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Self-organization properties of sustained magnetized plasma are applied to selected solar data to understand solar magnetic fields. Torsional oscillations are speed-up and slow-down bands of the azimuthal flow that correlate with the solar cycle, and they imply the existence of a symmetric solar dynamo with a measured polar flux of 3x10^14 Wb. It is shown that the solar dynamo is thin (~0.1 Mm gradient scale size) and powerful (~10^23 W). These properties are found from the amplitude of the torsional oscillations and the relationship of their velocity contours to solar magnetograms supports the result. The dynamo has enough power to heat the chromosphere and to power the corona and the solar wind. The dynamo also causes a rigid rotation of the heliosphere out to at least the corona and the relationship of the rotation of the corona to solar magnetograms supports this result as well. The thin solar dynamo sustains a thin stable minimum energy state that seems to be covering most of the solar surface just below the photosphere. The magnetic field lines of the minimum energy state should be parallel to the solar surface and rotate with distance from the surface with 2{pi} radians of rotation in ~1 Mm Resistive diffusion helps to push the magnetic fields to the surface and the global magnetic structure (GMS) seems to lose {pi} radians every 11 years, causing the observed 180 degree flipping of the solar magnetic field. The thin sheets of magnetized plasma in solar prominences may be the lost thin sheets of the GMS. For completeness, the formation of sunspots, CMEs and flares is discussed.
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We explore the suggestions by Uzdensky (2007) and Cassak et al. (2008) that coronal loops heated by magnetic reconnection should self-organize to a state of marginal collisionality. We discuss their model of coronal loop dynamics with a one-dimensional hydrodynamic calculation. We assume that many current sheets are present, with a distribution of thicknesses, but that only current sheets thinner than the ion skin depth can rapidly reconnect. This assumption naturally causes a density dependent heating rate which is actively regulated by the plasma. We report 9 numerical simulation results of coronal loop hydrodynamics in which the absolute values of the heating rates are different but their density dependences are the same. We find two regimes of behavior, depending on the amplitude of the heating rate. In the case that the amplitude of heating is below a threshold value, the loop is in stable equilibrium. Typically the upper and less dense part of coronal loop is collisionlessly heated and conductively cooled. When the amplitude of heating is above the threshold, the conductive flux to the lower atmosphere required to balance collisionless heating drives an evaporative flow which quenches fast reconnection, ultimately cooling and draining the loop until the cycle begins again. The key elements of this cycle are gravity and the density dependence of the heating function. Some additional factors are present, including pressure driven flows from the loop top, which carry a large enthalpy flux and play an important role in reducing the density. We find that on average the density of the system is close to the marginally collisionless value.
The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS) and space-born (for example Hinode and SDO) instruments. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV-images of the radiating coronal plasma.
Magnetic fields play a crucial role at all stages of the formation of low mass stars and planetary systems. In the final stages, in particular, they control the kinematics of in-falling gas from circumstellar discs, and the launching and collimation of spectacular outflows. The magnetic coupling with the disc is thought to influence the rotational evolution of the star, while magnetised stellar winds control the braking of more evolved stars and may influence the migration of planets. Magnetic reconnection events trigger energetic flares which irradiate circumstellar discs with high energy particles that influence the disc chemistry and set the initial conditions for planet formation. However, it is only in the past few years that the current generation of optical spectropolarimeters have allowed the magnetic fields of forming solar-like stars to be probed in unprecedented detail. In order to do justice to the recent extensive observational programs new theoretical models are being developed that incorporate magnetic fields with an observed degree of complexity. In this review we draw together disparate results from the classical electromagnetism, molecular physics/chemistry, and the geophysics literature, and demonstrate how they can be adapted to construct models of the large scale magnetospheres of stars and planets. We conclude by examining how the incorporation of multipolar magnetic fields into new theoretical models will drive future progress in the field through the elucidation of several observational conundrums.
Potential field extrapolations are widely used as minimum-energy models for the Suns coronal magnetic field. As the reference to which other magnetic fields are compared, they have -- by any reasonable definition -- no global (signed) magnetic helicity. Here we investigate the internal topological structure that is not captured by the global helicity integral, by splitting it into individual field line helicities. These are computed using potential field extrapolations from magnetogram observations over Solar Cycle 24, as well as for a simple illustrative model of a single bipolar region in a dipolar background. We find that localised patches of field line helicity arise primarily from linking between strong active regions and their overlying field, so that the total unsigned helicity correlates with the product of photospheric and open fluxes. Within each active region, positive and negative helicity may be unbalanced, but the signed helicity is only around a tenth of the unsigned helicity. Interestingly, in Cycle 24, there is a notable peak in unsigned helicity caused by a single large active region. On average, the total unsigned helicity at the resolution considered is approximately twice the typical signed helicity of a single real active region, according to non-potential models in the literature.
This paper is the second in a series of studies working towards constructing a realistic, evolving, non-potential coronal model for the solar magnetic carpet. In the present study, the interaction of two magnetic elements is considered. Our objectives are to study magnetic energy build up, storage and dissipation as a result of emergence, cancellation, and flyby of these magnetic elements. In the future these interactions will be the basic building blocks of more complicated simulations involving hundreds of elements. Each interaction is simulated in the presence of an overlying uniform magnetic field, which lies at various orientations with respect to the evolving magnetic elements. For these three small-scale interactions, the free energy stored in the field at the end of the simulation ranges from $0.2-2.1times 10^{26}$ ergs, while the total energy dissipated ranges from $1.3-6.3times 10^{26}$ ergs. For all cases, a stronger overlying field results in higher energy storage and dissipation. For the cancellation and emergence simulations, motion perpendicular to the overlying field results in the highest values. For the flyby simulations, motion parallel to the overlying field gives the highest values. In all cases, the free energy built up is sufficient to explain small-scale phenomena such as X-ray bright points or nanoflares. In addition, if scaled for the correct number of magnetic elements for the volume considered, the energy continually dissipated provides a significant fraction of the quiet Sun coronal heating budget.
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