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.     

Photospheric Magnetic Evolution in the WHI Active Regions

Sequences of line-of-sight (LOS) magnetograms recorded by the Michelson Doppler Imager are used to quantitatively characterize photospheric magnetic structure and evolution in three active regions that rotated across the Sun??s disk during the Whole Heliosphere Interval (WHI), in an attempt to relate the photospheric magnetic properties of these active regions to flares and coronal mass ejections (CMEs). Several approaches are used in our analysis, on scales ranging from whole active regions, to magnetic features, to supergranular scales, and, finally, to individual pixels. We calculated several parameterizations of magnetic structure and evolution that have previously been associated with flare and CME activity, including total unsigned magnetic flux, magnetic flux near polarity-inversion lines, amount of canceled flux, the ??proxy Poynting flux,?? and helicity flux. To catalog flare events, we used flare lists derived from both GOES and RHESSI observations. By most such measures, AR 10988 should have been the most flare- and CME-productive active region, and AR 10989 the least. Observations, however, were not consistent with this expectation: ARs 10988 and 10989 produced similar numbers of flares, and AR 10989 also produced a few CMEs. These results highlight present limitations of statistics-based flare and CME forecasting tools that rely upon line-of-sight photospheric magnetic data alone.     

Sunspot Rotations Derived from Magnetic and Velocity Fields Observations

The rotation of sunspot penumbrae has been investigated on the longitudinal magnetic and velocity fields, observed in the photospheric line Fe i λ5253 Å of five lone sunspots. We reconstructed the entire vectors of both fields from their line-of-sight components. All three components of both vectors revealed that the rotation of the sunspots was, in fact, a torsional oscillation. All components of each sunspot had the same rotational period. The penumbrae oscillation periods were distributed in the range from 3.4 days to 7.7 days. The phase of the velocity azimuthal component oscillation was ahead of the phases of all other components of both vectors. If the penumbra plasma density had been equal to the photospheric plasma density (10^?7 g cm^?3) then the oscillation magnetic energy of the components exceeded their kinetic energy approximately by a factor of 10–200. The obtained results led to the conclusion that these oscillations were constrained.     

Evolution of Active and Polar Photospheric Magnetic Fields During the Rise of Cycle 24 Compared to Previous Cycles

The evolution of the photospheric magnetic field during the declining phase and minimum of cycle 23 and the recent rise of cycle 24 are compared with the behavior during previous cycles. We used longitudinal full-disk magnetograms from the NSO??s three magnetographs at Kitt Peak, the Synoptic Optical Long-term Investigations of the Sun (SOLIS) vector spectro-magnetograph (VSM), the spectro-magnetograph and the 512-channel magnetograph instruments, and longitudinal full-disk magnetograms from the Mt. Wilson 150-foot tower. We analyzed 37 years of observations from these two observatories that have been observing daily, weather permitting, since 1974, offering an opportunity to study the evolving relationship between the active region and polar fields in some detail over several solar cycles. It is found that the annual averages of a proxy for the active region poloidal magnetic field strength, the magnetic field strength of the high-latitude poleward streams, and the time derivative of the polar field strength are all well correlated in each hemisphere. The active region net poloidal fields effectively disappeared in both hemispheres around 2004 and the polar fields have not become significantly stronger since this time. These results are based on statistically significant cyclical patterns in the active region fields and are consistent with the Babcock?CLeighton phenomenological model for the solar activity cycle. There was more hemispheric asymmetry in the total and maximum active region flux during late cycle 23 (after around 2004), when the southern hemisphere was more active, and the rise of cycle?24, when the northern hemisphere was more active, than at any other time since 1974. We see evidence that the process of cycle 24 field reversal has begun at both poles.     

