Evaluating (and Improving) Estimates of the Solar Radial Magnetic Field Component from Line-of-Sight Magnetograms

Although for many solar physics problems the desirable or meaningful boundary is the radial component of the magnetic field \(B_{\mathrm {r}}\), the most readily available measurement is the component of the magnetic field along the line of sight to the observer, \(B_{\mathrm {los}}\). As this component is only equal to the radial component where the viewing angle is exactly zero, some approximation is required to estimate \(B_{\mathrm {r}}\) at all other observed locations. In this study, a common approximation known as the “\(\mu\)-correction”, which assumes all photospheric field to be radial, is compared to a method that invokes computing a potential field that matches the observed \(B_{\mathrm {los}}\), from which the potential field radial component, \(B_{\mathrm {r}}^{\mathrm {pot}}\) is recovered. We demonstrate that in regions that are truly dominated by a radially oriented field at the resolution of the data employed, the \(\mu\)-correction performs acceptably if not better than the potential-field approach. However, it is also shown that for any solar structure that includes horizontal fields, i.e. active regions, the potential-field method better recovers both the strength of the radial field and the location of magnetic neutral line.     

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.     

Multifractal Analysis Of Solar Magnetograms

As solar observational techniques improve, fine small-scale structures observed on the solar surface become more pronounced. Complex filigree structures of solar granulation, sunspots, photospheric magnetic and velocity fields cannot be described adequately by a single parameter (e.g., filling factor, fractal dimension, or power-law index). Methods which incorporate parameters that are a function of scale (multiscale methods) to describe the complexity of a field under study, should be involved. The multifractal approach offers such a possibility. In this paper the scaling of structure functions is proposed in order to analyze multifractality. Application of the approach to SOHO/MDI high-resolution magnetograms of active regions show that the structure functions differ for all active regions studied. For a given active region, the functions may maintain their shape during several hours; however, they can significantly change during a day. Flare-quiet active regions tend to possess a lower degree of multifractality than flaring active regions do. The increase in multifractality is a signal that a magnetic structure is driven to a critical state, thus gaining tangential discontinuities of various length scales.     

Studies of Solar Helicity Using Vector Magnetograms

Observations of photospheric magnetic fields made with vector magnetographs have been used recently to study helicity on the Sun. In this paper we indicate what can and cannot be derived from vector magnetograms, and point out some potential problems in these data that could affect the calculations of `helicity'. Among these problems are magnetic saturation, Faraday rotation, low spectral resolution, and the method of resolving the ambiguity in the azimuth.     

Automated Boundary-extraction And Region-growing Techniques Applied To Solar Magnetograms

We present an automated approach to active region extraction from full-disc MDI longitudinal magnetograms. This uses a region-growing technique in conjunction with boundary-extraction to define a number of enclosed contours as belonging to separate regions of magnetic significance on the solar disc. This provides an objective definition of active regions and areas of plage on the Sun. A number of parameters relating to the flare potential of each region are discussed.     

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.     

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.     

Projection Effects on Physical Parameters Obtained from Solar Vector Magnetograms

1 INTRODUCTION Magnetic field plays an important role in solar activity. The stressing and subsequent partialrelaxation of magnetic fields in the active regions are generally accepted to be the energy sourceof solar flares. To quantitatively study the extent of stressed magnetic field as distinct from itspotential field, Hagyard et al. (1984) defined a magnetic shear angle膖he azimuth differencebetween the observed transverse magnetic field vector and the computed potential field vectorth…     

Solar Magnetograms at 12 μm Using the Celeste Spectrograph

We present the first solar vector magnetogram constructed from measurements of infra-red Mg I 12.32-μm line spectra. Observations were made at the McMath-Pierce Telescope using the Celeste spectrometer/polarimeter. Zeeman-split Stokes line spectra were fitted with Seares profiles to obtain the magnetic field parameters. Maps of absolute field strength, line-of-sight angle, and azimuth are presented. Analysis shows that the variation in field strength within a spatial resolution element, 2 arcseconds, is greatest in the sunspot penumbra and that this is most likely caused by vertical field strength gradients, rather than horizontal image smearing. Widths of the Zeeman-split σ components, assuming a formation layer thickness of 200 km, indicate that vertical field strength gradients can be as large as 6.5 G/km in a penumbra.     

