Artist’s impression of the ESA/ NASA Solar and Heliospheric Observatory, SOHO, with the Sun as seen by the satellite’s extreme-ultraviolet imaging telescope on 14 September 1999. Credit: Spacecraft: ESA/ ATG medialab; Sun: ESA/ NASA SOHO, CC BY-SA 3.0 IGO <https://creativecommons.org/licenses/by-sa/3.0/igo/deed.en>, via Wikimedia Commons.

Researchers have pioneered an innovative method using helioseismology, a discipline dedicated to studying the Sun’s acoustic oscillations, to measure solar radiative opacity under extreme conditions.

This groundbreaking work not only reveals gaps in our understanding of atomic physics but also confirms recent experimental results, thereby opening new perspectives in astrophysics and nuclear physics.

ScienceVega spoke to Dr Gaël Buldgen, of the Université de Liège in Belgium, about the research and what it could potentially mean for the future of nuclear fusion.

ScienceVega: Can you give a bit of background to the discipline of Helioseismology?

GB: The Sun is a very controlled environment in terms of what we know about it. We know the radius, we know the mass of the Sun very precisely from very simple first principles and we know the total energy that is irradiated from the Sun again from very simple principles. We also know the age of the Sun from the materials and history of the Solar System. It’s a very controlled environment.

The idea of helioseismology is you have global oscillation modes, like a bubble of gas oscillating. It is just like a musical instrument. You listen to the tones of the Sun and you try to reconstruct the internal structure from the dispersion relations that you have for these observations.

ScienceVega: How exactly do you study the Sun’s acoustic oscillations?

GB: The key thing is that you need to detect them and we do that through variations of luminosity at the surface. For example, if you have small variations in pressure, you’re going to have a variation of flux at the surface. Using this idea to look at the different harmonics of the spectrum and putting them all together, you can actually see from all the spherical harmonics of the modes these very chaotic and complex motions that make up what we call the solar spectrum.

For the Sun we have a periodic variation of luminosity and detecting oscillations is relatively simple. All we need to do is look at the Sun for a certain period of time and then mathematically you do a Fourier transform and look at the periodicities in that signal. From there we see spikes, that are essentially individual oscillation modes, and they spike at about five minutes. The spectrum actually looks like a comb.

Now, with the improvement of space observations, we have been able to get thousands of oscillation modes; the biggest data set I work with is about 7,000 individual frequencies, which is extreme, if we compare to other solar-like stars for which we have about 50, at best.

Also, the Sun has been continuously monitored from the ground for about 35 years, by different networks of telescopes. There were also people who went to Antarctica during the midnight Sun to actually have continuous observations; you want to look at the Sun for as long as possible with a sensitive detector so you can see these tiny variations and see the periodicity in them. You need a very long time series to detect the oscillations, and luckily enough for helioseismology, that is what we have.

A complementary tool to helioseismology are neutrino detection experiments, which have provided crucial constraints on what was actually powering the Sun (nuclear fusion). Two Nobel prizes (2002 and 2015) have been linked with the scientific progress made from these measurements.

SOHO’s EIT (Extreme ultraviolet Imaging Telescope) images the solar atmosphere at several wavelengths and, therefore, shows solar material at different temperatures. In the images taken at 304 Angstroms, the bright material is at 60 000 to 80 000K. In those taken at 171, at 1 million Kelvin. 195 Angstrom images correspond to about 1.5 million Kelvin. The hotter the temperature, the higher you look in the solar atmosphere. Credit: SOHO instrument consortium. Public Domain.

ScienceVega: What is solar radiative opacity?

GB: To understand the concept of opacity you have to think about transparency. If you think of a glass window, if the glass is more opaque, you will have less light going through it and you will get a darker picture of what’s happening. That is opacity.

In our case, it is the ability of the solar plasma to absorb radiation and, essentially, not let radiation go through. It is also about absorbing the energy of the radiation that is around; the more absorption you have, because it’s not always elastic, you are going to have energy that goes to the atoms and you’re going to see an increase in temperature in the plasma. This is what you see when you have a more opaque medium. It is a similar concept to putting your hand on a black car in sunlight – it’s going to be hotter than a white car, because there is greater absorption.

Radiative opacity is complicated especially in these conditions. It has been called one of the most tedious ingredients of astrophysics. From a theoretical point of view, there are only a couple of groups that compute radiative opacity tables and it takes years to do them.

