Live Stellar Oscillation and
Asteroseismic Inference Console
Live power spectrum synthesis with Harvey-profile granulation background, oscillation envelope, and Tassoul asymptotic p-mode pattern. Echelle diagram visualization with l=0,1,2,3 mode identification. Autocorrelation extraction of the large frequency separation. Scaling relation inference of stellar mass, radius, mean density, and surface gravity for the Kepler LEGACY sample, the Sun, 16 Cygni A and B, and selected red giants.
Overview
Asteroseismology is the study of stellar interiors through the analysis of stellar oscillations. Stars ring like bells. Acoustic pressure waves (p-modes) and buoyancy gravity waves (g-modes) propagate inside, with each mode probing a different depth. By measuring the frequencies of these modes at the surface we infer the mass, radius, age, and internal structure of the star without resolving it.
SEIS-01 implements the standard pipeline: synthesize a power spectrum with realistic granulation, white noise, and an oscillation envelope; identify the comb of solar-like p-modes via the Tassoul asymptotic relation; extract the large frequency separation by autocorrelation; and convert the global oscillation parameters into stellar mass and radius via the Kjeldsen-Bedding 1995 scaling relations.
Targets are drawn from the Kepler LEGACY sample (Lund et al. 2017), supplemented by the Sun (the only star whose oscillations have been measured to picohertz precision) and a representative red giant. All numerical work runs in Float64. Frequencies are reported in microhertz (uHz). One day of continuous observation gives a frequency resolution of about 11.6 uHz; four years of Kepler data resolves to about 8 nHz.
Quick Start
Guided Workflows
Workflow A :: Solar Twin Identification
Target: The Sun. The reference for every scaling relation in the field.
Workflow B :: Solar Analog Mass and Age
Target: 16 Cyg A. The brightest solar analog asteroseismic target. Its companion 16 Cyg B is the second brightest.
Workflow C :: Red Giant Branch
Target: KIC 4448777. A first-ascent red giant with mixed modes.
Tab Guide
Targets
Catalog of confirmed asteroseismic targets. Click a card to load it. The summary panel shows host parameters from the literature: effective temperature, surface gravity, metallicity, Kepler magnitude, and the asteroseismic globals nu_max and Delta_nu. Loading a target synthesizes a fresh power spectrum.
Power Spectrum
Two stacked plots:
- Power Spectral Density - power versus frequency in uHz on linear axes. The granulation background slopes from low frequencies, the oscillation envelope rises near nu_max, individual modes appear as Lorentzian peaks.
- Autocorrelation - ACF of the spectrum versus frequency lag. The first peak above lag zero marks Delta_nu. Subsequent peaks at 2 Delta_nu, 3 Delta_nu confirm the comb structure.
Echelle
The mode comb folded modulo Delta_nu produces vertical ridges by spherical degree l. l=0 forms the principal ridge; l=2 sits just to its left at offset delta_nu_02 (sensitive to the core); l=1 sits near the centre of the diagram offset by Delta_nu/2; l=3 is faint and adjacent to l=1.
Inference
Slider-driven scaling relation calculator. Adjust nu_max, Delta_nu, and Teff. The console reports inferred mass, radius, mean density, and surface gravity in real time alongside the catalog values for the loaded target.
Stack
Runtime probe of every capability the module can leverage. OK means available. FALLBACK means a graceful CPU substitute is active.
Method
Mathematical and algorithmic documentation with citations.
Controls Reference
| Control | Tab | Action |
|---|---|---|
| EXTRACT DELTA NU | Power Spectrum | Compute autocorrelation of the oscillation region; first peak gives Delta_nu. |
| INJECT NOISE | Power Spectrum | Multiply white noise floor by 1.5x. Tests detection robustness. |
| RESET | Power Spectrum | Regenerate the original synthetic spectrum. |
| l=0 / l=1 / l=2 / l=3 | Echelle | Toggle visibility of each spherical degree on the diagram. |
| nu_max slider | Inference | Frequency of maximum power (uHz). Solar value 3090. |
| Delta_nu slider | Inference | Large frequency separation (uHz). Solar value 135.1. |
| Teff slider | Inference | Effective temperature (K). Solar value 5777. |
| SCALING | Inference | Apply Kjeldsen-Bedding 1995 to derive mass and radius. |
Reading the Plots
Power Spectrum
From low to high frequency: a steep activity slope, a flatter granulation plateau, the bell-shaped oscillation envelope centred at nu_max, then white photon noise. Inside the envelope individual modes appear as Lorentzians whose widths reflect mode lifetimes (about 1 uHz for the Sun, narrower for cooler stars).
