A Time-Evolving 3D Method Dedicated to the Reconstruction of Solar Plumes and Results Using Extreme Ultraviolet Data

An important issue in the tomographic reconstruction of the solar poles is the relatively rapid evolution of the polar plumes. We demonstrate that it is possible to take into account this temporal evolution in the reconstruction. The difficulty of this problem comes from the fact that we want a four-dimensional reconstruction (three spatial dimensions plus time) whereas we only have three-dimensional data (two-dimensional images plus time). To overcome this difficulty, we introduce a model that describes polar plumes as stationary objects whose intensity varies homogeneously with time. This assumption can be physically justified if one accepts the stability of the magnetic structure. This model leads to a bilinear inverse problem. We describe how to extend linear inversion methods to these kinds of problems. Studies of simulations show the reliability of our method. Results for SOHO/EIT data show that we can estimate the temporal evolution of polar plumes to improve the reconstruction of the solar poles from only one point of view. We expect further improvements from STEREO/EUVI data when the two probes will be separated by about 60°.     

Differential Rotation of Strong Magnetic Flux During Solar Cycles 21 – 23

In the present investigation we measure the differential rotation of strong magnetic flux during solar cycles 21 – 23 with the method of wavelet transforms. We find that the cycle-averaged synodic rotation rate of strong magnetic flux can be written as ω=13.47−2.58sin ² θ or ω=13.45−2.06sin ² θ−1.37sin ⁴ θ, where θ is the latitude. They agree well with the results derived from sunspots. A north–south asymmetry of the rotation rate is found at high latitudes (28°<θ<40°). The strong flux in the southern hemisphere rotates faster than that in the northern hemisphere by 0.2 deg day⁻¹. The asymmetry continued for cycles 21 – 23 and may be a secular property.     

Reconstruction of the North–South Solar Asymmetry with a Kuramoto Model

This paper applies a Kuramoto model of coupled oscillators to investigate the north–south (N–S) solar asymmetry and properties of meridional circulation. We focus our study on the asymmetry of the 11-year phase, which is slight but persistent: only two changes of sign (around 1928 and 1968) are observed in the past century. We present a model of two non-linear coupled oscillators that links the hemispheric phase asymmetry of sunspots with the asymmetry of the meridional flow. We use a Kuramoto model with evolving frequencies and constant symmetric coupling to show how asymmetry in meridional circulation could produce a persistent phase lead of one solar hemisphere over the other. We associate the natural frequencies of the two oscillators with the velocities of the meridional flow cells in the northern and southern hemispheres. We assume the respective circulations to be independent and estimate the value of the relevant cross-equatorial coupling by the coupling coefficient in the Kuramoto model. We find that a persistent N–S asymmetry of sunspots and the change of the leading hemisphere could indeed both be the result of the evolving frequencies of meridional circulation; the necessary asymmetry of the meridional flow may be small; and the cross-equatorial coupling has an intermediate range value. Possible applications of these results in solar dynamo models are discussed.     

STEREO/Extreme Ultraviolet Imager (EUVI) Event Catalog 2006 – 2012

We generated an event catalog with an automated detection algorithm based on the entire EUVI image database observed with the two Solar Terrestrial Relations Observatory (STEREO)-A and -B spacecraft over the first six years of the mission (2006?–?2012). The event catalog includes the heliographic positions of some 20?000 EUV events, transformed from spacecraft coordinates to Earth-based coordinates, and information on associated GOES flare events (down to the level of GOES A5-class flares). The 304 Å wavelength turns out to be the most efficient channel for flare detection (79?% of all EUVI event detections), while the 171 Å (4?%), 195 Å (10?%), and the 284 Å channel (7?%) retrieve substantially fewer flare events, partially due to the suppressing effect of EUV dimming, and partially due to the lower cadence in the later years of the mission. Due to the Sun-circling orbits of STEREO-A and -B, a large number of flares have been detected on the farside of the Sun, invisible from Earth, or seen as partially occulted events. The statistical size distributions of EUV peak fluxes (with a power-law slope of α _P =2.5±0.2) and event durations (with a power-law slope of α _T =2.4±0.3) are found to be consistent with the fractal-diffusive self-organized criticality model. The EUVI event catalog is available on-line at secchi.lmsal.com/EUVI/euvi_autodetection/euvi_events.txt and may serve as a comprehensive tool to identify stereoscopically observed flare events for 3D reconstruction and to study occulted flare events.     

