Simulations Of Solar Convection Research Articles

Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids

We present two major improvements over the Compressible High-ORder Unstructured Spectral difference (CHORUS) code published in Wang et al., “A compressible high-order unstructured spectral difference code for stratified convection in rotating spherical shells,” J. Comput. Phys. 290, 90–111 (2015). The new code is named CHORUS++ in this paper. Subsequently, we perform a series of efficient simulations for rotationally constrained convection (RCC) in spherical shells. The first improvement lies in the integration of the high-order spectral difference method with a boundary-conforming transfinite mapping on cubed-sphere grids, thus ensuring exact geometric representations of spherical surfaces on arbitrary sparse grids. The second improvement is on the adoption of higher-order elements (sixth-order) in CHORUS++ vs third-order elements for the original CHORUS code. CHORUS++ enables high-fidelity RCC simulations using sixth-order elements on very coarse grids. To test the accuracy and efficiency of using elements of different orders, CHORUS++ is applied to a laminar solar benchmark, which is characterized by columnar banana-shaped convective cells. By fixing the total number of solution degrees of freedom, the computational cost per time step remains unchanged. Nevertheless, using higher-order elements in CHORUS++ resolves components of the radial energy flux much better than using third-order elements. To obtain converged predictions, using sixth-order elements is 8.7 times faster than using third-order elements. This significant speedup allows global-scale fully compressible RCC simulations to reach equilibration of the energy fluxes on a small cluster of just 40 cores. In contrast, CHORUS simulations were performed by Wang et al. on supercomputers using approximately 10 000 cores. Using sixth-order elements in CHORUS++, we further carry out global-scale solar convection simulations with decreased rotational velocities. Interconnected networks of downflow lanes emerge and surround broader and weaker regions of upflow fields. A strong inward kinetic energy flux compensated by an enhanced outward enthalpy flux appears. These observations are all consistent with those published in the literature. Furthermore, CHORUS++ can be extended to magnetohydrodynamic simulations with potential applications to the hydromagnetic dynamo processes in the interiors of stars and planets.

Theory of solar oscillations in the inertial frequency range: Amplitudes of equatorial modes from a nonlinear rotating convection simulation

Context. Several types of inertial modes have been detected on the Sun. Properties of these inertial modes have been studied in the linear regime, but have not been studied in nonlinear simulations of solar rotating convection. Comparing the nonlinear simulations, the linear theory, and the solar observations is important to better understand the differences between the models and the real Sun. Aims. Our aim is to detect and characterize the modes present in a nonlinear numerical simulation of solar convection, in particular to understand the amplitudes and lifetimes of the modes. Methods. We developed a code with a Yin-Yang grid to carry out fully nonlinear numerical simulations of rotating convection in a spherical shell. The stratification is solar-like up to the top of the computational domain at 0.96 R⊙. The simulations cover a duration of about 15 solar years, which is more than the observational length of the Solar Dynamics Observatory (SDO). Various large-scale modes at low frequencies (comparable to the solar rotation frequency) are extracted from the simulation. Their characteristics are compared to those from the linear model and to the observations. Results. Among other modes, both the equatorial Rossby modes and the columnar convective modes are seen in the simulation. The columnar convective modes, with north-south symmetric longitudinal velocity vϕ, contain most of the large-scale velocity power outside the tangential cylinder and substantially contribute to the heat and angular momentum transport near the equator. Equatorial Rossby modes with no radial nodes (n = 0) are also found; they have the same spatial structures as the linear eigenfunctions. They are stochastically excited by convection and have the amplitudes of a few m s−1 and mode linewidths of about 20−30 nHz, which are comparable to those observed on the Sun. We also confirm the existence of the “mixed” Rossby modes between the equatorial Rossby modes with one radial node (n = 1) and the columnar convective modes with north-south antisymmetric vϕ in our nonlinear simulation, as predicted by the linear eigenmode analysis. We also see the high-latitude mode with m = 1 in our nonlinear simulation, but its amplitude is much weaker than that observed on the Sun.

