Anti-solar Differential Rotation Research Articles

Investigation of the dependence of angular momentum transport on spatial scales for construction of differential rotation

ABSTRACT We investigate the dependence of the angular momentum transport (AMT) on the spatial scales with numerical simulation of solar-like stars. It is thought that turbulence has an essential role in constructing solar differential rotation (DR). In a widely used method to analyse the construction mechanism of DR, the flow is divided into two components, ‘mean flow’ and ‘turbulence’, where ‘turbulence’ includes a broad spectrum of spatial scales. The features of the AMT are expected to depend on the scale. In this study, we decompose the angular momentum flux (AMF) to investigate the dependence of the AMF on the spatial scale. We compare the results with anti-solar (fast pole) and solar-type (fast equator) DR. Our conclusions are summarized as (1) Radially outward AMT is seen on a large scale (60 Mm ≤ L < 120 Mm) in rotationally constrained systems. (2) Even when the scale-integrated AMF is negative, we sometimes observe positive AMF on certain scales. (3) Small-scale turbulence tends to transport the angular momentum radially inward and causes the anti-solar DR, indicating that high-resolution simulation is a negative factor for solar-like DR. Our method to decompose the AMF provides a deep understanding of the angular momentum and construction mechanism of DR.

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.

Hunting for anti-solar differentially rotating stars using the Rossby number

Context. Anti-solar differential rotation profiles have been found for decades in numerical simulations of convective envelopes of solar-type stars. These profiles are characterized by a slow equator and fast poles (i.e., reversed with respect to the Sun) and have been found in simulations for high Rossby numbers. Rotation profiles like this have been reported in evolved stars, but have never been unambiguously observed for cool solar-type stars on the main sequence. As solar-type stars age and spin down, their Rossby numbers increase, which could therefore induce a transition toward an anti-solar differential rotation regime before the end of the main sequence. Such a rotational transition will impact the large-scale dynamo process and the magnetic activity. In this context, detecting this regime in old main-sequence solar-type stars would improve our understanding of their magnetorotational evolution. Aims. The goal of this study is to identify the most promising cool main-sequence stellar candidates for anti-solar differential rotation in the Kepler sample. Methods. First, we introduce a new theoretical formula to estimate fluid Rossby numbers, Rof, of main-sequence solar-type stars. We derived it from observational quantities such as Teff and Prot, and took the influence of the internal structure into account. Then, we applied it on a subset of the most recent catalog of Kepler rotation periods, after removing subgiants and selecting targets with solar metallicity. Next, we considered the highest computed Rof and inspected each target individually to select the most reliable anti-solar candidate. Finally, we extended our study to stars with metallicities different from that of the Sun. To this end, we developed a formulation for Rof dependent on the metallicity index [Fe/H] by using 1D stellar grids, and we also considered this compositional aspect for the selection of the targets. Results. We obtain a list of the most promising stars that are likely to show anti-solar differential rotation. We identify two samples: one at solar metallicity, including 14 targets, and another for other metallicities, including 8 targets. We find that the targets with the highest Rof are likely to be early-G or late-F stars at about log10g = 4.37 dex. Conclusions. We conclude that cool main-sequence stellar candidates for anti-solar differential rotation exist in the Kepler sample. The most promising candidate is KIC 10907436, and two other particularly interesting candidates are the solar analog KIC 7189915 and the seismic target KIC 12117868. Future characterization of these 22 stars is expected to help us understand how dynamics can impact magnetic and rotational evolution of old solar-type stars at high Rossby number.

