Maarit J. Mantere

Cyclic Magnetic Activity due to Turbulent Convection in Spherical Wedge Geometry

We report on simulations of turbulent, rotating, stratified, magnetohydrodynamic convection in spherical wedge geometry. An initially small-scale, random, weak-amplitude magnetic field is amplified by several orders of magnitude in the course of the simulation to form oscillatory large-scale fields in the saturated state of the dynamo. The differential rotation is solar-like (fast equator), but neither coherent meridional poleward circulation nor near-surface shear layer develop in these runs. In addition to a poleward branch of magnetic activity beyond 50 degrees latitude, we find for the first time a pronounced equatorward branch at around 20 degrees latitude, reminiscent of the solar cycle.

Reynolds stress and heat flux in spherical shell convection

Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate. Aims. Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong banana cells. Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

Effects of enhanced stratification on equatorward dynamo wave propagation

We present results from simulations of rotating magnetized turbulent convection in spherical wedge geometry representing parts of the latitudinal and longitudinal extents of a star. Here we consider a set of runs for which the density stratification is varied, keeping the Reynolds and Coriolis numbers at similar values. In the case of weak stratification, we find quasi-steady dynamo solutions for moderate rotation and oscillatory ones with poleward migration of activity belts for more rapid rotation. For stronger stratification, the growth rate tends to become smaller. Furthermore, a transition from quasi-steady to oscillatory dynamos is found as the Coriolis number is increased, but now there is an equatorward migrating branch near the equator. The breakpoint where this happens corresponds to a rotation rate that is about three to seven times the solar value. The phase relation of the magnetic field is such that the toroidal field lags behind the radial field by about ?/2, which can be explained by an oscillatory ?2 dynamo caused by the sign change of the ?-effect about the equator. We test the domain size dependence of our results for a rapidly rotating run with equatorward migration by varying the longitudinal extent of our wedge. The energy of the axisymmetric mean magnetic field decreases as the domain size increases and we find that an m = 1 mode is excited for a full 2? azimuthal extent, reminiscent of the field configurations deduced from observations of rapidly rotating late-type stars.

SPOKE-LIKE DIFFERENTIAL ROTATION IN A CONVECTIVE DYNAMO WITH A CORONAL ENVELOPE

We report on the results of four convective dynamo simulations with an outer coronal layer. The magnetic field is self-consistently generated by the convective motions beneath the surface. Above the convection zone, we include a polytropic layer that extends to 1.6 solar radii. The temperature increases in this region to ≈8 times the value at the surface, corresponding to ≈1.2 times the value at the bottom of the spherical shell. We associate this region with the solar corona. We find solar-like differential rotation with radial contours of constant rotation rate, together with a near-surface shear layer. This non-cylindrical rotation profile is caused by a non-zero latitudinal entropy gradient that offsets the Taylor-Proudman balance through the baroclinic term. The meridional circulation is multi-cellular with a solar-like poleward flow near the surface at low latitudes. In most of the cases, the mean magnetic field is oscillatory with equatorward migration in two cases. In other cases, the equatorward migration is overlaid by stationary or even poleward migrating mean fields.

Flip-flops of FK Comae Berenices

Context. FK Comae Berenices is a rapidly rotating magnetically active star, the light curve of which is modulated by cool spots on its surface. It was the first star where the “flip-flop” phenomenon was discovered. Since then, flip-flops in the spot activity have been reported in many other stars. Follow-up studies with increasing length have shown, however, that the phenomenon is more complex than was thought right after its discovery. Aims. Therefore, it is of interest to perform a more thorough study of the evolution of the spot activity in FK Com. In this study, we analyse 15 years of photometric observations with two different time series analysis methods, with a special emphasis on detecting flip-flop type events from the data. Methods. We apply the continuous period search and carrier fit methods on long-term standard Johnson-Cousins V-observations from the years 1995−2010. The observations were carried out with two automated photometric telescopes, Phoenix-10 and Amadeus T7 located in Arizona. Results. We identify complex phase behaviour in 6 of the 15 analysed data segments. We identify five flip-flop events and two cases of phase jumps, where the phase shift is Δ φ 0.031. Conclusions. The flip-flop cannot be interpreted as a single phenomenon, where the main activity jumps from one active longitude to another. In some of our cases the phase shifts can be explained by differential rotation: two spot regions move with different angular velocity and even pass each other. Comparison between the methods show that the carrier fit utility is better in retrieving slow evolution especially from a low amplitude light curve, while the continuous period search is more sensitive in case of rapid changes.

STARSPOTS DUE TO LARGE-SCALE VORTICES IN ROTATING TURBULENT CONVECTION

We study the generation of large-scale vortices in rotating turbulent convection by means of Cartesian direct numerical simulations. We find that for sufficiently rapid rotation, cyclonic structures on a scale large in comparison to that of the convective eddies emerge, provided that the fluid Reynolds number exceeds a critical value. For slower rotation, cool cyclonic vortices are preferred, whereas for rapid rotation, warm anti-cyclonic vortices are favored. In some runs in the intermediate regime both types of cyclones coexist for thousands of convective turnover times. The temperature contrast between the vortices and the surrounding atmosphere is of the order of 5%. We relate the simulation results to observations of rapidly rotating late-type stars that are known to exhibit large high-latitude spots from Doppler imaging. In many cases, cool spots are accompanied with spotted regions with temperatures higher than the average. In this paper, we investigate a scenario according to which of the spots observed in the temperature maps could have a non-magnetic origin due to large-scale vortices in the convection zones of the stars.

