Topological and statistical properties of nonlinear force-free fields

We use our semi-analytic solution of the nonlinear force-free field equation to construct three-dimensional magnetic fields that are applicable to the solar corona and study their statistical properties for estimating the degree of braiding exhibited by these fields. We present a new formula for calculating the winding number and compare it with the formula for the crossing number. The comparison is shown for a toy model of two helices and for realistic cases of nonlinear force-free fields; conceptually the formulae are nearly the same but the resulting distributions calculated for a given topology can be different. We also calculate linkages, which are useful topological quantities that are independent measures of the contribution of magnetic braiding to the total free energy and relative helicity of the field. Finally, we derive new analytical bounds for the free energy and relative helicity for the field configurations in terms of the linking number. These bounds will be of utility in estimating the braided energy available for nano-flares or for eruptions.     

Modeling the (upper) solar atmosphere including the magnetic field

The atmosphere of the Sun is highly structured and dynamic in nature. From the photosphere and chromosphere into the transition region and the corona plasma-β changes from above to below one, i.e., while in the lower atmosphere the energy density of the plasma dominates, in the upper atmosphere the magnetic field plays the governing role – one might speak of a “magnetic transition”. Therefore the dynamics of the overshooting convection in the photosphere, the granulation, is shuffling the magnetic field around in the photosphere. This leads not only to a (re-)structuring of the magnetic field in the upper atmosphere, but induces also the dynamic reaction of the coronal plasma, e.g., due to reconnection events. Therefore the (complex) structure and the interaction of various magnetic patches is crucial to understand the structure, dynamics and heating of coronal plasma as well as its acceleration into the solar wind.

The present article will emphasize the need for three-dimensional modeling accounting for the complexity of the solar atmosphere to understand these processes. Some advances on 3D modeling of the upper solar atmosphere in magnetically closed as well as open regions will be presented together with diagnostic tools to compare these models to observations. This highlights the recent success of these models which in many respects closely match the observations.     

The relationship between inductive electric field and flares

We observationally deduce the inductive electric field in the photosphere for the first time from the horizontal velocities computed by local correlation tracking (LCT) technique and the vector magnetic fields derived from vector magnetograms. We study the relationship between E and powerful flares (X-class) of four active regions (ARs): NOAA 10720, 10486, 9077 and 8100. It is found that the kernels of flares are roughly located near the inversion lines where maxima of E are observed. Our results show that E relates to the accumulation of non-potentiality in the photosphere and the transportation of non-potentiality from the photosphere to the corona.     

Asymmetric precipitation in a coronal loop as explanation of a singular observed spectrum

Almost 10 years of solar submillimeter observations have shown new aspects of solar activity, such as the presence of rapid solar spikes associated with the launch of coronal mass ejections and an increasing submillimeter spectral component in flares. We analyse the singular microwave–submillimeter spectrum of an M class solar flare on 20 December, 2002. Flux density observations measured by Sun patrol telescopes and the Solar Submillimeter Telescope are used to build the radio spectrum, which is fitted using Ramaty’s code. At submillimeter frequencies the spectrum shows a component different from the microwave classical burst. The fitting is achieved proposing two homogeneous sources of emission. This theoretical fitting is in agreement with differential precipitation through a magnetically asymmetric loop or set of loops. From a coronal magnetic field model we infer an asymmetric magnetic structure at the flare location. The model proposed to quantify the differential precipitation rates due to the asymmetry results in a total precipitation ratio Q₂/Q₁≈10⁴–10⁵, where Q₁(Q₂) represents the total precipitation in the loop foot with the high (low) magnetic field intensity. This ratio agrees with the electron total number ratio of the two sources proposed to fit the radio spectrum.     

太阳宁静区色球磁场观测

利用中国科学院北京天文台怀柔太阳磁场望远镜,对日面中心宁静区光球和色球磁场进行了长时间的积分观测。通过对光球、色球以及色球不同层次的长时间积分的观测发现,网络磁元从光球到色球扩展不大,并且部分内网络磁元升到了色球。这些结果对描述太阳磁场的两大模型提出了挑战。      

Magnetic connectivity and solar energetic proton event intensity profiles at deka-MeV energy

