Solar-like Differential Rotation Research Articles

Scale-dependent analysis of angular momentum flux in high-resolution magnetohydrodynamic simulations for solar differential rotation

ABSTRACT In this work, we systematically investigate the scale-dependent angular momentum flux by analysing high-resolution three-dimensional magnetohydrodynamic simulations in which the solar-like differential rotation is reproduced without using any manipulations. More specifically, the magnetic angular momentum transport (AMT) plays a dominant role in the calculations. We examine the important spatial scales for the magnetic AMT. The main conclusions of our approach can be summarized as follows: 1. Turbulence transports the angular momentum radially inward. This effect is more pronounced in the highest resolution calculation. 2. The dominant scale for the magnetic AMT is the smallest spatial scale. 3. The dimensionless magnetic correlation is low in the high-resolution simulation. Thus, chaotic but strong small-scale magnetic fields achieve efficient magnetic AMT.

Magnetic topologies of two weak-line T Tauri stars TAP 4 and TAP 40

ABSTRACT We present a Zeeman–Doppler imaging study of two weak-line T Tauri stars TAP 4 and TAP 40, based on the high-resolution spectropolarimetric observations with ESPaDOnS at the Canada–France–Hawaii Telescope in November 2013, in the framework of the Magnetic Topologies of Young Stars and Survival of close-in giant Exoplanets large programme. We apply two Zeeman–Doppler imaging codes to the Stokes I and V profiles to reconstruct their brightness and large-scale magnetic field images. The results given by the two imaging codes are in good agreement with each other. TAP 4 shows a large polar cool spot and several intermediate-latitude warm spots on its surface, whereas TAP 40 exhibits very weak variations in its Stokes I profiles, suggesting a mostly unspotted photosphere. We detect Zeeman signatures in the Stokes V profiles of both stars. The reconstructed magnetic maps reveal dominantly toroidal fields, which enclose about 60 per cent of the total magnetic energy for both TAP 4 and TAP 40. Both stars show prominent circular ring features of the azimuthal magnetic field. We derive a solar-like surface differential rotation on TAP 4 from the tomographic modelling. The brightness image of TAP 4 is used to predict the radial velocity (RV) jitters induced by its activity. After filtering out the activity jitter, the rms of its RVs is reduced from 1.7 to 0.2 km s−1, but we do not detect any periodic signals in the filtered RVs of TAP 4, implying that it is unlikely to host a close-in exoplanet more massive than ∼3.5MJup at 0.1 au.

Transition from anti-solar to solar-like differential rotation: Dependence on Prandtl number

Context. Late-type stars such as the Sun rotate differentially due to the interaction of turbulent convection and rotation. Aims. The aim of the study is to investigate the effects of the effective thermal Prandtl number, which is the ratio of kinematic viscosity to thermal diffusivity, on the transition from anti-solar (slow equator, fast poles) to solar-like (fast equator, slow poles) differential rotation. Methods. Three-dimensional hydrodynamic and magnetohydrodynamic simulations in semi-global spherical wedge geometry were used to model the convection zones of solar-like stars. Results. The overall convective velocity amplitude increases as the Prandtl number decreases, in accordance with earlier studies. The transition from anti-solar to solar-like differential rotation is insensitive to the Prandtl number for Prandtl numbers below unity, but for Prandtl numbers greater than unity, solar-like differential rotation becomes significantly harder to excite. Magnetic fields and more turbulent regimes with higher fluid and magnetic Reynolds numbers help to achieve solar-like differential rotation in near-transition cases where anti-solar rotation is found in more laminar simulations. Solar-like differential rotation occurs only in cases with radially outward turbulent angular momentum transport due to the Reynolds stress at the equator. The dominant contribution to this outward transport near the equator is due to prograde propagating thermal Rossby waves. Conclusions. The differential rotation is sensitive to the Prandtl number only for large Prandtl numbers in the parameter regime explored in this study. Magnetic fields have a greater effect on the differential rotation, although the inferred presence of a small-scale dynamo did not lead to drastically different results. The dominance of the thermal Rossby waves in the simulations is puzzling because they are not detected in the Sun. The current simulations are shown to be incompatible with the currently prevailing mean-field theory of differential rotation.

