Interpretation of the coronal magnetic field configuration of the Sun

The origin of the heliospheric magnetic flux on the Sun,and hence the origin of the solar wind,is a topic of hot debate.While the prevailing view is that the solar wind originates from outside the coronal streamer helmets,there also exists the suggestion that the open magnetic field spans a far wider region.Without the definitive measurement of the coronal magnetic field,it is difficult to unambiguously resolve the conflict between the two scenarios.We present two 2-dimensional, Alfvénic-turbulence-based models of the solar corona and solar wind,one with and the other without a closed magnetic field region in the inner corona.The purpose of the latter model is to test whether it is possible to realize a picture suggested by polarimetric measurements of the corona using the Fe XⅢ 10747 line,where open magnetic field lines seem to penetrate the streamer base.The boundary conditions at the coronal base are able to account for important observational constraints,especially those on the magnetic flux distribution.Interestingly,the two models provide similar polarized brightness（pB）distributions in the field of view（FOV）of SOHO/LASCO C2 and C3 coronagraphs.In particular,a dome-shaped feature is present in the C2 FOV even for the model without a closed magnetic field.Moreover,both models fit the Ulysses data scaled to 1 AU equally well.We suggest that：1）The pB observations cannot be safely taken as a proxy for the magnetic field topology,as is often implicitly assumed.2）The Ulysses measurements,especially the one showing a nearly uniform distribution with heliocentric latitude of the radial magnetic field,do not rule out the ubiquity of open magnetic fields on the Sun.

Data-driven Simulations of Magnetic Field Evolution in Active Region 11429:Magneto-frictional Method Using PENCIL CODE

Coronal magnetic fields evolve quasi-statically over long timescales and dynamically over short timescales.As of now there exist no regular measurements of coronal magnetic fields,and therefore generating the coronal magnetic field evolution using observations of the magnetic field at the photosphere is a fundamental requirement to understanding the origin of transient phenomena from solar active regions(ARs).Using the magneto-friction(MF)approach,we aim to simulate the coronal field evolution in the solar AR 11429.The MF method is implemented in the open source PENCIL CODE along with a driver module to drive the initial field with different boundary conditions prescribed from observed vector magnetic fields at the photosphere.In order to work with vector potential and the observations,we prescribe three types of bottom boundary drivers with varying free-magnetic energy.The MF simulation reproduces the magnetic structure,which better matches the sigmoidal morphology exhibited by Atmospheric Imaging Assembly(AIA)images at the pre-eruptive time.We found that the already sheared field further driven by the sheared magnetic field will maintain and further build the highly sheared coronal magnetic configuration,as seen in AR 11429.Data-driven MF simulation is a viable tool to generate the coronal magnetic field evolution,capturing the formation of the twisted flux rope and its eruption.

Magnetic non-potentiality on the quiet Sun and the filigree

From the observed vector magnetic fields by the Solar Optical Telescope/ Spectro-Polarimeter aboard the satellite Hinode, we have examined whether or not the quiet Sun magnetic fields are non-potential, and how the G-band filigrees and Ca II network bright points （NBPs） are associated with the magnetic non-potentiality. A sizable quiet region in the disk center is selected for this study. The new findings by the study are as follows. （1） The magnetic fields of the quiet region are obviously non-potential. The region-average shear angle is 40°, the average vertical current is 0.016A m^-2, and the average free magnetic energy density, 2.7× 10^2erg cm^-3. The magnitude of these non-potential quantities is comparable to that in solar active regions. （2） There are overall correlations among current helicity, free magnetic energy and longitudinal fields. The magnetic non-potentiality is mostly concentrated in the close vicinity of network elements which have stronger longitudinal fields. （3） The filigrees and NBPs are magnetically characterized by strong longitudinal fields, large electric helicity, and high free energy density. Because the selected region is away from any enhanced network, these new results can generally be applied to the quiet Sun. The findings imply that stronger network elements play a role in high magnetic non-potentiality in heating the solar atmosphere and in conducting the solar wind.

