Artist's depiction of the life cycle of a Sun-like star, starting as a main-sequence star at lower left then expanding through the subgiant and giant phases, until its outer envelope is expelled to form a planetary nebula at upper right.

The faint young Sun paradox or faint young Sun problem describes the apparent contradiction between observations of liquid water early in Earth's history and the astrophysical expectation that the Sun's output would be only 70 percent as intense during that epoch as it is during the modern epoch.[1] The paradox is this: with the young sun's output at only 70 percent of its current output, early Earth would be expected to be completely frozen – but early Earth seems to have had liquid water.

The issue was raised by astronomers Carl Sagan and George Mullen in 1972.[2] Proposed resolutions of this paradox have taken into account greenhouse effects, changes to planetary albedo, astrophysical influences, or combinations of these suggestions.

An unresolved question is how a climate suitable for life was maintained on Earth over the long timescale despite the variable solar output and wide range of terrestrial conditions.[3]

## Solar evolution

Early in Earth's history, the Sun's output would have been only 70 percent as intense as it is during the modern epoch, owing to a higher ratio of hydrogen to helium in its core. Since then, the Sun has gradually brightened and consequently warmed Earth's surface, a process known as radiative forcing. During the Archaean age, assuming, constant albedo, and other surface features, such as greenhouse gases, Earth's equilibrium temperature would have been too low to sustain a liquid ocean. Astronomers Carl Sagan and George Mullen pointed out in 1972 that this is contrary to the geological and paleontological evidence.[2]

The sun is powered by nuclear fusion, which, for the Sun can be represented in the following way:

${\displaystyle {\ce {4^{1}H -> ^{4}He + 2e+ + 2\nu}}}$
${\displaystyle {\ce {4^{1}H + e- -> ^{4}He + e+ + 2\nu}}}$

In the equations above, e+ is a positron, e is an electron and ${\displaystyle {\ce {\nu}}}$ represents a neutrino (nearly massless). The net effect is three-fold: a release of energy by Einstein's formula ΔE = mc2 (since the helium nucleus is less massive than the four hydrogen nuclei), an increase in the density of the solar core (since the final product is contained in one nucleus as opposed to between four different protons), and an increase in the rate of fusion (since higher temperatures help increase the collision speed between the four protons and boost the likelihood that such reactions take place).[4][5] The net effect is an associated increase in solar luminosity. More recent modeling studies have shown that the Sun is currently 1.4 times brighter today than it was 4.6 billion years ago (Ga), and that it has brightened roughly linearly since then with time, though it has accelerated slightly.

Despite the reduced solar luminosity 4 billion (4 × 109) years ago and with greenhouse gas, the geological record shows a continually relatively warm surface in the full early temperature record of Earth, with the exception of a cold phase, the Huronian glaciation, about 2.4 to 2.1 billion years ago. Water-related sediments have been found dating to as early as 3.8 billion years ago.[6] This relationship between surface temperature and the balance of forcing mechanisms has implications for how scientists understand the evolution of early life forms, which have been dated from as early as 3.5 billion years.[7]

## Greenhouse gas solutions

### Ammonia as a greenhouse gas

Sagan and Mullen even suggested during their descriptions of the paradox that it might be solved by high concentrations of ammonia gas, NH3.[2] However, it has since been shown that while ammonia is an effective greenhouse gas, it is easily photochemically destroyed in the atmosphere and converted to nitrogen (N2) and hydrogen (H2) gases.[8] It was suggested (again by Sagan) that a photochemical haze could have prevented this destruction of ammonia and allowed it to continue acting as a greenhouse gas during this time,[9] however by 2001 this idea was tested using a photochemical model and discounted.[10] Furthermore, such a haze is thought to have cooled Earth's surface beneath it and counteracted the greenhouse effect.[citation needed] Around 2010 scholars at the University of Colorado revived the idea, arguing that the ammonia hypothesis is a viable contributor if the haze formed a fractal pattern.[11][12]

### Carbon dioxide as a greenhouse gas

This conceptual graph shows the relationship between solar radiation and the greenhouse effect – in this case dominated by modulations in carbon dioxide.