We present an analysis of the time-intensity profiles of 25 solar energetic proton events at 18.2 MeV, modelled by fitting an analytical function form (a modified Weibull function) to the observed intensities. Additionally relying on previous work that characterized the magnetic connectivity between the event-related solar flare and the observer in these events with three angular parameters, we investigate the fit function parameters, the connectivity parameters, and the iron-to-carbon ratio of the events for dependencies and correlations. We find that the fit parameter controlling the basic shape of the profile (parameter a) is not clearly dependent on the connectivity parameters or the Fe/C ratio, suggesting that the profile shapes of neither well and weakly connected nor generally “impulsive” and “gradual” events differ systematically during the early stages of the event at 1 AU. In contrast, the time scaling of the fit function (parameter b) is at least moderately correlated with both the magnetic connectivity parameters and the Fe/C ratio, in that well-connected and iron-rich events are typically shorter in relative duration than weakly connected and nominal-abundance events; intensity rise times display a similar correlation with the connectivity parameters. We interpret the former result as following from the combined effect of various transport processes acting on the particles in interplanetary space, while the latter is essentially consistent with established knowledge regarding the observed dependence of the time-intensity profile shapes of solar energetic particle events on their magnetic connectivity and heavy ion abundances. The desirability of modelling the particle transport effects in detail and extending the analysis to cover higher energies is indicated.     

Quasi-biennial oscillations in the cross-correlation of properties of macrospicules

Jets, whatever small (e.g. spicules) or large (e.g. macrospicules) their size, may play a key role in momentum and energy transport from photosphere to chromosphere and at least to the low corona. Here, we investigate the properties of abundant, large-scale dynamic jets observable in the solar atmosphere: the macrospicules (MS). These jets are observationally more distinct phenomena than their little, and perhaps more ubiquitous, cousins, the spicules. Investigation of long-term variation of the properties of macrospicules may help to a better understanding of their underlying physics of generation and role in coronal heating. Taking advantage of the high temporal and spatial resolution of the Solar Dynamics Observatory, a new dataset, with several hundreds of macrospicules, was constructed encompassing a period of observations over six years. Here, we analyse the measured properties and relations between these properties of macrospicules as function of time during the observed time interval. We found that cross-correlations of several of these macrospicule properties display a strong oscillatory pattern. Next, wavelet analysis is used to provide more detailed information about the temporal behaviour of the various properties of MS. For coronal hole macrospicules, a significant peak is found at around 2-year period. This peak also exists partially or is shifted to longer period, in the case of quiet Sun macrospicules. These observed findings may be rooted in the underlying mechanism generating the solar magnetic field, i.e. the global solar dynamo.     

A MHD-turbulence model for solar corona

The disposition of energy in the solar corona has always been a problem of great interest. It remains an open question how the low temperature photosphere supports the occurence of solar extreme phenomena. In this work, a turbulent heating mechanism for the solar corona through the framework of reduced magnetohydrodynamics (RMHD) is proposed. Two-dimensional incompressible long time simulations of the average energy disposition have been carried out with the aim to reveal the characteristics of the long time statistical behavior of a two-dimensional cross-section of a coronal loop and the importance of the photospheric time scales in the understanding of the underlying mechanisms. It was found that for a slow, shear type photospheric driving the magnetic field in the loop self-organizes at large scales via an inverse MHD cascade. The system undergoes three distinct evolutionary phases. The initial forcing conditions are quickly “forgotten” giving way to an inverse cascade accompanied with and ending up to electric current dissipation. Scaling laws are being proposed in order to quantify the nonlinearity of the system response which seems to become more impulsive for decreasing resistivity. It is also shown that few, if any, qualitative changes in the above results occur by increasing spatial resolution.     

Spectral analysis of 3D MHD models of coronal structures

We study extreme-ultraviolet emission line spectra derived from three-dimensional magnetohydrodynamic models of structures in the corona. In order to investigate the effects of increased magnetic activity at photospheric levels in a numerical experiment, a much higher magnetic flux density is applied at the photosphere as compared to the Sun. Thus, we can expect our results to highlight the differences between the Sun and more active, but still solar-like stars. We discuss signatures seen in extreme-ultraviolet emission lines synthesized from these models and compare them to observed signatures in the spatial distribution and temporal evolution of Doppler shifts in lines formed in the transition region and corona. This is of major interest to test the quality of the underlying magnetohydrodynamic model to heat the corona, i.e. currents in the corona driven by photospheric motions (flux braiding).     

暗条模型中暗条电流纵向分量的考虑

用暗条电流模型中矩形电流回路来研究NOAA131活动区暗条,结果得到暗条上升时弯曲成"U"形态,跟观测结果不符.因此本文推知:考虑暗条电流的纵向分量时一种椭圆形回路似乎比矩形回路更接近于暗条实际.      

