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D. O. Gough

Publications and source records attributed to D. O. Gough.

At least 19 recordsLinked to original sources
arXiv2025

Towards a self-consistent hydrodynamical model of the solar tachocline

The solar tachocline is an internal boundary layer in the Sun located between the differentially-rotating convection zone and the uniformly-rotating radiative interior beneath. Spiegel and Zahn (1992) 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, 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 Chini et al. (2022) and Shah et al. (2024), which has been numerically validated by Garaud et al. (2024). 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 $Ω_\odot / N_m$, where $Ω_\odot$ is the mean angular velocity of the Sun, and $N_m$ the 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.

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arXiv2023

The acoustic size of the Sun

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.

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arXiv2019

A Critical Evaluation of Recent Claims Concerning Solar Rotation

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.

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arXiv2018

On the hydrostatic stratification of the solar tachocline

We present an attempt to reconcile the solar tachocline glitch, a thin layer immediately beneath the convection zone in which the seismically inferred sound speed in the Sun exceeds corresponding values in standard solar models, with a degree of partial material mixing which we presume to have resulted from a combination of convective overshoot, wave transport and tachocline circulation. We first summarize the effects of either modifying in the models the opacity in the radiative interior or of incorporating either slow or fast tachocline circulation. Neither alone is successful. We then consider, without physical justification, incomplete material redistribution immediately beneath the convection zone which is slow enough not to disturb radiative equilibrium. It is modelled simply as a diffusion process. We find that, in combination with an appropriate opacity modification, it is possible to find a density-dependent diffusion coefficient that removes the glitch almost entirely, with a radiative envelope that is consistent with seismology.

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arXiv2015

Some glimpses from helioseismology at the dynamics of the deep solar interior

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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arXiv2015

Indications of r-mode Oscillations in SOHO/MDI Solar Radius Measurements

Analysis of solar radius measurements acquired by the Michelson Doppler Imager on the SOHO spacecraft supports previously reported evidence of solar internal r-mode oscillations in Mt Wilson radius data and in nuclear-decay data acquired at the Lomonosov Moscow State University. The frequencies of these oscillations are compatible with oscillations in a putative inner tachocline that separates a slowly rotating core from the radiative envelope.

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arXiv2012

On the magnetic field required for driving the observed angular-velocity variations in the solar convection zone

A putative temporally varying circulation-free magnetic-field configuration is inferred in an equatorial segment of the solar convection zone from the helioseismologically inferred angular-velocity variation, assuming that the predominant dynamics is angular acceleration produced by the azimuthal Maxwell stress exerted by a field whose surface values are consistent with photospheric line-of-sight measurements.

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arXiv2012

Heliophysics gleaned from seismology

Some of the principal heliophysical inferences that have been drawn from, or refined by, seismology, and the manner in which those inferences have been made, are very briefly described. Prominence is given to the use of simple formulae, derived either from simple toy models or from asymptotic approximations to more realistic situations, for tailoring procedures to be used for analysing observations in such a way as to answer specific questions about physics. It is emphasized that precision is not accuracy, and that confusing the two can be quite misleading.

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arXiv2011

Nonlocal model for the turbulent fluxes due to thermal convection in rectilinear shearing flow

We revisit a phenomenological description of turbulent thermal convection along the lines proposed by Gough (1977) in which eddies grow solely by extracting energy from the unstably stratified mean state and are subsequently destroyed by internal shear instability. This work is part of an ongoing investigation for finding a procedure to calculate the turbulent fluxes of heat and momentum in the presence of a shearing background flow in stars.

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arXiv2011

On the seismic age and heavy-element abundance of the Sun

We estimate the main-sequence age and heavy-element abundance of the Sun by means of an asteroseismic calibration of theoretical solar models using only low-degree acoustic modes from the BiSON. The method can therefore be applied also to other solar-type stars, such as those observed by the NASA satellite Kepler and the planned ground-based Danish-led SONG network. The age, 4.60+/-0.04 Gy, obtained with this new seismic method, is similar to, although somewhat greater than, today's commonly adopted values, and the surface heavy-element abundance by mass, Zs=0.0142+/-0.0005, lies between the values quoted recently by Asplund et al. (2009) and by Caffau et al. (2009). We stress that our best-fitting model is not a seismic model, but a theoretically evolved model of the Sun constructed with `standard' physics and calibrated against helioseismic data.

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arXiv2011

Bridges between helioseismological and asteroseismological inference

Exactly eighty years ago, a very young Yehudi Menuhin was invited by Bruno Walter to perform Beethoven's violin concerto with the Berlin Philharmonic Orchestra. Walking through the streets of Berlin he was unsure of his way, and asked a passer-by how he could get to the Konzerthaus. The man looked at him, looked down at the violin case that Yehudi was carrying, and said: `Practise, young man, practise'. It was with such advice in their minds, I am sure, that Margarida and Michael have asked me to try to build bridges between helioseismology and asteroseismology. Asteroseismology is new and fresh, and the young scientists who are entering the subject should be full of the expectation of the delights of discovery of untrodden ground. Where should they tread? They should be guided, perhaps, by our mature, well practised, experiences with the Sun.