Transition from multipolar to dipolar dynamos in stratified systems

ABSTRACT Observations of surface magnetic fields of cool stars reveal a large diversity of configurations. Although there is now a consensus that these fields are generated through dynamo processes occurring within the convective zone, the physical mechanism driving such a variety of field topologies is still debated. This paper discusses the possible origins of dipole- and multipole-dominated morphologies using three-dimensional numerical simulations of stratified systems where the magnetic feedback on the fluid motion is significant. Our main result is that dipolar solutions are found at Rossby numbers up to 0.4 in strongly stratified simulations, where previous works suggested that only multipolar fields should exist. We argue that these simulations are reminiscent of the outlier stars observed at Rossby numbers larger than 0.1, whose large-scale magnetic field is dominated by their axisymmetric poloidal component. As suggested in previous Boussinesq calculations, the relative importance of inertial over Lorentz forces is again controlling the dipolar to multipolar transition. Alternatively, we find that the ratio of kinetic to magnetic energies can equally well capture the transition in the field morphology. We test the ability of this new proxy to predict the magnetic morphology of a few M dwarf stars whose internal structure matches that of our simulations and for which homogeneous magnetic field characterization is available. Finally, the magnitude of the differential rotation obtained in our simulations is compared to actual measurements reported in the literature for M dwarfs. In our simulations, we find a clear relationship between antisolar differential rotation and the emergence of dipolar fields.

Impact of anti-solar differential rotation in mean-field solar-type dynamos

Context. Over the course of their lifetimes, the rotation of solar-type stars goes through different phases. Once they reach the zero-age main sequence, their global rotation rate decreases during the main sequence until at least the solar age, approximately following the empirical Skumanich’s law and enabling gyrochronology. Older solar-type stars might then reach a point of transition when they stop braking, according to recent results of asteroseismology. Additionally, recent 3D numerical simulations of solar-type stars show that different regimes of differential rotation can be characterized with the Rossby number. In particular, anti-solar differential rotation (fast poles, slow equator) may exist for high Rossby number (slow rotators). If this regime occurs during the main sequence and, in general, for slow rotators, we may consider how magnetic generation through the dynamo process might be impacted. In particular, we consider whether slowly rotating stars are indeed subject to magnetic cycles. Aims. We aim to understand the magnetic field generation of solar-type stars possessing an anti-solar differential rotation and we focus on the possible existence of magnetic cycles in such stars. Methods. We modeled mean-field kinematic dynamos in solar (fast equator, slow poles) and anti-solar (slow equator, fast poles) differential rotation, using the STELEM code. We consider two types of mean field dynamo mechanisms along with the Ω-effect: the standard α-effect distributed at various locations in the convective envelope and the Babcock-Leighton effect. Results. We find that kinematic αΩ dynamos allow for the presence of magnetic cycles and global polarity reversals for both rotation regimes, but only if the α-effect is saddled on the tachocline. If it is distributed in the convection zone, solar-type cases still possess a cycle and anti-solar cases do not. Conversely, we have not found any possibility for sustaining a magnetic cycle with the traditional Babcock-Leighton flux-transport dynamos in the anti-solar differential rotation regime due to flux addition. Graphic interpretations are proposed in order to illustrate these cases. However, we find that hybrid models containing both prescriptions can still sustain local polarity reversals at some latitudes. Conclusions. We conclude that stars in the anti-solar differential rotation regime can sustain magnetic cycles only for very specific dynamo processes. The detection of a magnetic cycle for such a star would therefore be a particularly interesting constraint in working to decipher what type of dynamo is actually at work in solar-type stars.

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.

Star-in-a-box simulations of fully convective stars

Context.Main-sequence late-type stars with masses of less than 0.35 M⊙are fully convective.Aims.The goal is to study convection, differential rotation, and dynamos as functions of rotation in fully convective stars.Methods.Three-dimensional hydrodynamic and magnetohydrodynamic numerical simulations with a star-in-a-box model, in which a spherical star is immersed inside of a Cartesian cube, are used. The model corresponds to a 0.2 M⊙main-sequence M5 dwarf. A range of rotation periods (Prot) between 4.3 and 430 d is explored.Results.The slowly rotating model withProt = 430 days produces anti-solar differential rotation with a slow equator and fast poles, along with predominantly axisymmetric quasi-steady large-scale magnetic fields. For intermediate rotation (Prot = 144 and 43 days) the differential rotation is solar-like (fast equator, slow poles), and the large-scale magnetic fields are mostly axisymmetric and either quasi-stationary or cyclic. The latter occurs in a similar parameter regime as in other numerical studies in spherical shells, and the cycle period is similar to observed cycles in fully convective stars with rotation periods of roughly 100 days. In the rapid rotation regime the differential rotation is weak and the large-scale magnetic fields are increasingly non-axisymmetric with a dominatingm = 1 mode. This large-scale non-axisymmetric field also exhibits azimuthal dynamo waves.Conclusions.The results of the star-in-a-box models agree with simulations of partially convective late-type stars in spherical shells in that the transitions in differential rotation and dynamo regimes occur at similar rotational regimes in terms of the Coriolis (inverse Rossby) number. This similarity between partially and fully convective stars suggests that the processes generating differential rotation and large-scale magnetism are insensitive to the geometry of the star.

