Mode selection mechanism and magnetic diffusivity in a non-axisymmetric solar dynamo model

The generation of solar non-axisymmetric magnetic fields is studied based on a linear α²–Ω dynamo model in a rotating spherical frame. The model consists of a solar-like differential rotation, a magnetic diffusivity varied with depth, and three types of α-effects with different locations, i.e. the tachocline, the whole convective zone and the sub-surface. Some comparisons of the critical α-values of axisymmetric (m = 0) and longitude-dependent modes (m = 1,2,3) are presented to show the roles of the magnetic diffusivity in the problem of modes selection. With the changing of diffusivity intensity for the given solar differential rotation system, the dominant mode possibly changes likewise and the stronger the diffusivity is, the easier the non-axisymmetric modes are excited. The influence of the diffusivity and differential rotation on the configurations of the dominant modes are also presented.     

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.     

Model of a fluxtube with a twisted magnetic field in the stratified solar atmosphere

We build a single vertical straight magnetic fluxtube spanning the solar photosphere and the transition region which does not expand with height. We assume that the fluxtube containing twisted magnetic fields is in magnetohydrostatic equilibrium within a realistic stratified atmosphere subject to solar gravity. Incorporating specific forms of current density and gas pressure in the Grad–Shafranov equation, we solve the magnetic flux function, and find it to be separable with a Coulomb wave function in radial direction while the vertical part of the solution decreases exponentially. We employ improved fluxtube boundary conditions and take a realistic ambient external pressure for the photosphere to transition region, to derive a family of solutions for reasonable values of the fluxtube radius and magnetic field strength at the base of the axis that are the free parameters in our model. We find that our model estimates are consistent with the magnetic field strength and the radii of Magnetic bright points (MBPs) as estimated from observations. We also derive thermodynamic quantities inside the fluxtube.     

Power-law spectra of energetic electrons in solar flares from the maximum entropy and dimensional considerations

The maximum entropy formalism and dimensional analysis are used to derive a power-law spectrum of accelerated electrons in impulsive solar flares, where the particles can contain a significant fraction of the total flare energy. Entropy considerations are used to derive a power-law spectrum for a particle distribution characterised by its order of magnitude of energy. The derivation extends an earlier one-dimensional argument to the case of an isotropic three-dimensional particle distribution. Dimensional arguments employ the idea that the spectrum should reflect a balance between the processes of energy input into the corona and energy dissipation in solar flares. The governing parameters are suggested on theoretical grounds and shown to be consistent with solar flare observations. The flare electron flux, differential in the non-relativistic electron kinetic energy E, is predicted to scale as $E^{-3}$. This scaling is in agreement with RHESSI measurements of the hard X-ray flux that is generated by deka-keV electrons, accelerated in intense solar flares.     

Kuafu and the studies of CME initiation

We first briefly review the current trend in the studies of coronal mass ejections (CMEs), then summarize some recent efforts in understanding the CME initiation. Emphasis has been put on the studies of Earth-directed CMEs whose associated surface activity and large scale magnetic source have been well identified. The data analysis by combining the MDI full disc magnetograms, vector magnetograms of active regions, EUV waves and dimmings, non-thermal radio sources, and the SOHO LASCO observations has shed new light in understanding the CME magnetism. However, the current studies seem to invoke new observations in a few aspects: (1) The observations which enable us to trace CMEs from the earliest associated surface activity to its initial acceleration and key development in the low corona in the height of 1–3 R; (2) The imaging spectroscopic observations which can be used to diagnose the early plasma outflow and the line-of-sight velocity in understanding the kinematics of CMEs; (3) The accurate timing from primary magnetic energy release, manifested by chromospheric activity, non-thermal radio bursts, and EUV, X-ray and γ-ray emissions, to the CME initiation, early acceleration and propagation, and the consequences in the interplanetary space and magnetosphere. The Kuafu Mission will meet the basic requirement for the new observations in CME initiation studies and serve as a monitor of space weather of the Sun–Earth system.     

Variations of the solar acoustic high-degree mode frequencies over solar cycle 23

Using full-disk observations obtained with the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) spacecraft, we present variations of the solar acoustic mode frequencies caused by the solar activity cycle. High-degree (100 < ? < 900) solar acoustic modes were analyzed using global helioseismology analysis techniques over most of solar cycle 23. We followed the methodology described in details in [Korzennik, S.G., Rabello-Soares, M.C., Schou, J. On the determination of Michelson Doppler Imager high-degree mode frequencies. ApJ 602, 481–515, 2004] to infer unbiased estimates of high-degree mode parameters ([see also Rabello-Soares, M.C., Korzennik, S.G., Schou, J. High-degree mode frequencies: changes with solar cycle. ESA SP-624, 2006]). We have removed most of the known instrumental and observational effects that affect specifically high-degree modes. We show that the high-degree changes are in good agreement with the medium-degree results, except for years when the instrument was highly defocused. We analyzed and discuss the effect of defocusing on high-degree estimation. Our results for high-degree modes confirm that the frequency shift scaled by the relative mode inertia is a function of frequency and it is independent of degree.     