Modeling of Local Magnetic Field Enhancements within Solar Flux Ropes

To model and study local magnetic-field enhancements in a solar flux rope we consider the magnetic field in its interior as a superposition of two linear (constant α) force-free magnetic-field distributions, viz. a global one, which is locally similar to a part of the cylinder, and a local torus-shaped magnetic distribution. The newly derived solution for a toroid with an aspect ratio close to unity is applied. The symmetry axis of the toroid and that of the cylinder may or may not coincide. Both the large and small radii of the toroid are set equal to the cylinder’s radius. The total magnetic field distribution yields a flux tube which has a variable diameter with local minima and maxima. In principle, this approach can be used for the interpretation and analysis of solar-limb observations of coronal loops.     

Are There Different Populations of Flux Ropes in the Solar Wind?

Flux ropes are twisted magnetic structures that can be detected by in-situ measurements in the solar wind. However, different properties of detected flux ropes suggest different types of flux-rope populations. As such, are there different populations of flux ropes? The answer is positive and is the result of the analysis of four lists of flux ropes, including magnetic clouds (MCs), observed at 1 AU. The in-situ data for the four lists were fitted with the same cylindrical force-free field model, which provides an estimate of the local flux-rope parameters such as its radius and orientation. Since the flux-rope distributions have a broad dynamic range, we went beyond a simple histogram analysis by developing a partition technique that uniformly distributes the statistical fluctuations across the radius range. By doing so, we found that small flux ropes with radius R<0.1 AU have a steep power-law distribution in contrast to the larger flux ropes (identified as MCs), which have a Gaussian-like distribution. Next, from four CME catalogs, we estimated the expected flux-rope frequency per year at 1 AU. We found that the predicted numbers are similar to the frequencies of MCs observed in-situ. However, we also found that small flux ropes are at least ten times too abundant to correspond to CMEs, even to narrow ones. Investigating the different possible scenarios for the origin of these small flux ropes, we conclude that these twisted structures can be formed by blowout jets in the low corona or in coronal streamers.     

Combined Analysis of Solar Neutrino and Solar Irradiance Data: Further Evidence for Variability of the Solar Neutrino Flux and Its Implications Concerning the Solar Core

A search for any particular feature in any single solar neutrino dataset is unlikely to establish variability of the solar neutrino flux since the count rates are very low. It helps to combine datasets, and in this article we examine data from both the Homestake and GALLEX experiments. These show evidence of modulation with a frequency of 11.85 year⁻¹, which could be indicative of rotational modulation originating in the solar core. We find that precisely the same frequency is prominent in power spectrum analyses of the ACRIM irradiance data for both the Homestake and GALLEX time intervals. These results suggest that the solar core is inhomogeneous and rotates with a sidereal frequency of 12.85 year⁻¹. From Monte Carlo calculations, it is found that the probability that the neutrino data would by chance match the irradiance data in this way is only 2 parts in 10 000. This rotation rate is significantly lower than that of the inner radiative zone (13.97 year⁻¹) as recently inferred from analysis of Super-Kamiokande data, suggesting that there may be a second, inner tachocline separating the core from the radiative zone. This opens up the possibility that there may be an inner dynamo that could produce a strong internal magnetic field and a second solar cycle.     

Is Null-Point Reconnection Important for Solar Flux Emergence?

The role of null-point reconnection in a three-dimensional numerical magnetohydrodynamic (MHD) model of solar emerging flux is investigated. The model consists of a twisted magnetic flux tube rising through a stratified convection zone and atmosphere to interact and reconnect with a horizontal overlying magnetic field in the atmosphere. Null points appear as the reconnection begins and persist throughout the rest of the emergence, where they can be found mostly in the model photosphere and transition region, forming two loose clusters on either side of the emerging flux tube. Up to 26 nulls are present at any one time, and tracking in time shows that there is a total of 305 overall, despite the initial simplicity of the magnetic field configuration. We find evidence for the reality of the nulls in terms of their methods of creation and destruction, their balance of signs, their long lifetimes, and their geometrical stability. We then show that due to the low parallel electric fields associated with the nulls, null-point reconnection is not the main type of magnetic reconnection involved in the interaction of the newly emerged flux with the overlying field. However, the large number of nulls implies that the topological structure of the magnetic field must be very complex and the importance of reconnection along separators or separatrix surfaces for flux emergence cannot be ruled out.     

Numerical Simulations of Torsional Alfvén Waves in Axisymmetric Solar Magnetic Flux Tubes

We numerically investigate Alfvén waves propagating along an axisymmetric and non-isothermal solar flux tube embedded in the solar atmosphere. The tube magnetic field is current-free and diverges with height, and the waves are excited by a periodic driver along the tube magnetic field lines. The main results are that the two wave variables, the velocity and magnetic field perturbations in the azimuthal direction, behave differently as a result of gradients of the physical parameters along the tube. To explain these differences in the wave behavior, the time evolution of the wave variables and the resulting cutoff period for each wave variable are calculated and used to determine regions in the solar chromosphere where strong wave reflection may occur.     

Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model

The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free “potential-field” extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.     

Solar S-bursts at Frequencies of 10 – 30 MHz

Solar S-bursts observed by the radio telescope UTR-2 in the period 2001 – 2002 are studied. The bursts chosen for a detailed analysis occurred in the periods 23 – 26 May 2001, 13 – 16 and 27 – 39 July 2002 during three solar radio storms. More than 800 S-bursts were registered in these days. Properties of S-bursts are studied in the frequency band 10 – 30 MHz. All bursts were always observed against a background of other solar radio activity such as type III and IIIb bursts, type III-like bursts, drift pairs and spikes. Moreover, S-bursts were observed during days when the active region was situated near the central meridian. Characteristic durations of S-bursts were about 0.35 and 0.4 – 0.6 s for the May and July storms, respectively. For the first time, we found that the instantaneous frequency width of S-bursts increased with frequency linearly. The dependence of drift rates on frequency followed the McConnell dependence derived for higher frequencies. We propose a model of S-bursts based on the assumption that these bursts are generated due to the confluence of Langmuir waves with fast magnetosonic waves, whose phase and group velocities are equal.     

Solar Flares and Coronal Mass Ejections: A Statistically Determined Flare Flux – CME Mass Correlation

In an effort to examine the relationship between flare flux and corresponding CME mass, we temporally and spatially correlate all X-ray flares and CMEs in the LASCO and GOES archives from 1996 to 2006. We cross-reference 6733 CMEs having well-measured masses against 12 050 X-ray flares having position information as determined from their optical counterparts. For a given flare, we search in time for CMEs which occur 10 – 80 minutes afterward, and we further require the flare and CME to occur within ± 45° in position angle on the solar disk. There are 826 CME/flare pairs which fit these criteria. Comparing the flare fluxes with CME masses of these paired events, we find CME mass increases with flare flux, following an approximately log-linear, broken relationship: in the limit of lower flare fluxes, log (CME mass)∝0.68×log (flare flux), and in the limit of higher flare fluxes, log (CME mass)∝0.33×log (flare flux). We show that this broken power-law, and in particular the flatter slope at higher flare fluxes, may be due to an observational bias against CMEs associated with the most energetic flares: halo CMEs. Correcting for this bias yields a single power-law relationship of the form log (CME mass)∝0.70×log (flare flux). This function describes the relationship between CME mass and flare flux over at least 3 dex in flare flux, from ≈ 10⁻⁷ – 10⁻⁴ W m⁻².     

An Extreme Solar Event of 20 January 2005: Properties of the Flare and the Origin of Energetic Particles

The famous extreme solar and particle event of 20 January 2005 is analyzed from two perspectives. Firstly, using multi-spectral data, we study temporal, spectral, and spatial features of the main phase of the flare, when the strongest emissions from microwaves up to 200 MeV gamma-rays were observed. Secondly, we relate our results to a long-standing controversy on the origin of solar energetic particles (SEP) arriving at Earth, i.e., acceleration in flares, or shocks ahead of coronal mass ejections (CMEs). Our analysis shows that all electromagnetic emissions from microwaves up to 2.22 MeV line gamma-rays during the main flare phase originated within a compact structure located just above sunspot umbrae. In particular, a huge (≈ 10⁵ sfu) radio burst with a high frequency maximum at 30 GHz was observed, indicating the presence of a large number of energetic electrons in very strong magnetic fields. Thus, protons and electrons responsible for various flare emissions during its main phase were accelerated within the magnetic field of the active region. The leading, impulsive parts of the ground-level enhancement (GLE), and highest-energy gamma-rays identified with π ⁰-decay emission, are similar and closely correspond in time. The origin of the π ⁰-decay gamma-rays is argued to be the same as that of lower-energy emissions, although this is not proven. On the other hand, we estimate the sky-plane speed of the CME to be 2 000 – 2 600 km s⁻¹, i.e., high, but of the same order as preceding non-GLE-related CMEs from the same active region. Hence, the flare itself rather than the CME appears to determine the extreme nature of this event. We therefore conclude that the acceleration, at least, to sub-relativistic energies, of electrons and protons, responsible for both the major flare emissions and the leading spike of SEP/GLE by 07 UT, are likely to have occurred nearly simultaneously within the flare region. However, our analysis does not rule out a probable contribution from particles accelerated in the CME-driven shock for the leading GLE spike, which seemed to dominate at later stages of the SEP event. S.N. Kuznetsov deceased 17 May 2007.     