Physically motivated heat-conduction treatment in simulations of solar-like stars: effects on dynamo transitions

Context.Results from global magnetoconvection simulations of solar-like stars are at odds with observations in many respects: simulations show a surplus of energy in the kinetic power spectrum at large scales; anti-solar differential rotation profiles with accelerated poles, and a slow equator for the solar rotation rate; and a transition from axi- to nonaxisymmetric dynamos at a much lower rotation rate than what is observed. Even though the simulations reproduce the observed active longitudes in fast rotators, their motion in the rotational frame (the so-called azimuthal dynamo wave, ADW) is retrograde, in contrast to the prevalent prograde motion in observations.Aims.We study the effect of a more realistic treatment of heat conductivity in alleviating the discrepancies between observations and simulations.Methods.We use physically motivated heat conduction by applying Kramers opacity law to a semi-global spherical setup that describes the convective envelopes of solar-like stars, instead of a prescribed heat conduction profile from mixing-length arguments.Results.We find that some aspects of the results now better correspond to observations: the axi- to nonaxisymmetric transition point is shifted towards higher rotation rates. We also find a change in the propagation direction of ADWs that means that prograde waves are also now found. However, the transition from an anti-solar to solar-like rotation profile is also shifted towards higher rotation rates, leaving the models in an even more unrealistic regime.Conclusions.Although Kramers-based heat conduction does not help in reproducing the solar rotation profile, it does help in the faster rotation regime, where the dynamo solutions now better match the observations.

Rotational dependence of turbulent transport coefficients in global convective dynamo simulations of solar-like stars

Context. For moderate and slow rotation, the magnetic activity of solar-like stars is observed to strongly depend on rotation, while for rapid rotation, only a very weak or no dependency is detected. These observations do not yet have a solid explanation in terms of dynamo theory. Aims. We aim to find such an explanation by numerically investigating the rotational dependency of dynamo drivers in solar-like stars, that is, stars that have a convective envelope of similar thickness to that of the Sun. Methods. We ran semi-global convection simulations of stars with rotation rates from 0 to 30 times the solar value, corresponding to Coriolis numbers, Co, of 0 to 110. We measured the turbulent transport coefficients contributing to the magnetic field evolution with the help of the test-field method, and compared with the dynamo effect arising from the differential rotation that is self-consistently generated in the models. Results. The trace of the α tensor increases for moderate rotation rates with Co0.5 and levels off for rapid rotation. This behavior is in agreement with the kinetic α based on the kinetic helicity, if one takes into account the decrease of the convective scale with increasing rotation. The α tensor becomes highly anisotropic for Co ≳ 1. Furthermore, αrr dominates for moderate rotation (1 < Co < 10), and αϕϕ for rapid rotation (Co ≳ 10). The effective meridional flow, taking into account the turbulent pumping effects, is markedly different from the actual meridional circulation profile. Hence, the turbulent pumping effect is dominating the meridional transport of the magnetic field. Taking all dynamo effects into account, we find three distinct regimes. For slow rotation, the α and Rädler effects are dominating in the presence of anti-solar differential rotation. For moderate rotation, α and Ω effects are dominant, indicative of αΩ or α2Ω dynamos in operation, producing equatorward-migrating dynamo waves with a qualitatively solar-like rotation profile. For rapid rotation, an α2 mechanism with an influence from the Rädler effect appears to be the most probable driver of the dynamo. Conclusions. Our study reveals the presence of a large variety of dynamo effects beyond the classical αΩ mechanism, which need to be investigated further to fully understand the dynamos of solar-like stars. The highly anisotropic α tensor might be the primary reason for the change of axisymmetric to non-axisymmetric dynamo solutions in the moderate rotation regime.

