Solar flare CME - 2D Sun-Earth plane

Drag-based coronal mass ejection transit to Earth with shock pressure and magnetopause compression.

Switch to 3D

Presets

Playback

Parameters

Model checks

The science

Drag-based CME propagation

Beyond a few solar radii a coronal mass ejection is pushed and pulled by the ambient solar wind: dv/dt = -γ (v - w) |v - w| with wind speed w and drag parameter γ (typically 0.1-0.3 × 10-7 km-1). For v>w the distance has a closed form r(t) = r0 + ln(1 + γ(v0 - w)t)/γ + w t, which the page checks against a numerical RK4 integration. Fast CMEs decelerate and slow ones are carried up to the wind speed, so arrival times are not simply 1 AU / v.

Does it hit Earth?

The ejection is a cone of half-width β; Earth is hit when the direction offset is smaller than β (a flat 2D cut of the real 3D geometry, so the true longitude-latitude geometry is simplified).

Shock, pressure, magnetosphere

The shock compression follows the Rankine-Hugoniot jump for a fast-mode shock, bounded by 4 for a monatomic gas. Solar-wind dynamic pressure Pd = mp n v2 squeezes the dayside magnetopause: r0 = (10.22 + 1.29 tanh(0.184 (Bz + 8.14))) Pd-1/6.6 Earth radii (Shue et al. 1998 form).

Honest simplifications: the 3D page animates a stylised cloud; here the CME is one cone in the ecliptic plane with a constant γ, a Gaussian-shaped sheath pressure pulse of about 10 h, and a rough illustrative storm-level index that is not an operational forecast. Real forecasting needs measured Bz inside the ejecta.

What to try
  • Launch the "Fast halo" preset and compare its drag deceleration with the "Slow CME" which accelerates toward 400 km/s.
  • Move the direction offset beyond the half-width to see a miss.
  • Set gamma to 0.02: the front becomes nearly ballistic and the numeric curve matches r0 + v t.
  • Make Bz more negative and see the magnetopause shrink during the pressure pulse.
CME front distance vs time
CME speed vs ambient wind
Pressure and magnetopause at Earth