Doppler images of II Pegasi for 2004-2010

Aims. We study the spot activity of II Peg during the years 2004–2010 to determine long- and short-term changes in the magnetic activity. In a previous study, we detected a persistent active longitude, as well as major changes in the spot configuration occurring on a timescale of shorter than a year. The main objective of this study is to determine whether the same phenomena persist in the star during these six years of spectroscopic monitoring. Methods. The observations were collected with the high-resolution SOFIN spectrograph at the Nordic Optical Telescope. The temperature maps were calculated using a Doppler imaging code based on Tikhonov regularization. Results. We present 12 new temperature maps that show spots distributed mainly over high and intermediate latitudes. In each image, 1–3 main active regions can be identified. The activity level of the star is clearly lower than during our previous study for the years 1994–2002. In contrast to the previous observations, we detect no clear drift of the active regions with respect to the rotation of the star. Conclusions. Having shown a systematic longitudinal drift of the spot-generating mechanism during 1994–2002, the star has clearly switched to a low-activity state for 2004–2010, during which the spot locations appear more random over phase space. It could be that the star is near to a minimum of its activity cycle.

AN AZIMUTHAL DYNAMO WAVE IN SPHERICAL SHELL CONVECTION

We report the discovery of an azimuthal dynamo wave of a low-order (m = 1) mode in direct numerical simulations (DNS) of turbulent convection in spherical shells. Such waves are predicted by mean-field dynamo theory and have been obtained previously in mean-field models. An azimuthal dynamo wave has been proposed as a possible explanation for the persistent drifts of spots observed on several rapidly rotating stars, as revealed through photometry and Doppler imaging. However, this has been judged unlikely because evidence for such waves from DNS has been lacking. Here we present DNS of large-scale magnetic fields showing a retrograde m = 1 mode. Its pattern speed is nearly independent of latitude and does not reflect the speed of the differential rotation at any depth. The extrema of magnetic m = 1 structures coincide reasonably well with the maxima of m = 2 structures of the temperature. These results provide direct support for the observed drifts being due to an azimuthal dynamo wave.

Ejections of Magnetic Structures Above a Spherical Wedge Driven by a Convective Dynamo with Differential Rotation

We combine a convectively driven dynamo in a spherical shell with a nearly isothermal density-stratified cooling layer that mimics some aspects of a stellar corona to study the emergence and ejections of magnetic field structures. This approach is an extension of earlier models, where forced turbulence simulations were employed to generate magnetic fields. A spherical wedge is used which consists of a convection zone and an extended coronal region to ≈ 1.5 times the radius of the sphere. The wedge contains a quarter of the azimuthal extent of the sphere and 150∘ in latitude. The magnetic field is self-consistently generated by the turbulent motions due to convection beneath the surface. Magnetic fields are found to emerge at the surface and are ejected to the coronal part of the domain. These ejections occur at irregular intervals and are weaker than in earlier work. We tentatively associate these events with coronal mass ejections on the Sun, even though our model of the solar atmosphere is rather simplistic.

Multiperiodicity, modulations and flip-flops in variable star light curves - II. Analysis of II Pegasus photometry during 1979–2010

Aims. According to previously published Doppler images of the magnetically active primary giant component of the RS CVn binary II Peg, the surface of the star was dominated by one single active longitude that was clearly drifting in the rotational frame of the binary system during 1994-2002; later imaging for 2004–2010, however, showed decreased and chaotic spot activity, with no signs of the drift pattern. Here we set out to investigate from a more extensive photometric dataset whether this drift is a persistent phenomenon, in which case it could be caused either by an azimuthal dynamo wave or be an indication that the binary system’s orbital synchronization is still incomplete. On a differentially rotating stellar surface, spot structures preferentially on a certain latitude band could also cause such a drift, the disruption of which could arise from the change of the preferred spot latitude. Methods. We analyzed the datasets using the carrier fit (CF) method, which is especially suitable for analyzing time series in which a fast clocking frequency (such as the rotation of the star) is modulated with a slower process (such as the stellar activity cycle). Results. We combined all collected photometric data into one single data set and analyzed it with the CF method. We confirm the previously published results that the spot activity has been dominated by one primary spotted region almost through the entire data set and also confirm a persistent, nearly linear drift. Disruptions of the linear trend and complicated phase behavior are also seen, but the period analysis reveals a rather stable periodicity with Pspot = 6. d 71054 ± 0. 00005. After removing the linear trend from the data, we identified several abrupt phase jumps, three of which are analyzed in more detail with the CF method. These phase jumps closely resemble what is called a flip-flop event, but the new spot configurations do not persist for longer than a few months in most cases. Conclusions. There is some evidence that the regular drift without phase jumps is related to the high state, while the complex phase behavior and disrupted drift pattern are related to the low state of magnetic activity. The most natural explanation of the drift is weak anti-solar (pole rotating faster than the equator) differential rotation with a coefficient k ≈ 0.002 combined with the preferred latitude of the spot structure.