An Exploration of Non-kinematic Effects in Flux Transport Dynamos

Recent global magnetohydrodynamical simulations of solar convection producing a large-scale magnetic field undergoing regular, solar-like polarity reversals also present related cyclic modulations of large-scale flows developing in the convecting layers. Examination of these simulations reveal that the meridional flow, a crucial element in flux transport dynamos, is driven at least in part by the Lorentz force associated with the cycling large-scale magnetic field. This suggests that the backreaction of the field onto the flow may have a pronounced influence on the long-term evolution of the dynamo. We explore some of the associated dynamics using a low-order dynamo model that includes this Lorentz force feedback. We identify several characteristic solutions which include single period cycles, period doubling and chaos. To emulate the role of turbulence in the backreaction process we subject the model to stochastic fluctuations in the parameter that controls the Lorentz force amplitude. We find that short term fluctuations produce long-term modulations of the solar cycle and, in some cases, grand minima episodes where the amplitude of the magnetic field decays to near zero. The chain of events that triggers these quiescent phases is identified. A subsequent analysis of the energy transfer between large-scale fields and flows in the global magnetohydrodynamical simulation of solar convection shows that the magnetic field extracts energy from the solar differential rotation and deposits part of that energy into the meridional flow. The potential consequences of this marked departure from the kinematic regime are discussed in the context of current solar cycle modeling efforts based on flux transport dynamos.     

Magnetic field, helicity and the 2000 July 14 flare in solar active region 9077

In this paper we analyse the non-potential magnetic field and the relationship with current (helicity) in the active region NOAA 9077 in 2000 July, using photospheric vector magnetograms obtained at different solar observatories and also coronal extreme-ultraviolet 171-Å images from the TRACE satellite.
We note that the shear and squeeze of magnetic field are two important indices for some flare-producing regions and can be confirmed by a sequence of photospheric vector magnetograms and EUV 171-Å features in the solar active region NOAA 9077. Evidence on the release of magnetic field near the photospheric magnetic neutral line is provided by the change of magnetic shear, electric current and current helicity in the lower solar atmosphere. It is found that the 'Bastille Day' 3B/5.7X flare on 2000 July 14 was triggered by the interaction of the different magnetic loop systems, which is relevant to the ejection of helical magnetic field from the lower solar atmosphere. The eruption of the large-scale coronal magnetic field occurs later than the decay of the highly sheared photospheric magnetic field and also current in the active region.     

A global numerical 3-D MHD model of the solar wind

A fully three-dimensional, steady-state global model of the solar corona and the solar wind is developed. A numerical, self-consistent solution for 3-D MHD equations is constructed for the region between the solar photosphere and the Earth's orbit. Boundary conditions are provided by the solar magnetic field observations. A steady-state solution is sought as a temporal relaxation to the dynamic equilibrium in the region of transonic flow near the Sun and then traced to the orbit of the Earth in supersonic flow region. The unique features of the proposed model are: (a) uniform coverage and self-consistent treatment of the regions of subsonic/sub-Alfvénic and supersonic/super-Alfvénic flows, (b) inferring the global structure of the interplanetary medium between the solar photosphere and 1 AU based on large-scale solar magnetic field data. As an experimental test for the proposed technique, photospheric magnetic field data for CR 1682 are used to prescribe boundary condition near the Sun and results of a simulation are compared with spacecraft measurements at 1 AU. The comparison demonstrates a qualitative agreement between computed and observed parameters. While the difference in densities is still significant, the 3-D model better reproduces variations of the solar wind velocity than does the 2-D model presented earlier (Usmanov, 1993).     

