This 2D companion runs the identical torsional shear-mode ring-down physics as the 3D crust view, but instead of rendering a lattice of patches on a rotatable sphere, it unrolls the crust onto a flat latitude (vertical) × longitude (horizontal) strip map — the same equirectangular projection seismologists use to plot a planet's surface wavefield — and pairs it with a live scrolling seismogram trace, exactly the kind of strip-chart record a real X-ray timing instrument produces. Neither panel is a camera view of a 3D scene; both are 2D-native data representations of the same field.
Shear wave speed: v_s = √(μ / ρ)
Fundamental (n=0) toroidal mode:
f_ℓ ≈ (v_s / 2πR) · √(ℓ(ℓ+1) − 2), ℓ = 2,3,4,…
Ring-down: A(t) = A₀ e^(−t/τ) sin(2π f_ℓ t), τ = Q / (π f_ℓ)
Surface field: u(θ,t) = A(t) · P_ℓ(cos θ) (tangential, φ-independent, m=0)
The strip map colors every (θ, φ) patch by the signed tangential displacement u(θ,t) and draws short horizontal arrows showing the azimuthal shear motion; because the real mode is axisymmetric (m=0), the pattern is identical across every column (longitude) at a given time and only varies with row (latitude) — so the map shows the same ℓ-node standing-wave rings as the 3D sphere, just unrolled flat. The seismogram panel plots u at the equator (θ=90°) against time on a scrolling strip, the same way a magnetar's real X-ray flux ring-down is read off a light curve to recover f_ℓ and τ (Israel et al. 2005; Watts & Strohmayer 2006, SGR 1806-20).
- ℓ buttons — pick the standing-wave pattern; the strip map redraws the row-wise |Pℓ(cos θ)| node structure immediately.
- Crust rigidity μ — a stiffer crust carries shear waves faster, raising the frequency for every ℓ (same v_s and f_ℓ formulas as the 3D version).
- Damping Q — sets how many cycles the ringing survives; higher Q rings longer, both on the map and the seismogram.
- Trigger Starquake — injects the impulsive kick and starts the exponentially-decaying ring-down on both panels simultaneously.
Real-world relevance: this is the mechanism behind the quasi-periodic oscillations (QPOs) discovered in the X-ray afterglow of the 27 December 2004 giant flare from SGR 1806-20 — frequencies near 18, 30, 92 and 150 Hz were read as direct seismograms of a neutron star crust, the first asteroseismology ever performed on a magnetar.