What Is Helioseismology? Listening to the Sun's Heartbeat

Helioseismology is the study of the Sun's interior through the way its surface heaves up and down. Convection beneath the surface keeps jostling the gas, and the jostling sets sound waves racing through the Sun, turning, and returning, so the whole star rings in millions of overlapping patterns. Astronomers read those patterns as tiny Doppler shifts in sunlight, then work backward to the temperature, rotation, and composition of layers no telescope can see. Here is how that works and what it has found.

How a star rings without anyone striking it

Sound needs a medium, so nothing about this reaches us as audible sound across space. The oscillations live inside the Sun and show up as slow, rhythmic movements of its visible surface, which we detect by measuring how sunlight from different spots is Doppler shifted.

The easiest way to picture the process is a bell, or better, an organ pipe. A bell does not need a musician with a perfect sense of timing: any irregular blow excites the notes the bell's shape and material allow, and nothing else. The Sun behaves the same way. The outer layers of the Sun boil continuously (the convection zone, the shell where hot gas rises and cooler gas sinks), and that churning acts like random tapping from all directions at once. The star responds only at its natural frequencies, so the noise sorts itself into a clean set of notes.

Those notes are called normal modes. In the Sun the dominant restoring force for most of them is pressure, which is why they are named p modes (p for pressure). A compressed pocket of gas pushes back, overshoots, and compresses the gas on the other side, and the wave travels on. Sound waves are the same thing as pressure waves, so the Sun is acting as a resonant cavity for sound.

Where the waves turn around

A wave inside a star does not travel in a straight line. Sound moves faster where the gas is hotter, and temperature rises steeply toward the center. A wave heading downward therefore bends gradually, like light entering denser glass at a slant, until it curves back toward the surface. That is the inner turning point, and its depth depends on how the wave is shaped around the Sun. Near the surface the wave is reflected from the outside by the rapid thinning of the gas, at a level set by the acoustic cutoff frequency, so the waves cannot simply leak into space (Basu, 2016).

The result is a standing wave pattern trapped between the surface and a turning point somewhere below. Waves that run nearly straight down reach deep and carry information about the core. Waves that skim sideways turn around just under the surface and tell us only about the outer layers. Having many modes with different turning points is what turns a list of frequencies into a map.

How fast the Sun rings

The motions are tiny compared with the Sun itself, so what matters for identifying them is timing. The dominant oscillation has a period of about five minutes, a frequency near 3 millihertz. More broadly, the p modes sit between roughly 1 and 5 millihertz, and the GONG network measures oscillations with periods from about 2 to 20 minutes (NSO). Human hearing starts near 20 hertz, so these frequencies are thousands of times too low to hear even if sound could reach us. Sonification projects that let people listen to the Sun have to speed the data up by factors of thousands.

Reading the notes: three numbers per mode

Every mode is labeled by three integers, borrowed from the mathematics of vibrating spheres (Basu, 2016):

• Radial order n: the number of nodes (points where the motion cancels) along the radius.
• Angular degree ℓ: the number of nodal lines on the surface. A mode with ℓ = 0 is purely radial: the whole Sun swells and shrinks together. Higher ℓ means a finer checkerboard on the surface.
• Azimuthal order m: how many of those nodal lines pass through the rotation axis, running from −ℓ to +ℓ.

In a perfectly spherical, nonrotating star, every mode with the same n and ℓ would have identical frequency, however m differs. Rotation, magnetic fields, and anything else that breaks spherical symmetry lifts that degeneracy and splits the frequency into a small multiplet. The Sun's rotation is by far the dominant cause of that splitting, which is how helioseismologists measure rotation without ever seeing inside.

Think of a swimmer crossing a river: swimming with the current and against it take different times, and the difference tells you how fast the water is flowing. Waves traveling with the Sun's rotation and against it likewise have slightly different frequencies, and the size of that difference tells you how fast the layer they cross is turning.

