The slender solar tachocline: a magnetic model

Rüdiger, G.; Kitchatinov, L. L.

doi:10.1002/asna.2113180504

Cited by 109 publications

(106 citation statements)

References 11 publications

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“…In the Sun, this would cause the slow rotation of the high-latitude convection zone to spread down into the radiative envelope, in the Haynes-Spiegel-Zahn burrowing process noted in § 1. We also note that the torque balance described by (3.17) is very different from the torque balance described by Rüdiger & Kitchatinov (1997) and Kitchatinov & Rüdiger (2006) in which there is no Coriolis effect, the Lorentz torque being balanced instead by a viscous torque. In fact for realistic solar parameter values it will be seen that, as already indicated, viscous torques are entirely negligible -perhaps counterintuitively for shear layers as thin as the confinement layer and the helium sublayer.…”

Section: The Model Equationsmentioning

confidence: 80%

Polar confinement of the Sun's interior magnetic field by laminar magnetostrophic flow

Wood

McIntyre

2011

J. Fluid Mech.

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The global-scale interior magnetic field Bi needed to account for the Sun's observed differential rotation can be effective only if confined below the convection zone in all latitudes including, most critically, the polar caps. Axisymmetric solutions are obtained to the nonlinear magnetohydrodynamic equations showing that such polar confinement can be brought about by a very weak downwelling flow U ~ 10−5cms−1 over each pole. Such downwelling is consistent with the helioseismic evidence. All three components of the magnetic field B decay exponentially with altitude across a thin, laminar ‘magnetic confinement layer’ located at the bottom of the tachocline and permeated by spiralling field lines. With realistic parameter values, the thickness of the confinement layer ~10−3 of the Sun's radius, the thickness scale being the magnetic advection–diffusion scale δ = η/U where the magnetic (ohmic) diffusivity η ≈ 4.1 × 102cm2s−1. Alongside baroclinic effects and stable thermal stratification, the solutions take into account the stable compositional stratification of the helium settling layer, if present as in today's Sun, and the small diffusivity of helium through hydrogen, χ ≈ 0.9 × 101cm2s−1. The small value of χ relative to η produces a double boundary-layer structure in which a ‘helium sublayer‘ of smaller vertical scale (χ/η)1/2δ is sandwiched between the top of the helium settling layer and the rest of the confinement layer. Solutions are obtained using both semi-analytical and purely numerical, finite-difference techniques. The confinement-layer flows are magnetostrophic to excellent approximation. More precisely, the principal force balances are between Lorentz, Coriolis, pressure-gradient and buoyancy forces, with relative accelerations negligible to excellent approximation. Viscous forces are also negligible, even in the helium sublayer where shears are greatest. This is despite the kinematic viscosity being somewhat greater than χ. We discuss how the confinement layers s at each pole might fit into a global dynamical picture of the solar tachocline. That picture, in turn, suggests a new insight into the early Sun and into the longstanding enigma of solar lithium depletion.

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Section: The Model Equationsmentioning

confidence: 80%

Polar confinement of the Sun's interior magnetic field by laminar magnetostrophic flow

Wood

McIntyre

2011

J. Fluid Mech.

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“…Moreover, the predicted value Ω SZ is sufficiently far from the observed value to be ruled out by the observations. In the past decade, magnetized models have become more widely accepted as the simplest explanation for the observed uniform rotation of the radiative zone (Rüdiger & Kitchatinov 1997;GM98;see Garaud 2007 for a review). A large-scale primordial magnetic field, strictly confined beneath the convection zone can indeed robustly maintain a state of uniform rotation through Ferraro's law of isorotation (Ferraro 1937).…”

Section: Introductionmentioning

confidence: 99%

The Rotation Rate of the Solar Radiative Zone

Garaud¹,

Guervilly²

2009

ApJ

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The rotation rate of the solar radiative zone is an important diagnostic for angular momentum transport in the tachocline and below. In this paper, we study the contribution of viscous and magnetic stresses to the global angular momentum balance. By considering a simple linearized toy model, we discuss the effects of field geometry and applied boundary conditions on the predicted rotation profile and rotation rate of the radiative interior. We compare these analytical predictions with fully nonlinear simulations of the dynamics of the radiative interior, as well as with observations. We discuss the implications of these results as constraints on models of the solar interior.

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“…There has also been extensive study of the influence of poloidal fields on global tachocline MHD (Charbonneau & MacGregor 1992;Rüdiger & Kitchatinov 1997;MacGregor 2000;Forgács-Dajka & Petrovay 2002;Garaud 2002). Here we take the next step in generality of model, moving us still closer to the full 3D MHD problem in a very similar way as Cally (2003) did.…”

Section: Introductionmentioning

confidence: 99%

Global MHD Instabilities in a Three‐dimensional Thin‐Shell Model of Solar Tachocline

Gilman

Dikpati

Miesch

2007

ASTROPHYS J SUPPL S

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We generalize the linear analysis of the global instability of coexisting differential rotation and toroidal magnetic fields in the solar tachocline to include continuous radial stratification, thermodynamics, and finite tachocline thickness, as perturbed by three-dimensional disturbances of longitudinal wavenumbers m ¼ 1, 2. For radiative tachocline stratification, the instability for both banded and broad toroidal field profiles is similar to the two-dimensional and shallow water cases studied previously, even though the unstable modes have substantial vertical structure. For overshoot tachocline stratification, instability for banded toroidal fields with peaks P20 kG is similar to the corresponding shallow water case, but for substantially higher ( perhaps unrealistic) toroidal fields there is no low-subadiabaticity cutoff, and modes appear with much higher growth rate and increasingly negative phase velocities in longitude, analogous to those found earlier by Cally. All of these results are only modestly sensitive to the tachocline thickness chosen. For broad toroidal field profiles, the instability results are similar to the two-dimensional and shallow water cases for toroidal field peaks up to at least 80 kG, unless the shell has a thickness that is a substantial fraction of a pressure scale height. For thinner shells, only above about 94 kG do the high growth rate, low phase velocity modes appear, with structure similar to the ''polar kink'' instability Cally found. But even in this case, we find that the slower growing ''clam-shell'' instability eventually replaces the faster growing polar kink modes. We conclude that for conditions most likely to occur in the solar tachocline, such as peak toroidal fields limited by the dynamo to 20 kG or less, the two-dimensional and shallow water type unstable modes are likely to predominate even when the tachocline has finite thickness and the modes can have radial structure.

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The slender solar tachocline: a magnetic model

Cited by 109 publications

References 11 publications

Polar confinement of the Sun's interior magnetic field by laminar magnetostrophic flow

Polar confinement of the Sun's interior magnetic field by laminar magnetostrophic flow

The Rotation Rate of the Solar Radiative Zone

Global MHD Instabilities in a Three‐dimensional Thin‐Shell Model of Solar Tachocline

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