Astronomy & Celestial Mechanics
the sky, computed
Concept

Faint young sun — where it appears

The Sun was about 30 per cent fainter four billion years ago, yet the young Earth had liquid water. Explaining that requires a stronger early greenhouse, and the carbonate–silicate cycle is the leading mechanism proposed to supply one.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The habitable zone of a 1 M☉ star, sweeping outwards. The inner and outer edges of the liquid-water zone against time, for a 1 solar-mass star whose main sequence lasts 10.0 Gyr. The star brightens as it burns hydrogen — a heavier core needs a hotter centre to hold the star up — so both edges move outward by a factor of 1.63 across the whole main sequence, and the band drawn here sweeps past any fixed orbit rather than containing it. Two quite different zones can be read off. The instantaneous zone at the age of the present-day Sun is 0.99 to 1.71 AU, which is the band a survey means by "in the habitable zone". The continuously habitable zone over the 10.0 Gyr drawn is the overlap of every instant in it — outside the inner edge at the end and inside the outer edge at the beginning — which is 1.37 to 1.44 AU, 10 per cent of the instantaneous width. The horizontal line is an orbit at 1 AU. It leaves the zone at 4.72 Gyr, when the inner edge overtakes it. None of these edges is a measurement: both come from one-dimensional climate models, and the inner one in particular is where a runaway greenhouse begins in a model whose clouds are prescribed.

The band moves and the orbit does not

A star brightens as it burns, so the distance at which water can be liquid sweeps outwards by a factor of one and a half across a main sequence. The band a survey quotes is an instant; the band a planet needs is the overlap of every instant, and for the Sun it is a tenth as wide and does not contain the Earth.

exoplanets · Habitable zone A thermostat that passes 40 per cent of the change it is meant to cancel. Surface temperature against the flux a planet absorbs, in units of the Earth's, for a planet round a 1 M☉ star, with and without the carbonate–silicate cycle. With carbon dioxide held at 280 µbar the temperature follows the flux directly. With weathering allowed to adjust — rock dissolves faster when it is warm and when there is more CO₂, and in the steady state it must remove exactly what volcanoes supply at 1 times today's rate — a colder planet accumulates CO₂ until the balance is restored. The feedback is real and it is not a set point. Near S = 1 it passes 40 per cent of a flux change through to the surface: the loop gain is k s / β = 1.49, with weathering rising one e-fold for every 9.7 K, a greenhouse of 4.33 K per e-folding of CO₂ and a CO₂ exponent of 0.3. The required CO₂ would reach 8.8 bar — the point at which more of it scatters sunlight faster than it traps heat, and the controller has nothing left to add — at S = 0.249. The steady state reaches 273 K at S = 0.531, before the CO₂ has run out — the outer edge of this planet's habitable zone is where the thermostat saturates or freezes, whichever comes first. The climate law is logarithmic in CO₂, which is right near today's values and only a calibration at several bar; ice-albedo feedback, which makes a cooling planet able to jump to a frozen state, is left out.

A thermostat that only halves the error

The carbonate–silicate cycle is credited with keeping a planet's water liquid across the whole width of its habitable zone. Written down with its own measured exponents, it is a proportional controller that cancels about three-fifths of a change in sunlight, takes half a million years to do it — and reaches the published outer edge only on a planet with an order of magnitude more volcanism than the Earth.

exoplanets · Habitable zone Oceans that a changing G would have boiled. The Earth's surface temperature in a crude climate — equilibrium temperature for a fixed albedo, scaled as the received flux to the quarter power, plus a fixed greenhouse warming of 33 K — against time before the present, if the Sun's luminosity goes as G⁷ and the Earth's orbit as 1/G, so the flux goes as G⁹, on top of the Sun's own brightening. With Dirac's G ∝ 1/t and an age of 13.8 Gyr, the oceans boil 1.9 Gyr ago; with G falling by 10⁻¹¹ of itself a year, the surface is 292 K at 3.8 Gyr. Rocks of that age were laid down in water. Constant G gives the faint young Sun's cooling, 270 K in this climate — a separate problem, which the real atmosphere solved.

A constant bounded by the oceans

In 1937 Dirac proposed that the gravitational constant falls as the universe ages. Eleven years later Teller pointed out what that would have done to the Earth: a star's luminosity depends on G to about the seventh power, the Earth's orbit shrinks as G grows, and the sunlight reaching the Earth goes as the ninth power. Run backwards, Dirac's G boils the oceans less than two billion years ago. The rocks were laid down in water, so G cannot have changed that fast — the first bound on a changing constant came from geology.

gravitation · Gravitational constant

Named alongside it

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

Carbonate silicate cycleHabitable zoneRunaway greenhouseAdiabatic invariantClimate modelClimate sensitivityContinuously habitable zoneEffective stellar fluxEquilibrium temperatureGravitational constantHelioseismologyLoop gain

All concepts