Implicit Large-eddy Simulations of Global Solar Convection: Effects of Numerical Resolution in Nonrotating and Rotating Cases

Simulating deep solar convection and its coupled mean-field motions is a formidable challenge where few observational results constrain models that suffer from the nonphysical influence of the grid resolution. We present hydrodynamic global implicit large-eddy simulations of deep solar convection performed with the EULAG-MHD code, and we explore the effects of grid resolution on the properties of rotating and nonrotating convection. The results, based on low-order moments and turbulent spectra, reveal that convergence in nonrotating simulations may be achieved at resolutions not much higher than these considered here. The flow is highly anisotropic, with the energy contained in horizontal divergent motions exceeding their radial counterpart by more than three orders of magnitude. By contrast, in rotating simulations, the largest energy is in the toroidal part of the horizontal motions. As the grid resolution increases, the turbulent correlations change in such a way that a solar-like differential rotation, obtained in the simulation with the coarser grid, transitions to an antisolar differential rotation. The reason for this change is the contribution of the effective viscosity to the balance of the forces driving large-scale flows. As the effective viscosity decreases, the angular momentum balance improves, yet the force balance in the meridional direction lessens, favoring a strong meridional flow that advects angular momentum toward the poles. The results suggest that obtaining the correct distribution of angular momentum may not be a mere issue of numerical resolution. Accounting for additional physics, such as magnetism or the near-surface shear layer, may be necessary in simulating the solar interior.

Constraining Global Solar Models through Helioseismic Analysis

Global hydrodynamic simulations of internal solar dynamics have focused on replicating the conditions for solar-like (equator rotating faster than the poles) differential rotation and meridional circulation using the results of helioseismic inversions as a constraint. Inferences of meridional circulation, however, have provided controversial results showing the possibility of one, two, or multiple cells along the radius. To help address this controversy and develop a more robust understanding of global flow regimes in the solar interior, we apply a “forward-modeling” approach to the analysis of helioseismic signatures of meridional circulation profiles obtained from numerical simulations. We employ the global acoustic modeling code GALE to simulate the propagation of acoustic waves through regimes of mean mass-flows generated by global hydrodynamic and magnetohydrodynamic models: EULAG, the Pencil code, and the Rayleigh code. These models are used to create synthetic Dopplergram data products, used as inputs for local time–distance helioseismology techniques. Helioseismic travel-time signals from solutions obtained through global numerical simulations are compared directly with inferences from solar observations, in order to set additional constraints on global model parameters in a direct way. We show that even though these models are able to replicate solar-like differential rotation, the resulting rotationally constrained convection develops a multicell global meridional circulation profile that is measurably inconsistent with local time–distance inferences of solar observations. However, we find that the development of rotationally unconstrained convection close to the model surface is able to maintain solar-like differential rotation, while having a significant impact on the helioseismic travel-time signal, replicating solar observations within one standard deviation of the error due to noise.

Generation of Solar-like Differential Rotation

We analyze the simulation result shown in Hotta & Kusano (2021) in which the solar-like differential rotation is reproduced. The Sun is rotating differentially with the fast equator and the slow pole. It is widely thought that the thermal convection maintains the differential rotation, but recent high-resolution simulations tend to fail to reproduce the fast equator. This fact is an aspect of one of the biggest problems in solar physics called the convective conundrum. Hotta & Kusano succeed in reproducing the solar-like differential rotation without using any manipulation with an unprecedentedly high-resolution simulation. In this study, we analyze the simulation data to understand the maintenance mechanism of the fast equator. Our analyses lead to conclusions that are summarized as follows. (1) The superequipatition magnetic field is generated by the compression, which can indirectly convert the massive internal energy to magnetic energy. (2) The efficient small-scale energy transport suppresses large-scale convection energy. (3) Non-Taylor–Proudman differential rotation is maintained by the entropy gradient caused by the anisotropic latitudinal energy transport enhanced by the magnetic field. (4) The fast equator is maintained by the meridional flow mainly caused by the Maxwell stress. The Maxwell stress itself also has a role in the angular momentum transport for the fast near-surface equator (we call it the P unching ball effect). The fast equator in the simulation is reproduced not due to the low Rossby number regime but due to the strong magnetic field. This study newly finds the role of the magnetic field in the maintenance of differential rotation.

