A hot Jupiter orbiting a few stellar radii from its star absorbs intense extreme-ultraviolet (XUV) radiation. That energy heats the upper atmosphere until thermal + bulk kinetic energy exceeds the gravitational binding energy, driving a hydrodynamic "planetary wind" — the atmosphere doesn't just leak, it flows off the planet like a rocket exhaust, escaping most easily through the day-side substellar point where the star's own gravity partially cancels the planet's.
The escape rate is commonly estimated with the energy-limited formula (Watson et al. 1981; Erkaev et al. 2007):
Ṁ = ε · π · R_p³ · F_XUV / (G · M_p · K_tide)
F_XUV = L_XUV / (4π a²) — XUV flux at the planet
K_tide = 1 − 3/(2ξ) + 1/(2ξ³) — Roche-lobe correction, ξ = R_Roche / R_p
R_Roche = a · (M_p / 3M★)^(1/3) — Roche lobe radius
ε is the fraction of absorbed XUV energy that goes into unbinding gas rather than radiating away (typically 0.1–0.3). Ktide < 1 because the star's gravity shrinks the planet's effective Roche lobe, making it easier to blow atmosphere off — closer orbits and lighter planets push Ktide toward zero, exactly where real ultra-hot Jupiters like WASP-12b sit.
- Orbital distance — sets both F_XUV (∝ 1/a²) and the Roche lobe size; closer orbits dramatically increase escape.
- Planet mass — a deeper gravitational well (larger M_p) suppresses Ṁ and raises K_tide toward 1.
- Stellar XUV activity — young, active stars emit far more XUV than the present Sun; this multiplies F_XUV.
- Heating efficiency ε — how effectively absorbed XUV photons convert into escaping gas versus radiative cooling/losses.
The particle stream you see is not just launched outward: each particle is integrated under the star's real gravity (same 1/r² law as the planet's own orbit). Escaping gas starts with roughly the planet's orbital velocity but drifts to larger radii, where Kepler's third law says the local orbital speed is slower — so the gas lags behind the planet's orbital motion and gets sheared into a trailing, comet-like tail, exactly as observed in Lyman-α and Hα transit spectroscopy of real evaporating hot Jupiters (e.g. HD 209458b, WASP-107b, GJ 3470b).