Small Solar Wind Transients and Their Connection to the Large-Scale Coronal Structure

It has been realized for some time that the slow solar wind with its embedded heliospheric current sheet often exhibits complex features suggesting at least partially transient origin. In this paper we investigate the structure of the slow solar wind using the observations by the Wind and STEREO spacecraft during two Carrington rotations (2054 and 2055). These occur at the time of minimum solar activity when the interplanetary medium is dominated by recurrent high-speed streams and large-scale interplanetary coronal mass ejections (ICMEs) are rare. However, the signatures of transients with small scale-sizes and/or low magnetic field strength (comparable with the typical solar wind value, ～?5 nT) are frequently found in the slow solar wind at these times. These events do not exhibit significant speed gradients across the structure, but instead appear to move with the surrounding flow. Source mapping using models based on GONG magnetograms suggests that these transients come from the vicinity of coronal source surface sector boundaries. In situ they are correspondingly observed in the vicinity of high density structures where the dominant electron heat flux reverses its flow polarity. These weak transients might be indications of dynamical changes at the coronal hole boundaries or at the edges of the helmet streamer belt previously reported in coronagraph observations. Our analysis supports the idea that even at solar minimum, a considerable fraction of the slow solar wind is transient in nature.     

The solar corona as a minimum energy system?

This paper is an exploration of the possibility that the large-scale equilibrium of plasma and magnetic fields in the solar corona is a minimum energy state. Support for this conjecture is sought by considering the simplest form of that equilibrium in a dipole solar field, as suggested by the observed structure of the corona at times of minimum solar activity. Approximate, axisymmetric solutions to the MHD equations are constructed to include both a magnetically closed, hydrostatic region and a magnetically open region where plasma flows along field lines in the form of a transonic, thermally-driven wind. Sequences of such solutions are obtained for various degrees of magnetic field opening, and the total energy of each solution is computed, including contributions from both the plasma and magnetic field. It is shown that along a sequence of increasingly closed coronal magnetic field, the total energy curve is a non-monotonic function of the parameter measuring the degree of magnetic field opening, with a minimum occurring at moderate field opening.For reasonable choices of model parameters (coronal temperature, base density, base magnetic field strength, etc.), the morphology of the minimum energy solution resembles the observed quiet, solar minimum corona. The exact location energy minimum along a given sequence depends rather sensitively on some of the adopted parameter values. It is nevertheless argued that the existence of an energy minimum along the sequences of solutions should remain a robust property of more realistic coronal wind models that incorporate the basic characteristics of the equilibrium corona- the presence of both open and closed magnetic regions.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Long term evolution of solar sector structure

The large-scale structure of the solar magnetic field during the past five sunspot cycles (representing by implication a much longer interval of time) has been investigated using the polarity (toward or away from the Sun) of the interplanetary magnetic field as inferred from polar geomagnetic observations. The polarity of the interplanetary magnetic field has previously been shown to be closely related to the polarity (into or out of the Sun) of the large-scale solar magnetic field. It appears that a solar structure with four sectors per rotation persisted through the past five sunspot cycles with a synodic rotation period near 27.0 days, and a small relative westward drift during the first half of each sunspot cycle and a relative eastward drift during the second half of each cycle. Superposed on this four-sector structure there is another structure with inward field polarity, a width in solar longitude of about 100° and a synodic rotation period of about 28 to 29 days. This 28.5 day structure is usually most prominent during a few years near sunspot maximum. Some preliminary comparisons of these observed solar structures with theoretical considerations are given.     

Current state of the problem of solar flares: New observations and new models

A review of current questions related to the problem of large solar flares is given. The basic physical principles applied in numerical simulation of flares are presented and illustrated. The main attention is given to the phenomenon of magnetic reconnection in large-scale current layers at separators of magnetic field in the corona. This phenomenon is demonstrated within the framework of the Rainbow topological model. The model provides the possibility of explaining specific features of large-scale reconnection as a physical process that makes it possible to accumulate large energy in the form of the magnetic energy of current layers before a flare and to quickly transform this energy to the kinetic energy of particles during a flare. The secondary effects in the solar atmosphere caused by energy fluxes from reconnecting current layers are also discussed. These consequences of the primary energy release are responsible for the flare pattern observed in X-ray, optical, UV, and other spectral ranges.     

