Theory and Modeling of Planetary Dynamos

Numerical dynamo models are increasingly successful in modeling many features of the geomagnetic field. Moreover, they have proven to be a useful tool for understanding how the observations connect to the dynamo mechanism. More recently, dynamo simulations have also ventured to explain the surprising diversity of planetary fields found in our solar system. Here, we describe the underlying model equations, concentrating on the Boussinesq approximations, briefly discuss the numerical methods, and give an overview of existing model variations. We explain how the solutions depend on the model parameters and introduce the primary dynamo regimes. Of particular interest is the dependence on the Ekman number which is many orders of magnitude too large in the models for numerical reasons. We show that a minor change in the solution seems to happen at $\mbox {E}=3\mbox {$\times 10^{-6}$}$ whose significance, however, needs to be explored in the future. We also review three topics that have been a focus of recent research: field reversal mechanisms, torsional oscillations, and the influence of Earth’s thermal mantle structure on the dynamo. Finally we discuss the possibility of tidally or precession driven planetary dynamos.     

Auroral Substorms: Search for Processes Causing the Expansion Phase in Terms of the Electric Current Approach

Auroral substorms are mostly manifestations of dissipative processes of electromagnetic energy. Thus, we consider a sequence of processes consisting of the power supply (dynamo), transmission (currents/circuits) and dissipations (auroral substorms-the end product), namely the electric current line approach. This work confirms quantitatively that after accumulating magnetic energy during the growth phase, the magnetosphere unloads the stored magnetic energy impulsively in order to stabilize itself. This work is based on our result that substorms are caused by two current systems, the directly driven (DD) current system and the unloading system (UL). The most crucial finding in this work is the identification of the UL (unloading) current system which is responsible for the expansion phase. A very tentative sequence of the processes leading to the expansion phase (the generation of the UL current system) is suggested for future discussions.

1. (1)
   The solar wind-magnetosphere dynamo enhances significantly the plasma sheet current when its power is increased above \(10^{18}~\mbox{erg}/\mbox{s}\) (\(10^{11}\) w).
    
2. (2)
   The magnetosphere accumulates magnetic energy during the growth phase, because the ionosphere cannot dissipate the increasing power because of a low conductivity. As a result, the magnetosphere is inflated, accumulating magnetic energy.
    
3. (3)
   When the power reaches \(3\mbox{--}5\times 10^{18}~\mbox{erg}/\mbox{s}\) (\(3\mbox{--}5\times 10^{11}\) w) for about one hour and the stored magnetic energy reaches \(3\mbox{--}5\times10^{22}\) ergs (\(10^{15}\) J), the magnetosphere begins to develop perturbations caused by current instabilities (the current density \({\approx}3\times 10^{-12}~\mbox{A}/\mbox{cm}^{2}\) and the total current \({\approx}10^{6}~\mbox{A}\) at 6 Re). As a result, the plasma sheet current is reduced.
    
4. (4)
   The magnetosphere is thus deflated. The current reduction causes \(\partial B/\partial t > 0\) in the main body of the magnetosphere, producing an earthward electric field. As it is transmitted to the ionosphere, it becomes equatorward-directed electric field which drives both Pedersen and Hall currents and thus generates the UL current system.
    
5. (5)
   A significant part of the magnetic energy is accumulated in the main body of the magnetosphere (the inner plasma sheet) between 4 Re and 10 Re, because the power (Poynting flux \([ \boldsymbol{E} \times \boldsymbol{B} ])\) is mainly directed toward this region which can hold the substorm energy.
    
6. (6)
   The substorm intensity depends on the location of the energy accumulation (between 4 Re and 10 Re), the closer the location to the earth, the more intense substorms becomes, because the capacity of holding the energy is higher at closer distances. The convective flow toward the earth brings both the ring current and the plasma sheet current closer when the dynamo power becomes higher.
    

This proposed sequence is not necessarily new. Individual processes involved have been considered by many, but the electric current approach can bring them together systematically and provide some new quantitative insights.

