We investigate the interaction of magneto-acoustic waves with magnetic network elements with the aim of finding possible signatures of the magnetic shadow phenomenon in the vicinity of network elements. We carried out three-dimensional numerical simu
lations of magneto-acoustic wave propagation in a model solar atmosphere that is threaded by a complexly structured magnetic field, resembling that of a typical magnetic network element and of internetwork regions. High-frequency waves of 10 mHz are excited at the bottom of the simulation domain. On their way through the upper convection zone and through the photosphere and the chromosphere they become perturbed, refracted, and converted into different mode types. We applied a standard Fourier analysis to produce oscillatory power-maps of the line-of-sight velocity. In the power maps of the upper photosphere and the lower chromosphere, we clearly see the magnetic shadow: a seam of suppressed power surrounding the magnetic network elements. We demonstrate that this shadow is linked to the mode conversion process and that power maps at these height levels show the signature of three different magneto-acoustic wave modes.
We review (i) observations and numerical simulations of vortical flows in the solar atmosphere and (ii) measurements of the horizontal magnetic field in quiet Sun regions. First, we discuss various manifestations of vortical flows and emphasize the r
ole of magnetic fields in mediating swirling motion created near the solar surface to the higher layers of the photosphere and to the chromosphere. We reexamine existing simulation runs of solar surface magnetoconvection with regard to vortical flows and compare to previously obtained results. Second, we review contradictory results and problems associated with measuring the angular distribution of the magnetic field in quiet Sun regions. Furthermore, we review the Stokes-V-amplitude ratio method for the lines Fe I 630.15 and 630.25 nm. We come to the conclusion that the recently discovered two distinct populations in scatter plots of this ratio must not bee interpreted in terms of uncollapsed and collapsed fields but they stem from weak granular magnetic fields and weak canopy fields located at the boundaries between granules and the intergranular space. Based on new simulation runs, we reaffirm earlier findings of a predominance of the horizontal field components over the vertical one, particularly in the upper photosphere and at the base of the chromosphere.
We present two-dimensional simulations of wave propagation in a realistic, non-stationary model of the solar atmosphere. This model shows a granular velocity field and magnetic flux concentrations in the intergranular lanes similar to observed veloci
ty and magnetic structures on the Sun and takes radiative transfer into account. We present three cases of magneto-acoustic wave propagation through the model atmosphere, where we focus on the interaction of different magneto-acoustic wave at the layer of similar sound and Alfven speeds, which we call the equipartition layer. At this layer the acoustic and magnetic mode can exchange energy depending on the angle between the wave vector and the magnetic field vector. Our results show that above the equipartition layer and in all three cases the fast magnetic mode is refracted back into the solar atmosphere. Thus, the magnetic wave shows an evanescent behavior in the chromosphere. The acoustic mode, which travels along the magnetic field in the low plasma-$beta$ regime, can be a direct consequence of an acoustic source within or outside the low-$beta$ regime, or it can result from conversion of the magnetic mode, possibly from several such
We present simulations of magneto-acoustic wave propagation in a magnetic, plane-parallel stratified solar model atmosphere, employing the CO5BOLD-code. The tests are carried out for two models of the solar atmosphere, which are similar to the ones u
sed by Cally (2007) and Schunker & Cally (2006). The two models differ only in the orientation of the magnetic field. A qualitative comparison shows good agreement between the numerical results and the results from ray theory. The tests are done in view of the application of the present numerical code for the computation of energy fluxes of propagating acoustic waves into a dynamically evolving magnetic solar atmosphere. For this, we consider waves with frequencies above the acoustic cut-off frequency.
We have investigated a time series of continuum intensity maps and corresponding Dopplergrams of granulation in a very quiet solar region at the disk center, recorded with the Imaging Magnetograph eXperiment (IMaX) on board the balloon-borne solar ob
servatory Sunrise. We find that granules frequently show substructure in the form of lanes composed of a leading bright rim and a trailing dark edge, which move together from the boundary of a granule into the granule itself. We find strikingly similar events in synthesized intensity maps from an ab initio numerical simulation of solar surface convection. From cross sections through the computational domain of the simulation, we conclude that these `granular lanes are the visible signature of (horizontally oriented) vortex tubes. The characteristic optical appearance of vortex tubes at the solar surface is explained. We propose that the observed vortex tubes may represent only the large-scale end of a hierarchy of vortex tubes existing near the solar surface.