Solar Energetic Particle Events in the 23rd Solar Cycle: Interplanetary Magnetic Field Configuration and Statistical Relationship with Flares and CMEs

We study the influence of the large-scale interplanetary magnetic field configuration on the solar energetic particles (SEPs) as detected at different satellites near Earth and on the correlation of their peak intensities with the parent solar activity. We selected SEP events associated with X- and M-class flares at western longitudes, in order to ensure good magnetic connection to Earth. These events were classified into two categories according to the global interplanetary magnetic field (IMF) configuration present during the SEP propagation to 1 AU: standard solar wind or interplanetary coronal mass ejections (ICMEs). Our analysis shows that around 20 % of all particle events are detected when the spacecraft is immersed in an ICME. The correlation of the peak particle intensity with the projected speed of the SEP-associated coronal mass ejection is similar in the two IMF categories of proton and electron events, ≈?0.6. The SEP events within ICMEs show stronger correlation between the peak proton intensity and the soft X-ray flux of the associated solar flare, with correlation coefficient r=0.67±0.13, compared to the SEP events propagating in the standard solar wind, r=0.36±0.13. The difference is more pronounced for near-relativistic electrons. The main reason for the different correlation behavior seems to be the larger spread of the flare longitude in the SEP sample detected in the solar wind as compared to SEP events within ICMEs. We discuss to what extent observational bias, different physical processes (particle injection, transport, etc.), and the IMF configuration can influence the relationship between SEPs and coronal activity.     

Kinematics and Evolution of Local Features of the Large-Scale Magnetic Field – I. Kinematical Characteristics

Kinematics of local magnetic features (LMFs) have been investigated by analyzing a 22-year series of synoptic maps of the radial magnetic field of the Sun (the term ‘local’ refers hereinafter to magnetic features with an effective size of the order of an arc min). We applied the cross-correlation technique to analyse separately each of the harmonics obtained by using a one-dimensional Fourier transform of the magnetic field in longitude. Such an approach allowed us to trace the motion of the LMFs for a time interval as long as 12 Carrington rotations. The analysis also has shown that the effective size of the magnetic tracers grows significantly with increasing age, which indicates that the local-scale magnetic features undergo diffusion-like expansion and weakening, in agreement with Leighton's model of magnetic field evolution. The LMFs emerging at latitudes between 10° and 55° reveal a poleward directed motion with a maximum velocity of about 14 m s^-1 near the latitude of 37°. The profile of the meridional velocity agrees approximately with that derived by Komm, Howard, and Harvey (1993) for small-scale, short-lived magnetic features. We have found that the LMFs rotate differentially at latitudes of up to 55°, and do not exhibit the ‘quasi-rigid’ rotation that is assumed to be characteristic of long-lived magnetic features. This disagrees with the results obtained by Stenflo (1989) and by Latushko (1994), who applied direct cross-correlation analysis of the synoptic maps. Such a discrepancy may be treated as being a consequence of inhomogeneity of the large-scale solar magnetic field that consists of several components with different kinematic characteristics.     

Real and virtual unipolar regions

Difficulties in relating magnetograph measurements to the actual solar magnetic field are discussed. After a brief review both of problems inherent in the nature of the measurements and of sources of instrumental error, we show that field measurements taken within the photosphere can map out large-scale regions of a single magnetic polarity even though these regions contain no footpoints of large-scale magnetic structures, but instead only aggregates of small, unresolved bipoles. This may occur wherever the density of unresolved bipoles has a preferred orientation and a spatial variation along the direction of that orientation. We call these regionsvirtual unipolar regions, as they are not connected to regions of opposite polarity by field loops or lines passing through the corona. Investigation of these regions shows that they can arise at widely separated locations, and that they may evolve into real unipolar magnetic regions which are connected to the chromospheric and coronal fields. These results can explain a number of puzzling aspects of magnetograph observations of the solar background magnetic field.     

Recurrent magnetic activity,sunspot number and its rate of decline

Power spectral densities computed from low-latitude horizontal intensity of the Earth's magnetic field over two-year periods of declining phases of solar cycles 16 to 19 show a close relationship with the maximum relative sunspot number of the following solar cycles. The maximum sunspot number shows an exponential rise with the power density near 1/27 cd^?1; maximum R _z,however, increases linearly with power density near 1/14 cd^?1. It is also shown that the rate of decline of sunspot number in a solar cycle is almost exactly related, linearly, to power spectral density for the preceding solar cycle. Power densities near 1/27 and 1/14 cd^?1 in declining phase of solar cycle appear to be satisfactory indices for the maximum relative sunspot number of the following cycle and its rate of decline thereafter.     

