From left to right: Jörn Warnecke, Petri Käpylä, Maarit Käpylä, Jyri Lehtinen & Mariangela Viviani
From left to right: Jörn Warnecke, Petri Käpylä, Maarit Käpylä, Jyri Lehtinen & Mariangela Viviani
Max Planck Research Group: Solar and stellar magnetic activity
SOLSTAR - Solar and stellar magnetic activity: observations and modelling
All activity phenomena in the Sun and stars originate from their magnetic fields, which arise due to a hydromagnetic dynamo that converts kinetic energy into magnetic form. Even the solar dynamo remains enigmatic due to the extreme complexity of phenomena related to it. Observations of other stars provide important constraints on the stellar dynamo mechanism(s). The work of the group aims at combining these observations with theory and models to gain better understanding of the solar dynamo.
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.
Stellar magnetic activity level and rotation are strongly connected. We studied the effect of increasing rotation rate on solar-like stars using magnetohydrodynamic simulations of stars with outer convective envelopes. At around 1.8 times the solar rotation rate, we found a transition point that separates slowly rotating, magnetically inactive stars, with rather axisymmetric large-scale magnetic fields (like our Sun), from more active, rapidly rotating, stars, with nonaxisymmetric large-scale magnetic fields. In the slow rotators we detected latitudinal dynamo waves reminiscent of the butterfly diagram of the Sun, while in the rapid rotators longitudinal dynamo waves were found. This essentially means that the nonaxisymmetric magnetic field modes rotate with a different speed than the stellar surface, that manifests itself as either prograde or retrograde migration of the magnetic structure. Such behaviour has also been observationally seen in active stars.
Our results also highlight the importance of maintaining high enough supercriticality of convection, in particular, in the rapid rotation regime, where a too low supercriticality results in axisymmetric field configuration instead of a nonaxisymmetric one.
The Sun, aside from its eleven year sunspot cycle is additionally subject to long term variation in its activity. We make use of a solar-like convective dynamo simulation of Käpylä et al. 2016, exhibiting equatorward propagation of the magnetic field, multiple frequencies, and irregular variability, including a missed cycle and complex parity transitions between dipolar and quadrupolar modes, to study the physical causes of such events. We use the test field analysis tool to measure and quantify the effects of turbulence in the generation and evolution of the large-scale magnetic field. The test-field analysis provides an explanation of the missing surface magnetic cycle in terms of the reduction of part of the alpha effect, the one of the key ingredients for dynamo action. Furthermore, we found an enhancement of downward turbulent pumping during the event to confine some of the magnetic field at the bottom of the convection zone, where local maximum of magnetic energy is observed during the event. At the same time, however, a quenching of the turbulent magnetic diffusivities is observed. For more detailed analysis, we will perform dedicated mean-field modelling with the measured turbulent transport coefficients in the future.[more]
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.
Observational characterization of solar and stellar dynamos
The existence of "activity branches", that is stellar cycles clustering in groups that show linear dependencies as function of rotation, has been debated for years. Such dependencies have crucial implications on how to explain stellar magnetism in terms of dynamo theory. In this study we applied novel time series analysis techniques (see Paper I for a Bayesian generalised Lomb-Scargle periodogram with trend) to one of the longest stellar activity database. We confirmed (Paper II) the clustering into inactive (solar-like) and active stars using a Gaussian mixture model. The inactive population exhibits a robust, positive slope in the activity diagram, while the previously claimed positive trend in the active population does not exist according to our analysis. Comparing to cycle data inferred for even more active stars (see the study of Lehtinen et al., 2016), the data is consistent with a negative trend that smoothly continues from active to super active stars. Hence, the positive slope for the inactive cluster, hosting the Sun itself, remains enigmatic for the prevailing solar dynamo paradigms, inexplicable by both the flux-transport concept and the classical turbulent dynamo mechanism. [more]
In a multidecade study of the photometric variability of 21 young solar-type stars we found systematic tendencies in the behavior of the spot cycles and active longitudes of active stars. The lengths of the identified spot cycles follow a sequence of branches as a function of Rossby number or the stellar activity level. A split into parallel sub-branches within the diagram may point to the excitation of different cycle modes in the dynamos of different stars. We found that active longitudes, or persistent non-axisymmetric spot distribution, are common on the fast rotating and strongly active stars but absent on the slow rotating and moderately active ones. This is indicative of a transition between axisymmetric and non-axisymmetric dynamo modes between slow and fast rotating stars. In many cases we observed a significant difference between the active longitude rotation periods and the stellar bulk rotation, which may suggest the presence of longitudinally moving dynamo waves in these stars.
We present the surface magnetic field and brightness maps of three active solar-type stars (AH Lep, HD 29615, V1358 Ori) using Zeeman-Doppler imaging for high resolution spectropolarimetry obtained with HARPSpol at the ESO 3.6m telescope. Two of the stars show dominance of the poloidal field over the toroidal one and in only one of them the non-axisymmetric field component dominates over the axisymmetric field. The maps reveal a magnetic polarity reversal on one of the stars (HD 29615) between 2009 and 2013 when compared with earlier published maps. We found only weak correlation between the reconstructed large scale magnetic field and the surface brightness of the stars. This may indicate a complex magnetic field structure within the spot areas, involving mixed magnetic polarities not retrievable by current methods.
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.
The formation of magnetic flux concentrations within the solar convection zone leading to sunspot formation remains poorly known. We study the self-organization of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection by performing magnetoconvection simulations in local domains. We find that super-equipartition magnetic flux concentrations are formed spontaneously from the turbulent flow. The size of the concentrations increases as the box size increases and the largest structures (20 Mm horizontally near the surface) are obtained in the models that are 24 Mm deep. The field strength in the concentrations is in the range of 3-5 kG, almost independent of the magnitude of the imposed field. The linear growth of large-scale flux concentrations implies that their dominant formation process is a tangling of the large-scale field rather than an instability. One plausible mechanism that can explain both the linear growth and the concentration of the flux in the regions of converging flow pattern is flux expulsion.
Turbulent effects play an important role in the magnetic generation of the Sun and stars. Unfortunately, at the moment observation are not able to reveal these effects. On way to understand how these turbulent effects can generate magnetic field via dynamo mechanisms is to study global 3 dimensional magnetohydrodynamic simulation of the Sun and stars. There the analysis tool 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.
We have developed an effective method for accelerating fluid dynamics calculations with high-order precision on graphics processing units (GPUs). This is done by efficient use of GPU memory with cache blocking and by dividing computation algorithms into memory efficient chunks. Our Nvidia CUDA based, proof of concept code 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). [more]