Sounds of Stars Script (Patreon)

Twinkle twinkle little star, how I wonder about your interior structure and dynamical properties. Believe it or not, we can now map the interiors of stars by “listening” to their harmonies as they vibrate with seismic waves.

Stars are among the best understood objects in astrophysics. This is impressive given the fact that they’re impossibly distant opaque balls of fiery plasma. Yet mathematical models emerged in the early 1900s that describe the balance between gravitational crush and the outward flow of energy from the fusion reactions in the core, These equations of hydrostatic equilibrium allow us to calculate things like the density and temperature of the core, the way energy flows to the surface, and even the lifespan of stars. These models are largely built around what little we can learn from the light we receive directly from the surface of stars. But how do we test these models if we can never see beneath those surfaces? We may not see light from beneath the stellar surface, but another type of wave travels freely throughout stars. I’m talking about seismic waves.

See, stars have a dynamical complexity far exceeding the simplest predictions of hydrostatic equilibrium. They resonate. Vast waves reflect around stellar interior, setting up global oscillations - natural resonant frequencies that carry information about stars’ impenetrable interiors. Stars ring like bells. And although we can’t hear this resonant vibration directly we can see its effect in the changing brightness and motion of the stellar surface. The fast growing field of asteroseismology uses these oscillations to probe the interiors of the distant stars. 

When we try to understand other stars we always start with our sun. While the distant stars are infinitesimal points of light to even our best telescopes, the surface of the sun can be resolved in incredible detail. The effects of seismic activity can be mapped across its surface. Understanding asteroseismology starts with understanding helioseismology. Actually, back up. Understanding helioseismology starts with regular old seismology on Earth - geoseismology. On Earth, seismic waves are generated by earthquakes and can travel around the planet as longitudinal pressure or P-waves, transverse shear or S-waves and surface waves which are a mixture of P- and S-waves.

Stars also support P-waves. These are true sound waves that echoing around their interiors. Because stars are fluid rather than solid they don’t support shear waves. However they do support two types of gravity waves. These are NOT gravitational waves - gravity waves result from the restoration of gravitational equilibrium - when some material is moved from its prefered depth, buoyancy forces try to push it back into place. In stars, these waves occur below the surface - G-waves - and on the surface - F-waves. The latter are closely analogous to ocean surface waves on Earth.

However it’s the pressure waves - the P-waves that really dominate in stars like the Sun. These acoustic waves are generated by turbulence just below the surface of a star; just as seismic waves on Earth are created by earthquakes just below the surface in the lithosphere. They start as traveling waves that can move throughout the stars inner structure. However, just as a single tap can set an entire bell ringing, a single traveling wave feeds its energy into  standing pressure waves that cause the entire star to vibrate. These P-mode oscillations follow the rules of spherical harmonics, taking the form of regular patterns of density oscillation throughout the star. The distribution of the pattern depends on the frequency - the mode - much like on the skin of a drum. Many modes vibrate at once, overlapping in a complex structure of resonance. The strongest oscillations are in the 2-4mHz range - these are the Sun’s 5-minute oscillations.

So what does this look like? For the sun we can map these oscillations in two ways: changes in brightness and changes in velocity. Brightness of spectral lines in the Sun’s atmosphere can change by around 1 part per million over the course of an oscillation; at the same time gas moves vertically in and out during the same oscillation, reaching velocities of 0.1 m/s. This can be detected in the Doppler shift of spectral lines. Because many different modes overlap, the complex, overlapping effects of these oscillations are separated using Fourier analysis. We’ve spoken already in depth about Fourier analysis in our recent episode on understanding the uncertainty principle so I won’t go into too much detail here. In short, the many overlapping modes form complex oscillations on the surface of a star. These can be deconstructed into simple sinusoidal oscillations, each of which corresponds to an individual mode resonating throughout the star.

Helio- and asteroseismology is all about determining and modeling the resonant modes within a star. See, the nature of these modes depends on the internal structure; specifically on how the speed of sound changes throughout the star, which in turn depends on the stratification of temperature, density, composition. The internal rotation of the star is also a key factor. Helioseismology has allowed us to verify and improve the models of the Sun’s internal structure. They have also revealed new things: for example, that the inner radiative zone rotates almost like a solid ball, while and outer convective zone rotates at different speeds depending on latitude. This differential rotation powers the Sun’s magnetic field, and is also responsible for twisting that magnetic field to drive the sunspot cycle. 

Helioseismology has also allowed us to measure the composition of the core, which tells us how much of the Sun’s hydrogen fuel source has already been turned into helium. In this way it has revealed that our Sun is currently around halfway through its 10 billion year lifespan; which is consistent with age-dating of the oldest meteorites.

Observations of the Sun’s surface are relatively easy. Seismological studies of the distant stars - asteroseismology - is much more difficult. They're too far away to resolve their surfaces, so we only on the global effects of their oscillations. The Doppler shifts due to local moving gas are completely washed out. However there is a global flickering - tiny changes in overall brightness that can allow us to figure out the strongest resonant modes. Those modes allow us to determine fundamental properties like radius, mass, density, and surface gravity. In red giant stars, asteroseismology has been used to determine the fusion activity in their dying cores, allowing us to learn just how close these stars are to their last flicker.

But asteroseismology is hard. To see that faint flickering we have to go to space. The Canadian MOST and French COROT satellites pioneered this work, while Kepler does asteroseismology as a side gig to finding alien planets. Future planet-hunting satellites like TESS and PLATO will continue this work with higher precision and for many more stars.

Most stellar seismology is focused on learning about the average, global structure of stars. But at least for the Sun, it’s possible to learn about current, local events that are hidden from our view. For example, we can map currents of plasma and density fluctuations as they shift beneath the solar surface. In helioseismic holography, the visible wavefield - so the distribution of Doppler velocities across the visible surface - is used to infer the current state of the standing waves throughout the Sun. That includes the far side of the sun. In fact helioseismic holography is capable of detecting sun spots long before the Sun rotates them into visibility. This can give us advance warning of potentially dangerous solar activity. 

Stars sing. Their harmonies are hidden in their flickering light and in the subtle in-out breathing of their surfaces. Woven into that music is knowledge of their mysterious depths, and of their pasts and futures. We’re only now learning to decipher the complex overlay of tones in stellar oscillations. We’re learning their lyrics. Twinkle, twinkle little star, and in doing so give up your secrets. Because the science of asteroseismology can now translate the messages of stars twinkling at us from across space time.