# SOLSTAR - Solare und Stellare Magnetische Aktivität: Beobachtungen und Modellierung

In our work, we combine state-of-the-art numerical simulations with sophisticated data analysis techniques. Our modelling efforts concentrate on high-accuracy modelling of turbulent flows, especially of compressible, rotating, and anisotropic convection, which process is of crucial importance in the outer envelope of the Sun and other late-type stars. Special data analysis tools are needed to process the massive data produced during our modelling efforts. In this realm, the emphasis of our work is in the development of methods that can directly measure collective effects arising from turbulence. These include for example the collective inductive action of turbulence contributing to the solar dynamo mechanism (studied with the test-field method) and turbulent angular momentum transport giving rise to solar and stellar differential rotation (studied with the test-flow method). Some more detailed research topics together with the latest publications are listed below.

## Understanding how solar and stellar dynamos work

#### Rotation-Activity relation in global convection simulations

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#### Hidden solar magnetic cycle explained with modifications in turbulent induction and pumping

#### Das versteckte Magnetfeld der Sonne während des großen Minimums

#### No asymptotic regime found in high-resolution stellar dynamo simulations

Three-dimensional magnetohydrodynamic simulations have recently been able to reproduce solar-like magnetic activity and non-axisymmetric large-scale magnetic fields self-consistently. The parameter regimes of such simulations are, however, still far removed from realistic conditions of stellar interiors. In our study we searched for an asymptotic regime where the large-scale features would no longer be dependent on the diffusion coefficients, and where the large-scale results would likely be representative of real stars. Instead, we found that as the turbulence becomes more vigorous, differential rotation is severely quenched and no clear indication of an asymptotic regime is found even at the highest resolution. A vigorous small-scale dynamo is a possible culprit for the behavior and our results call for even higher resolution follow-up studies.

[mehr]## Observational characterisation of solar and stellar activity cycles

#### Application of probabilistic methods to Mount Wilson Ca H&K data confirms robustness of the inactive branch

#### Activity trends in young solar-type stars

#### Zeeman-Doppler imaging of active young solar type stars

## Understanding solar and stellar convection

#### Extended subadiabatic layer in simulations of overshooting convection

Using three-dimensional simulations with smoothly varying heat conduction profile we found solutions where a substantial fraction of the lower part of the convection zone is stably stratified according to the Schwarzschild criterion. If these results carry over to the Sun, roughty 40 per cent of the lower part of the convection zone is stably startified. The existence of such a layer has possibly wide-ranging ramification in the theories of differential rotation and dynamos. Furthermore, a subadiabatic region is a possible solution to the so-called 'convective conundrum' which manifests itself as significantly too high convective velocities in traditional simulations.

[mehr]## Understanding sun- and starspot formation

#### Magnetic flux concentrations from turbulent stratified convection

## Test Field Method

#### Turbulent transport coefficients measured from stellar convective dynamos

*testified method*reveals the turbulent transport coefficients as a parametrization of the turbulent effects and therefore let us get an idea of the dynamo mechanism operating in these simulations. The most prominent mechanisms are the α effect, turbulent pumping and the turbulent diffusion. In our recent study, we find that the turbulent pumping is stronger than the meridional flow and therefore dominates the transport of magnetic field. Furthermore, all transport coefficients show strong temporal variation with the magnetic cycle, indicating a non-linear saturation mechanism for the dynamo. Only if we are able to understand the dynamos operating in simulation, we can achieve conclusion about the magnetic field generation in the Sun and stars. [mehr]

## Development of HPC and data analysis tools

#### The power of graphics processing units harnessed for high-accuracy turbulence modelling

*Astaroth*is able to achieve 3.6 times speedup in comparison to the reference code, which in practice allows for a week-long turbulence simulation to be performed within a couple of days. The method is published in Pekkilä, Väisälä et al. (2017). [mehr]