Three families of modes

Mode family	Restoring force	Where it lives	Status in the Sun
p modes (pressure)	Pressure gradient	Convection zone and outer radiative zone; low ℓ reach the core	Measured in enormous numbers; frequencies roughly 1 to 5 mHz
f modes (surface gravity)	Gravity acting on a surface wave	Thin layer near the surface	Measured; frequencies follow ω² ≈ gk, so they say little about deep structure but help pin down the solar radius
g modes (gravity or buoyancy)	Buoyancy	Radiative interior and core	Not unambiguously detected in individual modes

Sources: Basu (2016); Wikipedia, "Helioseismology."

Because the Sun's disk is observed from one side, only modes up to a limited angular degree can be resolved. GONG data reach about ℓ = 200 and MDI and HMI data about ℓ = 250. Beyond that, short-lived modes smear into ridges and spatial leakage mixes neighboring modes. This is the reason the outermost layers remain the hardest region to probe (Basu, 2016).

A short history of listening to the Sun

The field grew out of a surprise. Robert Leighton, Robert Noyes, and George Simon reported velocity oscillations with a period of about five minutes in 1962, and Evans and Michard confirmed them the same year. For a while these were assumed to be a local effect of the solar atmosphere. The decisive step was the theoretical proposal that they were global modes of the whole star.

Year	Milestone	Who
1962	Five-minute oscillations discovered	Leighton, Noyes, and Simon; confirmed by Evans and Michard
1970 to 1971	Oscillations interpreted as global modes that should form ridges in a frequency versus wavenumber diagram	Ulrich; Leibacher and Stein
1975	Ridges observed	Deubner
1979	Individual global modes resolved from Sun-as-a-star Doppler data	Claverie and colleagues
1980	Full-disk oscillation observations from the South Pole	Grec, Fossat, and Pomerantz
1984	Internal rotation first reported	Duvall and colleagues
1993	Time-distance helioseismology introduced	Duvall and colleagues
1995	GONG network installed; SOHO launched December 2	NSO; ESA and NASA
2001	Seismic imaging of the Sun's far side	Braun and Lindsey
2010	Solar Dynamics Observatory launched February 11, carrying HMI	NASA

Sources: Basu (2016); Wikipedia, "Helioseismology"; NASA SOHO mission page; Wikipedia, "Solar Dynamics Observatory."

The astronomer Arthur Eddington opened The Internal Constitution of the Stars by lamenting that the deep interior of the Sun was less accessible than the depths of space, since we had no instrument able to "pierce through the outer layers of a star" (quoted in Basu, 2016). Helioseismology is, in effect, the instrument he was asking for, and it is a close cousin of the seismology that uses earthquake waves to probe Earth. If you want the terrestrial version of the idea, how earthquakes work and what seismic waves reveal covers the same logic of reading structure from travel times.

The instruments that listen

Measuring a modulation of a few meters per second on a star 150 million kilometers away needs long, uninterrupted records. A gap in the data does the same thing to a frequency spectrum that a stuttering microphone does to a musical note: it creates false copies (sidelobes) next to each real peak and can bury a faint mode. That is why the field leans on networks and on spacecraft rather than a single telescope.

Project	Type	What it does
BiSON (Birmingham Solar Oscillations Network)	Ground network	Sun-as-a-star observations of the lowest degrees (ℓ of 0 to 3), valuable for the core
GONG (Global Oscillation Network Group)	Six identical telescopes: Teide (Canary Islands), Learmonth (Australia), Big Bear (California), Mauna Loa (Hawaii), Udaipur (India), Cerro Tololo (Chile)	Resolved full-disk Doppler images every minute, installed in 1995, with a duty cycle around 90 percent
SOHO (Solar and Heliospheric Observatory), ESA and NASA	Spacecraft launched December 2, 1995	Carries MDI (resolved Doppler imager), GOLF (global low-frequency oscillations), and VIRGO (irradiance variations)
SDO/HMI (Solar Dynamics Observatory, Helioseismic and Magnetic Imager)	Spacecraft launched February 11, 2010	Took over from MDI, which stopped acquiring data in April 2011, with Doppler images and magnetograms of the whole disk

Sources: Basu (2016); NSO GONG pages; Wikipedia, "Global Oscillation Network Group" and "Solar Dynamics Observatory"; NASA SOHO mission page.