Observational study of magnetic chirality of solar active regions

We present the evolution of magnetic field and relationship with the magnetic (current) helicity in solar active regions from a series of photospheric vector magnetograms obtained at Huairou Solar Observing Station near Beijing, and also longitudinal magnetograms by MDI of SOHO, white light and 171 Å images by TRACE and soft X-ray images by Yohkoh.The conclusions in the analysis of the formation process of complex and delta magnetic configuration in some super active regions are the following: (1) The magnetic shear and gradient provide the non-potentiality of the magnetic field of active regions reflecting the existence of electric current. (2) Some of large-scale delta active regions could be due to the emergence of highly sheared non-potential magnetic flux bundles from the subatmosphere with amount of magnetic helicity, in addition to the emergence of twisted magnetic ropes. (3) We also present some results on the study of the magnetic (current) helicity in solar active regions.     

Multi-scale reconnections in a complex CME

A series of three flares of GOES class M, M and C, and a CME were observed on 20 January 2004 occurring in close succession in NOAA 10540. Types II, III, and N radio bursts were associated. We use the combined observations from TRACE, EIT, Hα images from Kwasan Observatory, MDI magnetograms, GOES, and radio observations from Culgoora and Wind/ WAVES to understand the complex development of this event. We reach three main conclusions. First, we link the first two impulsive flares to tether-cutting reconnections and the launch of the CME. This complex observation shows that impulsive quadrupolar flares can be eruptive. Second, we relate the last of the flares, an LDE, to the relaxation phase following forced reconnections between the erupting flux rope and neighbouring magnetic field lines, when reconnection reverses and restores some of the pre-eruption magnetic connectivities. Finally, we show that reconnection with the magnetic structure of a previous CME launched about 8 h earlier injects electrons into open field lines having a local dip and apex (located at about six solar radii height). This is observed as an N-burst at decametre radio wavelengths. The dipped shape of these field lines is due to large-scale magnetic reconnection between expanding magnetic loops and open field lines of a neighbouring streamer. This particular situation explains why this is the first N-burst ever observed at long radio wavelengths.     

How far are we from a ‘Standard Model’ of the solar dynamo?

Over the last few years, dynamo theorists seem to be converging on a basic scenario as to how the solar dynamo operates. The strong toroidal component of the magnetic field is produced in the tachocline, from where it rises due to magnetic buoyancy to produce active regions at the solar surface. The decay of tilted bipolar active regions at the surface gives rise to the poloidal component, which is first advected poleward by the meridional circulation and then taken below the surface to the tachocline where it can be stretched to produce the toroidal component. The mathematical formulation of this basic model, however, involves the specification of some parameters which are still uncertain. We review these remaining uncertainties which have resulted in disagreements amongst various research groups and have made it impossible to still arrive at something that can be called a standard model of the solar dynamo.     

Solar atmosphere wave dynamics generated by solar global oscillating eigenmodes

The solar atmosphere exhibits a diverse range of wave phenomena, where one of the earliest discovered was the five-minute global acoustic oscillation, also referred to as the p-mode. The analysis of wave propagation in the solar atmosphere may be used as a diagnostic tool to estimate accurately the physical characteristics of the Sun’s atmospheric layers.In this paper, we investigate the dynamics and upward propagation of waves which are generated by the solar global eigenmodes. We report on a series of hydrodynamic simulations of a realistically stratified model of the solar atmosphere representing its lower region from the photosphere to low corona. With the objective of modelling atmospheric perturbations, propagating from the photosphere into the chromosphere, transition region and low corona, generated by the photospheric global oscillations the simulations use photospheric drivers mimicking the solar p-modes. The drivers are spatially structured harmonics across the computational box parallel to the solar surface. The drivers perturb the atmosphere at 0.5?Mm above the bottom boundary of the model and are placed coincident with the location of the temperature minimum. A combination of the VALIIIC and McWhirter solar atmospheres are used as the background equilibrium model.We report how synthetic photospheric oscillations may manifest in a magnetic field free model of the quiet Sun. To carry out the simulations, we employed the magnetohydrodynamics code, SMAUG (Sheffield MHD Accelerated Using GPUs).Our results show that the amount of energy propagating into the solar atmosphere is consistent with a model of solar global oscillations described by Taroyan and Erdélyi (2008) using the Klein-Gordon equation. The computed results indicate a power law which is compared to observations reported by Ireland et al. (2015) using data from the Solar Dynamics Observatory/Atmospheric Imaging Assembly.     