Three-dimensional magnetohydrodynamic simulations of the surface layers of the Sun intrinsically produce a predominantly horizontal magnetic field in the photosphere. This is a robust result in the sense that it arises from simulations with largely d
ifferent initial and boundary conditions for the magnetic field. While the disk-center synthetic circular and linear polarization signals agree with measurements from Hinode, their center-to-limb variation sensitively depends on the height variation of the horizontal and the vertical field component and they seem to be at variance with the observed behavior.
Three kinds of magnetic couplings in the quiet solar atmosphere are highlighted and discussed, all fundamentally connected to the Lorentz force. First the coupling of the convecting and overshooting fluid in the surface layers of the Sun with the mag
netic field. Here, the plasma motion provides the dominant force, which shapes the magnetic field and drives the surface dynamo. Progress in the understanding of the horizontal magnetic field is summarized and discussed. Second, the coupling between acoustic waves and the magnetic field, in particular the phenomenon of wave conversion and wave refraction. It is described how measurements of wave travel times in the atmosphere can provide information about the topography of the wave conversion zone, i.e., the surface of equal Alfven and sound speed. In quiet regions, this surface separates a highly dynamic magnetic field with fast moving magnetosonic waves and shocks around and above it from the more slowly evolving field of high-beta plasma below it. Third, the magnetic field also couples to the radiation field, which leads to radiative flux channeling and increased anisotropy in the radiation field. It is shown how faculae can be understood in terms of this effect. The article starts with an introduction to the magnetic field of the quiet Sun in the light of new results from the Hinode space observatory and with a brief survey of measurements of the turbulent magnetic field with the help of the Hanle effect.
Observations with the Hinode space observatory led to the discovery of predominantly horizontal magnetic fields in the photosphere of the quiet internetwork region. Here we investigate realistic numerical simulations of the surface layers of the Sun
with respect to horizontal magnetic fields and compute the corresponding polarimetric response in the Fe I 630 nm line pair. We find a local maximum in the mean strength of the horizontal field component at a height of around 500 km in the photosphere, where it surpasses the vertical component by a factor of 2.0 or 5.6, depending on the initial and boundary conditions. From the synthesized Stokes profiles we derive a mean horizontal field component that is, respectively, 1.6 and 4.3 times stronger than the vertical component. This is a consequence of both the intrinsically stronger flux density of, and the larger area occupied by the horizontal fields. We find that convective overshooting expels horizontal fields to the upper photosphere, making the Poynting flux positive in the photosphere, while this quantity is negative in the convectively unstable layer below it.
We study the structure of the magnetic elements in network-cell interiors. A quiet Sun area close to the disc centre was observed with the spectro-polarimeter of the Solar Optical Telescope on board the Hinode space mission, which yielded the best sp
atial resolution ever achieved in polarimetric data of the Fe I 630 nm line pair. For comparison and interpretation, we synthesize a similar data set from a three-dimensional magneto-hydrodynamic simulation. We find several examples of magnetic elements, either roundish (tube) or elongated (sheet), which show a central area of negative Stokes-V area asymmetry framed or surrounded by a peripheral area with larger positive asymmetry. This pattern was predicted some eight years ago on the basis of numerical simulations. Here, we observationally confirm its existence for the first time. We gather convincing evidence that this pattern of Stokes-V area asymmetry is caused by the funnel-shaped boundary of magnetic elements that separates the flux concentration from the weak-field environment. We also conclude that this kind of magnetic element of the internetwork is accompanied by electric current sheets.
In the first part of these lecture notes, new high-resolution observations of small-scale magnetic flux concentrations are presented and compared to results from new three-dimensional magnetohydrodynamic simulations. Special attention is paid to the
physics of faculae and to new three-dimensional radiation magnetohydrodynamic simulations of the integral layers from the top of the convection zone to the mid-chromosphere. The second part is devoted to a few basic properties of magnetic flux tubes, which can be considered to be an abstraction of the more complicated flux concentrations known from observations and numerical simulations. We treat electrical current sheets, the mechanical equilibrium condition at magnetic interfaces, the equations for constructing a magnetohydrostatic flux tube embedded in a gravitationally stratified atmosphere, the condition of radiative equilibrium, and the condition for interchange stability.
