Formation of starspots in self-consistent global dynamo models: Polar spots on cool stars

Kleeorin

et al. 2015

ApJ

Recent work by Mitra et al. (2014) has shown that in strongly stratified forced two-layer turbulence with helicity and corresponding large-scale dynamo action in the lower layer, and nonhelical turbulence in the upper, a magnetic field occurs in the upper layer in the form of sharply bounded bipolar magnetic spots. Here we extend this model to spherical wedge geometry covering the northern hemisphere up to 75°latitude and an azimuthal extent of 180°. The kinetic helicity and therefore also the large-scale magnetic field are strongest at low latitudes. For moderately strong stratification, several bipolar spots form that eventually fill the full longitudinal extent. At early times, the polarity of spots reflects the orientation of the underlying azimuthal field, as expected from Parker's Ω-shaped flux loops. At late times their tilt changes such that there is a radial field of opposite orientation at different latitudes separated by about 10°. Our model demonstrates the spontaneous formation of spots of sizes much larger than the pressure scale height. Their tendency to produce filling factors close to unity is argued to be reminiscent of highly active stars. We confirm that strong stratification and strong scale separation are essential ingredients behind magnetic spot formation, which appears to be associated with downflows at larger depths.

Section: High-latitude Spotssupporting

confidence: 54%

“…Figure 14 presents the formation of bipolar spots near the pole for run H2. By contrast, the work of Yadav et al (2015) showed just a single spot. However, in both cases the underlying dynamo process is a distributed one, so the lower boundary at the bottom of the domain is not critical for its operation.…”

Section: High-latitude Spotsmentioning

confidence: 89%

Bipolar Magnetic Spots From Dynamos in Stratified Spherical Shell Turbulence

Jabbari

Kleeorin

et al. 2015

ApJ

“…Given their size and further expansion when ascending to the surface, their role in sunspot formation remains inconclusive. An alternative to producing spots in a global dynamo simulation of rapidly rotating stars was found by Yadav et al (2015). These authors were able to generate a single polar spot without the help of rising tubes.…”

Section: Introductionmentioning

confidence: 99%

Bipolar region formation in stratified two-layer turbulence

Warnecke

Losada

et al. 2016

A&A

Aims. This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots. Methods. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In most cases, it is horizontal, but a vertical and an inclined field are also considered. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process. Results. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around 100 across the turbulent layer. For the fluid Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. A small imposed horizontal field component is necessary to generate bipolar structures. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations.

“…Furthermore, numerical simulations of convective dynamos produce diffuse magnetic fields throughout the convection zone (e.g. Ghizaru et al 2010;Käpylä et al 2012b;Yadav et al 2015;Augustson et al 2015), which could act as the seed field for NEMPI.…”

Section: Introductionmentioning

confidence: 99%

Magnetic flux concentrations from turbulent stratified convection

Käpylä

Kleeorin

et al. 2016

A&A

Context. The formation of magnetic flux concentrations within the solar convection zone leading to sunspot formation is unexplained. Aims. We study the self-organization of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods. We perform simulations of magnetoconvection in Cartesian domains representing the uppermost 8.5−24 Mm of the solar convection zone with the horizontal size of the domain varying between 34 and 96 Mm. The density contrast in the 24 Mm deep models is more than 3 × 10 3 or eight density scale heights, corresponding to a little over 12 pressure scale heights. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow in set-ups where no small-scale dynamos are present. In the most highly stratified cases we employ the reduced sound speed method to relax the time step constraint arising from the high sound speed in the deep layers. We model radiation via the diffusion approximation and neglect detailed radiative transfer in order to concentrate on purely magnetohydrodynamic effects. Results. We find that super-equipartition magnetic flux concentrations are formed near the surface in cases with moderate and high density stratification, corresponding to domain depths of 12.5 and 24 Mm. 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 amplitude of the concentrations grows approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in most of the domain, which is unfavourable for the operation of the negative effective magnetic pressure instability (NEMPI). Simulations in which a passive vector field is evolved do not show a noticeable difference from magnetohydrodynamic runs in terms of the growth of the structures. Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions. 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. A possible reason for the absence of NEMPI is that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign. Furthermore, there may not be sufficient scale separation, which is required for NEMPI to work.