Measure stellar oscillation frequencies and apply scaling relations—infer mass, radius, and age from asteroseismic data
Stellar oscillations reveal interior structure. The large frequency separation Δν measures the sound travel time across the star. The frequency of maximum power νmax reflects the acoustic cutoff frequency.
Asteroseismology is the study of stellar oscillations—acoustic waves that cause stars to pulsate. Solar-like oscillators exhibit stochastic oscillations driven by surface convection, similar to how the Sun rings like a bell. By measuring oscillation frequencies, we can precisely determine stellar masses, radii, and ages—properties that are otherwise difficult to measure for distant stars.
Stellar oscillations form a comb pattern in frequency space. The spacing between consecutive radial overtones (modes with the same angular degree l but different radial order n) is called the large frequency separation Δν. This quantity measures the sound travel time across the stellar diameter:
Δν ≈ (2 ∫0R dr/cs)-1 ∝ √(ρ̄) ∝ √(M/R³)
For the Sun, Δν☉ ≈ 135 μHz. Red giants have much larger radii and lower mean densities, so their Δν values are much smaller (1–10 μHz). This makes Δν a powerful diagnostic of stellar evolution.
Oscillation modes are not uniformly excited. There is a peak in the power spectrum envelope at a characteristic frequency νmax, which corresponds roughly to the acoustic cutoff frequency where waves transition from standing to evanescent. This frequency scales as:
νmax ∝ g/√Teff ∝ M/(R² √Teff)
For the Sun, νmax,☉ ≈ 3100 μHz. Combining Δν and νmax allows us to determine both mass and radius independently.
By normalizing to solar values, we obtain the empirical scaling relations:
These relations are remarkably accurate (typically ~3% in radius, ~7% in mass) and have been calibrated against eclipsing binaries and asteroseismic models. They work across a wide range of stellar types, from main-sequence stars to red giants.
When oscillation frequencies are folded modulo Δν (that is, plotted as ν mod Δν versus ν or n), modes of different angular degree l align in vertical ridges. This échelle diagram makes the overtone structure visually clear and helps identify mode identifications. Modes with l = 0 (radial), l = 1 (dipole), and l = 2 (quadrupole) form distinct ridges separated by small frequency offsets due to near-surface effects.
Solar oscillations were first detected in the 1960s and led to the field of helioseismology, which mapped the Sun's interior structure with exquisite detail. The extension to other stars became practical with space missions like CoRoT (2006), Kepler (2009), and TESS (2018), which provide the continuous, high-precision photometry needed to detect micromagnitude brightness variations from oscillations. Today, asteroseismology is a cornerstone of stellar astrophysics, providing "earthquakes" for distant stars.