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Final Report Summary - DYNACOR (From the Sun to stars - Interplay between dynamo and corona)

Most of solar-like stars show magnetic field on their surfaces similar to the Sun. In the atmosphere of these stars magnetic fields are able to generate enhanced X-ray and Ca K emissions, which are often used as a stellar activity indicators. One unique feature of cool stars is the relation of their activity and rotation rate. For slow rotating stars their activity increases with their rotation rate. However, for rapid rotating stars the activity show no dependence on rotation rate. This behavior is based on the two fundamental problems in stellar astrophysics: how the stars generate their magnetic field, and how magnetic energy is transformed into stellar activity indicators.

To solve these two interlinked problems it is necessary to understand to magnetic field generation by a dynamo mechanism operating in the stellar convection zone and its interaction with the outer atmosphere of the star. In this context the main objectives of the DynaCore have been:

1. Understand fundamental properties of stellar dynamos using accurate mean-field models of the direct numerical simulations,
2. Investigate the influence of the coronal envelope on stellar dynamos and stellar interiors,
3. Determine the role of stellar dynamos for the formation and evolution of coronal structures.

Following work has been performed during the DynaCore Project:

1. Performing several global convective dynamo simulation with and without a coronal envelope in large parameter range by varying rotation rate and Prandtl number (relation between magnetic, viscose and thermal diffusion).

2. Implementing and testing the test-field method for spherical coordinates with two-dimensional test-fields to be able to determine the mean-field dynamo transport coefficients from global dynamo simulations.

3. Performing mean-field simulation using transport coefficients obtained by test-field method.

4. Using mean-field simulations with combined model of the dynamo and a simplified treatment of the solar wind to study the process of helicity transport. The helicity plays an important role to alleviate the quenching of the dynamo process at high magnetic Reynolds numbers.

5. Performing simulations of stratified forced turbulence with weak imposed magnetic field to study the spontaneous formation of flux concentrations similar to sunspots or starspots. These simulation were performed with a large range of parameters, including rotation. Also we couple these simulation with a self-consistent dynamo. Such simulation will help us to understand the magnetic structure formation at the surface of the Sun and stars.

6. Performing and analyzing simulation of the solar corona to understand the structure formation in particular the relation between the emissivity and current topology in coronal loops.
This is important to understand the relation between magnetic activity, helicity and coronal emission.

Main results obtained during this project:

1. A realistic treatment of the upper boundary in spherical dynamo simulations is crucial for the dynamics of the flow and magnetic field evolution. We find the differential rotation as well as the dynamo solution changes in the presents of coronal envelope. This can be clearly seen in the responsible angular momentum transport coefficients (Warnecke et al. 2016b)

2. The dynamo solution obtained from global convective simulation show strong dependency on diffusivities and rotation rate. Solar-like behavior seems to occur only in a narrow parameter range and there is no indication of an asymptotic behavior for low and intermediate diffusivities (Käpylä et al. 2017).
Furthermore, the for some of the simulation we found long-time variation of the magnetic activity similar as seen on the Sun during the "Maunder Minimum". This is caused by a two dynamo modes operating on different timescales and their interaction (Käpylä et al. 2016).

3. The analysis of the dynamo mechanism in terms of the mean-field coefficients with the test-field method reveal a complex behavior. Besides the alpha-Omega dynamo also an alpha^2 dynamo can be locally present. The turbulent pumping, resulting in an effective velocity, just seen by the magnetic field, completely change the effective meridional circulation. This result challenges the broadly believed flux-transport dynamo model of the Sun and stars (Warnecke et al. 2017a).
The rotational dependence of these coefficients show that the alpha effect monotonically increased with higher rotation, however also its meridional distribution changes: for higher rotation its is more alined on cylinders. The turbulent pumping is found to be directed outwards for slow and medium rotation, which is in contrast to derivation from near-surface convection simulations.

4. We found from our simulations that for high rotation rate the dynamo solution becomes highly non-axisymmetric. For slow and medium rotation, the magnetic field is dominant in the m=0 (axisymmetric) mode, where as for fast rotation the m=1 mode dominates. Currently, we cannot find any indication of a increasing magnetic activity with rotation rate. This, however, can also be related to an increase in critical Rayleigh number for larger rotation.

5. We have shown that we can produce bipolar magnetic region similar to sunspots because of an hydromagnetic instability in stratified turbulence with a coronal envelope. This instability can operate in large parameter regime as long as enough stratification and scale-separation is present (Warnecke et al. 2016a). Including rotation leads to an inclination of the bipolar region as might be related to the observed Joy's law of sunspot tilt angles. The previously observed quenching of this instability is weaker using a coronal envelope. A combined model of helical dynamo action and this instability reveals the recurrent formation of bipolar region and the associated ejection of current helicity from the surface to the coronal envelope. These results are important to understand the formation of sunspots and starspots and the transport of helicity out of the dynamo domain to alleviate the quenching mechanism.

6. Using models of the solar corona, we have demonstrated that the current structure in coronal loop above an emerging active region is of complex nature. Even though there is no ejection of net helicity into the domain, the currents form helically structures in and around the coronal loop. This behavior is caused by the interaction of magnetic field movement as well as the plasma flow in and around the loop. The helical current structure also influence the temporal evolution of the loop and seems to be crucial for the emissivity in coronal lines (Warnecke et al. 2017b).
This seems to point to a direct relation between the current helicity and the emissivity in coronal lines and therefore is a key result to understand the rotation-activity relation of stars.
Furthermore, we found that the assumption of a low plasma-beta (ratio of magnetic to gas pressure) in the corona is not always true and 3D MHD simulation, which include the back-reaction of the plasma on the magnetic field are crucial to described the structure of the coronal magnetic field and current distribution (Peter et al. 2015).

Peter et al. 2015, Astron. Astrophys., 584, A68
Käpylä et al. 2016, Astron. Astrophys., 589, A56
Warnecke et al. 2016a, Astron. Astrophys., 589, A125
Warnecke et al. 2016b, Astron. Astrophys., 596, A115
Käpylä et al. 2017, Astron. Astrophys., 599, A4
Warnecke et al. 2017a, Astron. Astrophys., under revision, arXiv:1601.03730
Boro Saikia et al. 2017, Astron. Astrophys., under revision
Warnecke et al. 2017b, Astron. Astrophys., under revision, arXiv:1611.06170


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