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.

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 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.

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.

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 release mechanism. Based on observed vector magnetograms, we have determined the threedimensional （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 extraultraviolet （EUV） wavebands. We found clear evidence of topology eruptions which are referred 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 complexity 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 obscure 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.

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.

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.

Diagnostic Functions of Solar Coronal Magnetic Fields from Radio Observations

In solar physics,it is a big challenge to measure the magnetic fields directly from observations in the upper solar atmosphere,including the chromosphere and corona.Radio observations are regarded as the most feasible approach to diagnose the magnetic field in solar chromosphere and corona.However,because of the complexity and diversity of the emission mechanisms,the previous studies have only presented the implicit diagnostic functions of the magnetic field for specific mechanism from solar radio observations.This work collected and sorted out all methods for diagnosing coronal magnetic field from solar radio observations,which are expressed as a set of explicit diagnostic functions.In particular,this work supplemented some important diagnostic methods missed in other reviews.This set of diagnostic functions can completely cover all regions of the solar chromosphere and corona,including the quiet region,active region and flaring source regions.At the same time,it also includes incoherent radiation such as bremsstrahlung emission of thermal plasma above the quiet region,cyclotron and gyro-synchrotron emissions of magnetized hot plasma and mildly relativistic nonthermal electrons above the active regions,as well as coherently plasma emission around flaring source regions.Using this set of diagnostic functions and the related broadband spectral solar radio imaging observations,we can derive the magnetic fields of almost all regions in the solar atmosphere,which may help us to make full use of the spectral imaging observations of the new generation solar radio telescopes(such as MUSER,EVOSA and the future FASR,etc.) to study the solar activities,and provide a reliable basis for the prediction of disastrous space weather events.

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be so small (β = 10-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magnetic energy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magnetic energy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of the corresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as to whether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope. This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed to be detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.

Structure and evolution of magnetic fields associated with solar eruptions

This paper reviews the studies of solar photospheric magnetic field evo- lution in active regions and its relationship to solar flares. It is divided into two top- ics, the magnetic structure and evolution leading to solar eruptions and rapid changes in the photospheric magnetic field associated with eruptions. For the first topic, we describe the magnetic complexity, new flux emergence, flux cancelation, shear mo- tions, sunspot rotation and magnetic helicity injection, which may all contribute to the storage and buildup of energy that trigger solar eruptions. For the second topic, we concentrate on the observations of rapid and irreversible changes of the photospheric magnetic field associated with flares, and the implication on the restructuring of the three-dimensional magnetic field. In particular, we emphasize the recent advances in observations of the photospheric magnetic field, as state-of-the-art observing facilities （such as Hinode and Solar Dynamics Observatory） have become available. The link- ages between observations, theories and future prospectives in this research area are also discussed.

Analysis of sudden variations in photospheric magnetic fields during a large flare and their influences in the solar atmosphere

The solar active region NOAA 11719 produced a large two-ribbon flare on 2013 April 11. We have investigated sudden variations in the photospheric magnetic fields in this active region during the flare by employing magnetograms obtained in the spectral line Fe I 6173 A acquired by the Helioseismic and Magnetic Imager （HMI） onboard the Solar Dynamics Observatory （SDO） spacecraft. The analysis of the line-of-sight magnetograms from HMI show sudden and persistent magnetic field changes at different locations of the active region before the onset of the flare and during the flare. The vector magnetic field observations available from HMI also show coincident variations in the total magnetic field strength and its inclination angle at these locations. Using the simultaneous Dopplergrams obtained from HMI, we observe perturbations in the photospheric Doppler signals following the sudden changes in the magnetic fields in the aforementioned locations. The power spectrum analysis of these velocity signals shows enhanced acoustic power in these affected locations during the flare as compared to the pre-flare condition. Accompanying these observations, we have also used nearly simultaneous chromospheric observations obtained in the spectral line Ha 6562.8 A by the Global Oscillation Network Group （GONG） to study the evolution of flare- ribbons and intensity oscillations in this active region. The Ha intensity oscillations also show enhanced oscillatory power during the flare in the aforementioned locations. These results indicate that the transient Lorentz force associated with sudden changes in the magnetic fields could drive localized photospheric and chromospheric oscillations, like the flare-induced oscillations in the solar atmosphere.

