We present 2-D, fully compressible radiation-MHD simulations of the solar photospheric and subphotospheric layers that run for 2 hours of solar time starting from a magnetic configuration with mixed polarities. In the atmospheric layers the simulation reveals a correlation between field strength and inclination, with a nearly vertical strong-field magnetic component and a more horizontal weak-field component, in agreement with the observations. Our simulation also shows that magnetic flux is converted from one of these states to the other. In particular, magnetic flux sheets can also be formed when a new downflow lane starts due to granule fragmentation. The dynamics of the granulation and field-line reconnection are found to play a role in the initial stages of a magnetic element's formation. The simulation predicts that during or shortly after their formation magnetic elements could be associated with oppositely polarized flux at a small spatial scale.

We discuss an example of 'flux recycling' as seen in MHD simulations of the layers around the solar surface: convective motions bend two initially vertical flux elements of opposite polarity towards each other until they reconnect. The resulting flux loop then rises and the initial situation is restored. During this process, 'new' flux is neither created nor brought into the system from outside. The corresponding synthetic magnetogram, however, suggests the annihilation of two flux elements followed by the later emergence of magnetic flux at another location. Similar recycling events could contribute to the large flux emergence rates observed on small spatial scales.

We assess the diagnostic potential of the observed 'pathological' Stokes V profiles that differ strongly from the customary, nearly antisymmetric two-lobed shape. In particular, we consider the formation of one-lobed Stokes V profiles using the results of an MHD simulation. We find that the majority of one-lobed profiles is produced in regions of weak horizontal field with significant cancellation caused by mixed polarity along the line of sight. A minority of one-lobed profiles originates close to strong magnetic field concentrations with strong gradients of velocity and magnetic field strength.

Convection is the main form of energy transport in the subsurface layers of the sun and other cool stars. The imprint of cellular convection can be directly observed on the solar surface, with a hierarchy of four size scales. The smallest observed convection cells, called granules, have typical horizontal sizes of 1,000-2,000 km and have been successfully reproduced by numerical simulations (Spruit 1997; Stein & Nordlund 1998). Cells at three larger scales are also detected (Leighton et al. 1962; November et al. 1981; Beck et al. 1998), but these have so far not been amenable to numerical modelling, so that their formation scenarios remain untested. Here we present a numerical simulation which resolves both the granular and the next larger, mesogranular, scale. The mesogranules have horizontal extents of 5,000-10,000 km. Our 2D simulation reproduces key properties of both granules and mesogranules. In addition, our simulation demonstrates that the observed mesogranulation is driven close to the solar surface and therefore rules out the text-book explanation of mesogranulation as cellular convection driven by superadiabaticity in the deeper layer where neutral helium ionizes. By proxy, this result also casts doubt on the traditional explanation of supergranulation, even larger convection cells with diameters of 20,000-30,000 km, as being driven by the yet deeper second ionization of helium.

Two time-dependent sets of two-dimensional hydrodynamic models of solar granulation have been analyzed to obtain dependence of simulated thermal convection on the horizontal size of the convection cells. The two sets of models treat thermal convection either as fully non-stationary, multiscale convection (granular convection is a surface phenomenon) or as quasi-steady-state convection cells (they treat granular convection as a collection of deep-formed cells). The following results were obtained:1) quasi-steady convection cells can be divided into 3 groups according to their properties and evolution, namely small-scale (up to L similar to 900 km)? intermediate-scale (1000 - 1500 km) and large-scale (larger 1500 km) convection cells. For the first group thermal damping due to radiative exchange of energy, mostly ill the horizontal direction, is very important. Large-scale cells build up a pressure excess, which can lead to their total fragmentation. Similar precesses also acts on the fully non-stationary convection.2) The largest horizontal size of convection cells for which steady-state solutions can be obtained is about 1500 km. This corresponds to granules, i.e. the bright parts of the convection cells, with a diameter of about 1000 km.3) In addition to the zone of high convective instability associated with the partial ionization of hydrogen, we identify another layer harboring important dynamic processes in steady-state models. Just below the hydrogen-ionization layer pressure fluctuations and the acoustic flux are reduced. Steady-state models with reflecting lateral boundaries even exhibit an inversion of pressure fluctuations there.4) From observational point of view the surface convection differs from steady-state deep treatment of thermal convection in the dependence of vertical granular velocities on their sizes for small-scale inhomogeneous. However, they cannot be distinguished by the dependence of temperature or emergent intensity of brightness structures.5) Both kinds of models demonstrate the inversion of density in subphotospheric layers. It is more pronounced in small-scale cells and inside hot upflows.6) The brightness of simulated granules linearly increases with their size for small granules and is approximately constant or even decreases slightly for larger granules. For intergranular lanes the simulations predict a decrease of their brightness with increasing size. It falls very rapidly for narrow lanes and remains unchanged for broader lanes.7) A quantitative comparison of the brightness properties of simulated granulation with real observations shows that the strong size-dependence of the properties of the smallest simulated granules is not accessible to current observations due to their limited spatial resolution. The observed size dependences result rather from spatial smoothing and the granule-finding algorithm. We do not exclude, however, an influence of the limitations of the 2-D treatment of thermal convection on the present results.