     

Solar Wind Turbulence and the Role of Ion Instabilities

Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: (i) weakness of collisional dissipation and (ii) presence of several characteristic space and time scales. In this paper we discuss observational properties of solar wind turbulence in a large range from the MHD to the electron scales. At MHD scales, within the inertial range, turbulence cascade of magnetic fluctuations develops mostly in the plane perpendicular to the mean field, with the Kolmogorov scaling $k_{\perp}^{-5/3}$ for the perpendicular cascade and $k_{\|}^{-2}$ for the parallel one. Solar wind turbulence is compressible in nature: density fluctuations at MHD scales have the Kolmogorov spectrum. Velocity fluctuations do not follow magnetic field ones: their spectrum is a power-law with a ?3/2 spectral index. Probability distribution functions of different plasma parameters are not Gaussian, indicating presence of intermittency. At the moment there is no global model taking into account all these observed properties of the inertial range. At ion scales, turbulent spectra have a break, compressibility increases and the density fluctuation spectrum has a local flattening. Around ion scales, magnetic spectra are variable and ion instabilities occur as a function of the local plasma parameters. Between ion and electron scales, a small scale turbulent cascade seems to be established. It is characterized by a well defined power-law spectrum in magnetic and density fluctuations with a spectral index close to ?2.8. Approaching electron scales, the fluctuations are no more self-similar: an exponential cut-off is usually observed (for time intervals without quasi-parallel whistlers) indicating an onset of dissipation. The small scale inertial range between ion and electron scales and the electron dissipation range can be together described by $\sim k_{\perp}^{-\alpha}\exp(-k_{\perp}\ell_{d})$ , with α?8/3 and the dissipation scale ? _d close to the electron Larmor radius ? _d ?ρ _e . The nature of this small scale cascade and a possible dissipation mechanism are still under debate.     

CME Theory and Models

This chapter provides an overview of current efforts in the theory and modeling of CMEs. Five key areas are discussed: (1) CME initiation; (2) CME evolution and propagation; (3) the structure of interplanetary CMEs derived from flux rope modeling; (4) CME shock formation in the inner corona; and (5) particle acceleration and transport at CME driven shocks. In the section on CME initiation three contemporary models are highlighted. Two of these focus on how energy stored in the coronal magnetic field can be released violently to drive CMEs. The third model assumes that CMEs can be directly driven by currents from below the photosphere. CMEs evolve considerably as they expand from the magnetically dominated lower corona into the advectively dominated solar wind. The section on evolution and propagation presents two approaches to the problem. One is primarily analytical and focuses on the key physical processes involved. The other is primarily numerical and illustrates the complexity of possible interactions between the CME and the ambient medium. The section on flux rope fitting reviews the accuracy and reliability of various methods. The section on shock formation considers the effect of the rapid decrease in the magnetic field and plasma density with height. Finally, in the section on particle acceleration and transport, some recent developments in the theory of diffusive particle acceleration at CME shocks are discussed. These include efforts to combine self-consistently the process of particle acceleration in the vicinity of the shock with the subsequent escape and transport of particles to distant regions.     

Galaxien vom Magellanschen Typ

In the first part of this paper the morphological structure of Magellanic type galaxies (Irr I) is investigated. The galaxies of Magellanic type present a basic pattern consisting of a disk, a bar, stellar arms, rudimentary or well developed, spiral filaments and condensations in the disk. With the help of this pattern a well-defined classification scheme is set up. The subgroup of Irr II-systems consists of normal galaxies which are more or less tidally disturbed. Bursts of star formation have a great influence on structure and colour of irregular galaxies. Using the ESO-B Atlas, 580 galaxies of Magellanic type (out of a sample of 3187 galaxies) were classified; 57 are new SB(s)m systems (prototype Large Magellanic Cloud). The sample shows dominant bar structures at the classification stages d-, dm-, and m. A striking feature is the asymmetric position of bar and disk. This asymmetry is a general characteristic of galaxies of types SBd-SBm IB. The asymmetry can be discribed by a relative displacement parameter \(\tilde \Lambda \) = 0.78 ±0.15, defined as the quotient of small and great distance of the bar center to the optical edge of the disk. The displacement cannot be explained by tidal interaction with neighbouring galaxies. In the second part of the paper the kinematics and dynamics of the Large Magellanic Cloud (LMC) as the nearest and best-known example of a galaxy of Magellanic type is investigated. The main structural features of the LMC are disk, bar, rudimentary and well developed stellar arms as well as spiral filaments (not necessarily connected with density waves); the γ-structure is a broken up ring structure. Embedded into these features are young, asymmetrically located spiral arm filaments. As an explanation for these structures stochastic start formation in an ordered chain reaction is proposed. The pattern of the spiral arm filaments is determined by the rotation curve. The morphological peculiarities of the LMC can also be detected in other galaxies of that type. The mean absolute displacement of the centers of bar and disk, determined from 18 galaxies, is Λ = 800 pc. The displacement between the bar center and the symmetry center of the rotation curve is of the same order. The presently known radial velocities of planetary nebulae, star clusters, Hi and Hii regions and stars belonging to the LMC have been collected in a catalogue as the basis of a discussion of the kinematics and dynamics of the LMC. Contrary to earlier work, we have used, for the first time, the radial velocities of objects of all subgroups together by a proper weighting scheme. Thus the basic kinematics and dynamics of the LMC has been deduced. The radial velocity field shows no central symmetry; it is characterized by large scale (2–3 kpc) disturbances. By comparison with the velocity field of other galaxies three main disturbances are identified: an oval distortion of the velocity field in the bar region, a radial velocity field around 30 Doradus, and disturbances connected with a warp or material above the disk in the southern quadrants. The results of a detailed numerical analysis of these three facts can be summed up as follows:

1. The rotation curve is determined over 10° diameter; it shows differential rotation, an asymmetric behavior in the south and a double structure in its Hi component. The rotation center is displaced by 0°.7 from the bar center. The orientation of the kinematic line of nodes and the systemic velocity vary as functions of the distance from the center. Therefore, it is possible to show definitely that large scale disturbances (warping, z-structure and streaming motions) are existent.
2. By variation of the kinematical parameters (systemic velocity, inclination, orientation of the line of nodes, rotation center) the dispersion of the measured radial velocities was minimized and the basic rotation curve determined. The rotation curves for the north and south side of the LMC are significantly different. The south side is either warped or there is material above the main plane. There seems to be a connection between this structure, the Panmagellanic Gas and the Magellanic Stream. The north side appears to be free of distorsion.
3. The residual velocity field (observed minus model) deduced from a basic rotation curve shows that the displacement between the rotation center and the bar center is not caused by local streaming motions. The rotation center must be the mass center. The bar shows a radial velocity field; in the 30 Doradus region inward and outward motions are found.

The mean velocity dispersion of population I objects is 10.5 km s^-1 of population II objects 16.0 km s^-1. Red and blue globular clusters show different kinematical behavior. By comparison of eight mass models, taking into consideration thickness effects and controlled by surface photometric data, the mass of the LMC is found to be (0.5 ± 0.1) × 10¹⁰ \(\mathfrak{M}_ \odot \) (assuming the inclination 33°, the systemic velocity 46.9 km s^-1, and the distance 56 kpc). Dynamically, the LMC can be described by a dominating disk potential with an additional bar potential as a disturbance. The mass of the bar is 0.6 × 10⁹ \(\mathfrak{M}_ \odot \) . The stable neutral point of such a configuration can be found in the residual velocity field. The absorption feature crossing the bar coincides with the maximum velocity gradient of the computed radial velocity field in the plane of the system.     

S/WAVES: The Radio and Plasma Wave Investigation on the STEREO Mission

This paper introduces and describes the radio and plasma wave investigation on the STEREO Mission: STEREO/WAVES or S/WAVES. The S/WAVES instrument includes a suite of state-of-the-art experiments that provide comprehensive measurements of the three components of the fluctuating electric field from a fraction of a hertz up to 16 MHz, plus a single frequency channel near 30 MHz. The instrument has a direction finding or goniopolarimetry capability to perform 3D localization and tracking of radio emissions associated with streams of energetic electrons and shock waves associated with Coronal Mass Ejections (CMEs). The scientific objectives include: (i) remote observation and measurement of radio waves excited by energetic particles throughout the 3D heliosphere that are associated with the CMEs and with solar flare phenomena, and (ii) in-situ measurement of the properties of CMEs and interplanetary shocks, such as their electron density and temperature and the associated plasma waves near 1 Astronomical Unit (AU). Two companion papers provide details on specific aspects of the S/WAVES instrument, namely the electric antenna system (Bale et al., Space Sci. Rev., 2007) and the direction finding technique (Cecconi et al., Space Sci. Rev., 2007).     

Augmented Empirical Models of Plasmaspheric Density and Electric Field Using IMAGE and CLUSTER Data

Empirical models for the plasma densities in the inner magnetosphere, including plasmasphere and polar magnetosphere, have been in the past derived from in situ measurements. Such empirical models, however, are still in their initial phase compared to magnetospheric magnetic field models. Recent studies using data from CRRES, Polar, and Image have significantly improved empirical models for inner-magnetospheric plasma and mass densities. Comprehensive electric field models in the magnetosphere have been developed using radar and in situ observations at low altitude orbits. To use these models at high altitudes one needs to rely strongly on the assumption of equipotential magnetic field lines. Direct measurements of the electric field by the Cluster mission have been used to derive an equatorial electric field model in which reliance on the equipotential assumption is less. In this paper we review the recent progress in developing empirical models of plasma densities and electric fields in the inner magnetosphere with emphasis on the achievements from the Image and Cluster missions. Recent results from other satellites are also discussed when they are relevant.     