Echelle Diagram
Frequency on the y-axis, frequency mod Delta_nu on the x-axis. The same star produces stacked horizontal slabs each Delta_nu wide. Modes of the same degree align into vertical ridges. Curvature in a ridge indicates departure from the asymptotic relation - on the upper main sequence this is small; on the red giant branch the l=1 ridge twists into a characteristic mixed-mode pattern caused by coupling between the acoustic envelope and the gravity-mode core cavity.
Autocorrelation
Plot of ACF versus frequency lag. A clean solar-like spectrum gives a peak train at Delta_nu, 2 Delta_nu, 3 Delta_nu and so on. The first peak position is the most reliable estimate. For evolved stars mixed modes can introduce additional structure.
Troubleshooting
- Echelle ridges look scrambled or non-vertical
- Delta_nu is wrong. Try the EXTRACT DELTA NU button to recover it from the autocorrelation, or move the slider in the Inference tab until the ridges align.
- Inferred mass differs from catalog by more than 5 percent
- Either Teff is off, or the scaling relations are being pushed outside their calibrated regime (very hot stars, very evolved giants). Check the Teff input.
- Autocorrelation peak is faint
- Either the spectrum is dominated by white noise (press RESET) or the oscillation envelope falls outside the autocorrelation window. The console restricts ACF to the envelope plus or minus 2 sigma.
- Spectrum looks flat with no envelope
- For very evolved or very hot stars the envelope can be subtle. Switch to a main-sequence target like 16 Cyg A first to verify the pipeline.
- Stack tab shows WebGPU FALLBACK
- Browser does not advertise WebGPU yet, or the host page lacks COOP/COEP headers. The CPU path is fully functional and produces identical results.
Scientific References
The implementations in this console follow the original publications and are validated against published parameters.
- Tassoul 1980 - Asymptotic Approximations for Stellar Nonradial Pulsations. ApJS 43 469. Source for the asymptotic relation between p-mode frequencies, n, and l.
- Kjeldsen and Bedding 1995 - Amplitudes of stellar oscillations: the implications for asteroseismology. A&A 293 87. Source for the scaling relations between nu_max, Delta_nu, Teff and stellar M, R.
- Brown et al. 1991 - Detection of possible p-mode oscillations on Procyon. ApJ 368 599. Original empirical scaling relation.
- Stello et al. 2009 - The relation between Delta_nu and nu_max for solar-like oscillations. MNRAS 400 L80. Derivation of the Delta_nu vs nu_max power-law.
- Mosser et al. 2010 - The universal red-giant oscillation pattern. A&A 525 L9. Reference for the asymptotic mode pattern in red giants.
- Bedding et al. 2011 - Gravity modes as a way to distinguish between hydrogen- and helium-burning red-giant stars. Nature 471 608. Mixed-mode period spacing.
- Lund et al. 2017 - Standing on the Shoulders of Dwarfs: the Kepler asteroseismic LEGACY sample. ApJ 835 172. Source for all main-sequence target parameters in this catalog.
- Harvey 1985 - High-precision velocity measurements of very low-l solar oscillations. Source for the granulation profile.
- Sharma et al. 2016 - Stellar Population Synthesis Based Modeling of the Milky Way Using Asteroseismology of 13000 Kepler Red Giants. ApJ 822 15. Corrections to the scaling relations.
