Astronomy & Celestial Mechanics
the sky, computed
Concept

Effective flux — where it appears

The starlight a planet receives relative to what the Earth receives from the Sun, the single number that places a planet in its star's habitable zone. Its critical values differ slightly with the star's colour.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The habitable zone, and the radius inside which a day never ends. The conservative habitable zone — the runaway-greenhouse and maximum-greenhouse limits of Kopparapu's parameterisation — as a band in stellar mass against orbital distance, both logarithmic. For the Sun it runs from 0.99 to 1.71 AU, which is the published result and the check on the arithmetic here. The band moves inward far faster than the mass falls, because luminosity goes as roughly the fourth power of mass: a 0.2 M☉ star's zone is at 0.082–0.158 AU. The dashed line is the distance inside which a planet is tidally locked within 4.5 billion years, computed from τ = ω₀αmQa⁶/(3GM⋆²k₂R³) with an initial ten-hour spin, Q = 100 and k₂ = 0.3. It crosses the inner edge of the zone at 0.67 M☉ — so around every star below that, which is the great majority of stars, a planet in the habitable zone has one hemisphere in permanent daylight. The Earth is outside its own locking radius of 0.53 AU, and TRAPPIST-1e at 0.029 AU is inside its star's by a factor of 8.

One number sets the zone

The habitable zone is a band of stellar flux, so it scales as the square root of luminosity and moves inward far faster than mass falls. For most stars it lies inside the radius at which a planet is tidally locked.

exoplanets · Habitable zone Where the sunlight crosses the ceiling. The schematic emission of a wet planet against surface temperature, with the sunlight it absorbs at albedo 0.3 for 0.9×, 1×, 1.1×, 1.25× the Earth's present instellation (horizontal lines). Each line meets the emission curve at the planet's equilibrium temperature. Above 1.17 times the Earth's, the absorbed sunlight exceeds the ceiling and there is no equilibrium: the surface heats until the oceans have boiled into the atmosphere.

An inner edge set by a ceiling on outgoing heat

A planet keeps its temperature by radiating away the sunlight it absorbs, and a warmer planet radiates more. A planet with oceans does so only up to a point. Once its air holds enough water vapour, space sees only the level where the vapour becomes opaque, and that level's temperature is fixed by the boiling curve of water and the planet's gravity — not by the surface. The emission stops rising at about 280 watts a square metre, and a planet that absorbs more has no temperature at which it can balance.

exoplanets · Habitable zone

Named alongside it

The objects these essays reach for when they reach for this one.

AlbedoClimate modelEquilibrium temperatureHabitable zoneInsolationRunaway greenhouseM dwarfStellar luminosityTidal locking

All concepts