UniSDyn: Building up a Unified Theory of Stellar Dynamos
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
Results from global magnetoconvection simulations of solar-like stars are at odds with observations in many respects: They show a surplus of energy in the kinetic power spectrum at large scales, anti-solar differential rotation profiles, with accelerated poles and a slow equator, for the solar rotation rate, and a transition from axi- to non-axisymmetric dynamos at a much lower rotation rate than what is observed. Even though the simulations reproduce the observed active longitudes in fast rotators, their motion in the rotational frame (the so-called azimuthal dynamo wave, ADW) is retrograde, in contrast to the prevalent prograde motion in observations. Recently, we studied the effect of a more realistic treatment of heat conductivity in alleviating the discrepancies between observations and simulations. We used physically-motivated heat conduction, by applying Kramers opacity law, on a semi-global spherical setup describing convective envelopes of solar-like stars, instead of a prescribed heat conduction profile from mixing-length arguments. We found that some aspects of the results now better correspond to observations: The axi- to non-axisymmetric transition point is shifted towards higher rotation rates. We also found a change in the propagation direction of ADWs so that also prograde waves were now found (see figure). The transition from anti-solar to solar-like rotation profile, however, was also shifted towards higher rotation rates, leaving the models into an even more unrealistic regime.
Solar-like stars are more active when they are young and rotate more rapidly, while as they age, they spin down and also become magnetically less active. Hence, rotation rate is usually a reasonably good tracer of the star's age. We used this fact to probe the dynamo mechanism over time in solar-like partially convective stars using 3D MHD global convection simulations with varying rotation rates, and measured the turbulent effects taking part in the dynamo mechanism using the test-field method. As a result, we found three distinct dynamo regimes. Around solar rotation rate and age, we could reproduce solar-like magnetic activity with equatorward migrating activity belts forming the famous butterfly diagram. In this regime, the dynamo was again verified to be driven by differential rotation and an alpha effect (so called alpha-Omega dynamo), arising from the collective inductive action of rotationally affected convection cells. For rapid rotation and younger age, differential rotation is very inefficient and the dynamo becoming solely driven by the alpha effect. The tensor describing this effect becomes highly anisotropic, which may explain the preference of non-axisymmetric solutions in this regime. In the slow rotation regime and old age, the differential rotation swaps into fast-pole-slow-equator type, and other turbulent effects such as the Rädler effect becomes important. Our study reveals the presence of a large variety of dynamo effects beyond the classical alpha-Omega mechanism, which need to be investigated further to fully understand the dynamos of solar-like stars.
Observational characterization of solar and stellar dynamos
Different stars can exhibit very different levels of activity. The Sun’s coronal mass ejections, flares and sunspots – all signs of solar activity – are rather feeble on an astronomical scale. Other stars are up to ten times more active, for example sporting huge starspots that cover a large portion of their disc. While researchers have long identified the magnetic fields generated in the interior of stars in a dynamo process as drivers of activity, the exact workings of this dynamo are still unclear. A group of scientists led by the Max Planck Institute for Solar System Research (MPS) in Germany has now searched for an answer by applying the same analysis to a sample of both main sequence and more evolved stars. They find that a common, turbulence-dependent dynamo mechanism plays a crucial role for stellar activity in all stages of stellar evolution. The results are published in next week’s issue of Nature Astronomy. Read the full press release here .
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.
Understanding solar and stellar convection
The existence of large-scale dynamo action originating from other sources than the standard alpha Omega mechanism, requiring helicity, has been long debated. One such candidate is the shear-current effect, that has been postulated to exist in shear flows without helicity. While most of the numerical evidence has been against the existence of this effect, recent works showing some signatures of it in the presence of magnetic forcing, mimicking the small-scale dynamo action, have been presented. For gathering further evidence, we have developed a non-linear test-field method that is applicable in the presence of strong magnetic background turbulence, and applied it to measure the relevant transport coefficients in flows capable of exciting this “magnetic shear current effect”.
Our results, although still limited to simplified MHD equations neglecting the pressure gradient term in the Navier-Stokes equation (Burgulence), show that a weak shear-current effect is detected with kinematic forcing only, while in the magnetic forcing cases, the effect is not excited. The dynamos observed in the systems studied are rather found to be driven by the incoherent effects arising from turbulence.
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.
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, data analysis and scientific visualization 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 HD
37394 shown in the figure.