Solar-like Dynamos and Rotational Scaling of Cycles from Star-in-a-box Simulations

Magnetohydrodynamic star-in-a-box simulations of convection and dynamos in a solar-like star with different rotation rates are presented. These simulations produce solar-like differential rotation with a fast equator and slow poles and magnetic activity that resembles that of the Sun with equatorward migrating activity at the surface. Furthermore, the ratio of rotation to cycle period is almost constant, as the rotation period decreases in the limited sample considered here. This is reminiscent of the suggested inactive branch of stars from observations and differs from most earlier simulation results from spherical shell models. While the exact excitation mechanism of the dynamos in the current simulations is not yet clear, it is shown that it is plausible that the greater freedom that the magnetic field has due to the inclusion of the radiative core and regions exterior to the star are important in shaping the dynamo.

A Babcock–Leighton-type Solar Dynamo Operating in the Bulk of the Convection Zone

The toroidal magnetic field is assumed to be generated in the tachocline in most Babcock–Leighton (BL)-type solar dynamo models, in which the poloidal field is produced by the emergence and subsequent dispersal of sunspot groups. However, magnetic activity of fully convective stars and MHD simulations of global stellar convection have recently raised serious doubts regarding the importance of the tachocline in the generation of the toroidal field. In this study, we aim to develop a new BL-type dynamo model, in which the dynamo operates mainly within the bulk of the convection zone. Our 2D model includes the effect of solar-like differential rotation, one-cell meridional flow, near-surface radial pumping, strong turbulent diffusion, BL-type poloidal source, and nonlinear back-reaction of the magnetic field on its source with a vertical outer boundary condition. The model leads to a simple dipolar configuration of the poloidal field that has the dominant latitudinal component, which is wound up by the latitudinal shear within the bulk of the convection zone to generate the toroidal flux. As a result, the tachocline plays a negligible role in the model. The model reproduces the basic properties of the solar cycle, including (a) approximately 11 yr cycle period and 18 yr extended cycle period; (b) equatorward propagation of the antisymmetric toroidal field starting from high latitudes; and (c) polar field evolution that is consistent with observations. Our model opens the possibility for a paradigm shift in understanding the solar cycle to transition from the classical flux transport dynamo.

Generation mechanism of solar-like differential rotation in high-resolution simulations

We analyze the simulation result shown in Hotta & Kusano, 2021 in which the solar-like differential rotation is reproduced. The Sun is rotating differentially with the fast equator and the slow pole. It is widely thought that the thermal convection maintains the differential rotation, but recent high-resolution simulations tend to fail to reproduce the fast equator. This fact is an aspect of one of the biggest problems in solar physics called the convective conundrum. Hotta & Kusano, 2021 succeed in reproducing the solar-like differential rotation without using any manipulation with unprecedentedly high-resolution simulation. In this study, we analyze the simulation data to understand the maintenance mechanism of the fast equator. Our analyses lead to conclusions that are summarized as follows. 1. Superequipatition magnetic field is generated by the compression, which can indirectly convert the massive internal energy to magnetic energy. 2. The efficient small-scale energy transport suppresses large-scale convection energy. 3. Non-Taylor--Proudman differential rotation is maintained by the entropy gradient caused by the anisotropic latitudinal energy transport enhanced by the magnetic field. 4. The fast equator is maintained by the meridional flow mainly caused by the Maxwell stress. The Maxwell stress itself also has a role in the angular momentum transport for fast near-surface equator (we call it the Punching ball effect). The fast equator in the simulation is reproduced not due to the low Rossby number regime but due to the strong magnetic field. This study newly finds the role of the magnetic field in the maintenance of differential rotation.

