_{Poster Artistic Impression by Melissa Weiss}

When scientists describe the properties of other stars, they often use the Sun as a reference point. “This Star has five solar masses” or “Red Giants have a 1000 solar luminosities”. These are known quantities of the sun, used by astrophysicists the world over to describe our universe. Amongst non-solar physicists there is a sense that we understand the physics of the Sun, or understand it well enough, and that the mysteries of the universe lay in the workings of other “more-complex” stars. But this is far from the truth. The solar interior still holds many mysteries, questions that while remain unanswered could have a significant impact on our understanding of other stars. The challenge is that we cannot directly observe the interior of the Sun. Scientists must rely on sound waves (excited by ubiquitous sunquakes) to probe plasma flows in the hidden interior. This is known as helioseismology.

Solar convection is one challenging topic that  has been difficult to understand and relies on helioseismology to provide insights. The Sun is generating an enormous amount of energy every second due to the fusion of Hydrogen into Helium in the core. This energy must escape. In the inner 70% of the Sun’s radius, this energy is transported through radiation (light). In the outer 30%, the plasma becomes opaque to light, which means that radiation is not an efficient form of transport, and the most efficient method for heat transport is fluid motion — Convection. Think of the way hot air rises, while cold air sinks.

The standard theories used to describe convection in the Sun stipulate that there should exist a range of length scales for convection. Specifically, these theories predict that there should be small-scale convective motions (or flows) near the surface increasing all the way to large convective flows, comparable to the size of the sun, that turn over material deep in the interior. The problem for the Sun is that we don’t see this full cascade of scales. We can easily observe small scale motions, known as solar granules (convection cells 1,000 km wide that live for 10 min), intermediate scales known as supergranules (35,000 km wide flows that live for 2 days) but large scale structures are very weak and evade detection. Therefore,  for length-scales larger than supergranules, these standard theories do not match the observations. But convective cells smaller than supergranules are accurately described by theories and simulations. The question then becomes, where do supergranules fit in this picture? In order to find out we must see what's below the surface and fall back on helioseismology.

In order to image the depth of supergranules, we rely on the Sun’s internal wave field. Small scale turbulent convection at the surface generates a broad spectrum of acoustic (pressure or p modes) and surface gravity modes (f modes). See Figure 1. These waves travel into the interior, refract due to the increasing density and return to the surface. If these waves pass through supergranular flows, they are altered. Imagine you are swimming down river, you will travel the same distance in a shorter time than if you swam up river. It is the same with waves, as they pass through the flows they speed up, slow down or scatter into other modes. Helioseismologist’s measure these changes in the waves to infer what is below the surface. 

In our paper, we measured the full 3D flow fields of the average supergranule, a computationally demanding task that required the use of supercomputers.  Through measuring the altered wave field around 23,000 supergranules we found that the average solar supergranule extends to 20,000 km below the surface of the sun (see Figure 2). The peak upflow occurs around 10,000 km and tails off at around 20,000 km. The overlaid flow vectors, similar to wind patterns on a weather report, show that the supergranule forms a cell-like pattern. Material rises, reaches the surface and moves outward, descends into the interior and then returns to the up flow. 

Finding this cell-like pattern near the surface was not guaranteed, leading to the first surprising result. Computer simulations (similar to mixing length theory, a popular theory for convection in stars) depict a plume-like appearance for supergranules, where the cold sinking plasma goes deep into the interior after which it rises up again. We were also surprised to find that plasma rose fastest at around the same depth of 10,000 km regardless of the supergranule's diameter (30,000 km, 33,000 km, 38,000 km, etc). According to theory and simulations - larger convection cells should extend deeper into the Sun. We were most shocked when we realized that the cold, sinking material was moving 40% slower than the warm rising material. Is it possible that sound-waves of the Sun couldn't probe a part of this sinking material? Some studies in the past purport that the sinking plasma could be much smaller in size (~100 km), like raindrops. Sound waves, which in the Sun are at minimum ~5,000 km long, would be practically deaf to these raindrops, so to speak! Our research points to this missing component of the sinking plasma, that heretofore existed only in theory.

Using sound-waves of the Sun, we have achieved the most accurate characterization of supergranulation. Popular theories (mixing length) or simulations do not completely explain this supergranular structure and dynamics. Our observations challenge the way we traditionally describe convection in stellar atmospheres and require novel research efforts for a more holistic understanding of our Sun and consequently, other stars.

Acknowledgements: This research is based upon work supported by Tamkeen under the NYU Abu Dhabi Research Institute grants G1502 and CASS. S.H. acknowledges funding from the Department of Atomic Energy, India. K.R.S. and S.H. acknowledge support from the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under award OSR-CRG2020-4342. S.B.D acknowledges funding from the Elisabeth H. and F.A. Dahlen Award 2022 by the Department of Geosciences, Princeton University. S.B.D also acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413. Some data products were processed and downloaded from the German Data Center for SDO, which is funded by the German Aerospace Center under DLR grant 500L1701.