Magnetic Fields and Solar Activities

We discuss the study of solar magnetic fields based on the photospheric vector magnetograms of solar active regions which were obtained at Huairou Solar Observing Station near Beijing in the period of 22nd and 23th solar cycles. The measurements of the chromospheric magnetic field and the spatial configuration of the field at the lower solar atmosphere inferred by the distribution of the solar photospheric and chromospheric magnetic field. After the analysis on the formation process of delta configuration in some super active regions based on the photospheric vector magnetogram observations, 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, proposed to be generated in the subatmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and the relationship with magnetic shear in some delta active regions completely. (3) The proposition is that the large-scale delta active regions are formed from contribution by highly sheared non-potential magnetic flux bundles generated in the subatmosphere. We present some results of a study of the magnetic helicity. We also compare these results with other data sets obtained by magnetographs (or Stokes polarimeters) at different observatories, and analyze the basic chirality of the magnetic field in the solar atmosphere.     

Simulation of the Unusual Solar Minimum with 3D SIP-CESE MHD Model by Comparison with Multi-Satellite Observations

The observations both near the Sun and in the heliosphere during the activity minimum between solar cycles 23 and 24 exhibit different phenomena from those typical of the previous solar minima. In this paper, we have chosen Carrington rotation 2070 in 2008 to investigate the properties of the background solar wind by using the three-dimensional (3D) Solar?CInterPlanetary Conservation Element/Solution Element Magnetohydrodynamic (MHD) model. We also study the effects of polar magnetic fields on the characteristics of the solar corona and the solar wind by conducting simulations with an axisymmetric polar flux added to the observed magnetic field. The numerical results are compared with the observations from multiple satellites, such as the Solar and Heliospheric Observatory (SOHO), Ulysses, Solar Terrestrial Relations Observatory (STEREO), Wind and the Advanced Composition Explorer (ACE). The comparison demonstrates that the first simulation with the observed magnetic fields reproduces some observed peculiarities near the Sun, such as relatively small polar coronal holes, the presence of mid- and low-latitude holes, a tilted and warped current sheet, and the broad multiple streamers. The numerical results also capture the inconsistency between the locus of the minimum wind speed and the location of the heliospheric current sheet, and predict slightly slower and cooler polar streams with a relatively smaller latitudinal width, broad low-latitude intermediate-speed streams, and globally weak magnetic field and low density in the heliosphere. The second simulation with strengthened polar fields indicates that the weak polar fields in the current minimum play a crucial role in determining the states of the corona and the solar wind.     

Spatial distribution of solar flares in 23rd solar cycle

H-alpha flares accompanied by the X-radiation f ?? 10^?6 wm^?2 in power are examined; 2331 flares were registered during the first half of the 23rd solar cycle (1997?C2000). The specific power of the X-radiation of the flares monotonically doubles from the minimum to the maximum of the sunspot. An increase in the number of flares in each solar rotation is nonmonotonic and disproportional to the relative number of sunspots. Several longitudinal intervals with increased flare activity can be distinguished in the entire time interval of five to ten rotations. The longitudinal distributions of flares and boundaries of the sector structures of a large-scale magnetic field differ considerably. This confirms the existence of two types of zero lines; the first type is determined by active regions, and the second one is determined by large-scale structures with weak magnetic fields. The flares concentrate near Hale??s zero lines of the first type.     

Dayside induced magnetic field in the ionosphere of Mars

The Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) onboard the Mars Express spacecraft has occasionally displayed surprising features. One such feature is the occurrence of a series of broadband, low-frequency echoes at equally spaced delay times after the sounder transmitter pulse. The interval between the echoes has been shown to be at the cyclotron period of electrons orbiting in the local magnetic field. The electrons are believed to be accelerated by the large voltages applied to the antenna by the sounder transmitter. Measurements of the period of these “electron cyclotron echoes” provide a simple technique for determining the magnitude of the magnetic field near the spacecraft. These measurements are particularly useful because Mars Express carries no magnetometer, so this is the only method available for measuring the magnetic field magnitude. Using this technique, results are presented showing the large scale structure of the draped field inside the magnetic pile-up boundary. The magnitude of the draped field is shown to vary from about 40 nT at a solar zenith angle of about 25°, to about 25 nT at a solar zenith angle of 90°. The results compare favorably with similar results from the Mars Global Surveyor spacecraft. A fitting technique is developed to derive the vector direction and magnitude of the draped magnetic field in cases where the spacecraft passes through regions with significant variation in the crustal field. The magnetic field directions are consistent with current knowledge of the draping geometry of the magnetic field around Mars.     