Accurate Short-Characteristics Radiative Transfer in A Numerical Tool for Astrophysical RESearch (ANTARES)

We aim to improve the accuracy of radiative energy transport in three-dimensional radiation hydrodynamical simulations in ANTARES (A Numerical Tool for Astrophysical RESearch). We implement in the ANTARES short-characteristics numerical schemes a modification of the Bézier interpolant solver. This method yields a smoother surface structure in simulations of solar convection and reduces the artifacts appearing due to the limited number of rays along which the integration is done. Reducing such artifacts leads to increased stability of the code. We show that our new implementation achieves a better agreement of the temperature structure and its gradient with a semi-empirical model derived from observations, as well as of synthetic spectral-line profiles with the observed solar spectrum.

Grand Minima in a spherical non-kinematic α2Ω mean-field dynamo model

We present a non-kinematic axisymetric α2Ω mean-field dynamo model in which the complete α-tensor and mean differential rotation profile are both extracted from a global magnetohydrodynamical simulation of solar convection producing cycling large-scale magnetic fields. The nonlinear backreaction of the Lorentz force on differential rotation is the only amplitude-limiting mechanism introduced in the mean-field model. We compare and contrast the amplitude modulation patterns characterizing this mean-field dynamo, to those already well-studied in the context of non-kinematic αΩ models using a scalar α-effect. As in the latter, we find that large quasi-periodic modulation of the primary cycle are produced at low magnetic Prandtl number (Pm), with the ratio of modulation period to the primary cycle period scaling inversely with Pm. The variations of differential rotation remain well within the bounds set by observed solar torsional oscillations. In this low-Pm regime, moderately supercritical solutions can also exhibit aperiodic Maunder Minimum-like periods of strongly reduced cycle amplitude. The inter-event waiting time distribution is approximately exponential, in agreement with solar activity reconstructions based on cosmogenic radioisotopes. Secular variations in low-latitude surface differential rotation during Grand Minima, as compared to epochs of normal cyclic behavior, are commensurate in amplitude with historical inferences based on sunspot drawings. Our modeling results suggest that the low levels of observed variations in the solar differential rotation in the course of the activity cycle may nonetheless contribute to, or perhaps even dominate, the regulation of the magnetic cycle amplitude.

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.

Consequences of high effective Prandtl number on solar differential rotation and convective velocity

Observations suggest that the large-scale convective velocities obtained by solar convection simulations might be over-estimated (convective conundrum). One plausible solution to this could be the small-scale dynamo which cannot be fully resolved by global simulations. The small-scale Lorentz force suppresses the convective motions and also the turbulent mixing of entropy between upflows and downflows, leading to a large effective Prandtl number (Pr). We explore this idea in three-dimensional global rotating convection simulations at different thermal conductivity (κ), i.e., at different Pr. In agreement with previous non-rotating simulations, the convective velocity is reduced with the increase of Pr as long as the thermal conductive flux is negligible. A subadiabatic layer is formed near the base of the convection zone due to continuous deposition of low entropy plumes in low-κ simulations. The most interesting result of our low-κ simulations is that the convective motions are accompanied by a change in the convection structure that is increasingly influenced by small-scale plumes. These plumes tend to transport angular momentum radially inward and thus establish an anti-solar differential rotation, in striking contrast to the solar rotation profile. If such low diffusive plumes, driven by the radiative-surface cooling, are present in the Sun, then our results cast doubt on the idea that a high effective Pr may be a viable solution to the solar convective conundrum. Our study also emphasizes that any resolution of the conundrum that relies on the downward plumes must take into account the angular momentum transport and heat transport.

