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  Current Research Highlight :: December 2007 all highlights

Numerical sunspots

The structure of sunspots now reproduced in the computer.

Fig. 1: A (small, strip-shaped) sunspot as produced by a 3-dimensional radiative magnetohydrodynamical linkPfeil.gifsimulation (T. Heinemann et al. 2007).

Fig. 2: Crossection through the envelope of the Sun, at the location of a sunspot (sketch). The outer 30% are in convective motion (curls). The magnetic field of the 11-yr sunspot cycle is created at the base of the convective zone. A loop of magnetic field lines rising to the surface produces a sunspot.

Fig. 3: A sunspot observed with the Swedish 1-m solar telescope on La Palma. See also the linkPfeilExtern.gifmovie of this spot.

The dark patches on the solar surface called sunspots are magnetic: magnetic field lines cross the surface from below and extend up into the atmosphere (Fig 2). The presence of these field lines somehow causes a remarkably complex structure: dark and bright dots and filaments, all of them in motion in various directions (Fig 3). What does all this activity mean? The puzzle has now been deciphered with the aid of numerical simulations, which confirm a linkPfeil.giftheoretical model proposed earlier.

The patch we observe as a spot is not something 'painted on the surface' of the Sun. It is only a thin 2-dimensional slice through an extended 3-dimensional structure. If we could dig below the surface and look at its roots, we might get a better idea of what causes this complex looking structure. This is now becoming possible: with realistic numerical simulations. The first successful simulation of this kind is shown in Fig 1. It shows the computed brightness as it would be observed at the surface in a real sunspot. The spot simulated (actually a strip) is still rather small compared with typical well-developed spots, but its properties are already remarkably similar to the real thing. Compare them with Fig 3: the 'fingers' penetrating into the spot behave just like the structure seen around the dark central part (the 'umbra') of a real spot. They move in the same way, have the same bright 'head' and dark stripe over the tail. Like the real filaments, they often leave a longer-lived bright dot in the umbra where they fade away. A number of other details also fit very well, for example the pattern of outward motion seen in the granulation around the spot, and the changing appearance of the spot as it approaches the limb of the Sun. What does not fit well is the length of the filaments: they are much shorter than the long penumbral filaments seen in Fig. 3. This was to be expected, however: observed spots as small as the one calculated usually do not have such well developed penumbral filaments either. They are expected to show up in larger (more expensive) simulations.

What do we see below the surface, in these simulations? What is bright at the surface corresponds to a gap in the magnetic field below, which closes around the observed surface. In these gaps, the gas is in convective motion just like in the granulation around the spot. Between the gaps, the magnetic field is strong and suppress these motions, causing a darkening at the surface. This confirms earlier linkPfeil.gifpredictions of this structure.

The key to the success of these simulations lies in the word `realistic'. The fluid flows and the magnetic field have to be computed in a realistic model of the Sun. Critical, for example, is the correct inclusion of the steep drop in pressure from the interior to the vacuum outside, and of the radiation emitted from the surface. This realism is also possible: the physics of the solar plasma is known in detail, and the required numerical calculations have become possible with the present generation of computers.

Tobias Heinemann, Åke Nordlund, Göran Scharmer, Henk Spruit


Heinemann, T., Nordlund, Å., Scharmer, G., Spruit, H.C. "MHD simulations of penumbra fine structure"
linkPfeilExtern.gif Astrophysical Journal 669 (2007), 1390

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