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory

We derive an analytical approximation of nonlinear force-free magnetic field solutions (NLFFF) that can efficiently be used for fast forward-fitting to solar magnetic data, constrained either by observed line-of-sight magnetograms and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph data. The derived NLFFF solutions provide the magnetic field components B _x (x), B _y (x), B _z (x), the force-free parameter α(x), the electric current density j(x), and are accurate to second-order (of the nonlinear force-free α-parameter). The explicit expressions of a force-free field can easily be applied to modeling or forward-fitting of many coronal phenomena.     

Predicting the evolution of photospheric magnetic field in solar active regions using deep learning

The continuous observation of the magnetic field by the Solar Dynamics Observatory(SDO)/Helioseismic and Magnetic Imager(HMI) produces numerous image sequences in time and space.These sequences provide data support for predicting the evolution of photospheric magnetic field. Based on the spatiotemporal long short-term memory(LSTM) network, we use the preprocessed data of photospheric magnetic field in active regions to build a prediction model for magnetic field evolution. Because of the elaborate learning and memory mechanism, the trained model can characterize the inherent relationships contained in spatiotemporal features. The testing results of the prediction model indicate that(1) the prediction pattern learned by the model can be applied to predict the evolution of new magnetic field in the next 6 hours that have not been trained, and predicted results are roughly consistent with real observed magnetic field evolution in terms of large-scale structure and movement speed;(2) the performance of the model is related to the prediction time; the shorter the prediction time, the higher the accuracy of the predicted results;(3) the performance of the model is stable not only for active regions in the north and south but also for data in positive and negative regions. Detailed experimental results and discussions on magnetic flux emergence and magnetic neutral lines finally show that the proposed model could effectively predict the large-scale and short-term evolution of the photospheric magnetic field in active regions. Moreover, our study may provide a reference for the spatiotemporal prediction of other solar activities.     

Solar and geomagnetic activity on a long time scale: Reconstructions and possibilities for predictions

Using two mathematical methods based on the wavelet transform and nonlinear dynamics, we reconstructed the behavior of the aa-index of geomagnetic activity in the past. Two versions of the series are provided: for the last 400 years and on an almost 1000-year time scale. We consider typical values of the aa-index at grandiose extrema of solar activity. The same high level of geomagnetic activity as that observed in the last 50 years is shown to have also taken place in the early 12th and late 14th centuries. We suggest an extended time series of A-indices of the large-scale solar magnetic field. On the 400-year time scale, we confirmed that the large-scale magnetic field develops earlier than the magnetic fields of active regions. Ohl’s prediction method was verified on the same time scale.     

Structure and Cyclic Variations of Open Magnetic Fields in the sun

The structure and variations of open field regions (OFRs) are analyzed against the solar cycle for the time interval of 1970–1996. The cycle of the large-scale magnetic field (LSMF) begins in the vicinity of maximum Wolf numbers, i.e. during the polar field reversal. At the beginning of the LSMF cycle, the polar and mid-latitude magnetic field systems are connected by a narrow bridge, but later they evolve independently. The polar field at the latitudes above 60° has a completely open configuration and fills the whole area of the polar caps near the cycle minimum of local fields. At this time, essentially all of the open solar flux is from the polar caps. The mid-latitude open field regions (OFRs) occur at a latitude of 30–40° away from solar minimum and drift slowly towards the equator to form a typical 'butterfly diagram' at the periphery of the local field zone. This supports the concept of a single complex – 'large-scale magnetic field – active region – coronal hole'. The rotation characteristics of OFRs have been analyzed to reveal a near solid-body rotation, much more rigid than in the case of sunspots. The rotation characteristics are shown to depend on the phase of the solar cycle.