If you look at the publications and the data we use, there was one publication of tables in 1996, one in 2004, then one in 2015 and another one in 2016. That gives you an idea of the amount of computational scale that has to go into these quantities because when you look at the structure of an atom, you have different energy levels and electrons can jump on from one to another when they absorb the photon and so on. You need to take all energy levels for all the atoms at different range of energies in conditions that are almost impossible to simulate on Earth. We are talking about billions of computations of these transitions that have to be done accurately. It takes a huge amount of time and because of the computational scales involved, revisions of solar radiative opacity have always been very difficult and have taken a lot of time. The opacity tables are also used in all stellar evolutionary models for every star in the Universe, they are a fundamental constituent of stellar physics, just like the efficiency of nuclear reactions for example, or the equation of state describing the plasma.

It is a very complex quantity that translates the capability of the solar plasma to absorb high energy radiation.

ScienceVega: How does knowing more about solar radiative opacity help us understand the Sun’s interior?

GB: If you think about the Sun in terms of mass, 3% of its outer layers are convective. If you imagine a kettle on a stove, you know there will be an increase in temperature as you heat it and at some point you’re going to have turbulence and you’re going to have macroscopic motions taking over from simple heat diffusion taking place at the microscopic level. That is convection.

With the Sun, that takes place in the outer 3% of its layers – in 97% of the rest of the mass of the Sun, the transport of energy from inwards towards the outer layers is done by radiation, and therefore is dictated by the opacity of the solar material.

The Sun is essentially a gigantic nuclear fusion reactor. You have the energy generated in the core and it needs to be transported outwards and in 97% of its mass this transport is carried out by the high energy photons and so dictated by the capabilities of the plasma to absorb the energy, therefore by its opacity.

This has been a problem, not just for the Sun, but for astrophysics in general. In the paper we mentioned the Cepheid mass discrepancy of the 1980s, which was corrected when new opacity tables came out. There were also Beta Cephei stars, a class of massive pulsating stars, where you could see oscillation modes that were not explained theoretically, but when new opacity tables came out in 1996, they could be reproduced.

In the case of the Sun, we have an issue with chemical abundances or, at least, when we do a tomography of the internal structure, we see that models are failing to reproduce some key quantities. There is now more and more experimental evidence that this is due to a missing opacity, a missing amount of capability of the plasma to absorb radiation.

It’s going to be important in the sense that you need to understand how the Sun is capable of transporting its energy outwards and intrinsically, also, what is the fundamental principle dictating the fact that we’re missing opacity? None of the theoretical computations are able to reproduce the experiment. There is no code to this day, that can reproduce the helioseismology result. There is something missing in the way we model the atoms at these high energy levels. For the Sun’s interior, it is about the transport of energy and then the feedback loop in the transport of chemicals.

This is both a sociological problem and a scientific problem. Doing a structural model of the Sun is like a recipe of things that are needed to be included and a very important component is the amount of heavy elements, heavier atoms than helium, such as carbon, nitrogen, oxygen, iron, neon etc. They only make about 2% of the Sun in mass, but they are extremely important from an energetical point of view as they are the biggest contributors to opacity, because of their atomic structure: more electrons, more absorption can happen.

In the 1990s we had relatively high abundances of these elements that were used in solar models because the spectroscopists believed that you had a higher amount of, mostly, oxygen. Then in 2005, 2009 and also in 2021, the same group of spectroscopists revised their measures and said there is 30% less oxygen in the Sun than previously believed.

The problem was from a solar modelling perspective; the models of the 1990s, the so-called standard solar models, worked extremely well with helioseismology. There were those in the solar modelling community who were not so keen in letting go of the old abundances that worked extremely well, to move toward the newest ones that were raising questions about what was being put in the solar models. That has been a lasting debate ever since with competing groups claiming that the abundances of the 1990s were correct even in 2022. The measurements of 2021 have, however, been confirmed numerous times, even with independent techniques.

Scientifically, for me, there is no doubt that the abundances need to be revised. The problem then is, adopting this new composition raises questions about other ingredients like the opacities, like the way we actually model the Sun as stellar physicists. We have planetary formation models and if you consider that the Sun has formed with planets around it; in other words with the Solar System, then you have to be careful about their impact on the Sun itself. The standard models are also very simplified in the way they model turbulence and rotation (they fully neglect rotation) and we know the Sun is rotating, we actually have a map of the internal rotation of the Sun. That is never considered in standard models, and for me that is a problem. Others may of course have a different viewpoint.