Solar differential rotation reproduced with high-resolution simulation

The Sun rotates differentially with a fast equator and slow pole. Convection in the solar interior is thought to maintain the differential rotation. However, although many numerical simulations have been conducted to reproduce the solar differential rotation, previous high-resolution calculations with solar parameters fall into the anti-solar (fast pole) differential rotation regime. Consequently, we still do not know the true reason why the Sun has a fast-rotating equator. While the construction of the fast equator requires a strong rotational influence on the convection, the previous calculations have not been able to achieve the situation without any manipulations. The problem is called convective conundrum. The convection and the differential rotation in numerical simulations were different from the observations. Here, we show that a high-resolution calculation succeeds in reproducing the solar-like differential rotation. Our calculations indicate that the strong magnetic field generated by a small-scale dynamo has a significant impact on thermal convection. The successful reproduction of the differential rotation, convection, and magnetic field achieved in our calculation is an essential step to understanding the cause of the most basic nature of solar activity, specifically, the 11-year cycle of sunspot activity.

Observing the changing surface structures of the active K giant σ Geminorum with SONG

Aims. We aim to study the spot evolution and differential rotation in the magnetically active cool K-type giant star σ Gem from broadband photometry and continuous spectroscopic observations that span 150 nights. Methods. We use high-resolution, high signal-to-noise ratio spectra obtained with the Hertzsprung SONG telescope to reconstruct surface (photospheric) temperature maps with Doppler imaging techniques. The 303 observations span 150 nights and allow for a detailed analysis of the spot evolution and surface differential rotation. The Doppler imaging results are compared to simultaneous broadband photometry from the Tennessee State University T3 0.4 m Automated Photometric Telescope. The activity from the stellar chromosphere, which is higher in the stellar atmosphere, is also studied using SONG observations of Balmer Hα line profiles and correlated with the photospheric activity. Results. The temperature maps obtained during eight consecutive stellar rotations show mainly high-latitude or polar spots, with the main spot concentrations above latitude 45°. The spots concentrate around phase 0.25 near the beginning of our observations and around phase 0.75 towards the end. The photometric observations confirm a small jump in spot phases that occurred in February 2016. The cross-correlation of the temperature maps reveals rather strong solar-like differential rotation, giving a relative surface differential rotation coefficient of α = 0.10 ± 0.02. There is a weak correlation between the locations of starspots and enhanced emission in the chromosphere at some epochs.

Kepler-411 Differential Rotation from Three Transiting Planets

Abstract The differential rotation of the Sun is a crucial ingredient of the dynamo theory responsible for the generation of its magnetic field. Currently, the rotation profile of a star that hosts one or more transiting planet can be estimated. By detecting the same spot in a later transit, it is possible to infer the stellar rotation period at that latitude. In this work, we apply for the first time transit spot mapping to determine the differential rotation of Kepler-411, a K2V-type star with an average rotation period of 10.52 days, a radius of 0.79 R ⊙, and a mass of 0.83 M ⊙. Kepler-411 hosts at least four planets, the inner planet is a super-Earth with a radius of 1.88 R ⊕ and an orbital period of 3.0051 days, whereas the two larger transiting planets are mini Neptunes with radii of 3.27 and 3.31 R ⊕, and periods of 7.834435 and 58.0204 days, respectively. Their orbits are such that they transit the star at latitudes of −11°, −21°, and −49°. Analysis of the transit light curves of the three planets resulted in the detection of a total of 198 spots. For each transit latitude, the rotation period of the star was estimated and the differential rotation pattern estimated independently. Then a solar-like differential rotation profile was fit to the three rotation periods at the distinct latitudes, and the result agreed extremely well with the previous ones, resulting in a differential shear of 0.0500 ± 0.0006 rd day−1 or a relative differential rotation of 8.4% ± 0.1%.