The sites of GONG are spread around the globe so that when the Sun sets at one, it is still up at another. SOHO sits at the first Lagrange point, a gravitational balance spot between Earth and the Sun, which keeps the Sun in view without nights (how Lagrange points hold space telescopes explains why that spot is so useful).

From frequencies to a map: how inversions work

Measured frequencies are only the raw material. To find out what the inside of the Sun looks like, helioseismologists compare the observed set with the frequencies predicted by a solar model, then adjust the model until they agree. The adjustment is called an inversion.

The theory behind it is a little like checking a bell for flaws by tapping it. If a model's sound speed is wrong in some layer, every mode that passes through that layer shifts in frequency, and the amount depends on how much time the mode spends there. Each mode has a sensitivity function (a kernel) that says which depths it cares about. With thousands of modes, each with a different kernel, the data can be combined to estimate the sound speed at each depth (Basu, 2016).

Two practical details matter for how much to trust the answer:

1. The data are finite, but the Sun is continuous. No set of modes can pin down a function at every radius, so inversions return localized averages. Methods such as regularized least squares and optimally localized averages do this in complementary ways, and the most reliable results are those where both agree.
2. The surface is a problem. Models of the outermost layers are crude, which shifts model frequencies by a smooth function of frequency (the "surface term"). It has to be fitted and removed before the deeper structure is interpreted.

Inversions return sound speed more reliably than density, because mass conservation forces any density error in one layer to be compensated elsewhere. The usable range today is roughly 0.05 to 0.96 of the solar radius: the inner limit is set by how many low-degree modes have been measured, the outer by the scarcity of reliable high-degree ones (Basu, 2016).

What the Sun's interior looks like

Modern standard solar models agree with the Sun closely. In the inversion results in Basu's review, the squared sound speed in the models differs from the Sun by fractions of a percent through most of the interior, and density differences are at most about 2 percent. That is a strong check on the physics that goes into the models: the equation of state, nuclear reaction rates, and the way helium and heavier elements slowly settle.

Helium settling

A gas of heavier atoms sinks slowly through a gas of lighter ones. Over 4.6 billion years, helium and heavy elements have drained gradually out of the convection zone into the layers below. Models that leave this out predict a convection zone that is far too shallow and a helium abundance that is too high. Models that include it match the observed sound speed far better, and diffusion is now a standard ingredient (Basu, 2016).

Where convection stops

The boundary between convective and radiative energy transport leaves a clean signature. Gas in the convection zone follows a nearly adiabatic temperature gradient, and below it the gradient changes abruptly, producing a sharp feature in the sound speed profile (an acoustic "glitch"). Christensen-Dalsgaard and colleagues used it in 1991 to place the base of the convection zone at 0.713 ± 0.001 solar radii, and later work using GONG and MDI data found 0.7133 ± 0.0005 (Basu, 2016).

Because the solar radius is about 696,000 kilometers, the convection zone is roughly 200,000 kilometers deep, which is a little over 28 percent of the way from the surface to the center. Helioseismology has also set limits on how far convective motions overshoot below that boundary, and several analyses found no dependence of the boundary on latitude.

How much helium?

The Sun is too cool for helium to produce usable spectral lines in the photosphere, so its envelope abundance cannot be read from spectra. Helioseismology does it instead: helium changes the gas's mean molecular weight and therefore the sound speed, and it leaves a glitch in the helium ionization zone. Basu and Antia (2004) obtained an envelope helium mass fraction of Y = 0.2485 ± 0.0034. Working backward through the Sun's history, Serenelli and Basu (2010) estimated the initial helium abundance at Y₀ = 0.273 ± 0.006 (Basu, 2016).

The Sun's convection zone, measured through sound waves, starts at 0.713 of the solar radius, and the number is known to better than 0.2 percent.

The tachocline and the rotation map

Rotation splitting turns a list of frequencies into a rotation profile Ω(r, θ) as a function of radius and latitude. The picture it produced was not the one anyone expected.