The Effect of External Magnetic Field on Electron Scale Kelvin–Helmholtz Instability

We use particle-in-cell,fully electromagnetic,plasma kinetic simulation to study the effect of external magnetic field on electron scale Kelvin–Helmholtz instability(ESKHI).The results are applicable to collisionless plasmas when,e.g.,solar wind interacts with planetary magnetospheres or a magnetic field is generated in AGN jets.We find that as in the case of magnetohydrodynamic(MHD)KHI,in the kinetic regime,the presence of an external magnetic field reduces the growth rate of the instability.In the MHD case,there is a known threshold magnetic field for KHI stabilization,while for ESKHI this is to be analytically determined.Without a kinetic analytical expression,we use several numerical simulation runs to establish an empirical dependence of ESKHI growth rate,Γ(B_(0))ω_(pe),on the strength of the applied external magnetic field.We find the best fit is hyperbolic,Γ(B_(0))ω_(pe)=Γ_(0)ω_(pe)/(A+BB_(0)),where Γ_(0) is the ESKHI growth rate without an external magnetic field and B_(0)=B_(0)/B_(MHD)is the ratio of external and two-fluid MHD stability threshold magnetic field,derived here.An analytical theory to back up this growth rate dependence on the external magnetic field is needed.The results suggest that in astrophysical settings where a strong magnetic field pre-exists,the generation of an additional magnetic field by the ESKHI is suppressed,which implies that nature provides a“safety valve”—natural protection not to“over-generate”magnetic field by the ESKHI mechanism.Remarkably,we find that our two-fluid MHD threshold magnetic field is the same(up to a factor √γ_(0))as the DC saturation magnetic field,previously predicted by fully kinetic theory.

A Statistical Study of Magnetic Flux Emergence in Solar Active Regions Prior to Strongest Flares

Using the data on magnetic field maps and continuum intensity for Solar Cycles 23 and 24,we explored 100 active regions(ARs)that produced M5.0 or stronger flares.We focus on the presence/absence of the emergence of magnetic flux in these ARs 2-3 days before the strong flare onset.We found that 29 ARs in the sample emerged monotonically amidst quiet-Sun.A major emergence of a new magnetic flux within a pre-existing AR yielding the formation of a complex flare-productive configuration was observed in another 24 cases.For 30 ARs,an insignificant(in terms of the total magnetic flux of pre-existing AR)emergence of a new magnetic flux within the pre-existing magnetic configuration was observed;for some of them the emergence resulted in a formation of a configuration with a small δ-sunspot;11 out of 100 ARs exhibited no signatures of magnetic flux emergence during the entire interval of observation.In six cases the emergence was in progress when the AR appeared on the Eastern limb,so that the classification and timing of emergence were not possible.We conclude that the recent flux emergence is not a necessary and/or sufficient condition for strong flaring of an AR.The flux emergence rate of flare-productive ARs analyzed here was compared with that of flare-quiet ARs analyzed in our previous studies.We revealed that the flare-productive ARs tend to display faster emergence than the flare-quiet ones do.

A study of the relation between intensity oscillations and magnetic field parameters in a sunspot: Hinode observations

We present properties of intensity oscillations of a sunspot in the photo- sphere and chromosphere using G band and Ca u H filtergrams from Hinode. Intensity power maps as function of magnetic field strength and frequency reveal reduction of power in the G band with an increase in photospheric magnetic field strength at all frequencies. In Ca II H, however, stronger fields exhibit more power at high frequen- cies, particularly in the 4.5-8.0 mHz band. Power distributions in different locations of the active region show that the oscillations in Ca II H exhibit more power compared to that of the G band. We also relate the power in intensity oscillations with differ- ent components of the photospheric vector magnetic field using near simultaneous spectro-polarimetric observations of the sunspot from the Hinode spectropolarime- ter. The photospheric umbral power is strongly anti-correlated with the magnetic field strength and its line-of-sight component but there is a good correlation with the trans- verse component. A reversal of this trend is observed in the chromosphere except at low frequencies （V≤ 1.5 mHz）. The power in sunspot penumbrae is anti-correlated with the magnetic field parameters at all frequencies （1.0 ≤ v ≤ 8.0 mHz） in both the photosphere and chromosphere, except that the chromospheric power shows a strong correlation in the frequency range 3-3.5 mHz.

Physics-informed Neural Network for Force-free Magnetic Field Extrapolation

In this paper,we propose a physics-informed neural network extrapolation method that leverages machine learning techniques to reconstruct coronal magnetic fields.We enhance the classical neural network structure by introducing the concept of a quasi-output layer to address the challenge of preserving physical constraints during the neural network extrapolation process.Furthermore,we employ second-order optimization methods for training the neural network,which are more efficient compared to the first-order optimization methods commonly used in classical machine learning.Our approach is evaluated on the widely recognized semi-analytical model proposed by Low and Lou.The results demonstrate that the deep learning method achieves high accuracy in reconstructing the semianalytical model across multiple evaluation metrics.In addition,we validate the effectiveness of our method on the observed magnetogram of active region.

