Douglas Gough

High-resolution helioseismology observations with the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) provide a unique three-dimensional view of the solar interior structure and dynamics, revealing a tremendous complexity of the physical processes inside the Sun. We present an overview of the results of the HMI helioseismology program and discuss their implications for modern theoretical models and simulations of the solar interior.

The solar tachocline is a thin internal boundary layer in the Sun located between the differentially rotating convection zone and the uniformly rotating region of the radiative interior beneath. E. A. Spiegel & J. P. Zahn proposed the first hydrodynamical model, which here we call SZ92, arguing that the tachocline is essentially in a steady state of thermal-wind balance, angular-momentum balance, and thermal equilibrium. Angular momentum transport in their model is assumed to be dominated by strongly anisotropic turbulence, which is primarily horizontal, owing to the strong stable stratification of the radiative interior. By contrast, the heat transport is assumed to be dominated by a predominantly vertical diffusive heat flux, owing to the thinness of the tachocline. In this paper, we demonstrate that these assumptions are not consistent with the new model of stratified turbulence recently proposed by G. P. Chini et al. and K. Shah et al., which has been numerically validated by P. Garaud et al. We then propose a simple self-consistent alternative to the SZ92 model—namely, a scenario wherein angular momentum and heat transport are both dominated by horizontal turbulent diffusion. The thickness of the tachocline in the new model scales as Ω_⊙/N _m , where Ω_⊙ is the mean angular velocity of the Sun and N _m is the characteristic buoyancy frequency in the tachocline region. We discuss other properties of the model and show that it has several desirable features but does not resolve some of the other well-known problems of the SZ92 model.

Analysis of f-mode frequencies has provided a measure of the radius of the Sun which is lower, by a few hundredths per cent, than the photospheric radius determined by direct optical measurement. Part of this difference can be understood by recognizing that it is primarily the variation of density well beneath the photosphere of the star that determines the structure of these essentially adiabatic oscillation modes, not some aspect of radiative intensity. In this paper we attempt to shed further light on the matter, by considering a differently defined, and dynamically more robust, seismic radius, namely one determined from p-mode frequencies. This radius is calibrated by the distance from the centre of the Sun to the position in the subphotospheric layers where the first derivative of the density scale height changes essentially discontinuously. We find that radius is more-or-less consistent with what is suggested by the f modes. In addition, the interpretation of the radius inferred from p modes leads us to understand more deeply the role of the total mass constraint in the structure inversions. This enables us to reinterpret the sound-speed inversion, suggesting that the positions of the photosphere and the adiabatically stratified layers in the convective envelope differ non-homologously from those of the standard solar model.

Analysis of f-mode frequencies has provided a measure of the radius of the Sun which is lower, by a few hundredths per cent, than the photospheric radius determined by direct optical measurement. Part of this difference can be understood by recognizing that it is primarily the variation of density well beneath the photosphere of the star that determines the structure of these essentially adiabatic oscillation modes, not some aspect of radiative intensity. In this paper we attempt to shed further light on the matter, by considering a differently defined, and dynamically more robust, seismic radius, namely one determined from p-mode frequencies. This radius is calibrated by the distance from the centre of the Sun to the position in the subphotospheric layers where the first derivative of the density scale height changes essentially discontinuously. We find that that radius is more- or-less consistent with what is suggested by the f modes. In addition, the interpretation of the radius inferred from p modes leads us to understand more deeply the role of the total mass constraint in the structure inversions. This enables us to reinterpret the sound-speed inversion, suggesting that the positions of the photosphere and the adiabatically stratified layers in the convective envelope differ nonhomologously from those of the standard solar model.

This is a summary of my scientific career, biased by my personal view of events and unashamedly concentrating on those aspects of some of the scientific developments to which I have contributed. A selective unbiased alternative has been written by Christensen-Dalsgaard and Thompson (A selective overview. In: Thompson, M.J., Christensen-Dalsgaard, J. (Eds.) Stellar Astrophysical Fluid Dynamics, Cambridge University Press, pp. 1 – 19, 2003), followed by some further remarks by Christensen-Dalsgaard (Unsolved Problems in Stellar Physics: A Conference in Honour of Douglas Gough, American Institute of Physics Conference Series, 948, xii, 2007).

Fossat et al. recently reported detecting rotational splitting of g-modes indirectly via the interaction with p-modes observed directly by the Global Oscillations at Low Frequency (GOLF) instrument on the Solar and Heliospheric Observatory (SOHO). They concluded that the core of the Sun is rotating 3.8 ± 0.1 times faster than the surrounding radiative envelope. This is startling, partly because such rapid rotation almost contradicts direct inferences from the p-mode rotational splitting inferred from the same data. Moreover, the inferred amplitudes of the g-modes appear to exceed the upper bound reported by Appourchaux et al. It is also suspect because the theory of the procedure implies that the principal modes claimed to have been measured should be undetectable. We point out that there are other interpretations: one leads to a core rotation about twice as fast as the surrounding envelope; another, to a core rotating more slowly than the envelope. Here we also report on an independent assessment of the Fossat et al. analysis by applying their procedure to different representations of the GOLF data, expanding on Schunker et al. We also analyze seismic data obtained from LOI and MDI (both also on SOHO), from HMI (on SDO), and from the ground-based BiSON and GONG, and we find the evidence reported by Fossat et al. not to be robust. We also illustrate that merely fitting model spectra to observations, which Fossat et al. do to support their g-mode detections, and as Fossat & Schmider do for extracting additional g-mode splittings, is not necessarily reliable. We are therefore led to doubt the claim.

Fossat et al. (2017) recently reported detecting rotational splitting of g modes indirectly via the interaction with p modes observed directly by the GOLF instrument on SOHO. They concluded that the core of the Sun is rotating 3:8 ? 0:1 times faster than the surrounding radiative envelope. This is startling, partly because such rapid rotation almost contradicts direct inferences from the p-mode rotational splitting inferred from the same data. Moreover, the inferred amplitudes of the g modes appear to exceed the upper bound reported by Appourchaux et al. (2010). It is also suspect because the theory of the procedure implies that the principal modes claimed to have been measured should be undetectable. We point out that there are other interpretations: one leads to a core rotation about twice faster than the surrounding envelope; another, to a core rotating more slowly than the envelope. Here we also report on an independent assessment of the Fossat et al. analysis by applying their procedure to different representations of the GOLF data, expanding on Schunker et al. (2018). We also analyze seismic data obtained from LOI and MDI (both also on SOHO), from HMI (on SDO) and from the ground-based BiSON and GONG, and found the evidence reported by Fossat et al. not to be robust. We also illustrate that merely fitting model spectra to observations, which Fossat et al. do to support their g-mode detections and as Fossat & Schmider (2018) do for extracting additional g-mode splittings, is not necessarily reliable. We are therefore led to doubt the claim.