The surface rotates once every 25 days or so at the equator, with higher latitudes taking longer. Before helioseismology, models predicted that this differential rotation would continue inward on cylinders. Helioseismology showed instead that through most of the convection zone the rotation rate is nearly constant along cones of fixed latitude, so a pole-to-equator contrast persists all the way down (Basu, 2016).

Below the convection zone the Sun rotates almost like a solid body, at about the mid-latitude rate. In the GONG-based map shown in Basu's review the radiative zone turns at close to 430 nanohertz, a period of about 27 days. Nobody had predicted such rigid rotation, and explaining how the radiative zone stays that uniform is still an active area of work.

A thin layer carrying a lot of shear

The change from latitude-dependent rotation above to rigid rotation below happens across a thin layer called the tachocline, a term coined by Edward Spiegel and Jean-Paul Zahn in 1992 by analogy with the ocean's thermocline. Helioseismology places it at or just below the base of the convection zone, at a radius of at most about 0.70 solar radii, with a thickness near 0.04 solar radii, which is roughly 28,000 kilometers (Wikipedia, "Tachocline").

That is thin compared with the Sun, and it carries a great deal of shear. Many solar dynamo models, the models of how the Sun makes its magnetic field, rely on the tachocline to stretch weak poloidal (north-south) field lines into strong toroidal (east-west) ones, which later rise and form sunspot groups. Models that do not use a tachocline exist as well, so its role is not settled. Even so, the layer's existence and thickness are hard constraints that any dynamo theory has to respect. For how that field becomes visible at the surface, Solar Maximum 2025: how Solar Cycle 25 outran every prediction covers the cycle itself.

What lies at the very center

The rotation of the innermost 20 percent of the Sun is poorly known, because only low-degree p modes reach it and their splittings are small. Basu's review states plainly that the rotation of the innermost parts "is not really known." What is known is that nothing in the data suggests a rapidly spinning core. A detailed measurement would require g modes, whose detection is still contested (see the section on limits below).

The Sun is almost, but not quite, round

Rotation splits frequencies in a way that is odd in m. Centrifugal effects and magnetic fields produce an even-in-m component, and the even component is much smaller. The measured difference between the Sun's equatorial and polar radii is only about 1 part in 10⁵: space-based data from PICARD put it at around 6.1 kilometers, or about 9 parts in a million (Basu, 2016).

Limits on interior magnetic fields

The same frequency splittings give upper limits on hidden magnetic fields. The analysis in Basu's review puts an upper limit of about 0.3 megagauss on a toroidal field concentrated below the convection zone, and an upper limit of 10⁻⁵ on the ratio of magnetic pressure to gas pressure in the core.

The solar abundance problem

The sound-speed agreement described above depended on the heavy-element abundance that went into the models. Heavy elements make stellar gas more opaque, and opacity controls how deep convection reaches.

In the 2000s, Asplund and colleagues redid the spectroscopy of the solar surface with three-dimensional models of the atmosphere, which included the gas motions that earlier one-dimensional models ignored. The result was a lower carbon, nitrogen, and oxygen content, 35 to 45 percent below the older values of Grevesse and Sauval (1998), and a net reduction of the solar heavy-element fraction relative to hydrogen (Z/X) from 0.023 to 0.0165, about 28 percent lower (Basu, 2016).

The trouble came when models were rebuilt with the new composition. They no longer matched the Sun's acoustic structure:

Composition used in the model	Z/X	Convection zone base (solar radii)	Envelope helium Y	Source of values
Measured by helioseismology	not applicable	0.713 ± 0.001	0.2485 ± 0.0034	Basu and Antia (1997, 2004)
GS98	0.023	0.7139	0.2456	Basu (2016), Table 3
Caffau and colleagues (C11)	0.0209	0.7150	0.2415	Basu (2016), Table 3
AGSS09	0.018	0.7205	0.2352	Basu (2016), Table 3
AGS05	0.0165	0.7259	0.2286	Basu (2016), Table 3

The model built with the highest metal content (GS98) matches the measured convection zone base and helium within the quoted errors. As the assumed metal content drops, the modeled convection zone base moves outward, which means the zone is too shallow, and the modeled helium falls too low. The mismatch is one of the largest remaining puzzles in solar physics.