On the Measurements of Full-Disk Longitudinal Magnetograms at Huairou Solar Observing Station

Reliable information on the distribution of magnetic fields across the whole surface of the Sun is urgently needed to predict conditions in the solar corona, in the interplanetary medium, and in the near-Earth space (space weather). Several space- and ground-based solar instruments currently provide full-disk magnetograms. However, these measurements sometimes differ very significantly, which makes a cross-calibration of different datasets and searching for the reasons for such differences a very crucial task. Here, we analyze the Huairou Solar Observing Station (HSOS) Solar Magnetism and Activity Telescope (SMAT) full-disk line-of-sight magnetograms in comparison with magnetograms taken at the Solar Dynamic Observatory/Helioseismic and Magnetic Imager (SDO/HMI) and Solar Telescope for Operative Predictions (STOP) instruments. We show systematic differences between original SMAT magnetograms and those of other telescopes. The differences are caused by some SMAT instrumental problems, which we investigate. We suggest methods for compensating for these effects that have improved the quality of SMAT magnetograms. These methods will enable us to use SMAT measurements to solve many solar physics problems that are related to studying global solar magnetism and space weather.     

Uncertainties in Solar Synoptic Magnetic Flux Maps

Magnetic flux synoptic charts are critical for a reliable modeling of the corona and heliosphere. Until now, however, these charts were provided without uncertainty estimates. The uncertainties are due to instrumental noise in the measurements and to the spatial variance of the magnetic flux distribution that contributes to each bin in the synoptic chart. We describe here a simple method to compute synoptic magnetic flux maps and their corresponding magnetic flux spatial variance charts that can be used to estimate the uncertainty in the results of coronal models. We have tested this approach by computing a potential-field source-surface model of the coronal field for a Monte Carlo simulation of Carrington synoptic magnetic flux maps generated from the variance map. We show that these uncertainties affect both the locations of source-surface neutral lines and the distributions of coronal holes in the models.     

Investigation of Quasi-periodic Solar Oscillations in Sunspots Based on SOHO/MDI Magnetograms

In this work we study quasi-periodic solar oscillations in sunspots, based on the variation of the amplitude of the magnetic field strength and the variation of the sunspot area. We investigate long-period oscillations between three minutes and ten hours. The magnetic field synoptic maps were obtained from the SOHO/MDI. Wavelet (Morlet), global wavelet spectrum (GWS) and fast Fourier transform (FFT) methods are used in the periodicity analysis at the 95?% significance level. Additionally, the quiet Sun area (QSA) signal and an instrumental effect are discussed. We find several oscillation periods in the sunspots above the 95?% significance level: 3??C?5, 10??C?23, 220??C?240, 340 and 470 minutes, and we also find common oscillation periods (10??C?23 minutes) between the sunspot area variation and that of the magnetic field strength. We discuss possible mechanisms for the obtained results, based on the existing models for sunspot oscillations.     

Oscillations in Solar Faculae. III. The Phase Relations Between Chromospheric and Photospheric Line-of-Sight Velocities

An analysis of line-of-sight velocity oscillation in nine solar faculae was undertaken with the aim of studying phase relations between chromospheric (He?i 10830?Å line) and photospheric (Si?i 10827 Å line) five-minute oscillations. We found that the time lag of the chromospheric signal relative to photospheric one varies from ?12 to 100 seconds and is about 50 seconds on average. We assume that the small observed lag can have three possible explanations: i) convergence of formation levels of He?i 10830?Å and Si?i 10827?Å in faculae; ii) significant increase of five-minute oscillation propagation velocity above faculae; iii) simultaneous presence of standing and travelling waves.     

