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A close look at solar granulation

How would the surface of our Sun look like, if we had telescopes which have a resolution ten times that one of present instruments? Would the Sun look any different further inside? In an international collaboration scientists at the University of Vienna, Austria, and the Max Planck Institute for Astrophysics have used numerical simulations on high performance computers to answer this question and found a highly turbulent flow showing ever more details hidden underneath the smooth surface which we know from images of our Sun in visual light.

Fig. 1: The figure shows a region 2600 km wide and 2000 km deep. Horizontal and vertical resolution are 3 km and 2 km, respectively. The region is embedded in a domain 11200 km wide and 3000 km deep simulated at a resolution of 12 km by 8 km. The upper panel shows the simulated region, the lower panel illustrates the scales. The quantity displayed is entropy. It is tightly related to temperature and allows tracing the origin of the gas. High entropy gas is colored in red and originates from further inside. Low entropy gas is colored in blue and has been cooled at the surface layers. Intermediate values are shown in green and yellow. The latter are also found at the transition between the visible layers (near the top) and the hidden layers underneath as a sharp, but smooth boundary within the uppermost part of the figure.

Fig. 2: The movie shows the development of temperature in the same region for the same simulation as in Fig. 1, but at an earlier instant in time. It illustrates the development from a state as seen at lower resolution (first frame) to the development of small scale structures (already after the first 40 out of 262 frames). The quantity shown is the difference between local temperature and horizontally averaged temperature (both on a logarithmic scale). Regions hotter than average appear in red, regions colder than average in blue, regions close to the average in green. Narrow black lines connect locations with identical difference of pressure to its horizontal average, a bit similar to a chart in a weather forecast. But note that here the vertical direction (X) indeed corresponds to the vertical direction in the simulation (Y is the horizontal direction, indicated by arrows near the top) and in a forecast chart isolines would connect locations of identical local pressure. (Extended version of the linkPfeil.gifmovie, 32 MB)

Fig. 3: The movie shows a region 4000 km wide in each horizontal direction (Y, Z) and 2000 km deep (X). Horizontal and vertical resolution are 10 km and 7 km, respectively. The region is embedded in a domain 11200 km wide and 3000 km deep simulated at a resolution of 40 km horizontally and 28 km vertically. The dark yellow surface connects all points with a temperature of 8000 K. Volume rendering is used to visualize regions with large pressure gradients. The physical quantity chosen for this purpose is the norm (size) of the gradient of differences between local pressure and its horizontal average (both taken in logarithmic units). This way locations with strong local changes in pressure are shown in red. Moderate changes are in blue, while green and bright yellow denote values in between.

Observations of the surface of our Sun reveal a well-known granulation pattern of visually bright structures (the granules) embedded in a network of gas with a much lower visual brightness. On average such granules are about 1200 km wide. Within the granules gas is hotter than its environment. It moves upwards at some 2 km/s until radiation into space provides sufficient cooling. Pushed sidewards the cold and dense gas sinks downwards in a network surrounding the granules. The best instruments available for taking images of the solar surface can detect details as small as 70 km (examples: linkPfeilExtern.gifNAOJ linkPfeilExtern.gifInstitute for Solar Physics). At that resolution the granules appear remarkably smooth. This has also been found in numerical simulations of solar granulation at similar resolution. What if we looked at these layers, but were able to spot details as small as a few km? Since each granule is influenced also by its environment, numerical simulations of this process have to be performed for a much larger domain, more than 10000 km wide and 3000 km deep. Even on massively parallel computers a smaller region of interest has to be selected to predict the dynamical behavior of such tiny structures. This smaller region contains only a few granules. Its surroundings are simulated at lower resolution. Fig. 1 shows such a simulation, which has been performed taking into account only one horizontal direction. The solar surface is clearly visible as a vertically narrow and highly corrugated region which is thus located at various geometrical depths. Most small scale details are related to a few fronts moving upwards within the visible solar atmosphere. This picture agrees with images of the solar surface and physical explanations given for it in the literature, but here we look at that phenomenon at a much higher resolution. The region underneath the surface looks completely different: the longer the gas has had time to sink into the interior, the more details appear. The small scale structures mostly originate from shear stresses between the regions of upwards and downwards flowing gas.

Such small scale structures do not appear unless a minimum amount of resolution and advanced numerical methods are used for the simulations. This has been double-checked both with simulations at lower resolution and by using various numerical methods. The results just described are corroborated by the finding that once the resolution is high enough different numerical methods yield more and more similar results. Since the highly turbulent flow structures in Fig. 1 are hidden by layers of opaque gas (the visible solar surface), one has to look for indirect observational consequences. One possibility are oscillations and waves generated by the flow. The Sun is known to pulsate and these pulsations are the best "probe" available for the structure of the solar interior. They are (standing) sound waves trapped in the solar envelope. Most of the energy is transferred into these waves in the layers right underneath the solar surface, just where all the small scale structures appear (Fig. 1). An analysis of the simulations reveals numerous "acoustic events", pulses which are generated near regions where up- and downflows create large shearing forces and where regions of lower density are suddenly compressed. Fig. 2 shows a movie which illustrates these pulses as black lines connecting locations which have identical differences between local and horizontally averaged pressure. These pressure fluctuations travel usually non-aligned to the actual flow. The latter becomes visible through the development of the temperature fluctuations (color coded). The pulses cross each other, get damped or amplified, and some make their way up to the visible surface. How are they related to the observed oscillations, which in fact take place at length scales of at least a few granules and larger?

To answer this question requires more realistic simulations which account for both horizontal directions. The restriction to two dimensions creates features which are not expected (nor observed) for the real solar convection, such as the stable whirls notable in both Fig. 1 and the movie in Fig. 2 (which do not reach the surface). The computational requirements for such a three-dimensional simulation are considerable and to achieve the same resolution as in Fig. 2 means to push the top supercomputers of today to their very limits. Fig. 3 shows results from a first series of such simulations, at roughly one third of the resolution achieved in the case of two dimensions. The increase in complexity in the flow is evident by following the development from the initial stage (at a resolution which is effectively comparable to that one achieved in images of the solar surface by the most advanced instruments) to its final one. In real solar time this is just a few minutes later, slightly shorter than the development shown in Fig. 2. The smooth surface denotes a temperature region just underneath the visible layers of the Sun and its development illustrates, how upflows decay (and reappear) in time and how their boundaries to downflow regions become disrupted by shearing. In time, fronts of strong pressure differences (yellow-red) appear particularly at the boundary regions of upflows (the interior part of the granules) and they move further upwards. The appearance of these phenomena and the drastic increase in complexity within the regions of strong downflows motivates simulations similar in resolution to those in Fig. 2 to clarify the role of shear stresses in the generation of sound waves in the Sun. These are now conducted as part of an accepted linkPfeilExtern.gifDEISA proposal. However, already now it is clearly perceivable that what looks smooth from the outside at currently achievable observational resolution appears quite different, if studied with methods that can look into the Sun at higher resolution.

Friedrich Kupka, Herbert J. Muthsam, Christof Obertscheider, Florian Zaussinger


Muthsam et al., Mon. Not. Roy. Astr. Soc. 380, 1335-1340 (2007) doi:10.1111/j.1365-2966.2007.12185.x

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