The coupling of solar convection and rotation – (Invited Review)

In recent years, helioseismology has provided an unprecedented look at the dynamics of the solar interior. These new insights have been accompanied by tremendous advances in high-performance computing technology, prompting increasingly sophisticated and realistic numerical models of solar convection. Among the most important helioseismic constraints on global-scale convection models is the mean differential rotation profile of the solar envelope, which is established by convection under the influence of rotation. The highly turbulent nature of solar convection makes this rotational influence difficult to determine and model. I will begin this review by discussing the solar rotation profile inferred from helioseismic measurements and various theoretical and numerical approaches to account for it. Computational constraints limited early numerical models to relatively laminar flow regimes but more recent investigations have begun to explore the distinct nature of turbulent convection. After a brief overview of empirical and numerical results on the related Rayleigh-Bernard system, I will outline the current state of numerical modeling of turbulent convection in rotating, stratified fluids, first in Cartesian and then in spherical geometries. The emphasis throughout will be on how rotation influences the structure, evolution, and transport processes of turbulent convection and what type of differential rotation can result.     

Sunspot Oscillations: A Review – (Invited Review)

The current state of our knowledge, and ignorance, of the nature of oscillations in sunspots is surveyed. An effort is made to summarize the robust aspects of both the observational and theoretical components of the subject in a coherent, and common, conceptual framework. Detailed discussions of the various controversial issues are avoided except in instances where new viewpoints are advanced. Instead, extensive references are made to the growing literature on the subject, and generous explanatory remarks are made to guide the reader who wishes to delve more deeply into the underpinnings of the subject matter.     

Solar Magnetoconvection – (Invited Review)

In recent years the study of how magnetic fields interact with thermal convection in the Sun has made significant advances. These are largely due to the rapidly increasing computer power and its application to more physically relevant parameters regimes and to more realistic physics and geometry in numerical models. Here we present a survey of recent results following one line of investigations and discuss and compare the results of these with observed phenomena.     

Helioseismic Holography of Active-Region Subphotospheres – (Invited Review)

The development of solar acoustic holography has opened a major new diagnostic avenue in local helioseismology. It has revealed `acoustic moats' surrounding sunspots, `acoustic glories' surrounding complex active regions, and `acoustic condensations' suggesting the existence of significant seismic anomalies up to 20 Mm beneath active-region photospheres. Phase-sensitive seismic holography is now yielding high-resolution maps of sound travel-time anomalies caused by magnetic forces in the immediate subphotosphere, apparent thermal enhancements in acoustic moats, and Doppler signatures of subsurface flows. It has given us the first seismic images of a solar flare, and has uncovered a remarkable anomaly in the statistical distribution of seismic emission from acoustic glories. Seismic holography will probably give us the means for early detection of large active regions on the far-surface of the Sun, and possibly of deep subsurface activity as well. This powerful diagnostic now promises a new insight into the hydromechanical and thermal environments of the solar interior in the local perspective.     

Aspects of Three-Dimensional Magnetic Reconnection – (Invited Review)

In this review paper we discuss several aspects of magnetic reconnection theory, focusing on the field-line motions that are associated with reconnection. A new exact solution of the nonlinear MHD equations for reconnective annihilation is presented which represents a two-fold generalization of the previous solutions. Magnetic reconnection at null points by several mechanisms is summarized, including spine reconnection, fan reconnection and separator reconnection, where it is pointed out that two common features of separator reconnection are the rapid flipping of magnetic field lines and the collapse of the separator to a current sheet. In addition, a formula for the rate of reconnection between two flux tubes is derived. The magnetic field of the corona is highly complex, since the magnetic carpet consists of a multitude of sources in the photosphere. Progress in understanding this complexity may, however, be made by constructing the skeleton of the field and developing a theory for the local and global bifurcations between the different topologies. The eruption of flux from the Sun may even sometimes be due to a change of topology caused by emerging flux break-out. A CD-ROM attached to this paper presents the results of a toy model of vacuum reconnection, which suggests that rapid flipping of field lines in fan and separator reconnection is an essential ingredient also in real non-vacuum conditions. In addition, it gives an example of binary reconnection between a pair of unbalanced sources as they move around, which may contribute significantly to coronal heating. Finally, we present examples in TRACE movies of geometrical changes of the coronal magnetic field that are a likely result of large-scale magnetic reconnection. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005248007615     

