Stellar Convection Zones Research Articles

LAGRANGIAN COHERENT STRUCTURES IN NONLINEAR DYNAMOS

Turbulence and chaos play a fundamental role in stellar convective zones through the transportof particles, energy and momentum, and in fast dynamos, through the stretching, twisting and folding of magnetic flux tubes. A particularly revealing way to describe turbulent motions is through the analysis of Lagrangian coherent structures (LCS), which are material lines or surfaces that act as transport barriers in the fluid. We report the detection of Lagrangian coherent structures in helical MHD dynamo simulations with scale separation. In an ABC--flow, two dynamo regimes, a propagating coherent mean--field regime and an intermittent regime, are identified as the magnetic diffusivity is varied. The sharp contrast between the chaotic tangle of attracting and repelling LCS in both regimes permits a unique analysis of the impact of the magnetic field on the velocity field. In a second example, LCS reveal the link between the level of chaotic mixing of the velocity field and the saturation of a large--scale dynamo when the magnetic field exceeds the equipartition value.

Dynamos in Stellar Convection Zones: of Wreaths and Cycles

We live near a magnetic star whose cycles of activity are driven by dynamo action beneath the surface. In the solar convection zone, rotation couples with plasma motions to build highly organized magnetic fields that erupt at the surface and undergo relatively regular cycles of polarity reversal. Despite our proximity to the Sun, the nature of its dynamo remains elusive, but observations of other solar-type stars show that surface magnetism is a nearly ubiquitous feature. In recent time, numerical simulations of convection and dynamo action have taken tremendous strides forward. Global-scale organization and cyclic magnetism are being achieved by several groups in distinctly different solar and stellar simulations. Here I will talk about advances on the numerical front including wreath-building dynamos that may occupy stellar convection zones. I will discuss the interplay between the new simulations, various classes of mean-field models, and current and upcoming solar and stellar observations.

A model of the entropy flux and Reynolds stress in turbulent convection

We propose a closure model for the transport of entropy and momentum in astrophysical turbulence, intended for application to rotating stellar convective regions. Our closure model is first presented in the Boussinesq formalism, and compared with laboratory and numerical experimental results on Rayleigh-Benard convection and Homogeneous Rayleigh-Benard convection. The predicted angular momentum transport properties of the turbulence in the slowly rotating case recover the well-known Lambda-effect, with an amplitude uniquely related to the convective heat flux. The model is then extended to the anelastic case as well as the fully compressible case. In the special case of spherical symmetry, the predicted radial heat flux is equivalent to that of mixing-length theory. For rotating stars, our model describes the coupled transport of heat and angular momentum, and provides a unified formalism in which to study both differential rotation and thermal inhomogeneities in stellar convection zones.

Global-scale wreath-building dynamos in stellar convection zones

AbstractWhen stars like our Sun are young they rotate rapidly and are very magnetically active. We explore dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code. The magnetic fields built in these dynamos are organized on global-scales into wreath-like structures that span the convection zone. Wreath-building dynamos can undergo quasi-cyclic reversals of polarity and such behavior is common in the parameter space we have been able to explore. These dynamos do not appear to require tachoclines to achieve their spatial or temporal organization. Wreath-building dynamos are present to some degree at all rotation rates, but are most evident in the more rapidly rotating simulations.

Large-scale magnetic fields of low-mass dwarfs: the many faces of dynamo

AbstractMagnetic field are ubiquitous to low-mass stars and can potentially impact their evolution and their internal structure; yet the physical processes (called dynamo) that succeed at generating them in the stellar convective zones of cool dwarfs are still enigmatic. Although theoretical modelling and numerical simulations of stellar dynamo action showed breathtaking progress in the last decade, they are not yet in the state of accurately predicting the various magnetic topologies that different low-mass stars can generate.Thanks to the advent of new-generation instruments, spectropolarimetric observations can now reveal the large-scale magnetic topologies of cool dwarfs, from the brown dwarf threshold (spectral type M8) up to the limit beyond which outer convective zones get vanishingly small (spectral type F5). In particular, they can reconstruct through tomographic methods the poloidal and toroidal components of the large-scale field, hence offering a fresh option for guiding dynamo theories to a more mature state.We review here the latest observational advances, showing in particular that magnetic topologies of low-mass dwarfs can drastically vary with mass and rotation rate, and discuss their implications for our understanding of dynamo processes.

Hunting down giant cells in deep stellar convective zones

Abstract3D high resolution simulations for the convective zone of a 4Myr old 0.7 M⊙ pre-main sequence star in gravitational contraction are carried out with different radial density contrast using the pseudo spectral ASH code (Brun et al. 2004). We extract giant cells signal from the complex surface convective patterns by using a wavelet analysis. We then characterize them by estimating their lifetime and rotation rate according to the density contrast.