Photospheric Magnetic Free Energy Density of Solar Active Regions

We present the photospheric energy density of magnetic fields in two solar active regions (one of them recurrent) inferred from observational vector magnetograms, and compare it with other available differently defined energy parameters of magnetic fields in the photosphere. We analyze the magnetic fields in Active Regions NOAA 6580-6619-6659 and 11158. The quantity \(\frac{1}{4\pi}{\mathbf{B}}_{n}\cdot{\mathbf{B}}_{p}\) is an important energy parameter that reflects the contribution of magnetic shear to the difference between the potential (\(\mathbf{B}_{p}\)) and the non-potential magnetic field (\(\mathbf{B}_{n}\)), and also the contribution to the free magnetic energy near the magnetic neutral lines in the active regions. It is found that the photospheric mean magnetic energy density shows clear changes before the powerful solar flares in Active Region NOAA 11158, which is consistent with the change in magnetic fields in the flaring lower atmosphere.     

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.     

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.     

Correlation Between Solar Flare Productivity and Photospheric Magnetic Field Properties

From a large number of SOHO/MDI longitudinal magnetograms, three physical measures including the maximum horizontal gradient, the length of the neutral line, and the number of singular points are computed. These measures are used to describe photospheric magnetic field properties including nonpotentiality and complexity, which is believed to be closely related to solar flares. Our statistical results demonstrate that solar flare productivity increases with nonpotentiality and complexity. Furthermore, the relationship between the flare productivity and these measures can be well fitted with a sigmoid function. These results can be beneficial to future operational flare forecast models.     

Determination of the Topology Skeleton of Magnetic Fields in a Solar Active Region

Magnetic topology has been a key to the understanding of magnetic energy re-lease mechanism. Based on observed vector magnetograms, we have determined the three-dimensional (3D) topology skeleton of the magnetic fields in the active region NOAA 10720.The skeleton consists of six 3D magnetic nulls and a network of corresponding spines, fans,and null-null lines. For the first time, we have identified a spiral magnetic null in Sun's corona.The magnetic lines of force twisted around the spine of the null, forming a 'magnetic wreath'with excess of free magnetic energy and resembling observed brightening structures at extra-ultraviolet (EUV) wavebands. We found clear evidence of topology eruptions which are re-ferred to as catastrophic changes of topology skeleton associated with a coronal mass ejection(CME) and an explosive X-ray flare. These results shed new lights on the structural complex-ity and its role in explosive magnetic activity. The concept of flux rope has been widely used in modelling explosive magnetic activity, although their observational identity is rather ob-scure or, at least, lacking of necessary details up to date. We suggest that the magnetic wreath associated with the 3D spiral null is likely an important class of the physical entity of flux ropes.     

Automatic Recognition and Characterisation of Supergranular Cells from Photospheric Velocity Fields

We have developed an exceptionally noise-resistant method for accurate and automatic identification of supergranular cell boundaries from velocity measurements. Because of its high noise tolerance the algorithm can produce reliable cell patterns with only very small amounts of smoothing of the source data in comparison to conventional methods. In this paper we describe the method and test it with simulated data. We then apply it to the analysis of velocity fields derived from high-resolution continuum data from MDI (Michelson Doppler Imager) on SOHO. From this, we can identify with high spatial resolution certain basic properties of supergranulation cells, such as their characteristic sizes, the flow speeds within cells, and their dependence on cell areas. The effect of the noise and smoothing on the derived cell boundaries is investigated and quantified by using simulated data. We show in detail the evolution of supergranular cells over their lifetime, including observations of emerging, splitting, and coalescing cells. A key result of our analysis of cell internal velocities is that there is a simple linear relation between cell size and cell internal velocity, rather than the power law usually suggested. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Correlation between Solar Flare Productivity and Photospheric Magnetic Field Properties II. Magnetic Gradient and Magnetic Shear

With 1353 vector magnetograms observed at Huairou Solar Observing Station (HSOS), a statistical analysis is made on the relationship among solar flares, magnetic gradient, and magnetic shear. The results suggest that flare productivity has positive correlations with the gradient and the shear, which can be well fitted by the Boltzmann sigmoidal function. In the vicinity of neutral lines, high gradient and strong shear are roughly coincident in time but barely in position. In addition, flare productivity is more sensitive to the length of neutral lines with strong gradient and shear (L _gs) than independently with strong gradient (L _g) or strong shear (L _s), which means that L _gs can be a better parameter for solar flare forecasting models. Finally, an algorithm to evaluate projection effects on the statistical results is proposed.     

