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 and turbulent angular momentum transport giving rise to solar and stellar differential rotation. Our observational efforts concentrate on characterising stellar dynamo action through spectroscopic, spectropolarimetric, and photometric long-term datasets. In addition, we aim at devising observational tests to nail down how the solar dynamo operate by studying, for example, oscillations and the magnetic field at the solar surface. Our ultimate goal is to establish how dynamos operate and drive magnetism across all types of stars with convective envelopes.
Below we list our recent research highlights. Older research highlights can be found from our news archive.
Understanding how solar and stellar dynamos work
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.
Observational characterization of solar and stellar dynamos
We have determined magnetic helicity spectrum from the solar surface observations using the recently developed two-scale formalism. We analyzed synoptic vector magnetograms built with data from the Vector Spectromagnetograph (VSM) instrument on the Synoptic Optical Long-term Investigations of the Sun (SOLIS) telescope during January 2010–July 2016, hence covering a large fraction of the solar cycle 24. Our study includes the total of 74 synoptic Carrington rotation maps. We recover here bihelical spectra at different phases of solar cycle 24, where the net magnetic helicity in the majority of the data is consistent with a large-scale dynamo with helical turbulence operating in the Sun. More than 20 precent of the analyzed maps, however, show violations of the expected sign rule.
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 (Olspert et al., 2018, A&A, 615, A111 for a Bayesian generalised Lomb-Scargle periodogram with trend) to one of the longest stellar activity database. We confirmed 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, A&A, 588, A38), 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.
Understanding solar and stellar convection
We studied the effect of a subadiabatic layer at the base of the convection zone on convection itself and the associated large-scale dynamos in spherical wedge geometry. We used a heat conduction prescription, based on the Kramers opacity law for the first time in spherical semi-global geometry. Such setup allows the depth of the convection zone to dynamically adapt to changes in the physical characteristics such as rotation rate and magnetic fields. Furthermore, a stably stratified but still convective layer develops in the deep parts of the convection zone. This layer is named after James Deardorff who discovered the phenomenon from the Earth's atmosphere. In the rotating cases the location and depth of the Deardorff layer and the base of the convection zone are latitude dependent. We found that the latitude distribution of the convective heat flux, the rotation profiles, and dynamo solutions are sensitive to subtle changes in the dynamics in the lower part of the convection zone. A solar-like oscillatory dynamo solution with equatorward propagation of activity was found in a case where the Deardorff layer is particularly pronounced at mid-latitudes.
Three-dimensional simulations show that a non-diffusive contribution to the Reynolds stress, the Lambda effect, is present in rotating anisotropic turbulence. This effect is expected to be crucial for driving the solar large-scale differential rotation. The current simulations show that for slow rotation only the vertical component of the Lambda effect survives which is expected to maintain a constant radial gradient of angular velocity. This is the most likely explanation for the near-surface shear layer in the Sun. Furthermore, the magnetic quenching of the Lambda effect was computed from simulations for the first time. It was found that significant quenching is observed well before equipartition field strength. Overall the results as function of rotation and magnetic field are typically in qualitative agreement with analytic results although the latter are not formally valid even in the mildly turbulent regimes considered in the present simulations. Large-scale vortices were also found in the simulations for sufficiently rapid rotation. Such features may have relevance for starspots in rapidly rotating stars.
Understanding sun- and starspot formation
Recent observational work on f-modes from helioseismology has provided evidence for the strengthening of it a couple of days before the actual active region emergence (Singh et al., 2016). The effect of sub-surface magnetic fields on the f-mode had already been detected from numerical simulations, in the form of "fanning" of the f-mode power at large wavenumbers (Singh et al., 2014). The setups used were very idealised, treating the active region as a periodic disturbance to the magnetic field. Now we present an improvement to the setup, where we modulate this periodic variation with an envelope, giving thus more emphasis on localized bipolar magnetic structures in the middle of the domain. Our most notable finding is that, in this more realistic setting, the f-mode fanning is weaker, while we observe a significant strengthening of the f-mode at larger horizontal wavenumbers (as shown in figure), in agreement with observations. Hence, we argue that detections of f-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots.
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.
Development of HPC and data analysis tools
Linear trends appear in stellar time series either due to long periodicities, secular activity trends or instrumental effects. They make it even more difficult to detect the real periodicities in the data, already complicated due to the shortness and uneven sampling of the data. To solve this problem we developed a Bayesian method, which incorporates a linear trend component into the model. We showed that the introduced method is preferred both over detrending the data or leaving the data un-detrended. The method outperformed the generalized Lomb-Scargle periodogram with and without detrending, which was illustrated with several artificial examples. Selection of prior distributions for the regression coefficients was shown to play an important role in the analysis. In this paper, we give two examples from the Mount Wilson chromospheric activity data set, in which the way the linear trend is removed affects significantly the retrieved period, the case of HD37394 shown in the figure.
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).