Basic Principles of Solar Acoustic Holography – (Invited Review)

We summarize the basic principles of holographic seismic imaging of the solar interior, drawing on familiar principles in optics and parallels with standard optical holography. Computational seismic holography is accomplished by the phase-coherent wave-mechanical reconstruction of the p-mode acoustic field into the solar interior based on helioseismic observations at the solar surface. It treats the acoustic field at the solar surface in a way broadly analogous to how the eye treats electromagnetic radiation at the surface of the cornea, wave-mechanically refocusing radiation from submerged sources to render stigmatic images that can be sampled over focal surfaces at any desired depth. Holographic diagnostics offer a straight-forward assessment of the informational content of the observed p-mode spectrum independent of prospective physical models of the local interior anomalies that it represents. Computational holography was proposed as the optimum approach whereby to address the severe diffraction effects that confront standard tomography in the solar p-mode environment. It has given us a number of remarkable discoveries in the last two years and now promises a new insight into solar interior structure and dynamics in the local perspective. We compare the diagnostic roles of simple acoustic-power holography and phase-sensitive holography, and anticipate approaches to solar interior modeling based on holographic signatures. We identify simple computational principles that, applied to high-quality helioseismic observations, make it easy for prospective analysts to produce high-quality holographic images for practical applications in local helioseismology.     

Acoustic Imaging of Solar Active Regions – (Invited Review)

Acoustic imaging is a new method to construct the acoustic signal at a point on the solar surface or in the solar interior with the signals measured at the solar surface. The constructed signals contain both intensity information and phase information. The intensity is computed by summing the squared amplitude of the constructed signal over time. The phase of constructed signals can be studied by the cross-correlation function between the time series constructed with ingoing waves and outgoing waves. The location of the envelope peak of the cross-correlation function and the phase of the cross-correlation function contain different information on the physical conditions of the plasma along the wave path. From the constructed signals, one can form the two-dimensional outgoing intensity map, absorption map, phase-shift map, and envelope-shift map of a target region at different focal depths. The perturbed physical conditions caused by the magnetic fields of active regions manifest in these maps. The outgoing intensity is lower in magnetic regions than the quiet Sun. The group travel time and phase travel time are smaller in magnetic regions than in the quiet Sun. In this paper, we review the studies of active regions, including emerging flux regions, with acoustic imaging.     

Solar Spicules: A Review of Recent Models and Targets for Future Observations – (Invited Review)

Since their discovery over 100 years ago, there have been many suggestions for the origin and development of solar spicules. Because the velocities of spicules are comparable to the sound and Alfvén speeds of the low chromosphere, linear theory cannot fully describe them. Consequently, detailed tests of theoretical ideas had to await the development of computing power that only became available during the 1970s. This work reviews theories for spicules and spicule-like features over approximately the past 25 years, with an emphasis on the models based on nonlinear numerical simulations. These models have given us physical insight into wave propagation in the solar atmosphere, and have helped elucidate how such waves, and associated shock waves, may be capable of creating motions and structures on magnetic flux tubes in the lower solar atmosphere. So far, however, it has been difficult to reproduce the most-commonly-quoted parameters for spicules with these models, using what appears to be the most suitable input parameters. A key impediment to developing satisfactory models has been the lack of reliable observational information, which is a consequence of the small angular size and transient lifetime of spicules. I close with a list of key observational questions to be addressed with space-based satellites, such as the currently operating TRACE satellite, and especially the upcoming Solar-B mission. Answers to these questions will help determine which, if any, of the current models correctly explains spicules.     

