Present and Future Observing Trends in Atmospheric Magnetoseismology

With modern imaging and spectral instruments observing in the visible, EUV, X-ray, and radio wavelengths, the detection of oscillations in the solar outer atmosphere has become a routine event. These oscillations are considered to be the signatures of a wave phenomenon and are generally interpreted in terms of magnetohydrodynamic (MHD) waves. With multiwavelength observations from ground- and space-based instruments, it has been possible to detect waves in a number of different wavelengths simultaneously and, consequently, to study their propagation properties. Observed MHD waves propagating from the lower solar atmosphere into the higher regions of the magnetized corona have the potential to provide excellent insight into the physical processes at work at the coupling point between these different regions of the Sun. High-resolution wave observations combined with forward MHD modeling can give an unprecedented insight into the connectivity of the magnetized solar atmosphere, which further provides us with a realistic chance to reconstruct the structure of the magnetic field in the solar atmosphere. This type of solar exploration has been termed atmospheric magnetoseismology. In this review we will summarize some new trends in the observational study of waves and oscillations, discussing their origin and their propagation through the atmosphere. In particular, we will focus on waves and oscillations in open magnetic structures (e.g., solar plumes) and closed magnetic structures (e.g., loops and prominences), where there have been a number of observational highlights in the past few years. Furthermore, we will address observations of waves in filament fibrils allied with a better characterization of their propagating and damping properties, the detection of prominence oscillations in UV lines, and the renewed interest in large-amplitude, quickly attenuated, prominence oscillations, caused by flare or explosive phenomena.     

A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric  α²– Ω  dynamo model is derived to explore the characteristics of the axisymmetric  ( m = 0)  and the first non-axisymmetric  ( m = 1)  modes and to provide a theoretical basis with which to explain the 'active longitude', 'flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the  α²–Ω  and the  α–Ω  models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.     

Electromagnetic fields in jets

The magnetic fields and energy flows in an astronomical jet described by our earlier model are calculated in detail. Though the field distribution varies with the external pressure function   p ( z )  , it depends only weakly on the other boundary conditions. Individual field lines were plotted; the lines become nearly vertical at the bottom and are twisted at the top. An animation of a field line's motion was made, which shows the line being wound up by the accretion disc's differential rotation and rising as a result of this. The distribution of Poynting flux within the jet indicates that much of the energy flows up the jet from the inside of the accretion disc but a substantial fraction flows back down to the outside.     

Simulation of the Magnetothermal Instability

In many magnetized, dilute astrophysical plasmas, thermal conduction occurs almost exclusively parallel to magnetic field lines. In this case, the usual stability criterion for convective stability, the Schwarzschild criterion, which depends on entropy gradients, is modified. In the magnetized long mean free path regime, instability occurs for small wavenumbers when (∂ P/∂z) (∂ ln T/∂ z) > 0, which we refer to as the Balbus criterion. We refer to the convective-type instability that results as the magnetothermal instability (MTI). We use the equations of MHD with anisotropic electron heat conduction to numerically simulate the linear growth and nonlinear saturation of the MTI in plane-parallel atmospheres that are unstable according to the Balbus criterion. The linear growth rates measured from the simulations are in excellent agreement with the weak field dispersion relation. The addition of isotropic conduction, e.g. radiation, or strong magnetic fields can damp the growth of the MTI and affect the nonlinear regime. The instability saturates when the atmosphere becomes isothermal as the source of free energy is exhausted. By maintaining a fixed temperature difference between the top and bottom boundaries of the simulation domain, sustained convective turbulence can be driven. MTI-stable layers introduced by isotropic conduction are used to prevent the formation of unresolved, thermal boundary layers. We find that the largest component of the time-averaged heat flux is due to advective motions as opposed to the actual thermal conduction itself. Finally, we explore the implications of this instability for a variety of astrophysical systems, such as neutron stars, the hot intracluster medium of galaxy clusters, and the structure of radiatively inefficient accretion flows. J. M. Stone: Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544     