The Rotation Rates of Solar Magnetic Fields During Solar Cycles 21 – 23

Employing the synoptic maps of the photospheric magnetic fields from the beginning of solar cycle 21 to the end of 23, we first build up a time – longitude stackplot at each latitude between ±35°. On each stackplot there are many tilted magnetic structures clearly reflecting the rotation rates, and we adopt a cross-correlation technique to explore the rotation rates from these tilted structures. Our new method avoids artificially choosing magnetic tracers, and it is convenient for investigating the rotation rates of the positive and negative fields by omitting one kind of field on the stackplots. We have obtained the following results. i) The rotation rates of the positive and negative fields (or the leader and follower polarities, depending on the hemispheres and solar cycles) between latitudes ±35° during solar cycles 21–23 are derived. The reversal times of the leader and follower polarities are usually not consistent with the years of the solar minimum, nevertheless, at latitudes ±16°, the reversal times are almost simultaneous with them. ii) The rotation rates of the three solar cycles averaged over each cycle are calculated separately for the positive, negative and total fields. The latitude profiles of rotation of the positive and negative fields exhibit equatorial symmetries with each other, and those of the total fields lie between them. iii) The differences in rotation rates between the leader and follower polarities are obtained. They are very small near the equator, and increase as latitude increases. In the latitude range of 5° – 20°, these differences reach 0.05 deg day⁻¹, and the mean difference for solar cycle 22 is somewhat smaller than cycles 21 and 23 in these latitude regions. Then, the differences reduce again at latitudes higher than 20°.     

Energy Buildup,Flux Confinement and Helicity Accumulation in the Solar Corona

Starting from a dipole field and a given distribution of footpoint displace- ment of field lines on the photosphere,we find axisymmetric,force-free field solutions in spherical coordinates that have the same distribution of normal field on the photo- sphere and magnetic topology as the dipole field.A photospheric shear is introduced in the azimuthal direction in a region that strides across the equator and ends at latitude γ_s.The footpoint displacement has a sine distribution in latitude and a peak amplitude of (?)_m.The magnetic energy E,azimuthal flux F_(?),and magnetic helicity H_T in the solar corona are then calculated for each force-free field solution.It is found that for a given shear region range γ_s,all of the three quantities increase monotoni- cally with increasing (?)_m.In particular,both F_(?) and H_T have a linear dependence on (?)m.When (?)_m reaches a certain critical value (?)_(mc),the force-free field loses equilib- rium,leading to a partial opening of the field and the appearance of a current sheet in the equatorial plane.At this point,E,F_(?)and H_T reach their maximum values, E_c,F_((?)c) and H_(Tc).E_c increases,and F_((?)c) and H_(Tc)decrease with decreasing λ_s.It is found that E_c is always smaller than the open field energy,in agreement with the Aly conjecture.Of the three critical parameters,E_c has the weakest dependence on λ_s.Therefore,if one is interested in the transition of a magnetic configuration from a stable state to a dynamic one,the magnetic energy is probably the most appropriate marker of the transition.     

A Possible Cause of the Diminished Solar Wind During the Solar Cycle 23 – 24 Minimum

Interplanetary magnetic field and solar wind plasma density observed at 1 AU during Solar Cycle 23?–?24 (SC-23/24) minimum were significantly smaller than those during its previous solar cycle (SC-22/23) minimum. Because the Earth’s orbit is embedded in the slow wind during solar minimum, changes in the geometry and/or content of the slow wind region (SWR) can have a direct influence on the solar wind parameters near the Earth. In this study, we analyze solar wind plasma and magnetic field data of hourly values acquired by Ulysses. It is found that the solar wind, when averaging over the first (1995.6?–?1995.8) and third (2006.9?–?2008.2) Ulysses’ perihelion (\({\sim}\,1.4~\mbox{AU}\)) crossings, was about the same speed, but significantly less dense (\({\sim}\,34~\%\)) and cooler (\({\sim}\,20~\%\)), and the total magnetic field was \({\sim}\,30~\%\) weaker during the third compared to the first crossing. It is also found that the SWR was \({\sim}\,50~\%\) wider in the third (\({\sim}\,68.5^{\circ}\) in heliographic latitude) than in the first (\({\sim}\,44.8^{\circ}\)) solar orbit. The observed latitudinal increase in the SWR is sufficient to explain the excessive decline in the near-Earth solar wind density during the recent solar minimum without speculating that the total solar output may have been decreasing. The observed SWR inflation is also consistent with a cooler solar wind in the SC-23/24 than in the SC-22/23 minimum. Furthermore, the ratio of the high-to-low latitude photospheric magnetic field (or equatorward magnetic pressure force), as observed by the Mountain Wilson Observatory, is smaller during the third than the first Ulysses’ perihelion orbit. These findings suggest that the smaller equatorward magnetic pressure at the Sun may have led to the latitudinally-wider SRW observed by Ulysses in SC-23/24 minimum.