The evolution of solar granules is investigated on the basis of two dimensional numerical solutions of the hydrody- namic equations describing a compressible, radiatively coupled and gravitationally stratified medium representative of the so- lar surface layers. The simulation covers 17 Mm on the solar surface and was run for over 5 h of solar time, hence allowing the evolution of over 400 granules to be followed. A statisti- cal investigation of the temporal evolution of granules therefore becomes feasible. Two types of granules can be distinguished by their means of death: fragmenting and dissolving granules. Properties and average evolutionary histories of these two types of granules are considered. It is found that fragmenting granules are in general large at birth and expand further with time. It is confirmed that fragmentation into two (or more) parts is produced by buoyancy braking, which in turn is initiated by the stronger horizontal flows in larger granules. This last property, finally, is due to mass conservation. The expansion, however, is due to a pressure excess relative to neighbouring granules. The pressure excess is particularly marked if the neighbours are dissolving granules. In contrast, dissolving granules are born small and shrink be- fore finally disappearing. The shrinkage is caused by their neigh- bours which generally posses excess gas pressure and larger horizontal flows. In summary, according our findings the fate of a granule is decided by its properties at birth and the company it keeps. Evidence is presented suggesting that the evolution of both types of granules is driven by events near the solar surface.

The influence of torsional waves propagating along a thin, vertical, photospheric flux tube on Zeeman-split polarized line profiles (Stokes profiles) is investigated using a simple MI-ID model. In the presence of such a wave spatially resolved Stokes profiles are found to oscillate strongly in wavelength, amplitude and blue-red asymmetry. Qualitatively, torsional waves induce similar changes into the line profiles as kink waves (Ploner & Solanki 1997). The magnitude of the line parameter variation depends strongly on the observed location with respect to the Aux-tube axis.The spatially averaged Stokes V and Q profiles are found to follow the torsional wave with double the wave frequency, some parameters of Stokes U fluctuate directly at the wave frequency, however. The other main feature of the spatially averaged profiles is their comparatively small reaction to the wave. The reason for the latter is that most polarized light is produced near the centre of the flux tube where, however, the torsional wave produces only weak perturbations.Temporally and spatially, averaged Stokes profiles are found to be only negligibly shifted, but strongly broadened. The sign of the small remaining asymmetry is opposite in Stokes Q to that in V and U. The amplitude of the wave and the location of the flux tube on the solar disk, have a strong influence on the magnitude of the perturbation of the Stokes profiles.

The spectropolarimetric signature of models of small-scale magnetic features is well understood at the centre of the solar disc, but has been little studied near the solar limb, mainly because the detailed geometry of the flux tubes must then be taken into account in a realistic analysis. We present multi-ray calculations of Stokes profiles through arrays of 2-D magnetohydrostatic models of small flux tubes. We compare the Stokes profile shapes and Stokes based diagnostics ( Q to V ratio, V amplitude, magnetic line ratio, centre of gravity wave- lengths, etc.) resulting from plane-parallel and 2-D flux-tube models at different limb distances for two lines in the visible and an infrared H-band line. For the visible lines around 5250 ˚ A all the diagnostics we have studied, with the exception of the Q and U to V ratio, are significantly affected by the finite size of the flux tubes and the passage of the rays through non-magnetic material near the limb. We show that magnetic filling factors and the global magnetic flux may be underestimated using the usual calibration techniques. In addition, near the solar limb the magnetic line ratio can move into a regime that is forbidden ac- cording to simpler models. The spatially averaged longitudinal field derived from the centre-of-gravity method also becomes strongly model dependent. The thermal structure of the non- magnetic atmosphere appears to play a particularly important role in determining the values of these diagnostic parameters. The infrared line at 1.5648 m, on the one hand, reacts little to the external atmosphere and provides superior diagnostics of both the magnetic field strength and filling factor. On the other hand, for a flux tube with a sharp boundary this line shows little dependence on the flux-tube diameter, in contrast to the earlier findings of Zayer et al. (1989).

We study the evolution of artificial granulation on the basis of 2-D hydrodynamical simulations. These clearly show that granules die in two different ways. One route to death is the well known bifurcation or fragmentation of a large granule into 2 smaller ones (exploding granules). The other pathway to death is characterized by merging intergranular lanes and the accompanying dissolution of the granule located between them. It is found that the lifetime and maximum brightness is independent of the way in which granules evolve and die. They clearly differ in size, however, with exploding granules being in general significantly larger.