Time-Distance Inversion Methods and Results – (Invited Review)

The current interpretations of the travel-time measurements in quiet and active regions on the Sun are discussed. These interpretations are based on various approximations to the 3-D wave equation such as the Fermat principle for acoustic rays and the Born approximation. The ray approximation and its modifications have provided the first view of the 3-D structures and flows in the solar interior. However, more accurate and computationally efficient approximations describing the relation between the wave travel times and the internal properties are required to study the structures and flows in detail. Inversion of the large three-dimensional datasets is efficiently carried out by regularized iterative methods. Some results of time-distance inversions for emerging active regions, sunspots, meridional flows and supergranulation are presented. An active region which emerged on the solar disk in January 1998, was studied from SOHO/MDI for eight days, both before and after its emergence at the surface. The results show a complicated structure of the emerging region in the interior, and suggest that the emerging flux ropes travel very quickly through the depth range of our observations. The estimated speed of emergence is about 1.3 km s^–1. Tomographic images of a large sunspot reveal sunspot `fingers' - long narrow structures at a depth of about 4 Mm, which connect the sunspot with surrounding pores of the same polarity.     

Conditions for the Formation and Maintenance of Filaments – (Invited Review)

Observational conditions for the formation and maintenance of filaments are reviewed since 1989 in the light of recent findings on their structure, chirality, inferred magnetic topology, and mass flows. Recent observations confirm the necessary conditions previously cited: (1) their location at a boundary between opposite-polarity magnetic fields (2) a system of overlying coronal loops, (3) a magnetically-defined channel beneath, (4) the convergence of the opposite-polarity network magnetic fields towards their common boundary within the channel and (5) cancellation of magnetic flux at the common polarity boundary. Evidence is put forth for three additional conditions associated with fully developed filaments: (A) field-aligned mass flows parallel with their fine structure (B) a multi-polar background source of small-scale magnetic fields necessary for the formation of the filament barbs and (C) a handedness property known as chirality which requires them to be either of two types, dextral or sinistral. One-to-one relationships have been established between the chirality of filaments and the chirality of their filament channels and overlying coronal arcades. These findings reinforce earlier evidence that every filament magnetic field is separate from the magnetic field of the overlying arcade but both are parts of a larger magnetic field system. The larger system has at least quadrupolar footprints in the photosphere and includes the filament channel and subphotospheric magnetic fields, This ‘systems’ view of filaments and their environment enables new perspectives on why arcades and channels are invariable conditions for their existence. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005026814076     

Towards Understanding Solar Convection and Activity – (Invited Review)

The dynamics of the large-scale eddies which advect angular momentum through the convection zone is controlled in a significant way by the boundary conditions, which, if they are not modelled adequately, do not lead to a distribution of angular velocity that is consistent with observation. The transition boundary layer separating the convection zone from the radiative interior is thought to play a critical role in controlling the magnetic field in the convection zone, and is probably not wholly irrelevant to understanding the cycle of solar activity.     

Waves and Oscillations in the Corona – (Invited Review)

It has long been suggested on theoretical grounds that MHD waves must occur in the solar corona, and have important implications for coronal physics. An unequivocal identification of such waves has however proved elusive, though a number of events were consistent with an interpretation in terms of MHD waves. Recent detailed observations of waves in events observed by SOHO and TRACE removes that uncertainty, and raises the importance of MHD waves in the corona to a higher level. Here we review theoretical aspects of how MHD waves and oscillations may occur in a coronal medium. Detailed observations of waves and oscillations in coronal loops, plumes and prominences make feasible the development of coronal seismology, whereby parameters of the coronal plasma (notably the Alfvén speed and through this the magnetic field strength) may be determined from properties of the oscillations. MHD fast waves are refracted by regions of low Alfvén speed and slow waves are closely field-guided, making regions of dense coronal plasma (such as coronal loops and plumes) natural wave guides for MHD waves. There are analogies with sound waves in ocean layers and with elastic waves in the Earth's crust. Recent observations also indicate that coronal oscillations are damped. We consider the various ways this may be brought about, and its implications for coronal heating.     