“Oblique” Bernstein modes in solar preflare plasma: Generation of second harmonics

Process of second harmonics generation due to development of corresponding instability has been investigated for pure electron weakly oblique Bernstein mode. This mode was supposed to be modified by taking into account the influence of pair Coulomb collisions and weak large-scale electric field in flare loop. Investigated area was located near the loop foot-point in the “lower–middle” chromosphere of active region. It has been shown, that for the Fontenla–Avrett–Loeser model of solar atmosphere the investigated process of second harmonics generation starts at the extremely low threshold values of subdreicer electric field, well before the beginning of “preheating” phase of flare process.     

Non-stationarity and cross-correlation effects in the MHD solar activity

The analysis of turbulent processes in sunspots and pores which are self-organizing long-lived magnetic structures is a complicated and not yet solved problem. The present work focuses on studying such magneto-hydrodynamic (MHD) formations on the basis of flicker-noise spectroscopy using a new method of multi-parametric analysis. The non-stationarity and cross-correlation effects taking place in solar activity dynamics are considered. The calculated maximum values of non-stationarity factor may become precursors of significant restructuring in solar magnetic activity. The introduced cross-correlation functions enable us to judge synchronization effects between the signals of various solar activity indicators registered simultaneously.     

Tilts and polarity separation in the sunspot groups and active regions at the ascending and descending phases of the cycle 23

The Solar Feature Catalogues for sunspots and active regions measured with SOHO/MDI instrument and Ca II K3 spectroheliograph of the Paris-Meudon Observatory are analyzed with the automated classification technique for sunspot groups and active region polarities. We report the first classification results for daily variations of tilt angles (normal and trigonometric ones) in sunspot groups (SG) and active (AR) regions in the cycle 23. The average normal tilts are presented for every year at the ascending and descending phases of the cycle 23 which are similar to those deduced by other authors for the cycles 19–22. The normal tilts of both the sunspot groups and active regions are shown to increase in the ascending phase and a decrease in the descending phase. Similar to SG and AR areas, the trigonometric tilts are shown to have the noticeable North–South asymmetry with the Southern hemisphere dominant in the selected ascending and descending periods. The normal tilt variations with latitude follow Joy’s law revealing a periodicity along the meridian of about 10° and reaching the maximum of 14° at the latitude of about 32° corresponding to the top of the ‘royal zone’ where the sunspots appear. The variations of polarity separation with a latitude are in an anti-phase with those of the tilts reaching a maximum at the latitude of 35° and showing a small positive separation for the groups/active regions in a vicinity of the average tilts ±40°. The ratio R of the polarity separation to the trigonometric tilt fits the linear function of a latitude φ as R = −0.0213φ − 0.1245 confirming positive separation for the polarities of active regions with the average tilts, or the dominance of activity in the Southern hemisphere activity, for the selected period of observations.     

Driving major solar flares and eruptions: A review

This review focuses on the processes that energize and trigger M- and X-class solar flares and associated flux-rope destabilizations. Numerical modeling of specific solar regions is hampered by uncertain coronal-field reconstructions and by poorly understood magnetic reconnection; these limitations result in uncertain estimates of field topology, energy, and helicity. The primary advances in understanding field destabilizations therefore come from the combination of generic numerical experiments with interpretation of sets of observations. These suggest a critical role for the emergence of twisted flux ropes into pre-existing strong field for many, if not all, of the active regions that produce M- or X-class flares. The flux and internal twist of the emerging ropes appear to play as important a role in determining whether an eruption will develop predominantly as flare, confined eruption, or CME, as do the properties of the embedding field. Based on reviewed literature, I outline a scenario for major flares and eruptions that combines flux-rope emergence, mass draining, near-surface reconnection, and the interaction with the surrounding field. Whether deterministic forecasting is in principle possible remains to be seen: to date no reliable such forecasts can be made. Large-sample studies based on long-duration, comprehensive observations of active regions from their emergence through their flaring phase are needed to help us better understand these complex phenomena.     

The damping of small-amplitude oscillations in quiescent prominences

The presence of small-amplitude oscillations in prominences is well-known from long time ago. These oscillations, whose exciters are still unknown, seem to be of local nature and are interpreted in terms of magnetohydrodynamic (MHD) waves. During last years, observational evidence about the damping of these oscillations has grown and several mechanisms able to damp these oscillations have been the subject of intense theoretical modelling. Among them, the most efficient seem to be radiative cooling and ion-neutral collisions. Radiative cooling is able to damp slow MHD waves efficiently, while ion-neutral collisions, in partially ionised plasmas like those of solar prominences, can also damp fast MHD waves. In this paper, we plan to summarize our current knowledge about the time and spatial damping of small-amplitude oscillations in prominences.     