1984年2月18日耀斑后环速度场的分析

本文研究了耀斑后环内物质在太阳重力、磁压力梯度和气体压力梯度联合作用下的下落运动,并在非等温状态及定常假定下计算了环内物质分布。计算结果表明:在环的中上部,下落运动可当作太阳重力作用下的自由下落运动;在环的底部,环内物质密度和磁场强度对物质下落运动影响较显着。      

太阳质子耀斑的一个统计性质

本文研究太阳质子耀斑相对于太阳光球大尺度平均磁场中性线的分布, 给出一个新得到的质子耀斑的统计性质。研究太阳质子事件及其源耀斑的统计性质, 是太阳物理和空间物理学的重要前沿课题。从太阳活动预报及地球空间环境预报研究的角度看, 一个重要的问题是质子耀斑在      

Source investigation of impulsive He-rich particle events

We have investigated the source characteristic and coronal magnetic field structure of six impulsive solar energetic particle (SEP) events selected from Wang et al. [Wang, Y.-M., Pick, M., Mason, G.M. Coronal holes, jets, and the origin of ³He-rich particle events. ApJ 639, 495, 2006] and Pick et al. [Pick, M., Mason, G.M., Wang, Y.-M., Tan, C., Wang, L. Solar source regions for ³He-rich solar energetic particle events identified using imaging radio, optical, and energetic particle observations. ApJ 648, 1247, 2006]. Some results are obtained: first, 2 events are associated with wide (≈100°) CMEs (hereafter wide CME events), another 4 events are associated with narrow (?40°) CMEs (hereafter narrow CME events); second, the coronal magnetic field configuration of narrow CME events appear more simple than that of the wide CME events; third, the photospheric magnetic field evolutions of all these events show new emergence of fluxes, while one case also shows magnetic flux cancellation; fourth, the EUV jets usually occurred very close to the footpoint of the magnetic field loop, while meter type III bursts occurred near or at the top of the loop and higher than EUV jets. Furthermore, the heights of type III bursts are estimated from the result of the coronal magnetic field extrapolations.     

Analysis of a long-duration AR throughout five solar rotations: Magnetic properties and ejective events

Coronal mass ejections (CMEs), which are among the most magnificent solar eruptions, are a major driver of space weather and can thus affect diverse human technologies. Different processes have been proposed to explain the initiation and release of CMEs from solar active regions (ARs), without reaching consensus on which is the predominant scenario, and thus rendering impossible to accurately predict when a CME is going to erupt from a given AR. To investigate AR magnetic properties that favor CMEs production, we employ multi-spacecraft data to analyze a long duration AR (NOAA 11089, 11100, 11106, 11112 and 11121) throughout its complete lifetime, spanning five Carrington rotations from July to November 2010. We use data from the Solar Dynamics Observatory to study the evolution of the AR magnetic properties during the five near-side passages, and a proxy to follow the magnetic flux changes when no magnetograms are available, i.e. during far-side transits. The ejectivity is studied by characterizing the angular widths, speeds and masses of 108 CMEs that we associated to the AR, when examining a 124-day period. Such an ejectivity tracking was possible thanks to the multi-viewpoint images provided by the Solar-Terrestrial Relations Observatory and Solar and Heliospheric Observatory in a quasi-quadrature configuration. We also inspected the X-ray flares registered by the GOES satellite and found 162 to be associated to the AR under study. Given the substantial number of ejections studied, we use a statistical approach instead of a single-event analysis. We found three well defined periods of very high CMEs activity and two periods with no mass ejections that are preceded or accompanied by characteristic changes in the AR magnetic flux, free magnetic energy and/or presence of electric currents. Our large sample of CMEs and long term study of a single AR, provide further evidence relating AR magnetic activity to CME and Flare production.     

A solar wind driven model of geosynchronous plasma moments

We describe a tabular specification model of the density and temperature of ions and electrons at geosynchronous orbit as a function of magnetic local time and solar wind parameters. This model can be used to provide boundary conditions for numerical ring current models. Unlike previous specification models of geosynchronous plasma moments, this model is parameterized by upstream solar wind conditions. We find that solar wind parameters are a better predictor of geosynchronous ion density than magnetospheric indices, and as upstream parameters they are often more appropriate as model inputs since they causally precede the model outputs. Of the upstream parameters that were tested, the best predictors of geosynchronous conditions were the solar wind flow pressure and the magnitude and Z-component of the interplanetary magnetic field.     

Bayesian coronal seismology

In contrast to the situation in a laboratory, the study of the solar atmosphere has to be pursued without direct access to the physical conditions of interest. Information is therefore incomplete and uncertain and inference methods need to be employed to diagnose the physical conditions and processes. One of such methods, solar atmospheric seismology, makes use of observed and theoretically predicted properties of waves to infer plasma and magnetic field properties. A recent development in solar atmospheric seismology consists in the use of inversion and model comparison methods based on Bayesian analysis. In this paper, the philosophy and methodology of Bayesian analysis are first explained. Then, we provide an account of what has been achieved so far from the application of these techniques to solar atmospheric seismology and a prospect of possible future extensions.