Some properties of the kinetic energy flux and dissipation in turbulent stellar convection zones

We investigate simulated turbulent flow within thermally driven stellar convection zones. Different driving sources are studied, including cooling at the top of the convectively unstable region, as occurs in surface convection zones; and heating at the base by nuclear burning. The transport of enthalpy and kinetic energy, and the distribution of turbulent kinetic energy dissipation are studied. We emphasize the importance of global constraints on shaping the quasi-steady flow characteristics, and present an analysis of turbulent convection which is posed as a boundary value problem that can be easily incorporated into standard stellar evolution codes for deep, efficient convection. Direct comparison is made between the theoretical analysis and the simulated flow and very good agreement is found. Some common assumptions traditionally used to treat quasi-steady turbulent flow in stellar models are briefly discussed. The importance and proper treatment of convective boundaries are indicated.

DIRECT CALCULATION OF THE TURBULENT DISSIPATION EFFICIENCY IN ANELASTIC CONVECTION

The current understanding of the turbulent dissipation in stellar convective zones is based on the assumption that the turbulence follows Kolmogorov scaling. This assumption is valid for some cases in which the time frequency of the external shear is high (e.g., solar p modes). However, for many cases of astrophysical interest (e.g., binary orbits, stellar pulsations, etc.), the timescales of interest lie outside the regime of applicability of Kolmogorov scaling. We present direct calculations of the dissipation efficiency of the turbulent convective flow in this regime, using simulations of anelastic convection with external forcing. We show that the effects of the turbulent flow are well represented by an effective viscosity coefficient, we provide the values of the effective viscosity as a function of the perturbation frequency and compare our results to the perturbative method for finding the effective viscosity of Penev et al. that can be applied to actual simulations of the surface convective zones of stars.

Amplitudes of non-radial oscillations driven by turbulence

Turbulent motions in stellar convection zones generate acoustic energy, part of which is supplied to normal modes of the star. Amplitudes of these modes result from a balance between the efficiencies of excitation and damping processes in the convection zones. For radial oscillations, in the solar case, a good agreement between observations and theoretical modelling is reached (see for instance Belkacem et al. 2006b). We also compute the energy supplied by unit time by turbulent convection to the acoustic modes of α Cen A (HD 128620), a star which is similar but not identical to the Sun. In addition, we have developed a formalism that provides the excitation rates of non-radial modes excited by turbulent convection. It then allows us to investigate both p and g modes in the upper convection zones as well as in stellar convective cores. As a first application, we have estimated-and report here- the impact of non-radial effects on excitation rates and amplitudes of high-angular-degree solar p modes.

Lambda effect from forced turbulence simulations

Aims. We determine the components of the Λ-effect tensor that quantifies the contributions to the turbulent momentum transport even for uniform rotation. Methods. Three-dimensional numerical simulations are used to study turbulent transport in triply periodic cubes under the influence of rotation and anisotropic forcing. Comparison is made with analytical results obtained via the so-called minimal tau-approximation. Results. In the case where the turbulence intensity in the vertical direction dominates, the vertical stress is always negative. This situation is expected to occur in stellar convection zones. The horizontal component of the stress is weaker and exhibits a maximum at latitude 30 ◦ – regardless of how rapid the rotation is. The minimal tau-approximation captures many of the qualitative features of the numerical results, provided the relaxation time tau is close to the turnover time, i.e. the Strouhal number is of order unity.

Diamagnetic pumping near the base of a stellar convection zone

AbstractThe property of inhomogeneous turbulence in conducting fluids to expel large‐scale magnetic fields in the direction of decreasing turbulence intensity is shown as important for the magnetic field dynamics near the base of a stellar convection zone. The downward diamagnetic pumping confines a fossil internal magnetic field in the radiative core so that the field geometry is appropriate for formation of the solar tachocline. For the stars of solar age, the diamagnetic confinement is efficient only if the ratio of turbulent magnetic diffusivity ηT of the convection zone to the (microscopic or turbulent) diffusivity ηin of the radiative interior is ηT/ηin ≥ 105. Confinement in younger stars requires larger ηT/ηin. The observation of persistent magnetic structures on young solar‐type stars can thus provide evidence for the nonexistence of tachoclines in stellar interiors and on the level of turbulence in radiative cores. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modelling the time variation of the surface differential rotation in AB Doradus and LQ Hydrae

AbstractSequences of Doppler images of the young, rapidly rotating late‐type stars AB Dor and LQ Hya show that their equatorial angular velocity and the amplitude of their surface differential rotation vary versus time. Such variations can be modelled to obtain information on the intensity of the azimuthal magnetic stresses within stellar convection zones. We introduce a simple model in the framework of the mean‐field theory and discuss briefly the results of its application to those solar‐like stars. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Differential rotation and meridional circulation in global models of solar convection