Morphological Classification of the Convective Regimes in Rotating Stars

Abstract We present a set of numerical simulations that model the convection zones of solar-like stars. With this suite of numerical experiments, we explore how the nature of the convective structures transitions through a series of morphological regimes as the reduced Rayleigh number increases. Convection first manifests as a belt of rotationally aligned, convective, Taylor columns that circumscribes the equator. As the supercriticality increases, the poles begin to convect, initially in a cellular form, but eventually a plumy form emerges. Finally, at extremely high values of the Rayleigh number, a weakly rotating regime is achieved with antisolar differential rotation, i.e., the equator rotates more slowly than the poles. For all of these regimes, we provide theoretical and empirical scaling relations that summarize how global quantities—such as the bulk Rossby number and Reynolds number—scale with the Rayleigh and Ekman numbers. We demonstrate that a Rossby number based on the properties of the thermal boundary layer that clings to the outer surface of the convection zone works particularly well to predict the transition to antisolar differential rotation.

Assessment of Critical Convection and Associated Rotation States in Models of Sun-like Stars Including a Stable Layer

Abstract Recent numerical simulations of rotating stellar convection have suggested the possible existence of retrograde (slow equator, fast poles) or so-called antisolar differential rotation states in slowly rotating stars possessing a large Rossby number. We aim to understand whether such rotational states exist from the onset of convective instability or are the outcome of complex nonlinear interactions in the turbulent convective envelope. To this end, we have made a systematic linear analysis of the critical state of convection in a series of 15 numerical simulations published in Brun et al. We have assessed their degree of supercriticality and most-unstable mode properties, and computed the second-order mean zonal flow response. We find that none of the linear critical cases show a retrograde state at the onset of convection even when their nonlinear counterparts do. We also find that the presence of a stably stratified layer coupled to the convectively unstable upper layer leads to interesting gravity-wave excitation and angular momentum transport. We conclude that retrograde states of differential rotation are probably the outcome of complex mode–mode interactions in the turbulent convection layer and are, as a consequence, likely to exist in real stars.

Stellar dynamos with solar and antisolar differential rotations: Implications to magnetic cycles of slowly rotating stars

ABSTRACT Simulations of magnetohydrodynamics convection in slowly rotating stars predict antisolar differential rotation (DR) in which the equator rotates slower than poles. This antisolar DR in the usual αΩ dynamo model does not produce polarity reversal. Thus, the features of large-scale magnetic fields in slowly rotating stars are expected to be different than stars having solar-like DR. In this study, we perform mean-field kinematic dynamo modelling of different stars at different rotation periods. We consider antisolar DR for the stars having rotation period larger than 30 d and solar-like DR otherwise. We show that with particular α profiles, the dynamo model produces magnetic cycles with polarity reversals even with the antisolar DR provided, the DR is quenched when the toroidal field grows considerably high and there is a sufficiently strong α for the generation of toroidal field. Due to the antisolar DR, the model produces an abrupt increase of magnetic field exactly when the DR profile is changed from solar-like to antisolar. This enhancement of magnetic field is in good agreement with the stellar observational data as well as some global convection simulations. In the solar-like DR branch, with the decreasing rotation period, we find the magnetic field strength increases while the cycle period shortens. Both of these trends are in general agreement with observations. Our study provides additional support for the possible existence of antisolar DR in slowly rotating stars and the presence of unusually enhanced magnetic fields and possibly cycles that are prone to production of superflare.

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.

Antisolar differential rotation of slowly rotating cool stars

Rotating stellar convection transports angular momentum towards the equator, generating the characteristic equatorial acceleration of the solar rotation while the radial flux of angular momentum is always inwards. New numerical box simulations for the meridional cross-correlation ⟨uθuϕ⟩, however, reveal the angular momentum transport towards the poles for slow rotation and towards the equator for fast rotation. The explanation is that for slow rotation a negative radial gradient of the angular velocity always appears, which in combination with a so-far neglected rotation-induced off-diagonal eddy viscosity termν⊥provides “antisolar rotation” laws with a decelerated equator. Similarly, the simulations provided positive values for the rotation-induced correlation ⟨uruθ⟩, which is relevant for the resulting latitudinal temperature profiles (cool or warm poles) for slow rotation and negative values for fast rotation. Observations of the differential rotation of slowly rotating stars will therefore lead to a better understanding of the actual stress-strain relation, the heat transport, and the underlying model of the rotating convection.

