Runaway Greenhouse Limit | mysimulator.uk

Orbit & Star

Orbital distance 1.00 AU

Host-star luminosity 1.00 L☉

Planet

Bond albedo 0.30

Greenhouse-gas loading 1.0×

Energy Balance

STABLE

Absorbed flux S

–

OLR ceiling

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Equilibrium T

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Runaway edge

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How it works

A planet is stable when the starlight it absorbs equals the thermal radiation it emits to space (outgoing longwave radiation, OLR). For a moist, water-vapor-rich atmosphere this balance is not simple blackbody cooling — as the surface warms, more water evaporates, and that water vapor becomes so opaque in the infrared that the emitting layer rises in the atmosphere and its temperature stops tracking the surface. The result is the Simpson–Nakajima limit: OLR saturates near a fixed ceiling (≈282 W/m² for a CO₂-free atmosphere) no matter how hot the surface gets.

S(d) = L·S₀/d² · (1−A)/4      absorbed flux (global average)
OLR(T) = OLR_max·(1 − exp(−σT⁴ / OLR_max))
OLR_max = 282 − 25·(CO2 loading)   [W/m²]

Equilibrium exists only if S < OLR_max:
  T_eq = [ −OLR_max/σ · ln(1 − S/OLR_max) ]^(1/4)

If S ≥ OLR_max: no equilibrium — runaway greenhouse.

Orbital distance / luminosity — set the absorbed stellar flux S via the inverse-square law.
Albedo — reflected sunlight never enters the balance; higher albedo lowers S.
Greenhouse-gas loading — extra CO₂ adds opacity beyond what water vapor already saturates, pulling the OLR ceiling down and shrinking the safety margin.
Once S crosses OLR_max there is no stable surface temperature — this is the physical inner edge of the habitable zone (Kasting 1988; Kopparapu et al. 2013).

Ocean world Steam atmosphere Runaway / molten

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