Solar and stellar dynamos (SOLSTAR group)

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.

Go to a research topic:
How do solar and stellar dynamos work? -- Observational characterization of solar and stellar dynamos -- Understanding solar and stellar convection -- Sun- and starspot formation -- HPC, data analysis and scientific visualization tools

Understanding how solar and stellar dynamos work

<span>Dynamo drivers measured in Suns of different ages</span>
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. more
Slowly rotating stars with reversed butterfly diagrams: how to explain these dynamos?

We analysed a simulation of a solar-like star that is rotating slowly enough to revert its differential rotation profile from the solar-like one with a fast equator and slow poles into one with a slow equator and fast poles. In this simulation, the butterfly diagram, describing migration of the mean azimuthal magnetic field as function of time, also reversed from solar-like equatorward migration into a poleward one. Numerical solutions of this kind are unusual, but very interesting, as the Sun itself may approach such a regime, when it ages and slows down.

We used the test-field method to calculate the turbulent transport coefficients and found out that the turbulent alpha effect plays a major role in the generation of the mean toroidal magnetic field, therefore the dynamo is not an α Ω dynamo (where turbulence generates the poloidal magnetic field and differential rotation the toroidal magnetic field) as in the case of the Sun, but rather an α2 or α2Ω dynamo, where the differential rotation plays a marginal role.


Observational characterization of solar and stellar dynamos

<p><span>The Sun shows signatures of turbulent dynamo action </span></p>

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.

<p>Over 20-year long series of Doppler images of an active star published</p>

Over 20-year long series of Doppler images of an active star published

Our group has contributed significantly to the collection of a spectroscopic time series of active stars at the Nordic Optical Telescope (NOT) at La Palma, Spain, using the high-resolution spectrographs SOFIN and FIES. The former instrument has served at NOT since 1993, since 2004 including also  a polarimetric mode. The NOT observing programmes have resulted in a unique time series of spectroscopy over 24 years, enabling the study of both the long and short-term spot activity of the FK Comae-type star HD199178. These observations were recently published in a study containing the most extensive series of Doppler imaging temperature maps ever published: 41 DI maps covering the years 1994-2017 (Hackman et al., 2019) . The maps were used to extract a time-latitude diagram of the spot activity, i.e. the equivalent to the solar butterfly diagram. The study revealed a persistent cool spot region covering the rotation pole of the star.

The NOT data has also recently been used to study stars that can be regarded as young, rapidly rotating Suns. In V889 Her the spectroscopy reveals a constant polar spot, visible in all 19 data sets between 1999 and 2017, gathered with SOFIN, FIES and HARPSPol at the ESO 3.6m telescope (Willamo et al., 2019). The retrieved average temperature correlates well with photometric brightness variations, and both of these measures indicate that the star has recently entered a higher state of activity. Another young solar analogue monitored with NOT is LQ Hya. In a recently submitted study Doppler imaging temperature maps from 2006-2017 were presented (Cole-Kodikara et al., 2019). During this period, the spot activity of LQ Hya decreased and its luminosity consequently increased. The temperature maps reveal a somewhat erratic behaviour, but the previously reported bimodal latitudinal spot distribution remains.

Understanding solar and stellar convection

<p>Subadiabatic Deardorff layer shapes the dynamos and rotation profiles in stars</p>

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.

<p><span>Forced turbulence simulations prove the existence of Lambda effect</span></p>

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

<p><span>Simulations reveal f-mode strengthening from a localized bipolar subsurface magnetic field</span></p>

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.

<span>Magnetic flux concentrations from turbulent stratified convection</span>

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

<span>Do not get fooled by linear trends - new Bayesian periodogram method developed<br /></span>

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.


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