Shravan Hanasoge¹
1. Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Mumbai, India

The convective envelope of the Sun exhibits differential rotation, with a relatively fast-rotating equator, and supports a weak poleward meridional circulation. Both of these fluid circulations, thought to be driven by convective Reynolds stresses (correlations between convective velocities), likely play a central role in regulating the generation and sustenance of large-scale magnetic field in the Sun. Thus understanding the nature of convection in the interior is a problem of importance.

The dominant view has been that overturning convection is ubiquitous in the bulk of the convection zone, much as it is at surface layers, and is the primary coherent structure associated with convection. This flow field would likely possess large velocities and therefore significant Reynolds stresses, which in turn would fuel the observed large-scale fluid circulations in the Sun. A corollary of having vigorous overturning convection is that a total transport of some 10,000 solar luminosities (some M solar luminosities upwards, and M–1 downwards, where M is a very large number^[1]) would be required to achieve the net output of one solar luminosity.

Figure 1 |
Seismic upper bounds^[2] on large-scale lateral (horizontal) convective-velocity amplitudes in the solar interior at the depth r/R = 0.96. These constraints are compared with spectra derived at a similar depth from the global convection simulations (ASH^[3]). These low convective-velocity amplitudes throw into question our understanding of thermal and angular momentum transport in the Sun. How are differential rotation and meridional circulation sustained? How is a solar luminosity transported outwards through the convection zone?

For many decades, seismic and other investigations have attempted to record these large-scale motions with limited success. These failed efforts, in tandem with results from high-resolution surface convection simulations, led to alternate theories based on coherent descending plumes from the surface, in mass balance with weak upflow from the deep convection zone. These convective flows would possess much lower turbulent kinetic energy in the bulk, consistent with non-detections of large-scale coherent overturning convection. Motions with such low kinetic energy are associated with weak Reynolds stresses and there is no obvious means of sustaining large-scale solar fluid circulations. A more fundamental problem would be the thermal transport of one solar luminosity; contemporary numerical simulations cannot easily achieve this transport due to technical issues.

Increasingly, seismic investigations have turned towards inferring the nature of coherent convective structures in the bulk of the solar convection zone. Recently, [2] were able to place strong seismic upper bounds on the convective power spectrum at a depth of r/R = 0.96 (28 Mm or 28,000 km below the photosphere). They downsampled and synthesized 900 billion wavefield observations taken by HMI to produce 3 billion cross-correlations, which were averaged and fit to estimate 5 million wave travel times. Flows break the symmetry of wave propagation in that waves propagating in the direction of the flow are sped up and thus possess smaller travel times (and vice versa). Thus, the primary unit of measurement is the difference between the travel time from 1 –> 2 and 2 –> 1, where 1 and 2 are the points at which the cross correlation is measured. Using the statistics of these travel times, the underlying flow systems were measured and convective-velocity magnitudes were bounded in the interior of the Sun as a function of depth and spherical-harmonic degree. The constraints are shown in Figure 1.

Large-scale fluid motions at the photosphere of the Sun were claimed to have been discovered by [4], on the order of 8-20 m/s or so. Assuming that this estimate of convective velocities is accurate, magnitudes of flow velocities on these large scales at a depth of 28 Mm, where the density is about 10,000 times larger, are likely to be a factor of 10 or more smaller, consistent with the upper bounds shown in Figure 1. A greater puzzle is the photospheric convective spectrum, which shows a drop in power at spherical-harmonic degrees L < 120, and at very low spherical-harmonic degrees, the power drops linearly with L. Indeed, the reason for the lack of power on the largest scales is not well understood. Using numerical simulations, [5] attempted to model the peak of power at supergranular size scales and the subsequent fall in surface convective power spectrum at low L. In contrast with observations, they found that power would accumulate at low L, and concluded potently with: "These separate lines of evidence all suggest that the Sun transports energy through the convection zone while maintaining very low amplitude large-scale motions. Something is missing from our current theoretical understanding of solar convection below ∼10 Mm".

References

[1] Spruit, H., 1997, Astron. It., 68, 397
[2] Hanasoge, S.M, Duvall, T.L., Sreenivasan, K.R., 2012, PNAS, 109, 11928
[3] Miesch, M.S., Brun, A.S., De Rosa, M.L., Toomre, J., 2008, ApJ, 673, 557
[4] Hathaway, D.H., Upton, L., Colegrove, O., 2013, Science, 342, 1217
[5] Lord, J. W., Cameron, R. H., Rast, M.P., Rempel, M., Roudier, T., 2014, ApJ, 793, 24