Where it stands

Asplund, Amarsi, and Grevesse (2021) re-derived the composition and confirmed low carbon, nitrogen, and oxygen. They reported a surface heavy-element mass fraction of Z = 0.0139 ± 0.0006 and Z/X = 0.0187 ± 0.0009, and noted that the solar modeling problem persists, pointing to possible flaws in opacities or mixing in standard solar models.

Others have disagreed. Magg and colleagues (2022) reanalyzed the spectra with new oxygen atomic data and obtained Z/X = 0.0225, closer to the older high values, and reported that the mismatch with helioseismology was resolved when that composition was used. Those two groups have not converged, so the question should be treated as open until independent analyses agree.

Basu and Antia (2013) asked how much extra opacity the low-metal models would need to match the Sun: about 6 percent for the Caffau composition, 16.5 percent for AGSS09, and 26.5 percent for AGS05. Laboratory measurements of opacity at solar-interior conditions are therefore another place the answer might come from (Basu, 2016).

How a sound wave solved a neutrino puzzle

The Sun's core fuses hydrogen into helium, and the reactions release electron neutrinos that leave the Sun almost without interacting. In the late 1960s, Ray Davis and John Bahcall set out to count them. The chlorine detector in the Homestake mine registered only about a third of the flux that the standard solar model predicted. That disagreement is the solar neutrino problem, and it lasted for decades (Basu, 2016; Wikipedia, "Solar neutrino problem").

There were two broad possibilities. Either the model was wrong and the core was cooler than assumed, or the neutrinos changed identity on the way to Earth, so that the detector missed some of them. Helioseismology was the way to discriminate.

A cooler core would make sound travel more slowly in the core. Basu's review notes that a nonstandard solar model built to match the chlorine results would have a sound speed in the core off by about 10 percent from standard models, while the actual differences between standard models and the Sun are much smaller (Bahcall and colleagues, 1998, cited in Basu, 2016). In other words, the Sun's core was as hot as the standard model said. Independent neutrino measurements support the same conclusion: using a boron-8 neutrino flux, Fiorentini and Ricci (2002) estimated a central temperature of 15.7 million kelvin, with an uncertainty of about 1 percent (Wikipedia, "Standard solar model").

The answer was therefore in particle physics, not in the Sun. The Sudbury Neutrino Observatory published measurements in 2001 and 2002 that were sensitive to all neutrino flavors, and showed that the electron neutrinos were a fraction (about 34 percent) of a total flux that agreed with the solar model. Neutrinos had oscillated into other types. The 2015 Nobel Prize in Physics went to Takaaki Kajita and Arthur B. McDonald for evidence of neutrino oscillations, following the 2002 prize shared by Davis and Masatoshi Koshiba (Wikipedia, "Solar neutrino problem"). Few astronomical puzzles have been settled this completely, and the solar interior's acoustic properties were a key piece of the argument. For the nuclear reactions that make the neutrinos, see how the Sun makes energy through fusion.

Local helioseismology and the far side of the Sun

Global helioseismology uses modes of the entire star. Local helioseismology instead studies how waves travel across a small patch of the surface, which allows three-dimensional flows and structures to be mapped. Several methods are used (Wikipedia, "Helioseismology"):

Method	What it measures	First used
Ring-diagram analysis	Fits power in a small patch (around 15° by 15°) to get local horizontal flow	Hill, 1988
Time-distance helioseismology	Travel times of wave packets between pairs of surface points, giving flows and sound-speed variations beneath	Duvall and colleagues, 1993
Helioseismic holography	Reconstructs the wave field below the surface from the surface signal	Lindsey and Braun
Direct modeling	Recovers near-surface flows from correlations in the frequency and wavenumber plane	Woodard, 2002

These techniques have mapped supergranulation (large convective cells tens of thousands of kilometers across), the slow poleward drift of material near the surface called meridional circulation, and flows beneath sunspots. In 1999, Donea, Braun, and Lindsey produced seismic images of a solar flare, showing that these methods can pick up the Sun's response to an eruption on its surface.

