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The science
X-ray classes and statistics
GOES soft X-ray classes label the peak flux at 0.1-0.8 nm: A, B, C, M and X are 10−8, 10−7, 10−6, 10−5 and 10−4 W/m², so an M5 flare is 5×10−5. Flare peak fluxes follow a power law dN/dF ∝ F−α with α ≈ 1.8; the sampler draws F = Fmin (1 − u)−1/(α−1) and the maximum-likelihood estimate α = 1 + n / ∑ ln(F/Fmin) recovers it. The largest flare is capped by the free magnetic energy stored in the region.
Neupert effect and CMEs
The soft X-ray flux follows the time integral of the hard X-ray burst, dS/dt = H(t) − S/τ, so its derivative reproduces the hard X-ray shape. A coronal mass ejection leaving at speed v needs t = 1 AU / v to reach Earth: 41.6 hours at 1000 km/s. The storm level Kp is a crude function of speed and flare class.
Honest simplifications: a single active region, flares drawn as independent Poisson events, a hand-tuned flare-CME association, constant CME speed (no aerodynamic drag), no magnetic polarity or Bz dependence, and illustrative Kp scaling. Educational physics only; not a space-weather forecast.
What to try
- Press Quiet Sun versus Solar maximum and compare the record and the log-log counts.
- Press Flares, no CMEs: the aurora never appears.
- Raise free magnetic energy to allow bigger X-class flares.