Surface magnetic activity of the fast-rotating G5 giant IN Comae, central star of the faint planetary nebula LoTr 5

Context. On the asymptotic giant branch, low to intermediate mass stars blow away their outer envelopes, forming planetary nebulae. Dynamic interaction between the planetary nebula and its central progenitor is poorly understood. The interaction is even more complex when the central object is a binary star with a magnetically active component, as is the case for the target in this paper.Aims. We aim to quantify the stellar surface activity of the cool binary component of IN Com and aim to explain its origin. In general, we need a better understanding of how central binary stars in planetary nebulae evolve and how this evolution could develop such magnetically active stars as IN Com.Methods. We present a time series of 13 consecutive Doppler images covering six months in 2017 that we used to measure the surface differential rotation with a cross-correlation method. Hitherto unpublished high-precision photometric data from 1989 to 2017 are presented. We applied Fourier-transformation-based frequency analysis to both photometry and spectra. Very high resolution (R ≈ 200 000) spectra were used to update IN Com’s astrophysical parameters by means of spectral synthesis.Results. Our time-series Doppler images show cool and warm spots coexisting with an average surface temperature contrast of −1000 K and +300 K with respect to the effective temperature. Approximately 8% of the stellar surface is covered with cool spots and ∼3% with warm spots. A consistent cool polar spot is seen in all images. The average lifetime of the cool spots is not much more than a few stellar rotations (one month), while the warm spots appear to live longer (three months) and are mostly confined to high latitudes. We found anti-solar surface differential rotation with a shear coefficient ofα = −0.026 ± 0.005 suggesting an equatorial rotation period of 5.973 ± 0.008 d. We reconfirm the 5.9 day rotation period of the cool star from photometry, radial velocities, and Hαline-profile variations. A long-termV-brightness variation with a likely period of 7.2 yr is also found. It appears in phase with the orbital radial velocity of the binary system in the sense that it is brightest at highest velocity and faintest at lowest velocity, that is, at the two phases of quadrature. We redetermine [Ba/Fe], [Y/Fe], and [Sr/Fe] ratios and confirm the overabundance of theses-process elements in the atmosphere of IN Com.

The distance, rotation, and physical parameters of ζ Pup

We scrutinize the Hipparcos parallax for the bright O supergiant zeta Pup, and confirm that the implied distance of 332+/-11pc appears to be reliable. We then review the implications for the star's physical parameters, and the consequences for the interpretation of P(phot), the 1.78-d photometric period. The equatorial rotation period is <3.7d (with 95% confidence), ruling out a proposed ~5.1d value. If the photometric period is the rotation period then i, the inclination of the rotation axis to the line of sight, is 33.2+/-1.8 degrees. The inferred mass, radius, and luminosity are securely established to be less than canonical values for the spectral type, and are not in agreement with single-star evolution models. The runaway status, rapid rotation, and anomalous physical properties are all indicative of an evolutionary history involving binary (or multiple-star) interaction. We perform simple starspot modelling to show that the low axial inclination required if P(rot) = 1.78d has testable spectroscopic consequences, which have not been identified in existing time series. If P(phot) is directly related to drivers of systematic, high-velocity stellar-wind variability (`discrete absorption components') in zeta Pup, antisolar differential rotation is required. Model line profiles calculated on that basis are at variance with observations.

