Stellar Radiative Interiors Research Articles

Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone

Context. The interactions between magnetic fields and differential rotation in stellar radiative interiors could play a major role in achieving an understanding of the magnetism of intermediate-mass and massive stars and of the differential rotation profile observed in red-giant stars. Aims. The present study is aimed at studying the flow and field produced by a stellar radiative zone which is initially made to rotate differentially in the presence of a large-scale poloidal magnetic field threading the whole domain. We focus both on the axisymmetric configurations produced by the initial winding-up of the magnetic field lines and on the possible instabilities of those configurations. We investigate in detail the effects of the stable stratification and thermal diffusion and we aim, in particular, to assess the role of the stratification at stabilising the system. Methods. We performed 2D and 3D global Boussinesq numerical simulations started from an initial radial or cylindrical differential rotation and a large-scale poloidal magnetic field. Under the conditions of a large rotation frequency compared to the Alfvén frequency, we built a magnetic configuration strongly dominated by its toroidal component. We then perturbed this configuration to observe the development of non-axisymmetric instabilities. Results. The parameters of the simulations were chosen to respect the ordering of time scales of a typical stellar radiative zone. In this framework, the axisymmetric evolution is studied by varying the relative effects of the thermal diffusion, the Brunt-Väisälä frequency, the rotation, and the initial poloidal field strength. After a transient time and using a suitable adimensionalisation, we find that the axisymmetric state only depends on tes/tAp the ratio between the Eddington–Sweet circulation time scale and the Alfvén time scale. A scale analysis of the Boussinesq magnetohydrodynamical equations allows us to recover this result. In the cylindrical case, a magneto-rotational instability develops when the thermal diffusivity is sufficiently high to enable the favored wavenumbers to be insensitive to the effects of the stable stratification. In the radial case, the magneto-rotational instability is driven by the latitudinal shear created by the back-reaction of the Lorentz force on the flow. Increasing the level of stratification then leaves the growth rate of the instability mainly unaffected while its horizontal length scale grows. Conclusions. Non-axisymmetric instabilities are likely to exist in stellar radiative zones despite the stable stratification. They could be at the origin of the magnetic dichotomy observed in intermediate-mass and massive stars. They are also unavoidable candidates for the transport of angular momentum in red giant stars.

2D OR NOT 2D: THE EFFECT OF DIMENSIONALITY ON THE DYNAMICS OF FINGERING CONVECTION AT LOW PRANDTL NUMBER

Fingering convection (otherwise known as thermohaline convection) is an instability that occurs in stellar radiative interiors in the presence of unstable compositional gradients. Numerical simulations have been used in order to estimate the efficiency of mixing induced by this instability. However, fully three-dimensional (3D) computations in the parameter regime appropriate for stellar astrophysics (i.e., low Prandtl number) are prohibitively expensive. This raises the question of whether two-dimensional (2D) simulations could be used instead to achieve the same goals. In this work, we address this issue by comparing the outcome of 2D and 3D simulations of fingering convection at low Prandtl number. We find that 2D simulations are never appropriate. However, we also find that the required 3D computational domain does not have to be very wide: the third dimension only needs to contain a minimum of two wavelengths of the fastest-growing linearly unstable mode to capture the essentially 3D dynamics of small-scale fingering. Narrow domains, however, should still be used with caution since they could limit the subsequent development of any large-scale dynamics typically associated with fingering convection.

Modelling transport processes in stellar radiative interiors

I report here on the different transport processes redistributing angular momentum and nuclides in stellar radiative interiors and on their modelling in stellar evolution codes.

ENERGY CONSERVATION AND GRAVITY WAVES IN SOUND-PROOF TREATMENTS OF STELLAR INTERIORS. PART I. ANELASTIC APPROXIMATIONS

Typical flows in stellar interiors are much slower than the speed of sound. To follow the slow evolution of subsonic motions, various sound-proof equations are in wide use, particularly in stellar astrophysical fluid dynamics. These low-Mach number equations include the anelastic equations. Generally, these equations are valid in nearly adiabatically stratified regions like stellar convection zones, but may not be valid in the sub-adiabatic, stably stratified stellar radiative interiors. Understanding the coupling between the convection zone and the radiative interior is a problem of crucial interest and may have strong implications for solar and stellar dynamo theories as the interface between the two, called the tachocline in the Sun, plays a crucial role in many solar dynamo theories. Here we study the properties of gravity waves in stably-stratified atmospheres. In particular, we explore how gravity waves are handled in various sound-proof equations. We find that some anelastic treatments fail to conserve energy in stably-stratified atmospheres, instead conserving pseudo-energies that depend on the stratification, and we demonstrate this numerically. One anelastic equation set does conserve energy in all atmospheres and we provide recommendations for converting low-Mach number anelastic codes to this set of equations.