AbstractIn the outer envelope of the Sun and in other stars, differential rotation and meridional circulation are maintained via the redistribution of momentum and energy by convective motions. In order to properly capture such processes in a numerical model, the correct spherical geometry is essential. In this paper I review recent insights into the maintenance of mean flows in the solar interior obtained from high‐resolution simulations of solar convection in rotating spherical shells. The Coriolis force induces a Reynolds stress which transports angular momentum equatorward and also yields latitudinal variations in the convective heat flux. Meridional circulations induced by baroclinicity and rotational shear further redistribute angular momentum and alter the mean stratification. This gives rise to a complex nonlinear interplay between turbulent convection, differential rotation, meridional circulation, and the mean specific entropy profile. I will describe how this drama plays out in our simulations as well as in solar and stellar convection zones. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Differential rotation on rapidly rotating stars

AbstractTheories of meridional circulation and differential rotation in stellar convective zones predict trends in surface flow patterns on main‐sequence stars that are amenable to direct observational testing. Here I summarise progress made in the last few years in determining surface differential rotation patterns on rapidly‐rotating young main‐sequence stars of spectral types F, G, K and M. Differential rotation increases strongly with increasing effective temperature along the main sequence. The shear rate appears to increase with depth in the sub‐photospheric layers. Tidal locking in close binaries appears to suppress differential rotation, but better statistics are needed before this conclusion can be trusted. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Stochastic excitation of non-radial modes

Context.Turbulent motions in stellar convection zones generate acoustic energy, part of which is then supplied to normal modes of the star. Their amplitudes result from a balance between the efficiencies of excitation and damping processes in the convection zones.

The possible magnetic torus in stellar interior

Various possibilities of the structure of the magnetic field, which is driven by turbulent dynamo mechanisms, in the stellar convection zone are analysed, putting an emphasis on the cross-helicity dynamo effect. A relation between the cross-helicity dynamo and rotation is discussed. An evaluation is made for the cross-helicity-driven magnetic field, and the influence of the rotation is illustrated. A case in which the convection zone is lying just below the surface (like the solar convection zone) is analysed. The toroidal magnetic field structure is predicted to exist in stellar interior, and the analogy to laboratory toroidal plasmas is explained. The interior magnetic field is divided into two classes. One is dominated by the poloidal–radial component: activity may be seen near the polar region for this case. In the other, the magnetic field is dominated by the toroidal magnetic field as tokamaks in laboratory experiments.

Flow instabilities of magnetic flux tubes

Context.Flow-induced instabilities are relevant for the storage and dynamics of magnetic fields in stellar convection zones and possibly also in other astrophysical contexts.

Flow instabilities of magnetic flux tubes

Context. The stability properties of filamentary magnetic structures are relevant for the storage and dynamics of magnetic fields in stellar convection zones and possibly also in other astrophysical contexts. Aims. In a series of papers we study the effect of external and internal flows on the stability of magnetic flux tubes. In this paper we consider the effect of a flow perpendicular to a straight, horizontal flux tube embedded in a gravitationally stratified fluid. The flow acts on the flux tube by exerting an aerodynamic drag force and by modifying the pressure stratification in the background medium. Methods. We carry out a Lagrangian linear stability analysis in the framework of the approximation of thin magnetic flux tubes. Results. The external flow can drive monotonic and oscillatory instability (overstability). The stability condition depends on direction and magnitude of the external velocity as well as on its first and second derivatives with respect to depth. The range of the flow-driven instabilities typically extends to modes with much shorter wavelengths than for the buoyancy-driven undulatory Parker instability. Conclusions. Perpendicular flows with Alfvenic Mach number of order unity can drive monotonic as well as oscillatory instability of thin magnetic flux tubes. Such instability can affect the storage of magnetic flux in stellar interiors.

Round table discussion of session F: convection and rotation

AbstractThe Session F round table. and audience, considered the following questions: (i)what determines the differential rotation in stellar convective zones?(ii)If there really is a rapid inward increase in angular velocity in giants will it have significant effects in the late stages of stellar evolution?(iii)How effective is penetration above a convective core?(iv)Why is the solar core nearly uniformly rotating?

Possible Global Magneto-Fluid Structure of the Stellar Convection Zone

Structures of the magnetic field and velocity in stars are discussed based on the mean field MHD equations. A special case is presented, where the solution is constructed by the Beltrami solution in the stellar convection zone with the symmetry in the azimuthal direction. Magnetic field lines form concentric toroidal magnetic surfaces. The cross-helicity dynamo mechanism induces a mean flow of plasmas. The structure of this driven flow is also shown to constitute toroidal surfaces. Considering the symmetry and the relation of this toroidal magnetic structure with the polarity, it is shown that the latitudinal component of this flow is pole-ward in the northern as well as southern hemispheres. This gives an insight into the role of the magnetic field for the meridional flow.