Long-term evolution of magnetic fields in flaring Active Region NOAA 12673

During the lifetime of AR 12673,its magnetic field evolved drastically and produced numerous large flares.In this study,using full maps of the Sun observed by the Solar Dynamics Observatory and the Solar Terrestrial Relations Observatory,we identified that AR 12673 emerged in decayed AR 12665,which had survived for two solar rotations.Although both ARs emerged at the same location,they possessed different characteristics and different flare productivities.Therefore,it is important to study the long-term magnetic evolution of both ARs to identify the distinguishing characteristics of an AR that can produce large solar flares.We used the Space-weather Helioseismic and Magnetic Imager Active Region Patch data to investigate the evolution of the photospheric magnetic field and other physical properties of the recurring ARs during five Carrington rotations.All these investigated parameters dynamically evolved through a series of solar rotations.We compared the long-term evolution of AR 12665 and AR 12673 to understand the differences in their flare-producing properties.We also studied the relation of the long-term evolution of these ARs with the presence of active longitude.We found that the magnetic flux and complexity of AR12673 developed much faster than those of AR 12665.Our results confirmed that a strong emerging flux that emerged in the pre-existing AR near the active longitude created a very strong and complex AR that produced large flares.

Case studies of EUV cyclones and their associated magnetic fields

EUV cyclones are rotating structures in the solar corona, and they are usually rooted in the underlying rotating network magnetic fields in the photosphere. However, their connection with the surrounding magnetic fields remains unknown. Here we report an observational study of four typical cyclones which are rooted in different kinds of magnetic fields. We use Solar Dynamics Observatory^Atmospheric Imaging Assembly data to investigate the rotation of EUV features in cyclones and Helioseismic and Magnetic Imager data to study the associated magnetic fields. The results show that, （1） an EUV cyclone rooted in a sunspot rotates with the photo- spheric magnetic field; （2） two EUV cyclones in two faculae of an active region are connected to the same sunspot of the active region but rotate oppositely; （3） an EUV cyclone is rooted in a coronal hole with weak open magnetic fields; （4） a pair of con- jugated cyclones is rooted in magnetic fields that have opposite polarity with opposite directions of rotation. The differences in the spatial extent of a cyclone, characteristics of its rotation and underlying fields indicate that cyclones are ubiquitous over the solar atmosphere and that the magnetic structures relevant to the cyclones are more complicated than expected.

Linear Correlations between Peak Frequency of Gyrosynchrotron Spectrum and Photosphere Magnetic Fields

The gyrosynchrotron spectra are computed in a nonuniform magnetic field case, taking into account the self- and gyroresonance absorption. It is found that the peak frequency νp of the gyrosynchrotron spectrum systematically increases with the increasing photosphere magnetic field strength B0 and increasing viewing angle θ. It is also found for the first time that there are good positive linear correlations between νp and B0, and between log νp and log θ, with linear correlation coefficient 0.99 between νp and B0 and 0.95 between log νp and log θ. We apply the correlations to analyze two burst events observed with OVSA and find that the evolution tendencies of the photosphere magnetic field strength B0 estimated from the above expression are comparable with the observational results of SOHO/MDI. We also give a comparison of the diagnostic results of coronal magnetic field strength in both uniform and nonuniform source models.

Some issues in diagnostics of solar chromospheric magnetic fields with the Mg b_2 line

Up to now, exact measurements of chromospheric magnetic fields have not been as successful as those done in the photosphere. We are currently engaging in diagnostics of chromospheric magnetic fields with the Mg b2 line by employing the Multi-Channel Solar Telescope at Huairou Solar Observing Station. Therefore, how to improve accuracy in the measurement is the main issue of our present study. To this end, we first study linear calibration coefficients for longitudinal and transverse components of chromospheric fields, which vary with wavelength, in the case of a weak field assumption. Then the polarization crosstalk introduced by instruments is analyzed in detail with two numerical simulation methods. Comparisons of the po- larization signals between cases with and without correction are presented. The result indicates that polarization accuracy is greatly improved after crosstalk correction.