Magnetic field and prominences of the young, solar-like, ultra-rapid rotator V530 Persei

Context. Young solar analogs reaching the main sequence experience very strong magnetic activity, generating angular momentum losses through wind and mass ejections. Aims. We investigate signatures of magnetic fields and activity at the surface and in the prominence system of the ultra-rapid rotator V530 Per, a G-type solar-like member of the young open cluster α Persei. This object has a rotation period that is shorter than all stars with available magnetic maps. Methods. With a time-series of spectropolarimetric observations gathered with ESPaDOnS over two nights on the Canada-France-Hawaii Telescope, we reconstructed the surface brightness and large-scale magnetic field of V530 Per using the Zeeman-Doppler imaging method, assuming an oblate stellar surface. We also estimated the short term evolution of the brightness distribution through latitudinal differential rotation. Using the same data set, we finally mapped the spatial distribution of prominences through tomography of the Hα emission. Results. The brightness map is dominated by a large, dark spot near the pole, accompanied by a complex distribution of bright and dark features at lower latitudes. Taking the brightness map into account, the magnetic field map is reconstructed as well. Most of the large-scale magnetic field energy is stored in the toroidal field component. The main radial field structure is a positive region of about 500 G, at the location of the dark polar spot. The brightness map of V530 Per is sheared by solar-like differential rotation, with roughly a solar value for the difference in rotation rate between the pole and equator. It is important to note that Hα is observed in emission and it is mostly modulated by the stellar rotation period over one night. The prominence system is organized in a ring at the approximate location of the corotation radius, and displays significant evolution between the two observing nights. Conclusions. V530 Per is the first example of a solar-type star to have its surface magnetic field and prominences mapped together, which will bring important observational constraints to better understand the role of slingshot prominences in the angular momentum evolution of the most active stars.

Doppler Imaging and Differential Rotation of σ2 Coronae Borealis Using SONG*

Abstract We present new Doppler images of both components of the double-lined binary σ 2 CrB, based on the high-resolution spectroscopic data collected during 11 nights in 2015 March–April. The observed spectra form two independent data sets with sufficient phase coverage. We apply the least-squares deconvolution to all observed spectra to obtain high signal-to-noise mean profiles, from which we derive the Doppler images of both components of σ 2 CrB simultaneously. The surfaces of both F9 and G0 components are dominated by pronounced polar spots. The F9 component exhibits a weak spot at latitude 30° and its mid-to-low latitudes are relatively featureless. The G0 star shows an extended spot structure at latitude 30°, and its surface spot coverage is larger than that of the F9 star, which suggests a higher level of magnetic activity. With the cross-correlation method, we derive a solar-like surface differential rotation on the G0 star of σ 2 CrB for the first time, and the surface shear rate is ΔΩ = 0.180 ± 0.004 rad days−1 and α = ΔΩ/Ωeq = 0.032 ± 0.001. We do not obtain a clear surface shear law for the F9 star due to the lack of mid-to-low latitude features, but detect a systematic longitude shift of high-latitude spots, which indicates a slower rotation with respect to the corotating frame.

Stellar Dynamos in the Transition Regime: Multiple Dynamo Modes and Antisolar Differential Rotation

Abstract Global and semi-global convective dynamo simulations of solar-like stars are known to show a transition from an antisolar (fast poles, slow equator) to solar-like (fast equator, slow poles) differential rotation (DR) for increasing rotation rate. The dynamo solutions in the latter regime can exhibit regular cyclic modes, whereas in the former one, only stationary or temporally irregular solutions have been obtained so far. In this paper we present a semi-global dynamo simulation in the transition region, exhibiting two coexisting dynamo modes, a cyclic and a stationary one, both being dynamically significant. We seek to understand how such a dynamo is driven by analyzing the large-scale flow properties (DR and meridional circulation) together with the turbulent transport coefficients obtained with the test-field method. Neither an αΩ dynamo wave nor an advection-dominated dynamo are able to explain the cycle period and the propagation direction of the mean magnetic field. Furthermore, we find that the α effect is comparable or even larger than the Ω effect in generating the toroidal magnetic field, and therefore, the dynamo seems to be of α 2Ω or α 2 type. We further find that the effective large-scale flows are significantly altered by turbulent pumping.