Electric Fields and Magnetic Fields in the Plasmasphere: A Perspective From CLUSTER and IMAGE

The electric field and magnetic field are basic quantities in the plasmasphere measured since the 1960s. In this review, we first recall conventional wisdom and remaining problems from ground-based whistler measurements. Then we show scientific results from Cluster and Image, which are specifically made possible by newly introduced features on these spacecraft, as follows. 1. In situ electric field measurements using artificial electron beams are successfully used to identify electric fields originating from various sources. 2. Global electric fields are derived from sequences of plasmaspheric images, revealing how the inner magnetospheric electric field responds to the southward interplanetary magnetic fields and storms/substorms. 3. Understanding of sub-auroral polarization stream (SAPS) or sub-auroral ion drifts (SAID) are advanced through analysis of a combination of magnetospheric and ionospheric measurements from Cluster, Image, and DMSP. 4. Data from multiple spacecraft have been used to estimate magnetic gradients for the first time.     

Multi-Wavelength Observations of CMEs and Associated Phenomena

This chapter reviews how our knowledge of CMEs and CME-associated phenomena has been improved, since the launch of the SOHO mission, thanks to multi-wavelength analysis. The combination of data obtained from space-based experiments and ground based instruments allows us to follow the space-time development of an event from the bottom of the corona to large distances in the interplanetary medium. Since CMEs originate in the low solar corona, understanding the physical processes that generate them is strongly dependant on coordinated multi-wavelength observations. CMEs display a large diversity in morphology and kinematic properties, but there is presently no statistical evidence that those properties may serve to group them into different classes. When a CME takes place, the coronal magnetic field undergoes restructuring. Much of the current research is focused on understanding how the corona sustains the stresses that allow the magnetic energy to build up and how, later on, this magnetic energy is released during eruptive flares and CMEs. Multi-wavelength observations have confirmed that reconnection plays a key role during the development of CMEs. Frequently, CMEs display a rather simple shape, exhibiting a well known three-part structure (bright leading edge, dark cavity and bright knot). These types of events have led to the proposal of the ‘`standard model’' of the development of a CME, a model which predicts the formation of current sheets. A few recent coronal observations provide some evidence for such sheets. Other more complex events correspond to multiple eruptions taking place on a time scale much shorter than the cadence of coronagraph instruments. They are often associated with large-scale dimming and coronal waves. The exact nature of these waves and the physical link between these different manifestations are not yet elucidated. We also discuss what kind of shocks are produced during a flare or a CME. Several questions remain unanswered. What is the nature of the shocks in the corona (blast-wave or piston-driven?) How they are related to Moreton waves seen in Hα? How they are related to interplanetary shocks? The last section discusses the origin of energetic electrons detected in the corona and in the interplanetary medium. “Complex type III-like events,”which are detected at hectometric wavelengths, high in the corona, and are associated with CMEs, appear to originate from electrons that have been accelerated lower in the corona and not at the bow shock of CMEs. Similarly, impulsive energetic electrons observed in the interplanetary medium are not the exclusive result of electron acceleration at the bow shocks of CMEs; rather they have a coronal origin.     

Cosmological Distance Indicators

We review three distance measurement techniques beyond the local universe: (1) gravitational lens time delays, (2) baryon acoustic oscillation (BAO), and (3) HI intensity mapping. We describe the principles and theory behind each method, the ingredients needed for measuring such distances, the current observational results, and future prospects. Time-delays from strongly lensed quasars currently provide constraints on \(H_{0}\) with \(<4\%\) uncertainty, and with \(1\%\) within reach from ongoing surveys and efforts. Recent exciting discoveries of strongly lensed supernovae hold great promise for time-delay cosmography. BAO features have been detected in redshift surveys up to \(z\lesssim0.8\) with galaxies and \(z\sim2\) with Ly-\(\alpha\) forest, providing precise distance measurements and \(H_{0}\) with \(<2\%\) uncertainty in flat \(\Lambda\)CDM. Future BAO surveys will probe the distance scale with percent-level precision. HI intensity mapping has great potential to map BAO distances at \(z\sim0.8\) and beyond with precisions of a few percent. The next years ahead will be exciting as various cosmological probes reach \(1\%\) uncertainty in determining \(H_{0}\), to assess the current tension in \(H_{0}\) measurements that could indicate new physics.     