Convective Velocity Suppression via the Enhancement of the Subadiabatic Layer: Role of the Effective Prandtl Number

Abstract It has recently been recognized that the convective velocities achieved in current solar convection simulations might be overestimated. The newly revealed effects of the prevailing small-scale magnetic field within the convection zone may offer possible solutions to this problem. The small-scale magnetic fields can reduce the convective amplitude of small-scale motions through the Lorentz-force feedback, which concurrently inhibits the turbulent mixing of entropy between upflows and downflows. As a result, the effective Prandtl number may exceed unity inside the solar convection zone. In this paper, we propose and numerically confirm a possible suppression mechanism of convective velocity in the effectively high-Prandtl number regime. If the effective horizontal thermal diffusivity decreases (the Prandtl number accordingly increases), the subadiabatic layer which is formed near the base of the convection zone by continuous depositions of low entropy transported by adiabatically downflowing plumes is enhanced and extended. The global convective amplitude in the high-Prandtl thermal convection is thus reduced, especially in the lower part of the convection zone via the change in the mean entropy profile, which becomes more subadiabatic near the base and less superadiabatic in the bulk.

Magnetically Modulated Heat Transport in a Global Simulation of Solar Magneto-convection

Abstract We present results from a global MHD simulation of solar convection in which the heat transported by convective flows varies in-phase with the total magnetic energy. The purely random initial magnetic field specified in this experiment develops into a well-organized large-scale antisymmetric component undergoing hemispherically synchronized polarity reversals on a 40 year period. A key feature of the simulation is the use of a Newtonian cooling term in the entropy equation to maintain a convectively unstable stratification and drive convection, as opposed to the specification of heating and cooling terms at the bottom and top boundaries. When taken together, the solar-like magnetic cycle and the convective heat flux signature suggest that a cyclic modulation of the large-scale heat-carrying convective flows could be operating inside the real Sun. We carry out an analysis of the entropy and momentum equations to uncover the physical mechanism responsible for the enhanced heat transport. The analysis suggests that the modulation is caused by a magnetic tension imbalance inside upflows and downflows, which perturbs their respective contributions to heat transport in such a way as to enhance the total convective heat flux at cycle maximum. Potential consequences of the heat transport modulation for solar irradiance variability are briefly discussed.

A PROPOSED PARADIGM FOR SOLAR CYCLE DYNAMICS MEDIATED VIA TURBULENT PUMPING OF MAGNETIC FLUX IN BABCOCK–LEIGHTON-TYPE SOLAR DYNAMOS

ABSTRACT At present, the Babcock–Leighton flux transport solar dynamo models appear to be the most promising models for explaining diverse observational aspects of the sunspot cycle. The success of these flux transport dynamo models is largely dependent upon a single-cell meridional circulation with a deep equatorward component at the base of the Sun’s convection zone. However, recent observations suggest that the meridional flow may in fact be very shallow (confined to the top 10% of the Sun) and more complex than previously thought. Taken together, these observations raise serious concerns on the validity of the flux transport paradigm. By accounting for the turbulent pumping of magnetic flux, as evidenced in magnetohydrodynamic simulations of solar convection, we demonstrate that flux transport dynamo models can generate solar-like magnetic cycles even if the meridional flow is shallow. Solar-like periodic reversals are recovered even when meridional circulation is altogether absent. However, in this case, the solar surface magnetic field dynamics does not extend all the way to the polar regions. Very importantly, our results demonstrate that the Parker–Yoshimura sign rule for dynamo wave propagation can be circumvented in Babcock–Leighton dynamo models by the latitudinal component of turbulent pumping, which can generate equatorward propagating sunspot belts in the absence of a deep, equatorward meridional flow. We also show that variations in turbulent pumping coefficients can modulate the solar cycle amplitude and periodicity. Our results suggest the viability of an alternate magnetic flux transport paradigm—mediated via turbulent pumping—for sustaining solar-stellar dynamo action.