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arXiv2011

Variability in mode amplitudes in the rapidly oscillating Ap star HR 1217

HR 1217 is one of the best-studied rapidly oscillating Ap (roAp) stars, with eight known oscillation modes that are distorted by a strong, global magnetic field. We have reanalysed the multisite observations of HR 1217 taken in 1986 and 2000. We determined a weighting scheme for the 1986 and 2000 data to minimize the noise level. A wavelet analysis of the data has found that the modulation of the amplitude due to rotation for all frequencies is, in general, consistent with the expected modulation for modified l=1, 2 or 3 modes. Unexpected variations in the rotational modulation are also seen, with variations in the modulation profile, time of maximal pulsation, and pulsational energy in each mode. Interestingly, these changes take place on a short timescale, of the order of days. We consider potential explanations for these behaviours.

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arXiv2010

Modelling turbulent fluxes due to thermal convection in rectilinear shearing flow

We revisit a phenomenological description of turbulent thermal convection along the lines proposed originally by Gough (1965) in which eddies grow solely by extracting energy from the unstably stratified mean state and are subsequently destroyed by internal shear instability. This work is part of an ongoing investigation for finding a procedure to calculate the turbulent fluxes of heat and momentum in the presence of a shearing background flow in stars.

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arXiv2009

The quest for the solar g modes

Solar gravity modes (or g modes) -- oscillations of the solar interior for which buoyancy acts as the restoring force -- have the potential to provide unprecedented inference on the structure and dynamics of the solar core, inference that is not possible with the well observed acoustic modes (or p modes). The high amplitude of the g-mode eigenfunctions in the core and the evanesence of the modes in the convection zone make the modes particularly sensitive to the physical and dynamical conditions in the core. Owing to the existence of the convection zone, the g modes have very low amplitudes at photospheric levels, which makes the modes extremely hard to detect. In this paper, we review the current state of play regarding attempts to detect g modes. We review the theory of g modes, including theoretical estimation of the g-mode frequencies, amplitudes and damping rates. Then we go on to discuss the techniques that have been used to try to detect g modes. We review results in the literature, and finish by looking to the future, and the potential advances that can be made -- from both data and data-analysis perspectives -- to give unambiguous detections of individual g modes. The review ends by concluding that, at the time of writing, there is indeed a consensus amongst the authors that there is currently no undisputed detection of solar g modes.

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arXiv2009

Vainu Bappu Memorial Lecture: What is a sunspot?

Sunspots have been known in the West since Galileo Galilei and Thomas Harriot first used telescopes to observe the Sun nearly four centuries ago; they have been known to the Chinese for more than two thousand years. They appear as relatively dark patches on the surface of the Sun, and are caused by concentrations of magnetism which impede the flow of heat from deep inside the Sun up to its othewise brilliant surface. The spots are not permanent: the total number of spots on the Sun varies cyclically in time, with a period of about eleven years, associated with which there appear to be variations in our climate. When there are many spots, it is more dangerous for spacecraft to operate. The cause of the spots is not well understood; nor is it known for sure how they die. Their structure beneath the surface of the Sun is in some dispute, although much is known about their properties at the surface, including an outward material flow which was discovered by John Evershed observing the Sun from Kodaikanal a hundred years ago. I shall give you a glimpse of how we are striving to deepen our understanding of these fascinating features, and of some of the phenomena that appear to be associated with them.

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arXiv2009

Angular-momentum coupling through the tachocline

Astronomical observation of stellar rotation suggests that at least the surface layers of the Sun have lost a substantial amount of the angular momentum that they possessed at the beginning of the main-sequence phase of evolution; and solar-wind observations indicate that magnetic coupling is still draining angular momentum from the Sun today. In addition, helioseismological analysis has shown that the specific angular momentum at the top of the almost uniformly rotating radiative interior is approximately (although not exactly) the same as the spherically averaged value at the base of the (differentially rotating) convection zone, suggesting that angular momentum is being transported through the tachocline. The mechanism by which that transport is taking place is not understood. Nor is there a consensus of opinion. I review some of the suggestions that have been put forward, biassing my discussion, no doubt, according to my own opinions.

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arXiv2008

Progress report on solar age calibration

We report on an ongoing investigation into a seismic calibration of solar models designed for estimating the main-sequence age and a measure of the chemical abundances of the Sun. Only modes of low degree are employed, so that with appropriate modification the procedure could be applied to other stars. We have found that, as has been anticipated, a separation of the contributions to the seismic frequencies arising from the relatively smooth, glitch-free, background structure of the star and from glitches produced by helium ionization and the abrupt gradient change at the base of the convection zone renders the procedure more robust than earlier calibrations that fitted only raw frequencies to glitch-free asymptotics. As in the past, we use asymptotic analysis to design seismic signatures that are, to the best of our ability, contaminated as little as possible by those uncertain properties of the star that are not directly associated with age and chemical composition. The calibration itself, however, employs only numerically computed eigenfrequencies. It is based on a linear perturbation from a reference model. Two reference models have been used, one somewhat younger, the other somewhat older than the Sun. The two calibrations, which use BiSON data, are more-or-less consistent, and yield a main-sequence age $t_\odot=4.68\pm0.02 $Gy, coupled with a formal initial heavy-element abundance $Z=0.0169\pm0.0005$. The error analysis has not yet been completed, so the estimated precision must be taken with a pinch of salt.

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