Synoptic Solar Cycle 24 in Corona,Chromosphere, and Photosphere Seen by the Solar Dynamics Observatory

The Solar Dynamics Observatory provides multiwavelength imagery from extreme ultraviolet (EUV) to visible light as well as magnetic-field measurements. These data enable us to study the nature of solar activity in different regions of the Sun, from the interior to the corona. For solar-cycle studies, synoptic maps provide a useful way to represent global activity and evolution by extracting a central meridian band from sequences of full-disk images over a full solar Carrington rotation (≈?27.3 days). We present the global evolution during Solar Cycle 24 from 20 May 2010 to 31 August 2013 (CR?2097?–?CR?2140), using synoptic maps constructed from full-disk, line-of-sight magnetic-field imagery and EUV imagery (171 Å, 193 Å, 211 Å, 304 Å, and 335 Å). The synoptic maps have a resolution of 0.1 degree in longitude and steps of 0.001 in sine of latitude. We studied the axisymmetric and non-axisymmetric structures of solar activity using these synoptic maps. To visualize the axisymmetric development of Cycle 24, we generated time–latitude (also called butterfly) images of the solar cycle in all of the wavelengths, by averaging each synoptic map over all longitudes, thus compressing it to a single vertical strip, and then assembling these strips in time order. From these time–latitude images we observe that during the ascending phase of Cycle 24 there is a very good relationship between the integrated magnetic flux and the EUV intensity inside the zone of sunspot activities. We observe a North–South asymmetry of the EUV intensity in high-latitudes. The North–South asymmetry of the emerging magnetic flux developed and resulted in a consequential asymmetry in the timing of the polar magnetic-field reversals.     

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.     

Comparison of Ground-Based and Space-Based Longitudinal Magnetograms

We compare photospheric line-of-sight magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) instrument with observations from the 150-foot Solar Tower at Mt. Wilson Observatory (MWO), the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO), and the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO). We find very good agreement between VSM and the other data sources for both disk-averaged flux densities and pixel-by-pixel measurements. We show that the VSM mean flux density time series is of consistently high signal-to-noise ratio with no significant zero offsets. We discuss in detail some of the factors ?C spatial resolution, flux dependence, and position on the solar disk ?C affecting the determination of scaling between VSM and SOHO/MDI or SDO/HMI magnetograms. The VSM flux densities agree well with spatially smoothed data from MDI and HMI, although the scaling factors show a clear dependence on flux density. The factor to convert VSM to HMI increases with increasing flux density (from ??1 to ??1.5). The nonlinearity is smaller for the VSM vs. SOHO/MDI scaling factor (from ??1 to ??1.2).     

A Note on Saturation Seen in the MDI/SOHO Magnetograms

A type of saturation is sometimes seen in sunspot umbrae in MDI/SOHO magnetograms. In this paper, we present the underlying cause of such saturation. By using a set of MDI circular polarization filtergrams taken during an MDI line profile campaign observation, we derive the MDI magnetograms using two different approaches: the on-board data processing and the ground data processing, respectively. The algorithms for processing the data are the same, but the former is limited by a 15-bit lookup table. Saturation is clearly seen in the magnetogram from the on-board processing simulation, which is comparable to an observed MDI magnetogram taken one and a half hours before the campaign data. We analyze the saturated pixels and examine the on-board numerical calculation method. We conclude that very low intensity in sunspot umbrae leads to a very low depth of the spectral line that becomes problematic when limited to the 15-bit on-board numerical treatment. This 15-bit on-board treatment of the values is the reason for the saturation seen in sunspot umbrae in the MDI magnetogram. Although it is possible for a different type of saturation to occur when the combination of a strong magnetic field and high velocity moves the spectral line out of the effective sampling range, this saturation is not observed.     

Line-of-Sight Velocity Fluctuations of a Quiescent Prominence

Series of H spectra and slit-jaw H filtergrams of a quiescent prominence taken at Pic du Midi Observatory on 7 November 1977 are studied. The observations have been digitized by means of an automated Joyce Loebl microdensitometer. The image processing of the H filtergrams reveals an internal structure of the prominence consisting of several arches. Series of high-resolution H spectra obtained with the slit position located on a selected part of one of the prominence arches have been chosen for Doppler-shift analysis. The obtained time series of the line-of-sight velocity reveal large velocity variations near the periphery of the arch and a strong dependence of the velocity (in sign and magnitude) on the position along the slit. The prominence arch shows also cyclic displacements along the line-of-sight direction implying Alfvén string-mode oscillations.