GeV Particle Acceleration in Solar Flares and Ground Level Enhancement (GLE) Events

Ground Level Enhancement (GLE) events represent the most energetic class of solar energetic particle (SEP) events, requiring acceleration processes to boost ?1?GeV ions in order to produce showers of secondary particles in the Earth’s atmosphere with sufficient intensity to be detected by ground-level neutron monitors, above the background of cosmic rays. Although the association of GLE events with both solar flares and coronal mass ejections (CMEs) is undisputed, the question arises about the location of the responsible acceleration site: coronal flare reconnection sites, coronal CME shocks, or interplanetary shocks? To investigate the first possibility we explore the timing of GLE events with respect to hard X-ray production in solar flares, considering the height and magnetic topology of flares, the role of extended acceleration, and particle trapping. We find that 50% (6 out of 12) of recent (non-occulted) GLE events are accelerated during the impulsive flare phase, while the remaining half are accelerated significantly later. It appears that the prompt GLE component, which is observed in virtually all GLE events according to a recent study by Vashenyuk et al. (Astrophys. Space Sci. Trans. 7(4):459–463, 2011), is consistent with a flare origin in the lower corona, while the delayed gradual GLE component can be produced by both, either by extended acceleration and/or trapping in flare sites, or by particles accelerated in coronal and interplanetary shocks.     

Identifications of some highly-ionized iron and nickel lines in the 200–400 Å region of the solar spectrum

A number of previously unclassified multiplets of Fexiv, xiii, xii, and xi produced by transitions of the type 3s ²3p ⁿ -3s3p ⁿ⁺¹ are identified in the XUV spectrum of the Sun. The iron lines account for most of the previously unidentified strong lines between 330 and 370 Å. Solar observations of especial value for the investigation of the 300–400 Å region were the slitless spectroheliograms of September 22, 1968 (Purcell and Tousey, 1969) and November 4, 1969 (Tousey, 1971) — on which the image of a flare was recorded. Other solar identifications in the same spectral region include the resonance lines of Nixvii and Nixviii, and one 3p-3d multiplet of Fexiii. The solar blend at 417 Å involving the Fexv inter-combination line and Sxiv is resolved.     

The Solar Dynamo

It is generally accepted that the strong toroidal magnetic fields that emerge through the solar surface in sunspots and active regions are formed by the action of differential rotation on a poloidal field, and then stored in or near the tachocline at the base of the Sun’s convection zone. The problem is how to explain the generation of a reversed poloidal field from this toroidal flux—a process that can be parametrised in terms of an α-effect related to some form of turbulent helicity. Here we first outline the principal patterns that have to be explained: the 11-year activity cycle, the 22-year magnetic cycle and the longer term modulation of cyclic activity, associated with grand maxima and minima. Then we summarise what has been learnt from helioseismology about the Sun’s internal structure and rotation that may be relevant to our subject. The ingredients of mean-field dynamo models are differential rotation, meridional circulation, turbulent diffusion, flux pumping and the α-effect: in various combinations they can reproduce the principal features that are observed. To proceed further, it is necessary to rely on large-scale computation and we summarise the current state of play.     

Ion Composition of the Earth’s Radiation Belts in the Range from 100 keV to $100\mbox{ MeV}/\mbox{nucleon}$: Fifty Years of Research

Spatial, energy and angular distributions of ion fluxes in the Earth’s radiation belts (ERB) near the equatorial plane, at middle geomagnetic latitudes and at low altitudes are systematically reviewed herein. Distributions of all main ion components, from protons to Fe (including hydrogen and helium isotopes), and their variations under the action of solar and geomagnetic activity are considered. For ions with \(Z\geq 2\) and especially for ions with \(Z \geq 9\), these variations are much more than for protons, and these have no direct connection with the intensity of magnetic storms (\(Z\) is the charge of the atomic nucleus with respect to the charge of the proton). The main physical mechanisms for the generation of ion fluxes in the ERB and the losses of these ions are considered. Solar wind, Solar Cosmic Rays (SCR), Galactic Cosmic Rays (GCR), and Anomalous component of Cosmic Rays (ACR) as sources of ions in the ERB are considered.     

Plasma-physical aspects of the solar cycle

Mass motions below the photosphere drive the solar cycle which is associated with variations in the magnetic field structure and accompanying phenomena. In addition to semi-empirical models, dynamo theories have been used to explain the solar cycle. The emergence of magnetic field generated by these mechanisms and its expansion into the corona involves many plasma physical processes. Magnetic buoyancy aids the expulsion of magnetic flux. The corona may respond dynamically or by continually adjusting to a quasi-static force-free or pressure-balanced equilibrium. The formation and disruption of current sheets is significant for the overall structure of the coronal magnetic field and the physics of quiescent prominences. The corona has a fine structure consisting of magnetic loops. The structure and stability of these are important as they are one of the underlying elements which make up the corona.