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Some Glimpses from Helioseismology at the Dynamics of the Deep Solar Interior

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Abstract

Helioseismology has taught us a great deal about the stratification and kinematics of the solar interior, sufficient for us to embark upon dynamical studies more detailed than have been possible before. The most sophisticated studies to date have been the very impressive numerical simulations of the convection zone, from which, especially in recent years, a great deal has been learnt. Those simulations, and the seismological evidence with which they are being confronted, are reviewed elsewhere in this volume. Our understanding of the global dynamics of the radiative interior of the Sun is in a much more primitive state. Nevertheless, some progress has been made, and seismological inference has provided us with evidence of more to come. Some of that I summarize here, mentioning in passing hints that are pointing the way to the future.

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Notes

  1. Having deviated from its initial value by no more than 0.5 per cent.

  2. Yet hardly ever the flux of kinetic energy.

  3. Usually referred to as ‘heavy elements’, even though they include 3He.

  4. Rather than, for example, the solar abundance problem.

  5. Which is commonly doubted.

  6. Often, for computational convenience, Ω is expanded in orthogonal polynomials, such as Clebsch-Gordon coefficients (Ritzwoller and Lavely 1991).

  7. The oblateness Δv depends also on J 4 and the higher moments, but the additional contributions appear to be less than the observational uncertainty, so for clarity I do not take them explicitly into account here.

  8. In their paper, Fivian et al. (2008) actually claim a value that exceeds Δ Ω by about 2×10−7, which they offer as an estimate of Δ Φ , but their result was obtained with Dicke’s (1970) outdated underestimate of Δ Ω .

  9. Viscous stress operates also on the side walls, but there the boundary layer is not as thin as that at the bottom of the container, and removes negligible angular momentum (just as Bondi and Lyttleton had found, in the case of spin-down in a sphere, that negligible angular momentum is removed near the equator). The bottom boundary layer is thinner as a result of the vertical ‘rigidity’ imparted on the fluid immediately above by the vortex stretching (which is intimately related to a tendency towards local angular-momentum conservation) produced by the shear, and which is also responsible for the better-known Taylor-Proudman theorem for steady incompressible inviscid flow.

  10. And subsequently demonstrated it in the laboratory (unpublished) in a rotating beaker of water containing several layers of glass beads.

  11. Perhaps even in the face of the steep gradient of molecular weight (Huppert and Spiegel 1977) which had previously been regarded as isolating the angular momentum of the energy-generating core (Mestel 1953; Mestel 1957).

  12. Here I adopt the original Spiegel and Zahn (1992) definition of the tachocline: the gyroscopically pumped shear layer confined to only the stable region beneath the convection zone, despite the etymology of the appellation.

  13. And similar also to field intensities commonly discussed elsewhere in connection with the tachocline (e.g. Spruit 2002; Gilman and Cally 2007), although others (e.g. Gough and McIntyre 1998; Kitchatinov and Rüdiger 2007) have entertained weaker fields.

  14. The vertical component of the group velocity is directed oppositely to the phase velocity.

  15. As had both Kumar and Quataert (1997) and Zahn et al. (1997) earlier, in the mistaken belief that angular momentum transport by the waves would be in the reverse sense and would thus supply the reason for the observed uniform rotation of the radiative envelope.

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  1. Institute of Astronomy & Department of Applied Mathematics and Theoretical Physics, Madingley Road, Cambridge, CB3 0HA, UK

    D. O. Gough

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Gough, D.O. Some Glimpses from Helioseismology at the Dynamics of the Deep Solar Interior. Space Sci Rev 196, 15–47 (2015). https://doi.org/10.1007/s11214-015-0159-6

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