Lossless Compression Method for the Magnetic and Helioseismic Imager(MHI)Payload

The Solar Polar-orbit Observatory(SPO),proposed by Chinese scientists,is designed to observe the solar polar regions in an unprecedented way with a spacecraft traveling in a large solar inclination angle and a small ellipticity.However,one of the most significant challenges lies in ultra-long-distance data transmission,particularly for the Magnetic and Helioseismic Imager(MHI),which is the most important payload and generates the largest volume of data in SPO.In this paper,we propose a tailored lossless data compression method based on the measurement mode and characteristics of MHI data.The background out of the solar disk is removed to decrease the pixel number of an image under compression.Multiple predictive coding methods are combined to eliminate the redundancy utilizing the correlation(space,spectrum,and polarization)in data set,improving the compression ratio.Experimental results demonstrate that our method achieves an average compression ratio of 3.67.The compression time is also less than the general observation period.The method exhibits strong feasibility and can be easily adapted to MHI.

Sunspot rotation and magnetic transients associated with flares in NOAAAR 11429

We analyze sunspot rotation and magnetic transients in NOAA AR 11429 during two X-class(X5.4 and X1.3)flares using data from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory.A large leading sunspot with positive magnetic polarity rotated counterclockwise.As expected,the rotation was significantly affected by the two flares.Magnetic transients induced by the flares were clearly evident in the sunspots with negative polarity.They were moving across the sunspots with speed of order 3-7 km s-1.Furthermore,the trend of magnetic flux evolution in these sunspots exhibited changes associated with the flares.These results may shed light on understanding the evolution of sunspots.

A logistic model for magnetic energy storage in solar active regions

Previous statistical analyses of a large number of SOHO/MDI full disk longitudinal magnetograms provided a result that demonstrated how responses of solar flares to photospheric magnetic properties can be fitted with sigmoid functions. A logistic model reveals that these fitted sigmoid functions might be related to the free energy storage process in solar active regions. Although this suggested model is rather simple, the free energy level of active regions can be estimated and the probability of a solar flare with importance over a threshold can be forecast within a given time window.

Interaction between granulation and small-scale magnetic flux observed by Hinode

With the polarimetric observations obtained by the Spectro-Polarimeter on board Hinode, we study the relationship between granular development and magnetic field evolution in the quiet Sun. Six typical cases are displayed to exhibit interaction between granules and magnetic elements, and we have obtained the following results. （1） A granule develops centrosymmetrically when no magnetic flux emerges within the granular cell. （2） A granule develops and splits noncentrosymmetrically while flux emerges at an outer part of the granular cell. （3） Magnetic flux emergence in a cluster of mixed polarities is detected at the position of a granule as soon as the granule breaks up. （4） A dipole emerges accompanied by the development of a granule, and the two elements of the dipole are rooted in the adjacent intergranular lanes and face each other across the granule. Advected by the horizontal granular motion, the positive element of the dipole then cancels with the pre-existing negative flux. （5） Flux cancellation also takes place between a positive element, which is advected by granular flow, and its surrounding negative flux. （6） While magnetic flux cancellation takes place in a granular cell, the granule shrinks and then disappears. （7） Horizontal magnetic fields are enhanced at the places where dipoles emerge and where opposite polarities cancel each other, but only the horizontal fields between the dipolar elements point in an orderly way from the positive elements to the negative ones. Our results reveal that granules and small-scale magnetic fluxes influence each other. Granular flow advects magnetic flux, and magnetic flux evolution suppresses granular development. There exist extremely large Doppler blue-shifts at the site of one canceling magnetic element. This phenomenon may be caused by the upward flow produced by magnetic reconnection below the photosphere.

A comparison between magnetic shear and flare shear in a well-observed M-class flare

We give an extensive multi-wavelength analysis of an eruptive M1.0/1N class solar flare, which occurred in the active region NOAA 10044 on 2002 July 26. Our emphasis is on the relationship between magnetic shear and flare shear. Flare shear is defined as the angle formed between the line connecting the centroids of the two ribbons of the flare and the line perpendicular to the magnetic neutral line. The magnetic shear is computed from vector magnetograms observed at Big Bear Solar Observatory （BBSO）, while the flare shear is computed from Transition Region and Coronal Explorer （TRACE） 1700A images. By a detailed comparison, we find that; 1） The magnetic shear and the flare shear of this event are basically consistent, as judged from the directions of the transverse magnetic field and the line connecting the two ribbons＇ centroids. 2） During the period of the enhancement of magnetic shear, flare shear had a fast increase followed by a fluctuated decrease. 3） When the magnetic shear stopped its enhancement, the fluctuated decreasing behavior of the flare shear became very smooth. 4） Hard X-ray （HXR） spikes are well correlated with the unshearing peaks on the time profile of the rate of change of the flare shear. We give a discussion of the above phenomena.