SUPERGRANULATION AS THE LARGEST BUOYANTLY DRIVEN CONVECTIVE SCALE OF THE SUN

ABSTRACT The origin of solar supergranulation remains a mystery. Unlike granulation, the size of which is comparable to both the thickness of the radiative boundary layer and local scale-height in the photosphere, supergranulation does not reflect any obvious length scale of the solar convection zone. Moreover, recent observations of flows in the photosphere using Doppler imaging or correlation or feature tracking show a monotonic decrease in horizontal flow power at scales larger than supergranulation. Both local area and global spherical shell simulations of solar convection by contrast show the opposite, an increase in horizontal flow amplitudes to a low wavenumber. We examine these disparities and investigate how the solar supergranulation may arise as a consequence of nonlocal heat transport by cool diving plumes. Using three-dimensional anelastic simulations with surface driving, we show that the kinetic energy of the largest convective scales in the upper layers of a stratified domain reflects the depth of transition from strong buoyant driving to adiabatic stratification below caused by the dilution of the granular downflows. This depth is quite shallow because of the rapid increase of the mean density below the photosphere. We interpret the observed monotonic decrease in solar convective power at scales larger than supergranulation to be a consequence of this rapid transition, with the supergranular scale the largest buoyantly driven mode of convection in the Sun.

DOUBLE DYNAMO SIGNATURES IN A GLOBAL MHD SIMULATION AND MEAN-FIELD DYNAMOS

ABSTRACT The 11 year solar activity cycle is the most prominent periodic manifestation of the magnetohydrodynamical (MHD) large-scale dynamo operating in the solar interior, yet longer and shorter (quasi-) periodicities are also present. The so-called “quasi-biennial” signal appearing in many proxies of solar activity has been gaining increasing attention since its detection in p-mode frequency shifts, which suggests a subphotospheric origin. A number of candidate mechanisms have been proposed, including beating between co-existing global dynamo modes, dual dynamos operating in spatially separated regions of the solar interior, and Rossby waves driving short-period oscillations in the large-scale solar magnetic field produced by the 11 year activity cycle. In this article, we analyze a global MHD simulation of solar convection producing regular large-scale magnetic cycles, and detect and characterize shorter periodicities developing therein. By constructing kinematic mean-field α 2Ω dynamo models incorporating the turbulent electromotive force (emf) extracted from that same simulation, we find that dual-dynamo behavior materializes in fairly wide regions of the model’s parameters space. This suggests that the origin of the similar behavior detected in the MHD simulation lies with the joint complexity of the turbulent emf and differential rotation profile, rather that with dynamical interactions such as those mediated by Rossby waves. Analysis of the simulation also reveals that the dual dynamo operating therein leaves a double-period signature in the temperature field, consistent with a dual-period helioseismic signature. Order-of-magnitude estimates for the magnitude of the expected frequency shifts are commensurate with helioseismic measurements. Taken together, our results support the hypothesis that the solar quasi-biennial oscillations are associated with a secondary dynamo process operating in the outer reaches of the solar convection zone.

What drives the solar magnetic cycle?

Solar magnetic activities show an about 11-year cycle period with the variations of the amplitudes. The increasing technological advancement induces the stronger influence of the solar magnetic cycle on humans. The magnetic cycle is believed to be caused by a magnetohydrodynamic (MHD) dynamo process in the solar interior, where the flows and the magnetic fields interact in the strongly turbulent convective zone. The intrinsic features of the solar interior, e.g., the stratification, the turbulence and the nonlinearities, make the global MHD simulations of solar convection with the realistic parameters of the Sun extremely hard. The past substantial progress in understanding the solar magnetic cycle benefitted from the simplified models, e.g., the axisymmetric kinematic ones. The mean field electrodynamics and the helioseismology laid the foundation of the progress. Under the effects of the large-scale flows, the poloidal and the toroidal components of the magnetic field sustain each other, which persists the cycle variations of the solar magnetic field. The key ingredients in the dynamo process include the mechanism and the location of the toroidal field generation, the mechanism and the location of the poloidal field generation, the rising of toroidal field to form the sunspots with tilts and the mechanism for the equatorward migration of the sunspots. So far, only the generation of the toroidal field by differential rotations is less controversial. The current dynamo models usually do not include the toroidal flux tube emergence, which was investigated as a separated topic. As the workhorse to understand the solar cycle during the past decade, the Babcock-Leighton (BL) type flux transport dynamos is a popular paradigm for explaining the cyclic nature of solar magnetic activity. They were even used to predict future solar cycles by assimilating observed surface flows and fields into the models. Recently the flux transport dynamos faces some challenges, such as the depth variation of the equatorward flow, the strong turbulent diffusivity, and so on. But the BL mechanism which is due to the decay of the tilt sunspot groups on the solar surface to regenerate the poloidal field, is most probably at the heart of the solar cycle. The further understanding of the solar magnetic cycle will benefit from the constraints of the solar historical data, the helioseismology, the different magnetic cycles of different types of stars, and the global MHD numerical simulations. These fields will be developed in parallel with the kinematic dynamo and fertilize each other. The three dimensional Babcock-Leighton type dynamo models coupled with the toroidal flux tube emergence is expected to be the workhorse of the next generation of solar dynamo.