Seeing the back of the Sun

The best-known application is imaging the hemisphere facing away from us. Sound waves that cross the interior and return carry the imprint of whatever they passed beneath. Strong magnetic regions change how long waves take to travel, so a large active region on the far side shows up as a shift in travel time in the waves that come back to the near side. Braun and Lindsey published far-side imaging in 2001, and GONG now provides near-real-time seismic images of the far side (NSO).

The practical value is warning. A large sunspot group on the far side will rotate into view about two weeks later at the latest, since the Sun turns once in about a month. Forecasters therefore know in advance that a flare-producing region is on the way. Solar storms and space weather explains why that lead time matters for satellites and power grids.

Does the Sun's ringing change over the solar cycle?

It does. Mode frequencies shift as magnetic activity rises and falls, and the effect is measurable even in early data. Frequencies increase with solar activity, and the shifts correlate closely with changes in the strength of the surface magnetic field (Woodard and colleagues, 1991, cited in Basu, 2016). The effect appears chiefly in the outer layers, because the shifts behave like a function of frequency once mode inertia is accounted for, similar to the "surface term" error in the models. The 11-year solar cycle can therefore be tracked with sound alone, which provides an independent check on activity indices measured from the surface.

The same technique applied to other stars

Other stars cannot be resolved into spatial patterns, so only the lowest-degree modes can be detected, with angular degree up to about 3 in intensity measurements and about 4 in radial velocity. That is enough to do a good deal. The method is called asteroseismology, and it has grown with a series of space missions:

• MOST (launched 2003), the first spacecraft devoted to asteroseismology
• CoRoT (launched 2006), a French-led ESA mission
• Kepler (launched 2009), whose brightness data revealed oscillations in thousands of stars
• TESS (launched 2018), which surveys bright stars across most of the sky
• PLATO (ESA), planned for launch in 2027 with 26 cameras, to characterize planet-hosting stars

Sources: Wikipedia, "Asteroseismology"; ESA, "Plato."

Two measurements carry most of the weight. The large frequency separation, the spacing between modes of consecutive radial order, depends on the star's mean density: it is essentially a measurement of how long sound takes to cross the star. The small separation is sensitive to the composition gradient in the core and therefore to the star's age.

The red giants are the most dramatic case. Yu and colleagues (2018) characterized 16,094 oscillating red giants from Kepler data, with radii good to about 2.9 percent and masses to about 7.8 percent. In evolved stars some modes mix pressure and gravity-wave character and have a foot in the core, so they probe the interior in a way that is not possible for the Sun. This is the main reason the technique matters for dating stars in the Milky Way, and, since planets are measured relative to their stars, for characterizing exoplanets. See TESS and the search for worlds around nearby stars for how those planet surveys use stellar properties.

Pulsating stars with larger oscillations are older acquaintances. Variable stars such as Cepheids and RR Lyrae vibrate in much the same way, but in a few strong modes that are driven by a different mechanism and are easily seen.

What helioseismology cannot see yet

Three limits come up most often.

The core. Most helioseismic information comes from p modes, which pass through the core only briefly. Gravity modes, driven by buoyancy, would sample it directly, but their amplitude decays steeply through the convection zone, so they are tiny at the surface. García and colleagues (2007) reported a signal consistent with g modes in GOLF data, and Fossat and colleagues (2017) reported detecting them, but these claims have been challenged by Schunker and colleagues (2018) and by Scherrer and Gough (2019). As of the sources used here, no individual g mode has been unambiguously detected.

The outermost layers. High-degree modes are short lived and hard to separate, so the near-surface region is poorly constrained, and its modeling error contaminates the rest (the surface term).

The lack of a unique answer. Inversions give averages over a finite width, and the density result in particular changes when the low-degree mode set is improved. The sound speed is better known than the density.