Transport of angular momentum and chemical species by anisotropic mixing in stellar radiative interiors

AbstractSmall levels of turbulence can be present in stellar radiative interiors due to, e.g., the instability of rotational shear. In this paper we estimate turbulent transport coefficients for stably stratified rotating stellar radiation zones. Stable stratification induces strong anisotropy with a very small ratio of radial‐to‐horizontal turbulence intensities. Angular momentum is transported mainly due to the correlation between azimuthal and radial turbulent motions induced by the Coriolis force. This non‐diffusive transport known as the Λ‐effect has outward direction in radius and is much more efficient compared to the effect of radial eddy viscosity. Chemical species are transported by small radial diffusion only. This result is confirmed using direct numerical simulations combined with the test‐scalar method. As a consequence of the non‐diffusive transport of angular momentum, the estimated characteristic time of rotational coupling (≲100 Myr) between radiative core and convective envelope in young solar‐type stars is much shorter compared to the time‐scale of Lithium depletion (∼1 Gyr) (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A semi-analytic approach to angular momentum transport in stellar radiative interiors

A novel semi-analytic spectral method, based on eigenfunction expansions, is applied to model the angular momentum transport in stellar radiative interiors. The advantages of our approach are shown by applying it to a spin-down model for a 1M⊙ main-sequence star. The evolution of the coupling between core and envelope is investigated for different values of the viscosity and different geometries and intensities of the poloidal field. We suggest that a quadrupolar poloidal field may explain the short coupling timescale (τc∼10 Myr) needed to reproduce the observed rotational evolution of fast rotators on the zero age main sequence, while a dipolar geometry is indicated in the case of slow rotators (τc∼100 Myr). Our method provides a rigorous analytic treatment of a classic MHD problem and allows us to explore the influence of various parameters on the rotational history of radiative interiors.

A semi-analytic approach to angular momentum transport in stellar radiative interiors

We address the problem of angular momentum transport in stellar radiative interiors with a novel semi-analytic spectral technique, using an eigenfunction series expansion, that can be used to derive benchmark solutions in hydromagnetic regimes with very high Reynolds number (10^7 - 10^8). The error arising from the truncation of the series is evaluated analytically. The main simplifying assumptions are the neglect of meridional circulation and of non-axisymmetric magnetic fields. The advantages of our approach are shown by applying it to a spin-down model for a 1 M_sun main-sequence star. The evolution of the coupling between core and envelope is investigated for different values of the viscosity and different geometries and values of the poloidal field. We confirm that a viscosity enhancement by 10^4 with respect to the molecular value is required to attain a rigid rotation in the core of the Sun within its present age. We suggest that a quadrupolar poloidal field may explain the short coupling time-scale needed to model the observed rotational evolution of fast rotators on the ZAMS, while a dipolar geometry is indicated in the case of slow rotators. Our novel semi-analytic spectral method provides a conceptually simple and rigorous treatment of a classic MHD problem and allows us to explore the influence of various parameters on the rotational history of radiative interiors.

Solar spin-down with internal magnetic fields

view Abstract Citations (15) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Solar Spin-down with Internal Magnetic Fields Charbonneau, P. ; MacGregor, K. B. Abstract We investigate the rotational evolution of a solar-type star containing a large-scale poloidal magnetic field in its radiative core, in response to the torque applied to it by magnetically coupled wind. Our model takes into account both the generation of a toroidal magnetic component via shearing of the existing poloidal component by differential rotation, as well as the back-reaction on the differential rotation due to Lorentz forces associated with the toroidal field. Our computations demonstrate the existence of classes of large-scale poloidal magnetic fields allowing rapid spin-down of the surface layers shortly after the arrival on the zero-age main sequence, while producing weak internal differential rotation in the radiative core by the solar age. This indicates that the constraints brought about by rotational evolution of solar analogs in young clusters and by helioseismology are not incompatible with the existence of large-scale magnetic fields in stellar radiative interiors. The present surface solar rotation rate is also shown to be a poor indicator of the strength and geometry of hypothetical poloidal magnetic fields pervading the solar radiative interior. Publication: The Astrophysical Journal Pub Date: September 1992 DOI: 10.1086/186545 Bibcode: 1992ApJ...397L..63C Keywords: Late Stars; Spin Dynamics; Stellar Evolution; Stellar Magnetic Fields; Stellar Rotation; Magnetic Field Configurations; Stellar Interiors; Stellar Models; Stellar Winds; Astrophysics; STARS: INTERIORS; STARS: MAGNETIC FIELDS; STARS: ROTATION full text sources ADS | Related Materials (1) Erratum: 1993ApJ...403L..87C