Characterisation of the turbulent electromotive force and its magnetically-mediated quenching in a global EULAG-MHD simulation of solar convection

We perform a mean-field analysis of the EULAG-MHD millenium simulation of global magnetohydrodynamical convection presented in Passos and Charbonneau (2014). The turbulent electromotive force (emf) operating in the simulation is assumed to be linearly related to the cyclic axisymmetric mean magnetic field and its first spatial derivatives. At every grid point in the simulation’s meridional plane, this assumed relationship involves 27 independent tensorial coefficients. Expanding on Racine et al. (2011), we extract these coefficients from the simulation data through a least-squares minimization procedure based on singular value decomposition. The reconstructed α-tensor shows good agreement with that obtained by Racine et al. (2011), who did not include derivatives of the mean-field in their fit, as well as with the α-tensor extracted by Augustson et al. (2015) from a distinct ASH MHD simulation. The isotropic part of the turbulent magnetic diffusivity tensor β is positive definite and reaches values of 5.0×107m2s−1 in the middle of the convecting fluid layers. The spatial variations of both αϕϕ and βϕϕ component are well reproduced by expressions obtained under the Second Order Correlation Approximation, with a good matching of amplitude requiring a turbulent correlation time about five times smaller than the estimated turnover time of the small-scale turbulent flow. By segmenting the simulation data into epochs of magnetic cycle minima and maxima, we also measure α- and β-quenching. We find the magnetic quenching of the α-effect to be driven primarily by a reduction of the small-scale flow’s kinetic helicity, with variations of the current helicity playing a lesser role in most locations in the simulation domain. Our measurements of turbulent diffusivity quenching are restricted to the βϕϕ component, but indicate a weaker quenching, by a factor of ≃1.36, than of the α-effect, which in our simulation drops by a factor of three between the minimum and maximum phases of the magnetic cycle.

Velocity amplitudes in global convection simulations: The role of the Prandtl number and near-surface driving

Several lines of evidence suggest that the velocity amplitude in global simulations of solar convection, U, may be systematically over-estimated. Motivated by these recent results, we explore the factors that determine U and we consider how these might scale to solar parameter regimes. To this end, we decrease the thermal diffusivity κ along two paths in parameter space. If the kinematic viscosity ν is decreased proportionally with κ (fixing the Prandtl number Pr=ν/κ), we find that U increases but asymptotes toward a constant value, as found by Featherstone and Hindman (2016). However, if ν is held fixed while decreasing κ (increasing Pr), we find that U systematically decreases. We attribute this to an enhancement of the thermal content of downflow plumes, which allows them to carry the solar luminosity with slower flow speeds. We contrast this with the case of Rayleigh–Bénard convection which is not subject to this luminosity constraint. This dramatic difference in behavior for the two paths in parameter space (fixed Pr or fixed ν) persists whether the heat transport by unresolved, near-surface convection is modeled as a thermal conduction or as a fixed flux. The results suggest that if solar convection can operate in a high-Pr regime, then this might effectively limit the velocity amplitude. Small-scale magnetism is a possible source of enhanced viscosity that may serve to achieve this high-Pr regime.

