The Faint Young Sun Paradox

Summary

Standard models of how stars age put the Sun roughly thirty per cent fainter when it formed than it is now, brightening steadily since. Run that backwards with the Earth’s present reflectivity and atmosphere and the oceans should have been frozen until about 2.3 billion years ago. The rock record shows liquid water and life long before that.

Carl Sagan and George Mullen set the problem out in Science in 1972 and proposed that ammonia in the early atmosphere trapped the missing heat. Ammonia did not survive scrutiny, but the kind of answer did: an early atmosphere with more greenhouse warming than today’s. Carbon dioxide now carries most of the explanation, and a 2020 review states that the problem has essentially been solved. The friction that remains is between models and rocks, over how much carbon dioxide there actually was.

What is documented

The paper. Sagan, C. and Mullen, G., "Earth and Mars: Evolution of Atmospheres and Surface Temperatures", Science 177(4043), pp. 52 to 56, published 7 July 1972, received 17 December 1971 and revised 21 April 1972.

The paradox, in the authors’ own words. From the abstract: "Solar evolution implies, for contemporary albedos and atmospheric composition, global mean temperatures below the freezing point of seawater less than 2.3 aeons ago, contrary to geologic and paleontological evidence." An aeon here is a billion years. In other words, on those assumptions the Earth would have been frozen before about 2.3 billion years ago.

The luminosity figures they actually used. The paper states that "the luminosity, L, of the sun has increased by about 40 percent in geologic time", and gives "The best present estimate of [the change] is 40 plus or minus 10 percent." For most of the calculations they adopt a more conservative thirty per cent. With thirty per cent they obtain global temperatures of about 263 kelvin at 4.0 to 4.5 billion years ago; with fifty per cent, about 245 kelvin, and the freezing point of seawater is reached about 1.4 billion years ago.

Their proposed answer. An ammonia greenhouse. A volume mixing ratio of about one part in a hundred thousand at one bar provides appreciable absorption in the 8 to 13 micron window, and "Ammonia mixing ratios of the order of a few parts per million in the middle Precambrian atmosphere" would resolve the problem.

The curve usually quoted is not theirs. The 1972 paper gives no formula for luminosity against time and no figure of seventy per cent. The standard parameterisation, quoted in the 2012 review, is Gough’s, published in 1981. Evaluated at the Sun’s formation it gives about 71 per cent of the present luminosity.

The modern figures. A 2012 review gives the Sun as about thirty per cent less luminous at 4.57 billion years ago and takes early Archean luminosity as 0.75 of present. A 2020 review gives the Archean Sun, 3.8 to 2.5 billion years ago, as "typically 20-25% lower". The 2012 review expresses the deficit as energy rather than temperature: about 60 watts per square metre at 3.8 billion years ago and about 40 at 2.5 billion.

Who raised it first. Sagan and Mullen are usually credited with the problem, and the 2012 review notes that this is "not entirely true", pointing to statements of it by Ringwood in 1961 and Donn and colleagues in 1965. What Sagan and Mullen did was bring it to a wide audience and propose a mechanism.

Where the numbers now disagree. On the 2020 review’s figures, three-dimensional climate models want roughly 200 millibars of carbon dioxide at 3.8 billion years ago and about 40 millibars at 2.5 billion to reach present-day temperatures. Constraints from ancient soils, as that review summarises them, point to less than about 30 millibars in the late Archean. That gap is the live quantitative problem.

What the other agents contribute. On the 2020 review’s accounting: methane about 9 watts per square metre and up to about 14 kelvin; thinner low cloud about 5 watts and up to about 10 kelvin; less emerged land about 5 watts and up to 4 kelvin; a fourteen-hour day roughly nothing in forcing and about 1 kelvin. None of these is a solution alone, and together they are supporting players rather than the main agent.

Leading explanations

An enhanced carbon dioxide greenhouse (Charnay and colleagues, 2020; widely accepted). Much higher atmospheric carbon dioxide in the Archean trapped enough outgoing radiation to keep the oceans liquid, with the carbonate-silicate weathering cycle supplying the feedback that keeps the system stable. This is the leading component of the resolution. Its weakness is that geological limits on carbon dioxide sit below what the models want for the late Archean.

A methane greenhouse (contested). Biogenic methane supplementing carbon dioxide. Partially supported, and complicated by the fact that organic haze forming at high methane levels caps the warming. The 2012 review calls the methane route "considerably more complicated than previously thought".

Thinner low cloud (contributory). Fewer cloud condensation nuclei would thin the low cloud decks and lower the planet’s reflectivity. A real contribution on the published numbers, and not enough on its own.

A thicker nitrogen atmosphere (disfavoured for the Archean). Higher background pressure broadens the absorption lines of greenhouse gases, with one estimate of about 4.4 degrees per doubling of nitrogen. Judged unlikely for the Archean on pressure and nitrogen constraints, though possibly relevant earlier.

An ammonia greenhouse (Sagan and Mullen, 1972; rejected as the primary answer). The original proposal. Rated less likely than carbon dioxide or methane because ammonia is broken up by ultraviolet light, rains out, and dissolves readily, though the 2012 review concedes it "may not be completely out of the game".

A more massive, brighter young Sun (strongly disfavoured). That the Sun began heavier and lost mass, and so was brighter than standard models allow. About six per cent more initial mass would do it. It is disfavoured by a runaway-greenhouse limit at about seven per cent, by helioseismic constraints that are themselves disputed, and by the observed mass-loss rates of young stars like the Sun, which are too low.

Current status

Partially explained. The arithmetic is not in dispute. With today’s reflectivity and atmosphere and a Sun thirty to forty per cent fainter, the Earth’s mean temperature is below the freezing point of seawater before about 2.3 billion years ago, and the rock record contradicts that. What has changed since 1972 is the inventory of warming agents, and a 2020 review states the problem is essentially solved, with elevated Archean carbon dioxide doing most of the work and methane, thinner low cloud, less emerged land and faster rotation contributing. The remaining friction is quantitative and geological rather than conceptual: the models want roughly 200 millibars of carbon dioxide at 3.8 billion years ago and 40 at 2.5 billion, while soil-based proxies point to under about 30 millibars in the late Archean, and the 2012 review concluded, on the evidence then available, that carbon dioxide alone was most likely insufficient. Tighter and mutually consistent geochemical constraints on Archean carbon dioxide, fully coupled three-dimensional atmosphere and ocean simulations, and independent constraints on total atmospheric pressure would settle it. A proxy result firmly excluding the levels the models need would reopen the problem rather than close it.

Last reviewed: November 2026. Records are provisional. Where the evidence changes, the entry changes. Found an error? Tell us.