Influence of Ohmic diffusion on the excitation and dynamics of MRI

In this paper we make an effort to understand the interaction of turbulence generated by the magnetorotational instability (MRI) with turbulence from other sources, such as supernova explosions (SNe) in galactic disks. First we perform a linear stability analysis (LSA) of non‐ideal MRI to derive the limiting value of Ohmic diffusion that is needed to inhibit the growth of the instability for different types of rotation laws. With the help of a simple analytical expression derived under first‐order smoothing approximation (FOSA), an estimate of the limiting turbulence level and hence the turbulent diffusion needed to damp the MRI is derived. Secondly, we perform numerical simulations in local cubes of isothermal nonstratified gas with external forcing of varying strength to see whether the linear result holds for more complex systems. Purely hydrodynamic calculations with forcing, rotation and shear are made for reference purposes, and as expected, non‐zero Reynolds stresses are found. In the magnetohydrodynamic calculations, therefore, the total stresses generated are a sum of the forcing and MRI contributions. To separate these contributions, we perform reference runs with MRI‐stable shear profiles (angular velocity increasing outwards), which suggest that the MRI‐generated stresses indeed become strongly suppressed as function of the forcing. The Maxwell to Reynolds stress ratio is observed to decrease by an order of magnitude as the turbulence level due to external forcing exceeds the predicted limiting value, which we interpret as a sign of MRI suppression. Finally, we apply these results to estimate the limiting radius inside of which the SN activity can suppress the MRI, arriving at a value of 14 kpc (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The origin of our galactic magnetic field

A serious difficulty with the standard alpha‐omega theory of the origin of galactic magnetic fields involves the question of flux expulsion. This is intimately related to flux freezing. The alpha‐omega theory is shown in the context of the giant superbubble explosions that have a large impact on the physics of the interstellar medium. It is shown that superbubbles alone can duplicate the processes of the alpha‐omega dynamo and produce exponential growth of the galactic magnetic field. The possibility of the blow‐out of pieces of the magnetic field is discussed and it is shown that they have the potential to solve the flux‐expulsion problem. However, such an explanation must lead to apparent ‘gaps’ in the field in the galactic disc. These gaps are probably unavoidable in any dynamo theory and should have important observable consequences, one of which is an explanation for the escape of cosmic rays from the disc (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probability distribution functions for the Sun's magnetic field

Magnetoconvection structures the Sun's magnetic field cover a vast range of scales, down to the magnetic diffusion scale that is orders of magnitude smaller than the resolution of current telescopes. The statistical properties of this structuring are governed by probability density functions (PDFs) for the flux densities and by the angular distribution functions for the orientations of the field vectors. The magnetic structuring on sub‐pixel scales greatly affects the field properties averaged over the resolution element due to the non‐linear relation between polarization and magnetic field. Here we use a Hinode SOT/SP data set for the quiet Sun disk center to explore the complex behavior of the 6301–6302 Å Stokes line profile system and identify the observables that allow us to determine the distribution functions in the most robust and least model dependent way. The angular distribution is found to be strongly peaked around the vertical direction for large flux densities but widens with decreasing flux density to become isotropic in the limit of zero flux density. The noise‐corrected PDFs for the vertical, horizontal, and total flux densities all have a narrowly peaked maximum at zero flux density that can be fitted with a stretched exponential, while the extended wings decline quadratically (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The origin of cutoff frequencies for torsional tube waves propagating in the solar atmosphere

Torsional waves supported by magnetic flux tubes have long been thought to bear a high potential for supplying energy and momentum to the upper solar atmosphere, thereby contributing to its heating and to the driving of dynamic events like spicules. This hope rested on the belief that their propagation is not impeded by cutoff restrictions, unlike longitudinal and kink waves. We point out that this applies only to thin, isothermal tubes. When they widen in the chromosphere, and as a result of temperature gradients, cutoff restrictions arise. We compare them to recent observational reports of such waves and of vortex motions and find that their long period components are already affected by cutoff restrictions. An observational strategy is proposed that should permit the derivation of better information on vortex flows from off‐center observations with next generation telescopes (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)