Magnetic Buoyancy and Magnetorotational Instabilities in Stellar Tachoclines for Solar- and Antisolar-type Differential Rotation

Abstract We present results from an analytical model for magnetic buoyancy and rotational instabilities in full spherical shell stellar tachoclines that include rotation, differential rotation of either solar or antisolar type, and toroidal field. We find that in all cases, for latitudes where the tachocline vertical rotation gradient is positive, toroidal fields can be stored against magnetic buoyancy up to a limit that is proportional to the square root of the local vertical rotation gradient. For solar magnitude differential rotation, this limit is about 9 kG. For fixed percentage differential rotation, storage capacity varies linearly with the rotation rate. Faster rotators with the same percentage differential rotation can store larger fields, and slower rotators can store smaller fields. At latitudes where the vertical rotation gradient is negative, vigorous magnetorotational instability for even weak (≪1 kG) toroidal fields prevents such storage. We infer from these results that for stars with solar-type latitudinal differential rotation (fast equator, slow poles), any starspots present should be found in low latitudes, similar to the Sun. For antisolar differential rotation, any spots present should be found in mid- and high latitudes, perhaps with a peak of occurrence near 55°. These results hopefully provide some guidance for making and interpreting observations of stellar activity and differential rotation on stars with convection zones and tachoclines.

On the Differential Rotation of Stars

We discussmethods for analyzing the observational manifestations of differential rotation (DR). Based on the literary sources and our estimates (for 4 cool dwarfs), a list containing 75 stars was compiled. Using an example of analysis of the ‘ΔΩ–Teff’, ‘ΔΩ–rotation period’ and ‘ΔΩ–Rossby number’ diagrams we compared the determined parameters of DR stars with the results of theoretical studies. Particular attention is paid to the problems of measurements of DR parameters in low-mass dwarf stars, including the completely convective ones.We analyzed the measured parameters of solar-type DR stars. The objects having anti-solar DR (α < 0), and possiblemethods allowing to determine the sign of α are considered.We distinguish the areas of research that in the future may expand our understanding of DR manifestations: a study of DR in the inner regions of stars and an analysis of manifestations of the rotational brightness modulation caused by the spottedness of components in eclipsing-variable systems (subsynchronized systems).

Superflares on Giant Stars

The Kepler mission identified huge flares on various stars including some of solar type. These events are substantially more energetic than solar flares, and so they are referred to as superflares. Even a small probability of such a superflare on the Sun would be a menace to modern society. A flare comparable in energy with that of superflares was observed on 24th and 25th September on the binary HK Lac. Unlike the Kepler stars, there are observations of differential rotation for HK Lac. This differential rotation appears to be anti-solar. For anti-solar differential rotation, dynamo models can give magnetic activity waves of dipole symmetry as well as quasi-stationary magnetic configurations with quadrupole symmetry. The magnetic energy of such stationary configurations is usually about two orders of magnitude higher than that associated with activity waves. We believe that this mechanism could provide sufficient energy to produce superflares on late type stars, and present some simple models in support of this idea.

Driving Solar Giant Cells through the Self-organization of Near-surface Plumes

Abstract Global 3D simulations of solar giant-cell convection have provided significant insight into the processes which yield the Sun’s observed differential rotation and cyclic dynamo action. However, as we move to higher-resolution simulations a variety of codes have encountered what has been termed the convection conundrum. As these simulations increase in resolution and hence the level of turbulence achieved, they tend to produce weak or even anti-solar differential rotation patterns associated with a weak rotational influence (high Rossby number) due to large convective velocities. One potential culprit for this convection conundrum is the upper boundary condition applied in most simulations, which is generally impenetrable. Here we present an alternative stochastic plume boundary condition which imposes small-scale convective plumes designed to mimic near-surface convective downflows, thus allowing convection to carry the majority of the outward solar energy flux up to and through our simulated upper boundary. The use of a plume boundary condition leads to significant changes in the convective driving realized in the simulated domain and thus to the convective energy transport, the dominant scale of the convective enthalpy flux, and the relative strength of the strongest downflows, the downflow network, and the convective upflows. These changes are present even far from the upper boundary layer. Additionally, we demonstrate that, in spite of significant changes, giant cell morphology in the convective patterns is still achieved with self-organization of the imposed boundary plumes into downflow lanes, cellular patterns, and even rotationally aligned banana cells in equatorial regions. This plume boundary presents an alternative pathway for 3D global convection simulations where driving is non-local and may provide a new approach toward addressing the convection conundrum.