A Confined Two-peaked Solar Flare Observed by EAST and SDO

The solar flare is one of the most violent explosions,and can disturb the near-Earth space weather.Except for commonly single-peaked solar flares in soft X-ray,some special flares show intriguing a two-peak feature that is deserved much more attentions.Here,we reported a confined two-peaked solar flare and analyzed the associated eruptions using high-quality observations from Educational Adaptive-optics Solar Telescope and Solar Dynamics Observatory.Before the flare,a magnetic flux rope(MFR)formed through partially tether-cutting reconnection between two sheared arches.The flare occurred after the MFR eruption that was confined by the overlying strong field.Interestingly,a small underlying filament immediately erupted,which was possibly destabilized by the flare ribbon.The successive eruptions were confirmed by the analysis of the emission measure and the reconnection fluxes.Therefore,we suggest that the two peaks of the confined solar flare are corresponding to two episodes of magnetic reconnection during the successive eruptions of the MFR and the underlying filament.

ENSO Index Variations and Links with Solar and Volcanic Activity

In this paper, we investigated the Oceanic Niño Index (ONI), for simplicity called in this paper an El Nino Southern Oscillation (ENSO) index in 1950-2023 by applying the wavelet spectral transform and the IBM SPSS correlations analysis. ONI follows the three months’ current measurements of the average temperature of the sea surface in the East-Central tropical part of the Pacific Ocean nearby the international line of the date change over the average sea surface temperature over the past 30 years. The ENSO index is found to have a strong (>87%) correlation with the Global Land-Ocean Temperature (GLOT). The scatter plots of the ENSO-GLOT correlation with the linear and cubic fits have shown that the ENSO index is better fit by the cubic polynomial increasing proportionally to a cubic power of the GLOT variations. The wavelet analysis allowed us to detect the two key periods in the ENSO (ONI) index: 4 - 5 years and 12 years. The smaller period of 4.5 years can be linked to the motion of tectonic plates while the larger period of 12 years is shown to have a noticeable correlation of 25% with frequencies of the underwater (submarine) volcanic eruptions in the areas with ENSO occurrences. Not withholding any local terrestrial factors considered to contribute to the ENSO occurrences, we investigated the possibility of the volcanic eruptions causing ENSO to be also induced by the tidal forces of Jupiter and Sun showing the correlation of the underwater volcanic eruption frequency with the Jupiter-Earth distances to be 12% and with the Sun-Earth distances, induced by the solar inertial motion, in January, when the Earth is turned to the Sun with the southern hemisphere where the ENSO occurs, to become 15%. Hence, the underwater volcanic eruptions induced by tidal forces of Jupiter and Sun can be the essential additional factors imposing this 12 year period of the ENSO (ONI) index variations.

Correlations between the Rotations and Magnetospheres of the Terrestrial Planets and the Sun’s Formation in Our Solar System

Correlations between the rotations of the terrestrial planets in our solar system and the magnetic field of the Sun have been previously noted. These correlations account for the opposite rotation of Venus as a result of the magnetic field of the Sun being dragged across the conducting core of Venus. Currently, the Sun’s magnetic field is not sufficiently strong to account for the proposed correlations. But recently meteorite paleomagnetism measurements have indicated that during the Sun’s formation the magnetic field of the Sun was of sufficient strength to have resulted in the observed correlations. Also, dating back to the Sun’s formation are measurements showing that the Sun’s core rotates four times faster than the Sun’s surface. Both the counter rotation of Venus and the initial period of strong Sun magnetic fields are believed to be relics of the time period when the Sun’s core to surface differential rotation was established. As a part of these correlations, it was hypothesized that for a terrestrial planet to exhibit a magnetosphere, the average density must be ≥5350 ± 50 kg/m3. On this basis, only the Earth and Mercury would have formed initial magnetospheres, while Venus, Mars, and the “Moon” would not have developed magnetospheres. For such correlations to still be present today requires our Sun to have been formed as a sole star and with what might be termed a friendly Jupiter. Otherwise, the observed correlations would have been disrupted over time.

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.