4π Models of CMEs and ICMEs (Invited Review)

Coronal mass ejections (CMEs), which dynamically connect the solar surface to the far reaches of interplanetary space, represent a major manifestation of solar activity. They are not only of principal interest but also play a pivotal role in the context of space weather predictions. The steady improvement of both numerical methods and computational resources during recent years has allowed for the creation of increasingly realistic models of interplanetary CMEs (ICMEs), which can now be compared to high-quality observational data from various space-borne missions. This review discusses existing models of CMEs, characterizing them by scientific aim and scope, CME initiation method, and physical effects included, thereby stressing the importance of fully 3D (??4????) spatial coverage.     

The differential rotation of ε Eri from MOST data

From high-precision MOST photometry spanning 35 days the existence of two spots rotating with slightly differing periods is confirmed. From the marginal probability distribution of the derived differential rotation parameter k its expectation value as well as confidence limits are computed directly from the data. The result depends on the assumed range in inclination i, not on the shape of the prior distributions. Two cases have been considered: (a) The priors for angles, inclination i of the star and spot latitudes β 1,2, are assumed to be constant over i, β 1, and β 2; (b) the priors are assumed to be constant over cos i, sin β 1, and sin β 2. In both cases the full range of inclination is considered: 0° ≤ i ≤ 90°. Scalefree parameters, i. e. periods and spot areas (in case of small spots) are taken logarithmically. Irrespective of the shape of the prior, k is restricted to 0.03 ≤ k ≤ 0.10 (1 σ limits). The inclination i of the star is photometrically ill-defined. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid Dynamics and MHD of the Solar Convection Zone and Tachocline: Current Understanding and Unsolved Problems – (Invited Review)

We review recent progress and define unanswered scientific questions in five related topics: granulation- to supergranulation-scale convection and magnetic structures; global convection and circulation; the rise of magnetic flux tubes to the photosphere, and their injection into the base of the convection zone; tachocline fluid dynamics and MHD; and the solar dynamo. We close with a set of observational `targets' for helioseismologists to aim for.     

Short-term periodicities of the sun's ‘mean’ and differential rotation

We have looked for periodicities in solar differential rotation on time scales shorter than the 11-year solar cycle through the power- spectrum analysis of the differential rotation parameters determined from Mt. Wilson velocity data (1969–1994) and Greenwich sunspot group data (1879–1976). We represent the differential rotation by a set of Gegenbauer polynomials (()= + (5sin₂–1)+ (21sin₄–14sin₂+1)). For the Mt. Wilson data, we focus on observations obtained after 1981 due to the reduced instrumental noise and have binned the data into intervals of 19 days. We calculated annual averages for the sunspot data to reduce the uncertainty and corrected for outliers occuring during solar cycle minima. The power spectrum of the photospheric mean rotation , determined from the velocity data during 1982–1994, shows peaks at the periods of 6.7–4.4 yr, 2.2 ± 0.4 yr, 1.2 ± 0.2 yr, and 243 ± 10 day with 99.9% confidence level, which are similar to periods found in other indicators of solar activity suggesting that they are of solar origin. However, this result has to be confirmed with other techniques and longer data sets. The 11-yr periodicity is insignificant or absent in . The power spectra of the differential rotation parameters and , determined from the same subset, show only the solar cycle period with a 99.9% confidence level.The time series of determined from the yearly sunspot group data obtained during 1879–1976 is very similar to the corresponding time series of . After correcting for data with large error bars (occurring during cycle minima), we find periods, which are most likely harmonics of the solar cycle, such as 18.3 ± 3.0 yr and 7.5 ± 0.5 yr in and confirmed these and the 3.0 ± 0.1 yr period in . The original time series show in addition some shorter periods, absent in the corrected data, representing temporal variations during cycle minimum. Given their large error bars, it is uncertain whether they represent a solar variation or not. The results presented here show considerable differences in the periodicities of and determined from the velocity data and the spot group data. These differences may be explained by assuming that the rotation rates determined from velocity and sunspot data represent the rotation rates of the Sun's surface layers and of somewhat deeper layers.     