It is now thought that carbon dioxide was present in higher concentrations during this period of lower solar radiation. It was first proposed and tested as part of Earth's atmospheric evolution in the late 1970s. An atmosphere that contained about 1000 times the Present Atmospheric Level (or PAL) was found to be consistent with the evolutionary path of Earth's carbon cycle and solar evolution.[13][14][15]

The primary mechanism for attaining such high CO2 concentrations is the carbon cycle. On large timescales, the inorganic branch of the carbon cycle, which is known as the carbonate–silicate cycle is responsible for determining the partitioning of CO2 between the atmosphere and the surface of Earth. In particular, during a time of low surface temperatures, rainfall and weathering rates would be reduced, allowing for the build-up of carbon dioxide in the atmosphere on timescales of 0.5 million years (Myr).[16]

Specifically, using 1-D models, which represent Earth as a single point (instead of something that varies across 3 dimensions) scientists have determined that at 4.5 Ga, with a 30% dimmer Sun, a minimum partial pressure of 0.1 bar of CO2 is required to maintain an above-freezing surface temperature. At a maximum, 10 bar of CO2 has been suggested as a plausible upper limit.[14][17]

The exact amount of carbon dioxide levels is still under debate, however. In 2001, Sleep and Zahnle suggested that increased weathering on the seafloor on a young, tectonically active Earth could have reduced carbon dioxide levels.[18] Then in 2010, Rosing et al. analyzed marine sediments called banded iron formations (BIFs), and found large amounts of various iron-rich minerals, including magnetite (Fe3O4), an oxidized mineral alongside siderite (FeCO3), a reduced mineral and saw that they formed during the first half of Earth's history (and not afterward). The minerals' relative coexistence suggested an analogous balance between CO2 and H2. In the analysis, Rosing et al. connected the atmospheric H2 concentrations with regulation by biotic methanogenesis. Anaerobic, single-celled organisms that produced methane (CH4) may therefore have contributed to the warming in addition to carbon dioxide.[19][20]

## Other proposed explanations

### Tidal heating

The moon was originally much closer to the Earth, which rotated faster than it does today, resulting in greater tidal heating than the tidal heating experienced today. Original estimates found that even early tidal heating would be minimal, perhaps 0.02 watts per square meter. (For comparison, the solar energy incident on the Earth's atmosphere is on the order of 1000 watts per square meter.) However, around 2021, a team led by René Heller in Germany argued that such estimates were simplistic, and that in some plausible models tidal heating might have initially been on the order of a hundred watts per square meter (though decreasing rapidly as the Moon pulled away). This could have increased the equilibrium temperature by several degrees Celsius around the first hundred million years of the Earth's existence. Such a contribution would partially resolve the paradox, but is insufficient to solve the faint young paradox on its own without additional factors such as greenhouse heating.[21][22]

### Cosmic rays

A minority view, propounded by the Israeli-American physicist Nir Shaviv, uses climatological influences of solar wind, combined with a hypothesis of Danish physicist Henrik Svensmark for a cooling effect of cosmic rays, to explain the paradox.[23] According to Shaviv, the early Sun had emitted a stronger solar wind that produced a protective effect against cosmic rays. In that early age, a moderate greenhouse effect comparable to today's would have been sufficient to explain an ice-free Earth. Evidence for a more active early Sun has been found in meteorites.[24]

The temperature minimum around 2.4 billion years goes along with a cosmic ray flux modulation by a variable star formation rate in the Milky Way. The reduced solar impact later results in a stronger impact of cosmic ray flux, which is hypothesized to lead to a relationship with climatological variations.

### Mass loss from Sun

It has been proposed several times that mass loss from the faint young Sun in the form of stronger solar winds could have compensated for the low temperatures from greenhouse gas forcing.[25] In this framework, the early Sun underwent an extended period of higher solar wind output. Based on exoplanetary data, this caused a mass loss from the Sun of 5−6 percent over its lifetime,[26] resulting in a more consistent level of solar luminosity (as the early Sun had more mass, resulting in more energy output than was predicted). In order to explain the warm conditions in the Archean era, this mass loss must have occurred over an interval of about one billion years. Records of ion implantation from meteorites and lunar samples show that the elevated rate of solar wind flux only lasted for a period of 0.1 billion years. Observations of the young Sun-like star π1 Ursae Majoris matches this rate of decline in the stellar wind output, suggesting that a higher mass loss rate can not by itself resolve the paradox.[27][28][29]