Distribution of Helical Properties of Solar Magnetic Fields

We summarize studies of helical properties of solar magnetic fields such as current helicity and twist of magnetic fields in solar active regions (ARs), that are observational tracers of the alpha-effect in the solar convective zone (SCZ). Information on their spatial distribution is obtained by analysis of systematic magnetographic observations of active regions taken at Huairou Solar Observing Station of National Astronomical Observatories of Chinese Academy of Sciences. The main property is that the tracers of the alpha-effect are antisymmetric about the solar equator. Identifying longitudinal migration of active regions with their individual rotation rates and taking into account the internal differential rotation law within the SCZ known from helioseismology, we deduce the distribution of the effect over depth. We have found evidence that the alpha-effect changes its value and sign near the bottom of the SCZ, and this is in accord with the theoretical studies and numerical simulations. We discuss other regularities which can be revealed by further analysis such as possible dependence on longitude, time, and magnetic field strength, etc.

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

Employing the Poincar6 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 nullpoint 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.

Magnetic flux ropes in the solar corona: structure and evolution toward eruption

Magnetic flux ropes are characterized by coherently twisted magnetic field lines,which are ubiquitous in magnetized plasmas.As the core structure of various eruptive phenomena in the solar atmosphere,flux ropes hold the key to understanding the physical mechanisms of solar eruptions,which impact the heliosphere and planetary atmospheres.The strongest disturbances in the Earth’s space environments are often associated with large-scale flux ropes from the Sun colliding with the Earth’s magnetosphere,leading to adverse,sometimes catastrophic,space-weather effects.However,it remains elusive as to how a flux rope forms and evolves toward eruption,and how it is structured and embedded in the ambient field.The present paper addresses these important questions by reviewing current understandings of coronal flux ropes from an observer’s perspective,with an emphasis on their structures and nascent evolution toward solar eruptions,as achieved by combining observations of both remote sensing and in-situ detection with modeling and simulation.This paper highlights an initiation mechanism for coronal mass ejections(CMEs)in which plasmoids in current sheets coalesce into a’seed’flux rope whose subsequent evolution into a CME is consistent with the standard model,thereby bridging the gap between microscale and macroscale dynamics.

Coronal Flux Rope Equilibria in Closed Magnetic Fields

Using a 2.5-dimensional ideal MHD model in Cartesian coordinates, weinvestigate the equilibrium properties of coronal magnetic flux ropes in background magnetic fieldsthat are completely closed. The background fields are produced by a dipole, a quadrupole, and anoctapole, respectively, located below the photosphere at the same depth. A magnetic flux rope isthen launched from below the photosphere, and its magnetic properties, i.e., the annular magneticflux Φ_p and the axial magnetic flux Φ_z, are controlled by a single emergence parameter. Thewhole system eventually evolves into equilibrium, and the resultant flux rope is characterized bythree geometrical parameters: the height of the rope axis, the half-width of the rope, and thelength of the vertical current sheet below the rope. It is found that the geometrical parametersincrease monotonically and continuously with increasing Φ_p and Φ_z: no catastrophe occurs.Moreover, there exists a steep segment in the profiles of the geometrical parameters versus eitherΦ_p or Φ_z, and the faster the background field decays with height, the larger both the gradientand the growth amplitude within the steep segment will be.

Flares and magnetic non-potentiality of NOAA AR 11158

Magnetic non-potentiality is important for understanding flares and other solar activities in active regions （ARs）. Five non-potential parameters, i.e. electric current, current helicity, source field, photospheric free energy, and angular shear, are calculated to quantify the non-potentiality of NOAA AR 11158. Benefitting from the high spatial resolution, high cadence and continuous temporal coverage of vector mag- netograms from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory, both the long-term evolution of the AR and the rapid change during flares are studied. We confirm that, compared with the magnetic flux, the magnetic non-potentiality has a closer connection with the flare, and the emerging flux regions are important for understanding the magnetic non-potentiality and flares. The main re- suits are as follows. （1） The vortex in the source field directly displays the deflection of the horizontal magnetic field. The deflection corresponds to the fast rotating sunspot with a time delay, which suggests that the sunspot rotation leads to an increase in the non-potentiality. （2） Two areas that have evident changes in the azimuth of the vector magnetic field are found near the magnetic polarity inversion line. The change rates of the azimuth are about 1.3° h-1 and 3.6° h-1, respectively. （3） Rapid and prominent increases are found in the variation of helicity during four flares in the regions where their initial brightening occurs. The recovery of the increases takes 3-4 h for the two biggest flares （X2.2 and M6.6）, but only takes about 2 h for the two other smaller flares （M2.2 and M1.6）.

