A Multi-Observatory Inter-Comparison of Line-of-Sight Synoptic Solar Magnetograms

The observed photospheric magnetic field is a crucial parameter for understanding a range of fundamental solar and heliospheric phenomena. Synoptic maps, in particular, which are derived from the observed line-of-sight photospheric magnetic field and built up over a period of 27 days, are the main driver for global numerical models of the solar corona and inner heliosphere. Yet, in spite of 60 years of measurements, quantitative estimates remain elusive. In this study, we compare maps from seven solar observatories (Stanford/WSO, NSO/KPVT, NSO/SOLIS, NSO/GONG, SOHO/MDI, UCLA/MWO, and SDO /HMI) to identify consistencies and differences among them. We find that while there is a general qualitative consensus, there are also some significant differences. We compute conversion factors that relate measurements made by one observatory to another using both synoptic map pixel-by-pixel and histogram-equating techniques, and we also estimate the correlation between datasets. For example, Wilcox Solar Observatory (WSO) synoptic maps must be multiplied by a factor of 3?–?4 to match Mount Wilson Observatory (MWO) estimates. Additionally, we find no evidence that the MWO saturation correction factor should be applied to WSO data, as has been done in previous studies. Finally, we explore the relationship between these datasets over more than a solar cycle, demonstrating that, with a few notable exceptions, the conversion factors remain relatively constant. While our study was able to quantitatively describe the relationship between the datasets, it did not uncover any obvious “ground truth.” We offer several suggestions for how this may be addressed in the future.     

Comparison of Line-of-Sight Magnetograms Taken by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager and Solar and Heliospheric Observatory/Michelson Doppler Imager

We compare line-of-sight magnetograms from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) and the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). The line-of-sight magnetic signal inferred from the calibrated MDI data is greater than that derived from the HMI data by a factor of 1.40. This factor varies somewhat with center-to-limb distance. An upper bound to the random noise for the 1′′ resolution HMI 720-second magnetograms is 6.3 Mx?cm^?2, and 10.2 Mx?cm^?2 for the 45-second magnetograms. Virtually no p-mode leakage is seen in the HMI magnetograms, but it is significant in the MDI magnetograms. 12-hour and 24-hour periodicities are detected in strong fields in the HMI magnetograms. The newly calibrated MDI full-disk magnetograms have been corrected for the zero-point offset and underestimation of the flux density. The noise is 26.4 Mx?cm^?2 for the MDI one-minute full-disk magnetograms and 16.2 Mx?cm^?2 for the five-minute full-disk magnetograms observed with four-arcsecond resolution. The variation of the noise over the Sun’s disk found in MDI magnetograms is likely due to the different optical distortions in the left- and right-circular analyzers, which allows the granulation and p-mode to leak in as noise. Saturation sometimes seen in sunspot umbrae in MDI magnetograms is caused by the low intensity and the limitation of the onboard computation. The noise in the HMI and MDI line-of-sight magnetic-field synoptic charts appears to be fairly uniform over the entire map. The noise is 2.3 Mx?cm^?2 for HMI charts and 5.0 Mx?cm^?2 for MDI charts. No evident periodicity is found in the HMI synoptic charts.     

Active Region Photospheric Magnetic Properties Derived from Line-of-Sight and Radial Fields

The effect of using two representations of the normal-to-surface magnetic field to calculate photospheric measures that are related to the active region (AR) potential for flaring is presented. Several AR properties were computed using line-of-sight (\(B_{\mathrm{los}}\)) and spherical-radial (\(B_{r}\)) magnetograms from the Space-weather HMI Active Region Patch (SHARP) products of the Solar Dynamics Observatory, characterizing the presence and features of magnetic polarity inversion lines, fractality, and magnetic connectivity of the AR photospheric field. The data analyzed correspond to \({\approx\,}4{,}000\) AR observations, achieved by randomly selecting 25% of days between September 2012 and May 2016 for analysis at 6-hr cadence. Results from this statistical study include: i) the \(B_{r}\) component results in a slight upwards shift of property values in a manner consistent with a field-strength underestimation by the \(B_{\mathrm{los}}\) component; ii) using the \(B_{r}\) component results in significantly lower inter-property correlation in one-third of the cases, implying more independent information as regards the state of the AR photospheric magnetic field; iii) flaring rates for each property vary between the field components in a manner consistent with the differences in property-value ranges resulting from the components; iv) flaring rates generally increase for higher values of properties, except the Fourier spectral power index that has flare rates peaking around a value of \(5/3\). These findings indicate that there may be advantages in using \(B_{r}\) rather than \(B_{\mathrm{los}}\) in calculating flare-related AR magnetic properties, especially for regions located far from central meridian.     

Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×10¹⁶ – 10¹⁹ Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×10¹⁶ Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.     

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.     

Solar Magnetic Carpet III: Coronal Modelling of Synthetic Magnetograms

This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. (Solar Phys. 272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5?–?0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.     

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.     

Principal Component Analysis of the Solar Magnetic Field I: The Axisymmetric Field at the Photosphere

A principal component analysis, or proper orthogonal decomposition, of the axisymmetric magnetic field at the photosphere is carried out to find an optimal representation of the observed solar cycle. The 22-year periodic field requires just two modes. NSO Kitt Peak synoptic maps for Carrington rotations 1664–2007 were reduced by taking both the mean and the median field over longitude to produce two sequences of functions of sine latitude spanning 25.7 years. The lowest modes of each are determined by the polar fields. The mean field is most efficient at representing the periodic field, but the median field is more efficient at representing the evolution of the diffuse field patterns.     

基于支持向量机的太阳磁场活动区极性反转线位置的探测

太阳磁场的极性反转线(Polarity Inversion Line, PIL)是研究太阳活动、分析太阳磁场结构演变和预测太阳耀斑最重要的日面特征之一.磁场极性反转的位置是太阳耀斑和暗条可能出现的位置."先进天基太阳天文台(ASO-S)"是中国首颗空间太阳专用观测卫星,其搭载的"全日面矢量磁像仪(Full-Disk Vector Magnetograph, FMG)"主要任务是探测高空间、高时间分辨率的全日面矢量磁场.为了提高观测数据使用效率、快速监测太阳活动水平、提高太阳耀斑与日冕物质抛射的预报水平以及更好地服务于FMG数据处理与分析系统,采用了图像自动识别与处理技术,更加精确有效地检测极性反转线.从支持向量机(Support Vector Machine, SVM)的模型出发,将极性反转线位置的探测问题转化为一个模式识别中的二分类问题,提出了一种基于支持向量机的极性反转线检测算法,自动探测与识别太阳动力学天文台(Solar Dynamics Observatory, SDO)日震和磁成像仪(Helioseismic and Magnetic Imager, HMI)磁图的极性反转线位置.与现有算法的对比结果表明,此算法可以精确直观地检测太阳活动区的极性反转线.     

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.     

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.     

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.     

Differential Rotation of the Solar Corona from Magnetic Field Data

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75? with a 5? step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.     

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.     

Calculations of Coronal Magnetic Field Parallel and Perpendicular to Line-of-Sight in Microwave Bursts

Based on the approximations of the non-thermal gyro-synchrotron radiation used by G.A. Dulk, and K.A. Marsh, Astrophs. J. 259, 350, 1982, the author analyses calculations of the propagation angle and coronal magnetic field self-consistently with brightness temperature, spectral index, frequency, turnover frequency, and polarization degree in solar microwave bursts. Hence, the coronal magnetic fields parallel and perpendicular to the line-of-sight in the sources of microwave bursts are calculated theoretically, and discussed in an event observed by the Nobeyama Radio Polarimeters (NoRP).     

