Rainer Arlt

Digitization of sunspot drawings by Spörer made in 1861–1894

Most of our knowledge about the Suns activity cycle arises from sunspot observations over the last centuries since telescopes have been used for astronomy. The German astronomer Gustav Sporer observed almost daily the Sun from 1861 until the beginning of 1894 and assembled a 33-year collection of sunspot data covering a total of 445 solar rotation periods. These sunspot drawings were carefully placed on an equidistant grid of heliographic longitude and latitude for each rotation period, which were then copied to copper plates for a lithographic reproduction of the drawings in astronomical journals. In this article, we describe in detail the process of capturing these data as digital images, correcting for various effects of the aging print materials, and preparing the data for contemporary scientific analysis based on advanced image processing techniques. With the processed data we create a butterfly diagram aggregating sunspot areas, and we present methods to measure the size of sunspots (umbra and penumbra) and to determine tilt angles of active regions. A probability density function of the sunspot area is computed, which conforms to contemporary data after rescaling.

Physics of the solar cycle

The theory of the solar/stellar activity cycles is presented, based on the mean-field concept in magnetohydrodynamics. A new approach to the formulation of the electromotive force and the theory of differential rotation and meridional circulation is described. Dynamo cycles in the overshoot layer and distributed dynamos are compared, with the latter including the influence of meridional flow. The overshoot layer dynamo reproduces the solar cycle periods and the butterfly diagram only if alpha=0 in the convection zone (CZ). The distributed dynamo including meridional flows shows the observed butterfly diagram even with a positive dynamo-alpha in CZ. The nonlinear feedback of strong magnetic fields on differential rotation leads to grand minima in the cyclic activity similar to those observed. Our 2D model contains the large- and small-scale feedback of magnetic fields on diff. rotation and induction in a mean-field formulation (Lambda-, alpha-quenching). Grand minima may also occur if a dynamo occasionally falls below its critical eigenvalue. We never found any indication that such an on-off dynamo collapses by this effect after being excited. The full quenching of turbulence by strong magnetic fields as reduced induction (alpha) and reduced turbulent diffusivity (eta_T) is studied in 1D. We find a stronger dependence of cycle period on dynamo number compared with a pure alpha-quenching model giving a very weak cycle period dependence. Also the temporal fluctuations of alpha and eta_T from a random-vortex simulation were applied to a dynamo. Then the low `quality of the solar cycle can be explained with a small number of giant cells as dynamo-active turbulence. The transition from almost regular magnetic oscillations (many vortices) to a more or less chaotic time series (very few vortices) is shown.

Digitization of Spörer's sunspot drawings

Much of our knowledge about the solar dynamo is based on sunspot observations. It is thus desirable to extend the set of positional and morphological data of sunspots into the past. Gustav Sporer observed in Germany from Anklam (1861-1873) and Potsdam (1874-1894). He left detailed prints of sunspot groups, which we digitized and processed to mitigate artifacts left in the print by the passage of time. After careful geometrical correction, the sunspot data are now available as synoptic charts for almost 450 solar rotation periods. Individual sunspot positions can thus be precisely determined and spot areas can be accurately measured using morphological image processing techniques. These methods also allow us to determine tilt angles of active regions (Joys law) and to assess the complexity of an active region.

On radiation-zone dynamos

It is shown that the magnetic current-driven (`kink-type) instability produces flow and field patterns with helicity and even with alpha-effect but only if the magnetic background field possesses non-vanishing current helicity bar{vec{B}}cdot curl bar{vec{B}} by itself. Fields with positive large-scale current helicity lead to negative small-scale kinetic helicity. The resulting alpha-effect is positive. These results are very strict for cylindric setups without z/I>-dependence of the background fields. The sign rules also hold for the more complicated cases in spheres where the toroidal fields are the result of the action of differential rotation (induced from fossil poloidal fields) at least for the case that the global rotation is switched off after the onset of the instability.

MHD Taylor-Couette Flow for Small Magnetic Prandtl Number and With Hall Effect

Rotating shear flows are very common in astrophysics. Rotation profiles of stars, accretion disks, and galaxies are shear flows. The Rayleigh criterion for stability of a given rotation profile requires an increasing specific angular momentum with distance from the rotation axis. This criterion is fulfilled in nearly all astrophysical objects. The rotation profile in accretion disks obeys roughly Ω ∼ r−3/2, where r is the axis distance. A powerful ingredient to rotating shear flows are magnetic fields, which excite a linear instability even if they are weak in terms of energy compared with the thermal energy. The magnetorotational instability (MRI) has been proven by analytical and numerical studies to be very efficient in generating turbulence. The turbulent flows emerging from the instability lead to outward transport of angular momentum (see e.g. [1], [2], [3]). This is a very promising finding for the problem of the formation of stars. The MRI had not yet been observed in the laboratory at the time of the Conference. Taylor-Couette (TC) experiments study the flow between two coaxial cylinders with one of them, or both, rotating. If the inner cylinder is rotating – by far the most often studied case in the laboratory – the rotation profile Ω = A + B/r2 looks similar to the Keplerian one, but is Rayleigh unstable whence not comparable to accretion disks. Nevertheless, the TC flow bears the chance to reproduce the MRI in an experiment.