Charged particles in the solar wind carry a frozen-in magnetic field. When it points south (negative Bz) it partially cancels Earth's own northward field at the dayside magnetopause, letting the two reconnect and funnel solar-wind energy into the magnetosphere — the same E = v×B induction that makes a moving-conductor electric field:
Bs = max(0, −Bz) southward component (nT)
Em = V · Bs × 10⁻³ merging electric field (mV/m)
Pdyn = 1.6726×10⁻⁶ · n · V² solar-wind dynamic pressure (nPa)
From that coupling, an approximate Kp index and auroral-oval equatorward boundary (both simplified, empirically-shaped fits — not the official NOAA model) drive what you see:
Kp ≈ clamp(0..9, 1 + 7·(1 − e^(−Em/3)))
φ_b ≈ clamp(40..70°, 67 − 2.2·Kp) oval boundary, geomagnetic latitude
Faster, more energetic electrons penetrate deeper into the atmosphere before colliding with oxygen and nitrogen, so the characteristic precipitation energy sets the emission altitude and hence the colour — a real, well-established relationship:
Ep ≈ clamp(0.5..15 keV, 1 + 0.02·(V−300) + 3·Em)
h ≈ clamp(90..250 km, 250 − 12·Ep)
h < 120 km → blue-violet (N2⁺, 427.8 nm)
120–180 km → green (atomic O, 557.7 nm)
h > 180 km → red (atomic O, 630.0 nm)
- Side panel (main view) — solar-wind particles stream in along field lines and collide at the computed altitude, building a persistent coloured curtain.
- Polar inset — the auroral oval expands equatorward as Kp rises; the observer dot turns green when their latitude falls inside the oval.