THE SPECTRAL AMPLITUDE OF STELLAR CONVECTION AND ITS SCALING IN THE HIGH-RAYLEIGH-NUMBER REGIME

ABSTRACT Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from theoretical and computational models. The Sun is, however, exceptional in that regard. The wealth of observational data afforded by its proximity provides a unique test bed for comparing convection models against observations. When such comparisons are carried out, surprising inconsistencies between those models and observations become apparent. Both photospheric and helioseismic measurements suggest that convection simulations may overestimate convective flow speeds on large spatial scales. Moreover, many solar convection simulations have difficulty reproducing the observed solar differential rotation owing to this apparent overestimation. We present a series of three-dimensional stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star’s interior. While these simulations are nonmagnetic and nonrotating in nature, they demonstrate two robust phenomena. When run with sufficiently high Rayleigh number, the integrated kinetic energy of the convection becomes effectively independent of thermal diffusion, but the spectral distribution of that kinetic energy remains sensitive to both of these quantities. A simulation that has converged to a diffusion-independent value of kinetic energy will divide that energy between spatial scales such that low-wavenumber power is overestimated and high-wavenumber power is underestimated relative to a comparable system possessing higher Rayleigh number. We discuss the implications of these results in light of the current inconsistencies between models and observations.

MERIDIONAL CIRCULATION DYNAMICS FROM 3D MAGNETOHYDRODYNAMIC GLOBAL SIMULATIONS OF SOLAR CONVECTION

The form of the solar meridional circulation is a very important ingredient for mean field flux transport dynamo models. Yet a shroud of mystery still surrounds this large-scale flow, given that its measurement using current helioseismic techniques is challenging. In this work we use results from 3D global simulations of solar convection to infer the dynamical behavior of the established meridional circulation. We make a direct comparison between the meridional circulation that arises in these simulations and the latest observations. Based on our results we argue that there should be an equatorward flow at the base of the convection zone at mid latitudes, below the current maximum depth helioseismic measures can probe (0.75 R). We also provide physical arguments to justify this behaviour. The simulations indicate that the meridional circulation undergoes substantial changes in morphology as the magnetic cycle unfolds. We close by discussing the importance of these dynamical changes for current methods of observation that involve long averaging periods of helioseismic data. Also noteworthy is the fact that these topological changes indicate a rich interaction between magnetic fields and plasma flows, which challenges the ubiquitous kinematic approach used in the vast majority of mean field dynamo simulations.

Hemispheric Coupling: Comparing Dynamo Simulations and Observations

Numerical simulations that reproduce solar-like magnetic cycles can be used to generate long-term statistics. The variations in N-S hemispheric cycle synchronicity and amplitude produced in simulations has not been widely compared to observations. The observed limits on asymmetry show that hemispheric sunspot area production is no more than 20% asymmetric for cycles 12-23 and phase lags do not exceed 20% (2 yrs) of the total cycle period. Independent studies have found a long-term trend in phase values as one hemisphere leads the other for ~four cycles. Such persistence in phase is not indicative of a stochastic phenomenon. We compare the findings to results from a numerical simulation of solar convection recently produced with the EULAG-MHD model. This simulation spans 1600 yrs and generated 40 regular, sunspot-like cycles. While the simulated cycle length is too long and the toroidal bands remain at too high of latitudes, some solar-like aspects of hemispheric asymmetry are reproduced. The model reproduces the synchrony of polarity inversions and onset of cycle as the simulated phase lags do not exceed 20% of the cycle period. Simulated amplitude variations between the N and S hemispheres are larger than observed in the Sun. The simulations show one hemisphere persistently leads the other for several successive cycles, placing an upper bound on the efficiency of transequatorial magnetic coupling mechanisms. These include magnetic diffusion, cross-equatorial mixing within elongated convective rolls and transequatorial meridional flow cells. One or more of these processes may lead to magnetic flux cancellation whereby the oppositely directed fields come in close proximity and cancel each other across the magnetic equator late in the solar cycle. We discuss the discrepancies between model and observations and the constraints they pose on possible mechanisms of hemispheric coupling.