### Changes in clouds

If greenhouse gas concentrations did not compensate completely for the fainter sun, the moderate temperature range may be explained by a lower surface albedo. At the time, a smaller area of exposed continental land would have resulted in fewer cloud condensation nuclei both in the form of wind-blown dust and biogenic sources. A lower albedo allows a higher fraction of solar radiation to penetrate to the surface. Goldblatt and Zahnle (2011) investigated whether a change in cloud fraction could have been sufficiently warming and found that the net effect was equally likely to have been negative as positive. At most the effect could have raised surface temperatures to just above freezing on average.[30]

Another proposed mechanism of cloud cover reduction relates a decrease in cosmic rays during this time to reduced cloud fraction.[31] However, this mechanism does not work for several reasons, including the fact that ions do not limit cloud formation as much as CCN, and cosmic rays have been found to have little impact on global mean temperature.[32]

Clouds continue to be the dominant source of uncertainty in 3-D global climate models, and a consensus has yet to be reached on exactly how changes in cloud spatial patterns and cloud type may have affected Earth's climate during this time.[33]

### Local Hubble expansion

Although both simulations and direct measurements are of effects of Hubble's law on gravitationally bound systems are returning inconclusive results as in 2022,[34] it was noted what orbital expansion with a fraction of local Hubble expansion rate may explain the observed anomalies in orbital evolution, including a faint young Sun paradox.[35]

## Gaia hypothesis

The Gaia hypothesis holds that biological processes work to maintain a stable surface climate on Earth to maintain habitability through various negative feedback mechanisms. While organic processes, such as the organic carbon cycle, work to regulate dramatic climate changes, and that the surface of Earth has presumably remained habitable, this hypothesis has been criticized as intractable. Furthermore, life has existed on the surface of Earth through dramatic changes in climate, including Snowball Earth episodes. There are also strong and weak versions of the Gaia hypothesis, which has caused some tension in this research area.[33]

## On other planets

### Mars

Mars has its own version of the faint young Sun paradox. Martian terrains show clear signs of past liquid water on the surface, including outflow channels, gullies, modified craters, and valley networks. These geomorphic features suggest Mars had an ocean on its surface and river networks that resemble current Earth's during the late Noachian (4.1–3.7 Ga).[36][37] It is unclear how Mars's orbital pattern, which places it even further from the Sun, and the faintness of the young Sun could have produced what is thought to have been a very warm and wet climate on Mars.[38] Scientists debate over which geomorphological features can be attributed to shorelines or other water flow markers and which can be ascribed to other mechanisms.[33] Nevertheless, the geologic evidence, including observations of widespread fluvial erosion in the southern highlands, are generally consistent with an early warm and semi-arid climate.[39]

Given the orbital and solar conditions of early Mars, a greenhouse effect would have been necessary to boost surface temperatures at least 65 K in order for these surface features to have been carved by flowing water.[38][39] A much denser, CO2-dominated atmosphere has been proposed as a way to produce such a temperature increase. This would depend upon the carbon cycle and the rate of volcanism throughout the pre-Noachian and Noachian, which is not well known. Volatile outgassing is thought to have occurred during these periods.[38]

One way to ascertain whether Mars possessed a thick CO2-rich atmosphere is to look at carbonate deposits. A primary sink for carbon in Earth's atmosphere is the carbonate–silicate cycle. It is however hard for CO2 to have built up in the Martian atmosphere in this way because the greenhouse effect would have been outstripped by CO2 condensation.[40]

A volcanically-outgassed CO2-H2 greenhouse is one of the most potent warming solutions recently suggested for early Mars.[41] Intermittent bursts of methane may have been another possibility. Such greenhouse gas combinations appear necessary because carbon dioxide alone, even at pressures exceeding a few bar, cannot explain the temperatures required for the presence of surface liquid water on early Mars.[42][39]

### Venus

Venus's atmosphere is composed of 96% carbon dioxide, and during this time, billions of years ago, when the Sun was 25 to 30% dimmer, Venus's surface temperature could have been much cooler, and its climate could have resembled current Earth's, complete with a hydrological cycle – before it experienced a runaway greenhouse effect.[43]

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