Common confusions

• "The Sun produces sound we could hear." The oscillations are sound waves inside the Sun, with frequencies about four orders of magnitude below the audible range, and sound does not cross space.
• "Helioseismology looks inside with a telescope." It does not. It uses only light from the surface, and the interior information comes from the physics of how the waves must have traveled.
• "The Sun is a perfect sphere." It is nearly one, but rotation makes it very slightly oblate, and its oscillation frequencies carry the signature of rotation, magnetic fields, and flows.
• "The solar abundance problem means the models are broken." The models match the Sun well when given the older composition. The tension is about whether the surface composition measurements or the opacity physics are at fault.

Frequently asked questions

Q: What is helioseismology in simple terms? A: It is the study of the Sun's interior using the sound waves that make its surface oscillate. Astronomers measure the Doppler shifts of the surface, break the pattern into thousands of vibration modes, and use the frequencies of those modes to infer temperature, composition, and rotation at different depths.

Q: Can we actually hear the Sun? A: Not directly. The p modes have frequencies of roughly 1 to 5 millihertz, thousands of times below the lowest audible frequency, and sound cannot travel through space anyway. Sonifications speed the recorded oscillations up by large factors so that people can listen to them.

Q: How deep into the Sun can helioseismology see? A: Inversions of p-mode data are reliable from about 0.05 to 0.96 of the solar radius, so they reach close to the core but not the very center. The very deepest part of the core, and its rotation, are constrained mostly by low-degree modes and remain uncertain.

Q: How did helioseismology help solve the solar neutrino problem? A: It showed that sound speed in the Sun's core matches standard models closely. A cooler core, which would have explained the missing neutrinos, would have changed the core sound speed by about 10 percent, which the observations rule out. That shifted attention to neutrino oscillations, later confirmed by the Sudbury Neutrino Observatory.

Q: What is the tachocline? A: It is a thin shear layer, roughly 0.04 solar radii thick, at or just below the base of the convection zone, where rotation changes from latitude dependent (above) to nearly rigid (below). Many models of the solar dynamo use it to build strong magnetic fields, although its exact role is still debated.

Q: Has helioseismology detected g modes? A: Claims have been made, including by García and colleagues (2007) and Fossat and colleagues (2017), but they have been challenged, and no individual g mode has been unambiguously detected. Confirming them would give a direct view of the core.

The takeaway

The Sun's interior is out of reach of any telescope, yet it can be measured the way a luthier measures a bell, by listening to how it rings. A few decades of continuous observation have turned small shifts in surface velocity into a profile of sound speed, a measurement of the convection zone's base to better than a thousandth of the solar radius, and a rotation map that no model had predicted. The same measurements ruled out a cooler core and handed the neutrino deficit to particle physics.

What remains open is just as instructive. The surface composition and the interior structure do not yet fit together without a fix, the core's rotation is uncertain, and the g modes that would settle it have not been confirmed. Each of those questions is now being worked on from two directions, with better spectra and opacity data on one side and longer and more sensitive oscillation records on the other.

Sources

• Basu, S. (2016). "Global seismology of the Sun." Living Reviews in Solar Physics 13, 2. arXiv:1606.07071
• Asplund, M., Amarsi, A. M., and Grevesse, N. (2021). "The chemical make-up of the Sun: A 2020 vision." Astronomy & Astrophysics. arXiv:2105.01661
• Magg, E., and colleagues (2022). "Observational constraints on the origin of the elements IV." Astronomy & Astrophysics. arXiv:2203.02255
• Yu, J., and colleagues (2018). "Asteroseismology of 16,000 Kepler red giants: global oscillation parameters, masses, and radii." arXiv:1802.04455
• NASA, SOHO mission overview: soho.nascom.nasa.gov/about/about.html
• NSO, Global Oscillation Network Group: nso.edu/telescopes/nisp/gong
• ESA, Plato mission: esa.int/Science_Exploration/Space_Science/Plato
• Wikipedia, "Helioseismology", "Tachocline", "Solar neutrino problem", "Standard solar model", "Global Oscillation Network Group", and "Asteroseismology", used for dates and for the primary references each page cites.

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