The calculation of coronal magnetic field and density of nonthermal electrons in the 2003 October 27 microwave burst

Based on Dulk and Marsh＇s approximate theory about nonthermal gyrosyn- chrotron radiation, one simple impulsive microwave burst with a loop-like structure is selected for radio diagnostics of the coronal magnetic field and column density of non- thermal electrons, which are calculated from the brightness temperature, polarization degree, and spectral index, as well as the turnover frequency, observed by using the Nobeyama Radioheliograph and the Nobeyama Radio Polarimeters, respectively. Very strong variations （up to one or two orders of magnitude） of the calculated transverse and longitudinal magnetic fields with respect to the line-of-sight, as well as the cal- culated electron column density, appear in the looptop and footpoint sources during the burst. The absolute magnitude and varied range of the transverse magnetic field are evidently larger than those of the longitudinal magnetic field. The time evolution of the transverse magnetic field is always anti-correlated with that of the longitudi- nal magnetic field, but positively correlated with that of the electron column density. These results strongly support the idea that quantifying the energy released in a flare depends on a reconstruction of the coronal magnetic field, especially for the trans- verse magnetic field, and they are basically consistent with the recent theoretical and observational studies on the photospheric magnetic field in solar flares.

Formation of Solar Delta Active Regions:Twist and Writhe of Magnetic Ropes

We analyze the process of formation of delta configuration in some well-known super active regions based on photospheric vector magnetogram observations. It is found that the magnetic field in the initial developing stage of some delta active regions shows a potential-like configuration in the solar atmosphere, the magnetic shear develops mainly near the magnetic neutral line with magnetic islands of opposite polarities, and the large-scale photospheric twisted field forming gradually later. Some results are obtained: (1) The analysis of magnetic writhe of whole active regions cannot be limited in the strong field of sunspots, because the contribution of the fraction of decayed magnetic field is non-negligible. (2) The magnetic model of kink magnetic ropes, supposed to be generated in the subatmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and not entirely consistent with the relationship with magnetic shear in some delta active regions. (3) The proposition is that the large-scale delta active regions are formed from contribution by small-scale non-potential magnetic flux bundles generated in the subatmosphere.

On the Relation Between Coronal Green Line Brightness and Magnetic Fields Intensity

Two-dimensional(2 D) solar coronal magnetogram is difficult to be measured directly until now.From the previous knowledge,a general relation has been noticed that the brighter green-line brightness for corona,the higher coronal magnetic field intensity may correspond to.To try to further reveal the relationship between coronal green line brightness and magnetic field intensity,we use the 2 D coronal images observed by Yunnan Observatories Greenline Imaging System(YOGIS) of the 10 cm Lijiang coronagraph and the coronal magnetic field maps calculated from the current-free extrapolations with the photospheric magnetograms taken by Helioseismic and Magnetic Imager(HMI) on board the Solar Dynamics Observatory(SDO) spacecraft.In our analysis,we identified the coronal loop structures and construct two-dimensional maps of the corresponding magnetic field intensity in the plane of the sky(POS) above the limb.We derive the correlation coefficients between the coronal brightness and the magnetic field intensity for different heights of coronal layers.We further use a linear combination of a Gaussian and a quadratic profile to fit the correlation coefficients distribution,finding a largest correlation coefficient of 0.82 near 1.1 R(solar radii) where is almost the top of the closed loop system.For the small closed loop system identified,the correlation coefficient distributions crossing and covering the loop are calculated.We also investigate the correlation with extended heliocentric latitude zones and long period of one whole Carrington Rotation,finding again that the maximum correlation coefficient occurs at the same height.It is the first time for us to find that the correlation coefficients are high(all are larger than 0.8) at the loop-tops and showing poor correlation coefficients with some fluctuations near the feet of the coronal loops.Our findings indicate that,for the heating of the low-latitude closed loops,both DC(dissipation of currents) and AC(dissipation of Alfvén and magnetosonic waves) mechanisms should act simultaneously on the whole closed loop system while the DC mechanisms dominate in the loop-top regions.Therefore,in the distributions of the correlation coefficients with different heights of coronal layers,for both large-and small-scale latitude ranges,the coefficients can reach their maximum values at the same coronal height of 1.1 R,which may indicate the particular importance of the height of closed loops for studying the coupling of the local emission mechanism and the coronal magnetic fields,which maybe helpful for studying the origin of the low-speed solar wind.