This still image was taken from a new NASA movie of the Sun based on data from NASA’s Solar Dynamics Observatory, or SDO, showing the wide range of wavelengths – invisible to the naked eye – that the telescope can view. SDO converts the wavelengths into an image humans can see, and the light is colourised into a rainbow. Yellow light of 5,800 Angstroms, for example, generally emanates from material of about 10,000°F (5700°C), which represents the surface of the Sun. Extreme ultraviolet light of 94 Angstroms, which is typically colourised in green in SDO images, comes from atoms that are about 11million°F (6.3million°C) and is a good wavelength for looking at solar flares, which can reach such high temperatures. By examining pictures of the Sun in a variety of wavelengths – as is done not only by SDO, but also by NASA’s Interface Region Imaging Spectrograph, NASA’s Solar Terrestrial Relations Observatory and the European Space Agency/ NASA Solar and Heliospheric Observatory – scientists can track how particles and heat move through the Sun’s atmosphere. Credit: NASA Goddard Space Flight Center, Public domain, via Wikimedia Commons.

ScienceVega: Are we able to use helioseismology on other stars, or are they too far away?

GB: In those cases we call it asteroseismology. The problem with it is that since these are much more distant objects, you can’t resolve their surface. If you think about the oscillations, you are going to have what we call geometric cancellation. If you look at the Sun, you can see different areas on the surface of the Sun changing; you can resolve the surface.

But if you have a point-like source, it is much trickier. If you have huge motions, that’s ok, but if you have small motions in terms of geometric scale, you have a lot of cancellation. And if you do the integral on the surface of the star of such small variations, it is essentially going to be zero. You won’tsee the variations if they are very localised.

Asteroseismology is really a tool to probe the internal structure of other stars and it has also been a huge success in terms of dating structures in the Universe. If you are looking at structures in the galaxy/ Milky Way, the golden path to date objects is to use stellar models, but if you want to use stellar models you need observational constraints to know what kind of physical ingredients you’re going to put in your model, just like for the Sun, and that is how asteroseismology really helps you.

ScienceVega: The Plato mission will launch next year. How will it add to information available to you?

GB: Plato is going to be extremely helpful for solar twins, stars very similar to the Sun. If you look at the output of satellites like CoRoT, Kepler and TESS (Transiting Exoplanet Survey Satellite), they have been extremely helpful for what we call red giants, which are evolved suns after they have exhausted the hydrogen in their core.

Plato is going to focus on very bright stars that are still burning hydrogen in their core. They are also going to be located mostly in the southern hemisphere, which is going to allow for high-quality follow-up to determine the chemical abundances at the surface of these stars. Currently that is not provided by asteroseismology; it is provided by spectroscopy. The problem with Kepler is that it was mostly looking at the northern hemisphere and so we didn’t have the instruments like ESO’s Very Large Telescope to do high-quality spectroscopic follow up. Plato is going to allow for that.

We are going to have a large sample of solar twins, possibly hundreds. We are just going to be in the right physical conditions, which are going to be slightly different than the Sun for most of the cases. We will also have very good determinations of the chemical composition and with that we will be able sometimes to use interferometry to get the actual radius of the star, which is a very strong constraint too.

With the data of these additional stars, Plato is going to be extremely interesting in putting the Sun into an evolutionary perspective regarding its neighbours and the twins of the Sun in the Galaxy.

ScienceVega: How is this research helping nuclear fusion research?

GB: When you go into the world of people doing fusion experiments at institutions such as the Lawrence Livermore National Laboratory in California, the Sandia National Laboratories, the CEA in Paris, you realise how a lot of the things we do in stellar physics are interconnected to really fundamental questions in quantum mechanics and in nuclear physics.

Stars are really just fusion reactors, the Sun is the only really stable nuclear fusion reactor in the Solar System that has been going for almost five Giga years, and the fact we can probe the internal structure of the Sun in great detail is going to impact the way we model and understand these extreme conditions in which nuclear fusion is taking place. We have with the Sun a laboratory essentially of fundamental physics under very extreme conditions and that is how it’s going to help nuclear fusion research.

The Z machine, the largest X-ray generator in the world, is located in Albuquerque, New Mexico. As part of the Pulsed Power Program, which started at Sandia National Laboratories in the 1960s, the Z machine concentrates electrical energy and turns it into short pulses of enormous power, which can then be used to generate X-rays and gamma rays. Credit: Randy Montoya/ Sandia National Laboratories.

The link to the original paper can be found here.

Dr Gaël Buldgen, Theoretical Stellar Astrophysics and Asteroseismology, Department of Astrophysics, Geophysics and Oceanography and STAR Institute, Université de Liège.

Portrait credit: Gaël Buldgen.