Short-term Forecast of Solar Proton Events With Characteristic Phyiscal Quantities of Photospheric Magnetic Fields

Via the three physical quantities (i.e., the maximal horizontal gradient of longitudinal magnetic field |Δ_hB_z|_m, the length of neutral line with a large gradient L, and the number of isolated singular points η), which are used to represent the characteristics of the complexity and non-potentiality of the photospheric magnetic fields in solar active regions, a model of the shortterm forecast of proton events is built. The effectivity of the short-term forecast of proton events by means of the characteristic physical quantities of magnetic fields is verified. In the nowadays commonly used models of short-term forecast of solar proton events, until present the characteristic physical quantituieas of magnetic fields are not formally taken to be the factors of forecast. Because the solar proton events are low probability events, the physical mechanism of their occurrence is still not well understood. In the models of their prediction, the problems of high rates of false alarm or low rates of right alarm often exist. In this paper the traditional factors used in the existing models of forecast of proton events and the characteristic physical quantities of magnetic fields are combined together. By using the method of neural network, a more effective method of the short-term prediction of proton events is established. With the 1871 sample data in 1997-2001, we have set up Model A with the traditional forecast factors as the input layer, and also Model B with the traditional forecast factors plus the characteristic physical quantities of magnetic fields as the input layer. Via the set of 973 sample data of the years 2002 and 2003, we have carried out a simulative forecast, and found that under the condition that these two models possess the same rate of accuracy in the forecast of proton events, the rate of false alarm of Model B becomes evidently lower. This has further verified the effectiveness of the characteristic physical quantities of magnetic fields in shortterm prediction. Furthermore, this may improve the actual ability of forecast of solar proton events.     

Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields

We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad – Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced “photospheric” and more force-free “chromospheric” vector magnetic field boundary data derived from the model. When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field’s free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though, like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution. On 07/07/2007, the NLFFF team was saddened by the news that Tom Metcalf had died as the result of an accident. We remain grateful for having had the opportunity to benefit from his unwavering dedication to the problems encountered in attempting to understand the Sun’s magnetic field; Tom had completed this paper several months before his death, leading the team through the many steps described above.     

Observations of Unresolved Photospheric Magnetic Fields in Solar Flares Using Fe i and Cr i Lines

The structure of the photospheric magnetic field during solar flares is examined using echelle spectropolarimetric observations. The study is based on several Fe i and Cr i lines observed at locations corresponding to brightest Hα emission during thermal phase of flares. The analysis is performed by comparing magnetic-field values deduced from lines with different magnetic sensitivities, as well as by examining the fine structure of I±V Stokes-profiles’ splitting. It is shown that the field has at least two components, with stronger unresolved flux tubes embedded in weaker ambient field. Based on a two-component magnetic-field model, we compare observed and synthetic line profiles and show that the field strength in small-scale flux tubes is about 2?–?3 kG. Furthermore, we find that the small-scale flux tubes are associated with flare emission, which may have implications for flare phenomenology.     

太阳活动区的磁场观测

我们利用北京天文台太阳磁场望远镜在1983年投入试观测期间取得的资料,对该年6月份的一群黑子的磁场以及耀斑作了综合分析,得到一些结论。以光球纵场为边界条件,计算了常α无力场。根据挤压无力场耀斑模式,我们认为耀斑爆发的能量,来自异极性黑子的相互靠近。磁中性线的扭曲程度,反映了无力场的状态。     

A Comparative Analysis of Photospheric Bright Points in an Active Region and in the Quiet Sun

We present a comparative study of photometric and dynamic properties of photospheric bright points (BPs) observed at the disk centre in the active region (AR) NOAA 10912 and in the quiet Sun. We found that the average concentration of BPs is 54% larger in the AR than in the quiet Sun. We also measure a decrease of the BP concentration and an increase of their size moving away from the AR centre. However, these variations can be ascribed to the variation of the spatial resolution and image quality in the field of view of the AR dataset. We also found that BPs in the quiet Sun are associated with larger downflow motions than those measured within the AR. Finally, from our measurements of contrast and velocity along the line of sight, we deduced that BPs are less bright in high magnetic flux density regions than in quiet regions, due to a lower efficiency of convection in the former regions.