Flux Transport Dynamos: From Kinematics to Dynamics

Over the past several decades, Flux-Transport Dynamo (FTD) models have emerged as a popular paradigm for explaining the cyclic nature of solar magnetic activity. Their defining characteristic is the key role played by the mean meridional circulation in transporting magnetic flux and thereby regulating the cycle period. Most FTD models also incorporate the so-called Babcock-Leighton (BL) mechanism in which the mean poloidal field is produced by the emergence and subsequent dispersal of bipolar active regions. This feature is well grounded in solar observations and provides a means for assimilating observed surface flows and fields into the models in order to forecast future solar activity, to identify model biases, and to clarify the underlying physical processes. Furthermore, interpreting historical sunspot records within the context of FTD models can potentially provide insight into why cycle features such as amplitude and duration vary and what causes extreme events such as Grand Minima. Though they are generally robust in a modeling sense and make good contact with observed cycle features, FTD models rely on input physics that is only partially constrained by observation and that neglects the subtleties of convective transport, convective field generation, and nonlinear feedbacks. Here we review the formulation and application of FTD models and assess our current understanding of the input physics based largely on complementary 3D MHD simulations of solar convection, dynamo action, and flux emergence.

Characteristics of magnetic solar-like cycles in a 3D MHD simulation of solar convection

We analyse the statistical properties of the stable magnetic cycle unfolding in an extended 3D magnetohydrodynamic simulation of solar convection produced with the EULAG-MHD code. The millennium simulation spans over 1650 years, in the course of which forty polarity reversals take place on a regular ∼40 yr cadence, remaining well-synchronized across solar hemispheres. In order to characterize this cycle and facilitate its comparison with measures typically used to represent solar activity, we build two proxies for the magnetic field in the simulation mimicking the solar toroidal field and the polar radial field. Several quantities that characterize the cycle are measured (period, amplitudes, etc.) and correlations between them are computed. These are then compared with their observational analogs. From the typical Gnevyshev-Ohl pattern, to hints of Gleissberg modulation, the simulated cycles share many of the characteristics of their observational analogs even though the simulation lacks poloidal field regeneration through active region decay, a mechanism nowadays often considered an essential component of the solar dynamo. Some significant discrepancies are also identified, most notably the in-phase variation of the simulated poloidal and toroidal large-scale magnetic components, and the low degree of hemispheric coupling at the level of hemispheric cycle amplitudes. Possible causes underlying these discrepancies are discussed.

Thermodynamic fluctuations in solar photospheric three-dimensional convection simulations and observations

Numerical 3D radiative (M)HD simulations of solar convection are used to understand the physical properties of the solar photosphere. To validate this approach, it is important to check that no excessive thermodynamic fluctuations arise as a consequence of the partially incomplete treatment of radiative transfer. We investigate the realism of 3D convection simulations carried out with the Stagger code. We compared the characteristic properties of several spectral lines in solar disc centre observations with spectra synthesized from the simulations. We degraded the synthetic spectra to the spatial resolution of the observations using the continuum intensity distribution. We estimated the necessary spectral degradation by comparing atlas spectra with averaged observed spectra. In addition to deriving a set of line parameters directly, we used the SIR code to invert the spectra. Most of the line parameters from the observational data are matched well by the degraded simulation spectra. The inversions predict a macroturbulent velocity below 10 m/s for the simulation at full spatial resolution, whereas they yield ~< 1000 m/s at a spatial resolution of 0.3". The temperature fluctuations in the inversion of the degraded simulation do not exceed those from the observational data (of the order of 100-200 K rms for -2<log tau<-0.5). The comparison of line parameters in spatially averaged profiles with the averaged values of line parameters in spatially resolved profiles indicates a significant change of (average) line properties at a spatial scale between 0.13" and 0.3". Up to a spatial resolution of 0.3", we find no indications of the presence of excessive thermodynamic fluctuations in the 3D HD simulation. To definitely confirm that simulations without spatial degradation contain fully realistic thermodynamic fluctuations requires observations at even better spatial resolution.