发生之前、期间以及之后一直存在;并且观测到,该耀斑的两个亮带的位置几乎刚好与两个电流带重叠,它们的形状也极其相似. 9月6日电流总强度演化曲线表明,电流强度在X9.3级强耀斑爆发期间出现快速增加的现象,这种现象持续了几个小时.这一研究结果有力支持了磁准分界面(Quasi-Separatrix Layer, QSL) 3维重联模型.     

A New Method of Identifying 3D Null Points in Solar Vector Magnetic Fields

Employing the Poincare index of isolated null-points in a vector field, we worked out a mathematical method of searching for 3D null-points in coronal magnetic fields. After introducing the relevant differential topology, we test the method by using the analytical model of Brown & Priest. The location of null-point identified by our method coincides precisely with the analytical solution. Finally we apply the method to the 3D coronal magnetic fields reconstructed from an observed MDI magnetogram of a super-active region (NOAA 10488). We find that the 3D null-point seems to be a key element in the magnetic topology associated with flare occurrence.     

Two Early Sunspots Observers: Teodoro de Almeida and José Antonio Alzate

We present the sunspot ideas and observations of the 18th century Portuguese scholar Teodoro de Almeida (1722 – 1804) and Mexican scientist José Antonio Alzate (1737 – 1799). We describe the implications of dating a single sunspot observation performed by Almeida in the early 1760s, during the maximum of cycle number 1. A possible solar cycle peak in 1760 (instead of 1761) is investigated. We present several observations of sunspots obtained by Alzate during 1769 (partially associated with the Venus and Mercury transits) and also on 20 July 1786. We estimate 100±34 as the Group Sunspot Number for this date. These records were unknown and, therefore, not included in the database compiled by Hoyt and Schatten (1998).     

The Magnetic Field of the Solar Corona from Pulsar Observations

We present a novel experiment with the capacity to independently measure both the electron density and the magnetic field of the solar corona. We achieve this through measurement of the excess Faraday rotation resulting from propagation of the polarised emission from a number of pulsars through the magnetic field of the solar corona. This method yields independent measures of the integrated electron density, via dispersion of the pulsed signal and the magnetic field, via the amount of Faraday rotation. In principle this allows the determination of the integrated magnetic field through the solar corona along many lines of sight without any assumptions regarding the electron density distribution. We present a detection of an increase in the rotation measure of the pulsar J1801-2304 of approximately 170 rad m² at an elongation of 0.96° from the centre of the solar disc. This corresponds to a lower limit of the magnetic field strength along this line of sight of >41.8 nT. The lack of precision in the integrated electron density measurement restricts this result to a limit, but application of coronal plasma models can further constrain this to approximately 0.5 μT, along a path passing 2.7 solar radii from the solar limb, which is consistent with predictions obtained using extensions to the source surface models published by the Wilcox Solar Observatory.     

On the interaction of internal gravity waves with a magnetic field – I. Artificial wave forcing

We present results from numerical simulations of the interaction of internal gravity waves (IGW) with a magnetic field. In accordance with the dispersion relation governing IGW in the presence of magnetism and rotation, when the IGW frequency is approximately that of the Alfvén frequency, strong reflection of the wave occurs. Such strong reflection markedly changes the angular momentum transport properties of the waves. In these simple models a strong, time-independent shear layer develops, in contrast to the oscillating shear layer that develops in the purely hydrodynamic case.