Magnetic activity of the young solar analog V1358 Orinis

Context. Young, fast-rotating single stars can show dramatically different magnetic signatures and levels of magnetic activity as compared with the Sun. While losing angular momentum due to magnetic breaking and mass loss through stellar winds, the stars gradually spin down resulting in decreasing levels of activity. Studying magnetic activity on such solar analogues plays a key role in understanding the evolution of solar-like stars and allows a glimpse into the past of the Sun as well. Aims. In order to widen our knowledge of the magnetic evolution of the Sun and solar-like stars, magnetic activity of the young solar analog V1358 Ori is investigated. Methods. Fourier analysis of long-term photometric data is used to derive rotational period and activity cycle length, while spectral synthesis is applied to high-resolution spectroscopic data in order to derive precise astrophysical parameters. Doppler imaging is performed to recover surface-temperature maps for two subsequent intervals. Cross-correlation of the consecutive Doppler maps is used to derive surface differential rotation. The rotational modulation of the chromospheric activity indicators is also investigated. Results. An activity cycle of ~1600 days is detected for V1358 Ori. Doppler imaging revealed a surface-temperature distribution dominated by a large polar cap with a few weaker features around the equator. This spot configuration is similar to other maps of young solar analogs from the literature, and supports recent model predictions. We detected solar-like surface differential rotation with a surface shear parameter of α = 0.016 ± 0.010, which is in close agreement with our recently proposed empirical relation between rotation and differential rotation. The chromospheric activity indicators showed rotational modulation.

A Model of a Tidally Synchronized Solar Dynamo

We discuss a solar dynamo model of Tayler-Spruit type whose Omega-effect is conventionally produced by a solar-like differential rotation but whose alpha-effect is assumed to be periodically modulated by planetary tidal forcing. This resonance-like effect has its rationale in the tendency of the current-driven Tayler instability to undergo intrinsic helicity oscillations which, in turn, can be synchronized by periodic tidal perturbations. Specifically, we focus on the 11.07 years alignment periodicity of the tidally dominant planets Venus, Earth, and Jupiter, whose persistent synchronization with the solar dynamo is briefly touched upon. The typically emerging dynamo modes are dipolar fields, oscillating with a 22.14 years period or pulsating with a 11.07 years period, but also quadrupolar fields with corresponding periodicities. In the absence of any constant part of alpha, we prove the subcritical nature of this Tayler-Spruit type dynamo. The resulting amplitude of the alpha oscillation that is required for dynamo action turns out to lie in the order of 1 m/s, which seems not implausible for the sun. When starting with a more classical, non-periodic part of alpha, even less of the oscillatory alpha part is needed to synchronize the entire dynamo. Typically, the dipole solutions show butterfly diagrams, although their shapes are not convincing yet. Phase coherent transitions between dipoles and quadrupoles, which are reminiscent of the observed behaviour during the Maunder minimum, can be easily triggered by long-term variations of dynamo parameters, but may also occur spontaneously even for fixed parameters. Further interesting features of the model are the typical second intensity peak and the intermittent appearance of reversed helicities in both hemispheres.

A 3D kinematic Babcock Leighton solar dynamo model sustained by dynamic magnetic buoyancy and flux transport processes