Constraints on the Solar Internal Magnetic Field from a Buoyancy Driven Solar Dynamo

We report here results from a dynamo model developed on the lines of the Babcock-Leighton idea that the poloidal field is generated at the surface of the Sun from the decay of active regions. In this model magnetic buoyancy is handled with a realistic recipe – wherein toroidal flux is made to erupt from the overshoot layer wherever it exceeds a specified critical field B _c (10⁵ G). The erupted toroidal field is then acted upon by the α-effect near the surface to give rise to the poloidal field. In this paper we study the effect of buoyancy on the dynamo generated magnetic fields. Specifically, we show that the mechanism of buoyant eruption and the subsequent depletion of the toroidal field inside the overshoot layer, is capable of constraining the magnitude and distribution of the magnetic field there. We also believe that a critical study of this mechanism may give us new information regarding the solar interior and end with an example, where we propose a method for estimating an upper limit of the difusivity within the overshoot layer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Determination of the Coronal and Interplanetary Magnetic Field Strength and Radial Profiles from Large-Scale Photospheric Magnetic Fields

We propose a new model for the magnetic field at different distances from the Sun during different phases of the solar cycle. The model depends on the observed large-scale non-polar (\({\pm}\, 55^{\circ }\)) photospheric magnetic field and on the magnetic field measured at polar regions from \(55^{\circ }\) N to \(90^{\circ }\) N and from \(55^{\circ }\) S to \(90^{\circ }\) S, which are the visible manifestations of cyclic changes in the toroidal and poloidal components of the global magnetic field of the Sun. The modeled magnetic field is determined as the superposition of the non-polar and polar photospheric magnetic field and considers cycle variations. The agreement between the model predictions and magnetic fields derived from direct in situ measurements at different distances from the Sun, obtained with different methods and at different solar activity phases, is quite satisfactory. From a comparison of the magnetic fields as observed and calculated from the model at 1 AU, we conclude that the model magnetic field variations adequately explain the main features of the interplanetary magnetic field (IMF) radial, \(B_{\mathrm{x}}\), component cycle evolution at Earth’s orbit. The modeled magnetic field averaged over a Carrington rotation (CR) correlates with the IMF \(B_{\mathrm{x}}\) component also averaged over a CR at Earth’s orbit with a coefficient of 0.691, while for seven CR-averaged data, the correlation reaches 0.81. The radial profiles of the modeled magnetic field are compared with those of already existing models. In contrast to existing models, ours provides realistic magnetic-field radial distributions over a wide range of heliospheric distances at different cycle phases, taking into account the cycle variations of the solar toroidal and poloidal magnetic fields. The model is a good approximation of the cycle behavior of the magnetic field in the heliosphere. In addition, the decrease in the non-polar and polar photospheric magnetic fields is shown. Furthermore, the magnetic field during solar cycle maxima and minima decreased from Cycle 21 to Cycle 24. This implies that both the toroidal and poloidal components, and therefore the solar global magnetic field, decreased from Cycle 21 to Cycle 24.     

Magnetic Field Strengths and Structures from Radio Observations of Solar Active Regions

Radio observations of some active regions (ARs) obtained with the Nobeyama radioheliograph at λ=1.76cm are used for estimating the magnetic field strength in the upper chromosphere, based on thermal bremsstrahlung. The results are compared with the magnetic field strength in the photosphere from observations with the Solar Magnetic Field Telescope (SMFT) at Huairou Solar Observing Station of Beijing Astronomical Observatory. The difference in the magnetic field strength between the two layers seems reasonable. The solar radio maps of active regions obtained with the Nobeyama radioheliograph, both in total intensity (I-map) and in circular polarizations (V-map), are compared with the optical magnetograms obtained with the SMFT. The comparison between the radio map in circular polarization and the longitudinal photospheric magnetogram of a plage region suggest that the radio map in circular polarization is a kind of magnetogram of the upper chromosphere. The comparison of the radio map in total intensity with the photospheric vector magnetogram of an AR shows that the radio map in total intensity gives indications of magnetic loops in the corona, thus we have a method of defining the coronal magnetic structure from the radio I-maps at λ=1.76 cm. Analysing the I-maps, we identified three components: (a) a compact bright source; (b) a narrow elongated structure connecting two main magnetic islands of opposite polarities (observed in both the optical and radio magnetograms); (c) a wide, diffuse, weak component that corresponds to a wide structure in the solar active region which shows in most cases an S or a reversed S contour, which is probably due to the differential rotation of the Sun. The last two components suggest coronal loops on different spatial scales above the neutral line of the longitudinal photospheric magnetic field.