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Register a new userOn magnetic instabilities and dynamo action in stellar radiation zones
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J.-P. Zahn
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We examine the MHD instabilities arising in the radiation zone of a differentially rotating star, in which a poloidal field of fossil origin is sheared into a toroidal field. We focus on the non-axisymmetric instability that affects the toroidal magnetic field in a rotating star, which was first studied by Pitts and Tayler in the non-dissipative limit. According to Spruit, it could also drive a dynamo. The Pitts & Tayler instability is manifestly present in our simulations, with its conspicuous m=1 dependence in azimuth. But its analytic treatment used so far is too simplified to be applied to the real stellar situation. Although the instability generated field reaches an energy comparable to that of the mean poloidal field, that field seems unaffected by the instability: it undergoes Ohmic decline, and is neither eroded nor regenerated by the instability. The toroidal field is produced by shearing the poloidal field and it draws its energy from the differential rotation. The small scale motions behave as Alfven waves; they cause negligible eddy-diffusivity and contribute little to the net transport of angular momentum. In our simulations we observe no sign of dynamo action, of either mean field or fluctuation type, up to a magnetic Reynolds number of 10^5. However the Pitts & Tayler instability is sustained as long as the differential rotation acting on the poloidal field is able to generate a toroidal field of sufficient strength.
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Helicity and alpha effect driven by the nonaxisymmetric Tayler instability of toroidal magnetic fields in stellar radiation zones are computed. In the linear approximation a purely toroidal field always excites pairs of modes with identical growth rates but with opposite helicity so that the net helicity vanishes. If the magnetic background field has a helical structure by an extra (weak) poloidal component then one of the modes dominates producing a net kinetic helicity anticorrelated to the current helicity of the background field. The mean electromotive force is computed with the result that the alpha effect by the most rapidly growing mode has the same sign as the current helicity of the background field. The alpha effect is found as too small to drive an alpha^{2} dynamo but the excitation conditions for an alphaOmega dynamo can be fulfilled for weak poloidal fields. Moreover, if the dynamo produces its own alpha effect by the magnetic instability then problems with its sign do not arise. For all cases, however, the alpha effect shows an extremely strong concentration to the poles so that a possible alphaOmega dynamo might only work at the polar regions. Hence, the results of our linear theory lead to a new topological problem for the existence of large-scale dynamos in stellar radiation zones on the basis of the current-driven instability of toroidal fields.
Rotational mixing, the key process in stellar evolution, transports angular momentum and chemical elements in stellar radiative zones. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities in the context of stellar radiative zones. The eigenvalue problem describing linear instabilities of a flow with a hyperbolic-tangent horizontal shear profile was solved numerically for a wide range of parameters. As a first step, we consider a polar $f$-plane where the gravity and rotation vector are aligned. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposed-flow direction. The three-dimensional inflectional instability is destabilized by stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum $sqrt{f(1-f)}$ in the inviscid limit as the vertical wavenumber goes to infinity, where $f$ is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a self-similarity in both the inflectional and inertial instabilities based on the rescaled parameter $PeN^2$ with the P{e}clet number $Pe$ and the Brunt-V{a}is{a}l{a} frequency $N$.
Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. Understanding the dependence of the turbulent transport triggered by the shear instabilities due to the differential rotation in stellar radiation zones is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. We investigate horizontal shear instabilities in stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal component $tilde{f}$ and the vertical component $f$. We performed a linear stability analysis for a horizontal shear flow with a hyperbolic tangent profile, both numerically and asymptotically using the WKBJ approximation. As in the traditional approximation, we identified the inflectional and inertial instabilities. The inflectional instability is destabilized as $tilde{f}$ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is extended in the non-diffusive limit as $0<f<1+tilde{f}^{2}/N^{2}$, where $N$ is the dimensionless Brunt-Vaisala frequency. More strikingly, in the high-thermal-diffusivity limit, it is always inertially unstable at any colatitude $theta$ except at the poles (i.e., $0^{circ}<theta<180^{circ}$). Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the instabilities to be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough to redistribute efficiently angular momentum and mix chemicals in the radiation zones.
Young solar-type stars rotate rapidly and are very magnetically active. The magnetic fields at their surfaces likely originate in their convective envelopes where convection and rotation can drive strong dynamo action. Here we explore simulations of global-scale stellar convection in rapidly rotating suns using 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. We explore one case rotates five times faster than the Sun in detail. This dynamo simulation, called case D5, has repeated quasi-cyclic reversals of global-scale polarity. We compare this case D5 to the broader family of simulations we have been able to explore and discuss how future simulations and observations can advance our understanding of stellar dynamos and magnetism.
Upper bounds are derived on the amount of magnetic energy that can be generated by dynamo action in collisional and collisionless plasmas with and without external forcing. A hierarchy of mathematical descriptions is considered for the plasma dynamics: ideal MHD, visco-resistive MHD, the double-adiabatic theory of Chew, Goldberger and Low (CGL), kinetic MHD, and other kinetic models. It is found that dynamo action is greatly constrained in models where the magnetic moment of any particle species is conserved. In the absence of external forcing, the magnetic energy then remains small at all times if it is small in the initial state. In other words, a small seed magnetic field cannot be amplified significantly, regardless of the nature of flow, as long as the collision frequency and gyroradius are small enough to be negligible. A similar conclusion also holds if the system is subject to external forcing as long as this forcing conserves the magnetic moment of at least one plasma species and does not greatly increase the total energy of the plasma (i.e., in practice, is subsonic). Dynamo action therefore always requires collisions or some small-scale kinetic mechanism for breaking the adiabatic invariance of the magnetic moment.
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