Chaotic winds from a dying world: a one-dimensional map for evolving atmospheres

Planets which are smaller than Mercury and heated to sublimation temperatures of $\sim$2000 K lose mass catastrophically in dusty evaporative winds. The winds are observed to gust and recede largely without pattern; transit depths from the Kepler mission vary randomly from orbit to orbit by up to a factor of 10 or more. We explain how chaotic outflows may arise by constructing a map for the wind mass-loss rate as a function of time. The map is built on three statements: (1) The wind mass-loss rate scales in proportion to the surface equilibrium vapor pressure, rising exponentially with ground temperature. (2) Because the wind takes a finite time to escape the planet's gravity well, the surface mass-loss rate at any time determines the wind optical depth at a later time -- the atmosphere has hysteresis. (3) The ground temperature increases with optical depth (greenhouse effect) when the atmosphere is optically thin, and decreases with optical depth when the atmosphere is optically thick (nuclear winter). Statement (3) follows from how dust condenses in the face of intense stellar irradiation. As discussed recently, condensates initially naked before the star must be silicate-rich and iron-poor, staying cool enough for condensation by absorbing weakly in the visible and emitting strongly in the infrared. Later, when grains are numerous enough to self-shield from starlight, they may accrete more iron and reverse their visible-to-infrared opacity ratio. Depending on parameters, the map for the wind can regularly boom and bust between a greenhouse and a nuclear winter, or erupt into chaos. Lyapunov times are measured in orbital periods, the time for the wind to turn by Coriolis forces away from the planet's dayside, out of the Hill sphere.