EMRI Orbits

Interactive 3D visualization of Extreme Mass Ratio Inspirals (EMRIs) — a stellar-mass compact object spiraling into a massive Kerr black hole — together with the source-frame gravitational-wave strain it emits.

The orbital evolution and waveform are computed live in the browser using the Analytic Kludge (AK) of

Barack & Cutler, "LISA capture sources: Approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy", Phys. Rev. D 69, 082005 (2004). arXiv:gr-qc/0310125

Run it

It's a single HTML file — no build, no server.

open index.html        # macOS
xdg-open index.html    # Linux

Or drop it on any static host (GitHub Pages, S3, etc.).

What it does

• Integrates the AK orbital ODEs for (Φ, ν, e, γ̃, α) with RK4 (Eqs. 27–31 of the paper).
• Computes source-frame h₊ and h_× from the Peters–Mathews quadrupole harmonic sum (Eqs. 7–10), with a numerically stable Bessel J_n via Miller's downward recurrence and a bucketed harmonic count (6 → 60, depending on eccentricity).
• Renders the orbit in 3D with Three.js: Kerr horizon, equatorial ISCO ring, spin axis Ŝ, orbital angular momentum L̂ (precessing around Ŝ).
• Shows the modern Kerr-EMRI parameters: p/M, e, cos ι, and the three fundamental frequencies f_r, f_θ, f_φ.

Controls

• Presets: Generic Kerr, Spherical Kerr (inclined circular), High-e generic, Near plunge.
• System: MBH mass, CO mass.
• Initial orbit: spin a/M, semi-latus rectum p₀/M, eccentricity e₀, inclination ι.
• Animation: time speedup (×10 to ×100,000), play/pause, reset, freeze inspiral (hold orbital elements; orbit keeps cycling — useful at high e where the system would otherwise plunge in seconds of viz time).
• View: snap to side / top-along-Ŝ / plane-of-sky; toggles for trail, L̂, Ŝ, ISCO ring.

Caveats

• Source-frame strain only — no LISA detector response (Eqs. 11–17 not included).
• ISCO ring uses the closed-form Kerr equatorial-prograde formula; for inclined or eccentric orbits the true LSO differs slightly.
• Pericenter angle in the waveform uses γ ≈ γ̃ (skips the observer-dependent β term in Eq. 21); visually negligible.
• Near plunge the AK breaks down; the animation auto-freezes the slow elements rather than letting the integrator blow up.

Author

Daniel Oliver. Built with assistance from Claude Code.