Synthetic Observations from Flip-Flop dynamos

Heidi Korhonen and Detlef Elstner

Photometrische Langzeitbeobachtungen und Dopplertomographie zeigen für einige aktive Sterne einen periodischen Wechsel der Fleckenaktivität zwischen zwei gegenüberliegenden Längenbereichen. Wir untersuchten dieses sogenannte Flip-Flop Phänomen mit synthetischen photometrischen Abbildungen, die aus numerischen Dynamo-Simulationen gewonnen wurden. Auch mögliche koronale Strukturen aktiver Sterne wurden mittels einer Potenzialfeld-Extrapolation aus dem Oberflächenfeld der Dynamomodelle hergeleitet.

We model the dynamo with a turbulent fluid in a spherical shell. A rotation law similar to the solar one is chosen, but with a smaller difference between core and surface rotation. This also leads to a reduced surface differential rotation. The mean electromotive force contains an anisotropic alpha-effect and a turbulent diffusivity. The nonlinear feed back of the magnetic field acts on the turbulence only. The boundary conditions describe a perfect conducting fluid at the bottom of the convection zone and at the stellar surface the magnetic field matches the vacuum field. For such models we find similar excitation conditions for oscillating axisymmetric and azimuthal migrating bisymmetric modes. The superposition of both modes shows a typical flip-flop phenomenon on the surface of the star. With our simulation we can follow this behaviour in the non-linear regime over thousands of cycles.


Figure 1: Snapshots of the surface magnetic field strength for one flip-flop cycle.

We have investigated in detail two flip-flop dynamo models, one with a thick convection zone and one with a thin one. The model calculations have been converted into temperature maps. This has been done by setting magnetic pressure values that are larger than 70% of the maximum value to 3500 K (umbra), values smaller than 70 % and larger 30 % of the maximum to 4250 K (penumbra) and the rest to 5000 K (unspotted surface). Long time sequences of these maps with short time steps in between have been converted into long-term light-curves that span in real time approximately 30 years. Many active stars show similar long-term light-curve behaviour as we see in the models, i.e. behaviour where time periods with small and large amplitude in the photometry alternate.

The types of possible coronal structure have also been investigated through potential field extrapolation of the model prediction of the surface magnetic field (Figure 2). The model confirms that the high latitude spots, being of opposite polarity, will harbour connecting loops that would tend to give rise to pole-dominated emission. However, the model also shows the connection of these polarised high-latitude regions to lower latitudes whose polarity is opposite to that of the dominant spot. These lower latitude fields would give rise to significant rotational broadening as appears to be seen in rapidly rotating active stars.


Figure 2: A potential field extrapolation of the surface magnetic field predicted by the flip-flop models. Shown are the resulting surface flux distribution and 100 randomly selected closed field lines representing the hot corona (from Drake et al. 2006).