The nonlinear solar dynamo and differential rotation: A Taylor number puzzle?

We consider dynamically consistent mean-field dynamos in a spherical shell of incompressible fluid. The generation of magnetic field and differential rotation is parameterized by the - and -effects, respectively. Extending previous investigations, we include now the cases of moderate and rapid rotation in the sense that the inverse Rossby number can approach or exceed unity: This can lead to disk-shaped -contours, which are in better accordance with recent results of helioseismology than cylindrical -contours. On the other hand, in order to obtain -dynamo cycles the Taylor number has to be so large, that eventually cylindrical -contours become unavoidable (cf. Taylor-Proudman theorem). We discuss the different possibilities in a state diagram, where the inverse Rossby number and the relative correlation length are taken as the elementary parameters for mean-field dynamos.     

Pick-up Ion Measurements in the Heliosphere – A Review

Measurements of the composition and spatial distribution of pick-up ions inside the heliosphere are reviewed. The first interstellar ⁴He⁺pick-up ions were detected with the SULEICA instrument on the AMPTE spacecraft near Earth's orbit. Most data on pick-up ions were taken in the solar-wind and suprathermal energy range of SWICS on Ulysses while the spacecraft cruised from 1.4 to 5.4 AU and explored the high-latitude heliosphere and solar wind from the ecliptic to ± 80^° heliolatitude. This includes the discovery of H⁺, ⁴He⁺⁺, ³He⁺, N⁺,O⁺, and Ne⁺ pick-up ions that originate from the interstellar neutralgas penetrating the heliosphere. From their fluxes properties of the interaction region between the heliosphere and the Local Interstellar Cloud such as the limits on filtration and the strength of the interstellar magnetic field have been revealed. Detailed analysis of the velocity distributions of pick-up ions led to 1) the discovery of a new distinct source, the so-called Inner Source, consisting of atoms released from interstellar and interplanetary dust inside the heliosphere, 2) the determination of pick-up ion transport parameters such as the long mean free path for pitch-angle scattering of order1 AU, and 3) detailed knowledge on the very preferential injection and acceleration of pick-up ions during interplanetary energetic particle events such as Co-rotating Interaction Regions and Coronal Mass Ejections. SWICS measurements have fully confirmed the theory of Fisk, Koslovsky, and Ramaty that pick-up ions derived from the interstellar gas are the dominant source of the Anomalous Cosmic Rays; they are pre-accelerated inside the heliosphere and re-accelerated at the solar-wind Termination Shock according to Pesses, Eichler, and Jokipii. The data indicate that the Inner Source of pick-up ionsis largely responsible for the occurence of C⁺ in the Anomalous Cosmic Rays. The abundances of recently discovered Inner-Source Mg⁺ and Si⁺ are solar-wind like and consistent with their abundances in the energetic particles associated with Co-rotating Interaction Regions. Knowledge on the injection and acceleration processes in Co-rotating Interaction Regions is applied to discuss the current observational evidence for the Interplanetary Focusing Cone of the interstellar neutral gas due to the Sun's gravitational force. The 25–150 keV/amu suprathermal ⁴He⁺ pick-up ion fluxes measured by CELIAS/STOF on board SOHO over 360^° of ecliptic longitude represent a `local' ionization and acceleration of interstellar atoms at 1 AU or smaller heliocentric distances. Completing the first limited data set of SULEICA/AMPTE on ⁴He⁺ pick-up ions they indicate a density enhancement in the Interplanetary Focusing Cone which is confirmed by recent SWICS/ACE data. Clear evidence for signatures in ecliptic longitude are found in the data on energetic neutral H fluxes observed with the CELIAS/HSTOF sensor on board SOHO. These fluxes are enhanced in the upstream and downstream directions of the interstellar wind. Detection of energetic H atoms, which propagate unaffected by the Heliospheric Magnetic Field, provided for the first time a diagnostic tool for observations near Earth to analyze the structure in ecliptic longitude of the interface region between the heliosphere and the Local Interstellar Cloud. This revised version was published online in July 2006 with corrections to the Cover Date.