Probing the method of correcting Faraday rotation in vector magnetograms

By analyzing the vector magnetograms of Huairou Solar Observing Station (HSOS) taken at the line center (0.0 Å) and the line wing (−0.12 Å) of FeI λ5324.19 Å, we make an estimate of the measured errors in transversal azimuths (δ?) caused by Faraday rotation. Since many factors, such as the magnetic saturation and scattered light, can affect the measurement accuracy of the longitudinal magnetic field in the umbrae of sunspots, we limit our study in the region ∣B_z∣ < 800 G. The main mean azimuth rotations are about 4°, 6°, 7° and 9°, while ∣B_z∣ are in the ranges of 400–500 G, 500–600 G, 600–700 G and 700–800 G, respectively. Moreover, we find there is also an azimuth rotation of about 8° at the wavelength offset −0.12 Å of the line compared against a previous numerical simulation.     

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.     

A statistical study of CME-associated flare during the solar cycle 24

We investigate on the relationship between flares and coronal mass ejections (CMEs) in which a flare started before and after the CME events which differ in their physical properties, indicating potentially different initiation mechanisms. The physical properties of two types flare-correlated CME remain an interesting and important question in space weather. We study the relationship between flares and CMEs using a different approach requiring both temporal and spatial constraints during the period from December 1, 2008 to April 30, 2017 in which the CMEs data were acquired by SOHO/LASCO (Solar and Heliospheric Observatory/Large Angle Spectrometric Coronagraph) over the solar cycle 24. The soft X-ray flare flux data, such as flare class, location, onset time and integrated flux, are collected from Geostationary Environmental satellite (GOES) and XRT Flare catalogs. We selected 307 CMEs-flares pairs applying simultaneously temporal and spatial constraints in all events for the distinguish between two associated CME-flare types. We study the correlated properties of coincident flares and CMEs during this period, specifically separating the sample into two types: flares that precede a CME and flares that follow a CME. We found an opposite correlation relationship between the acceleration and velocity of CMEs in the After- and Before-CMEs events. We found a log-log relation between the width and mass of CMEs in the two associated types. The CMEs and flares properties show that there were significant differences in all physical parameters such as (mass, angular width, kinetic energy, speed and acceleration) between two flare-associated CME types.     

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.     

What is the role of magnetic null points in large flares?

We have performed the analysis of the magnetic topology of active region NOAA 10486 before two large flares occurring on October 26 and 28, 2003. The 3D extrapolation of the photospheric magnetic field shows the existence of magnetic null points when using two different methods. We use TRACE 1600 Å and 195 Å brightenings as tracers of the energy release due to magnetic reconnections. We conclude on the three following points:

1. The small events observed before the flares are related to low lying null points. They are long lasting and associated with low energy release. They are not triggering the large flares.

2. On October 26, a high altitude null point is found. We look for bright patches that could correspond to the signatures of coronal reconnection at the null point in TRACE 1600 Å images. However, such bright patches are not observed before the main flare, they are only observed after it.

3. On October 28, four ribbons are observed in TRACE images before the X17 flare. We interpret them as due to a magnetic breakout reconnection in a quadrupolar configuration. There is no magnetic null point related to these four ribbons, and this reconnection rather occurs at quasi-separatrix layers (QSLs).

We conclude that the existence of a null point in the corona is neither a sufficient nor a necessary condition to give rise to large flares.     

A theoretical model for the magnetic helicity of solar active regions

Active regions on the solar surface are known to possess magnetic helicity, which is predominantly negative in the northern hemisphere and positive in the southern hemisphere. Choudhuri et al. [Choudhuri, A.R. On the connection between mean field dynamo theory and flux tubes. Solar Phys. 215, 31–55, 2003] proposed that the magnetic helicity arises due to the wrapping up of the poloidal field of the convection zone around rising flux tubes which form active regions. Choudhuri [Choudhuri, A.R., Chatterjee, P., Nandy, D. Helicity of solar active regions from a dynamo model. ApJ 615, L57–L60, 2004] used this idea to calculate magnetic helicity from their solar dynamo model. Apart from getting broad agreements with observational data, they also predict that the hemispheric helicity rule may be violated at the beginning of a solar cycle. Chatterjee et al. [Chatterjee, P., Choudhuri, A.R., Petrovay, K. Development of twist in an emerging magnetic flux tube by poloidal field accretion. A&A 449, 781–789, 2006] study the penetration of the wrapped poloidal field into the rising flux tube due to turbulent diffusion using a simple 1-d model. They find that the extent of penetration of the wrapped field will depend on how weak the magnetic field inside the rising flux tube becomes before its emergence. They conclude that more detailed observational data will throw light on the physical conditions of flux tubes just before their emergence to the photosphere.