Context. Magnetohydrodynamic interactions between plasma flows and magnetic fields is fundamental to the origin and sustenance of the 11-year sunspot cycle. These processes are intrinsically three-dimensional (3D) in nature. Aims. Our goal is to construct a 3D solar dynamo model that on the one hand captures the buoyant emergence of tilted bipolar sunspot pairs, and on the other hand produces cyclic large-scale field reversals mediated via surface flux-transport processes – that is, the Babcock-Leighton mechanism. Furthermore, we seek to explore the relative roles of flux transport by buoyancy, advection by meridional circulation, and turbulent diffusion in this 3D dynamo model. Methods. We perform kinematic dynamo simulations where the prescribed velocity field is a combination of solar-like differential rotation and meridional circulation, along with a parametrized turbulent diffusivity. We use a novel methodology for modeling magnetic buoyancy through field-strength-dependent 3D helical up-flows that results in the formation of tilted bipolar sunspots. Results. The bipolar spots produced in our simulations participate in the process of poloidal-field generation through the Babcock-Leighton mechanism, resulting in self-sustained and periodic large-scale magnetic field reversal. Our parameter space study varying the amplitude of the meridional flow, the convection zone diffusivity, and parameters governing the efficiency of the magnetic buoyancy mechanism reveal their relative roles in determining properties of the sunspot cycle such as amplitude, period, and dynamical memory relevant to solar cycle prediction. We also derive a new dynamo number for the Babcock-Leighton solar dynamo mechanism which reasonably captures our model dynamics. Conclusions. This study elucidates the relative roles of different flux-transport processes in the Sun’s convection zone in determining the properties and physics of the sunspot cycle and could potentially lead to realistic, data-driven 3D dynamo models for solar-activity predictions and exploration of stellar magnetism and starspot formation in other stars.

Transition from axi- to nonaxisymmetric dynamo modes in spherical convection models of solar-like stars

Context. Both dynamo theory and observations of stellar large-scale magnetic fields suggest a change from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation. Aims. We seek to understand this transition using numerical simulations. Methods. We use three-dimensional simulations of turbulent magnetohydrodynamic convection in spherical shell wedges and considered rotation rates between 1 and 31 times the solar value. Results. We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration consists of an axisymmetric oscillatory field accompanied by an m = 1 azimuthal mode (two active longitudes), which also shows temporal variability. At slow (rapid) rotation, the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric mode produces latitudinal dynamo waves with polarity reversals, while the nonaxisymmetric mode often exhibits a slow drift in the rotating reference frame and the strength of the active longitudes changes cyclically over time between the different hemispheres. In the majority of cases we find retrograde waves, while prograde waves are more often found from observations. Most of the obtained dynamo solutions exhibit cyclic variability either caused by latitudinal or azimuthal dynamo waves. In an activity-period diagram, the cycle lengths normalized by the rotation period form two different populations as a function of rotation rate or magnetic activity level. The slowly rotating axisymmetric population lies close to what in observations is called the inactive branch, where the stars are believed to have solar-like differential rotation, while the rapidly rotating models are close to the superactive branch with a declining cycle to rotation frequency ratio and an increasing rotation rate. Conclusions. We can successfully reproduce the transition from axi- to nonaxisymmetric dynamo solutions for high rotation rates, but high-resolution simulations are required to limit the effect of rotational quenching of convection at rotation rates above 20 times the solar value.

Differential Rotation in Solar-like Convective Envelopes: Influence of Overshoot and Magnetism

Abstract We present a set of four global Eulerian/semi-Lagrangian fluid solver (EULAG) hydrodynamical (HD) and magnetohydrodynamical (MHD) simulations of solar convection, two of which are restricted to the nominal convection zone, and the other two include an underlying stably stratified fluid layer. While all four simulations generate reasonably solar-like latitudinal differential rotation profiles where the equatorial region rotates faster than the polar regions, the rotational isocontours vary significantly among them. In particular, the purely HD simulation with a stable layer alone can break the Taylor–Proudman theorem and produce approximately radially oriented rotational isocontours at medium to high latitudes. We trace this effect to the buildup of a significant latitudinal temperature gradient in the stable fluid immediately beneath the convection zone, which imprints itself on the lower convection zone. It develops naturally in our simulations as a consequence of convective overshoot and rotational influence of rotation on convective energy fluxes. This favors the establishment of a thermal wind balance that allows evading the Taylor–Proudman constraint. A much smaller latitudinal temperature gradient develops in the companion MHD simulation that includes a stable fluid layer, reflecting the tapering of deep convective overshoot that occurs at medium to high latitudes, which is caused by the strong magnetic fields that accumulate across the base of the convection zone. The stable fluid layer also has a profound impact on the large-scale magnetic cycles developing in the two MHD simulations. Even though both simulations operate in the same convective parameter regime, the simulation that includes a stable layer eventually loses cyclicity and transits to a non-solar, steady quadrupolar state.