Glossary
| Asteroseismology | The study of stellar interiors through stellar oscillations. |
| p-mode | Pressure mode. Acoustic standing wave; pressure is the restoring force. |
| g-mode | Gravity mode. Standing wave restored by buoyancy. Confined to radiative interior of low-mass stars. |
| f-mode | Fundamental mode. Surface gravity wave with no radial node. |
| Mixed mode | Hybrid p-g mode in evolved stars. Probes the core directly. |
| nu_max | Frequency of maximum oscillation power. Scales as g/sqrt(Teff). Solar value 3090 uHz. |
| Delta_nu | Large frequency separation. Spacing between consecutive radial overtones of same l. Scales as sqrt(rho). Solar value 135.1 uHz. |
| delta_nu_02 | Small frequency separation. Distance between l=0 and l=2 modes of consecutive n. Sensitive to core hydrogen abundance. |
| epsilon | Phase term in the asymptotic relation. Around 1.4 for the Sun. |
| l, n, m | Spherical degree, radial order, azimuthal number of a mode. |
| Echelle diagram | Mode frequency plotted versus (frequency mod Delta_nu). Reveals ridges by l. |
| Granulation | Convective surface motion. Produces a Harvey-profile background in the power spectrum. |
| uHz | Microhertz. 10^-6 Hz. Standard frequency unit in asteroseismology. |
| LEGACY | The 66 best-characterized main-sequence and subgiant Kepler targets (Lund et al. 2017). |
| RGB | Red Giant Branch. First post-main-sequence ascent. |
All numerical results carry a provenance hash recording the asymptotic relation, scaling relation, solar reference values, and target catalog used to produce them. Manifest is persisted to IndexedDB for cross-session reproducibility.
- Solar reference: nu_max = 3090 uHz, Delta_nu = 135.1 uHz, Teff = 5777 K
- Asymptotic: Tassoul 1980 with epsilon from White et al. 2011
- Scaling: Kjeldsen-Bedding 1995 in standard form
- Background: Harvey 1985 super-Lorentzian granulation profile
- Target values: Lund et al. 2017 LEGACY sample, IAU 2015 nominal solar values
Tassoul Asymptotic Relation
For high radial order n the p-mode frequencies follow nu_n,l = Delta_nu (n + l/2 + epsilon) - l(l+1) D0 + O(1/n). The console implements this with a White et al. 2011 calibration of epsilon against Delta_nu and a small separation delta_nu_02 = 6 D0 empirically fit to the LEGACY sample.
Granulation Background
The Harvey 1985 profile parametrises convective granulation as a super-Lorentzian P_g(nu) = 4 sigma^2 tau / [1 + (2 pi nu tau)^c] with c = 4. The timescale tau and amplitude sigma scale with nu_max as tau prop nu_max^-0.89 and sigma prop nu_max^-0.45 following Kallinger et al. 2014.
Oscillation Envelope
The total oscillation power is concentrated in a Gaussian envelope centred at nu_max with FWHM 0.66 * nu_max^0.88 uHz (Mosser et al. 2010). Individual mode amplitudes follow this envelope; mode visibilities are V0 = 1.0, V1 = 1.50, V2 = 0.53, V3 = 0.03 (Ballot et al. 2011).
Mode Profile
Each mode is rendered as a Lorentzian with FWHM Gamma. For solar-like dwarfs Gamma is around 1 uHz; for evolved subgiants it narrows to 0.1 uHz reflecting longer mode lifetimes. The console uses Gamma = 1 uHz for all main-sequence targets and 0.3 uHz for red giants.
Autocorrelation Extraction
The large frequency separation is recovered by computing the autocorrelation function of the oscillation region (nu_max plus or minus 2 sigma_env). The first peak above lag zero gives Delta_nu. The console restricts the search range to plus/minus 30 percent of the catalog Delta_nu to avoid spurious peaks at half or twice the true value.
Scaling Relations
The Kjeldsen-Bedding 1995 relations connect global oscillation parameters to stellar M and R via
M/Msun = (nu_max/nu_max_sun)^3 * (Delta_nu/Delta_nu_sun)^-4 * (Teff/Teff_sun)^1.5
R/Rsun = (nu_max/nu_max_sun) * (Delta_nu/Delta_nu_sun)^-2 * (Teff/Teff_sun)^0.5
with solar references nu_max_sun = 3090 uHz, Delta_nu_sun = 135.1 uHz, Teff_sun = 5777 K. Mean density and surface gravity follow as derived quantities. For very evolved giants a few-percent correction (Sharma et al. 2016) is required; the console reports the uncorrected value.
Compute Pipeline
Power spectrum synthesis, mode placement, autocorrelation, and scaling-relation evaluation all dispatch through Float64 buffers. State vectors are held in Float64Array views. Where the runtime advertises WebGPU and SharedArrayBuffer the autocorrelation kernel is offloaded to a WGSL compute shader operating on Float64-emulated buffers; otherwise a CPU loop executes inline.