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 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.

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.

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

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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 the 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 ν 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 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 this idea was later tested using a photochemical model and discounted.[10] Furthermore, such a haze is thought to have cooled the Earth's surface beneath it and counteracted the greenhouse effect.

### 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 70s. An atmosphere that contained about 1000 times the Present Atmospheric Level (or PAL) was found to be consistent with the evolutionary path of the Earth's carbon cycle and solar evolution.[11][12][13]

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 the 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).[14]

Specifically, using 1-D models, which represent the 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.[12][15]

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.[16] 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), and 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.[17][18]

## Other proposed explanations

Phanerozoic Climate Change

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.[19] 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.[20]

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 (CRF), 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.[21] In this framework, the early Sun underwent an extended period of higher solar wind output. This caused a mass loss from the Sun on the order of 5−10 percent over its lifetime, 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.[22][23][24]

### 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.[25]

Another proposed mechanism of cloud cover reduction relates a decrease in cosmic rays during this time to reduced cloud fraction.[26] 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.[27]

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.[28]

## 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 the 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.[28]

## 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).[29][30] 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.[31] Scientists debate over which geomorphological features can be attributed to shorelines or other water flow markers and which can be ascribed to other mechanisms.[28] 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.[32]

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.[31][32] 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.[31]

One way to ascertain whether Mars possessed a thick CO2-rich atmosphere is to look at carbonate deposits. A primary sink for carbon in the Earth 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.[33]

A volcanically-outgassed CO2-H2 greenhouse is one of the most potent warming solutions recently suggested for early Mars.[34] 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.[35][32]

### 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.[36]

## References

1. ^ Feulner, Georg (2012). "The faint young Sun problem". Reviews of Geophysics. 50 (2): RG2006. arXiv:1204.4449. Bibcode:2012RvGeo..50.2006F. doi:10.1029/2011RG000375. S2CID 119248267.
2. ^ a b c Sagan, C.; Mullen, G. (1972). "Earth and Mars: Evolution of Atmospheres and Surface Temperatures". Science. 177 (4043): 52–56. Bibcode:1972Sci...177...52S. doi:10.1126/science.177.4043.52. PMID 17756316. S2CID 12566286.
3. ^ David Morrison, NASA Lunar Science Institute, "Catastrophic Impacts in Earth's History", video-recorded lecture, Stanford University (Astrobiology), 2010 Feb. 2, access 2016-05-10.
4. ^ Gough, D. O. (1981). "Solar Interior Structure and Luminosity Variations". Solar Physics. 74 (1): 21–34. Bibcode:1981SoPh...74...21G. doi:10.1007/BF00151270. S2CID 120541081.
5. ^ Wolszczan, Alex; Kuchner, Marc J. (2010). Seager, Sara (ed.). Exoplanets. pp. 175–190. ISBN 978-0-8165-2945-2.
6. ^ Windley, B. (1984). The Evolving Continents. New York: Wiley Press. ISBN 978-0-471-90376-5.
7. ^ Schopf, J. (1983). Earth's Earliest Biosphere: Its Origin and Evolution. Princeton, N.J.: Princeton University Press. ISBN 978-0-691-08323-0.
8. ^ Kuhn, W. R.; Atreya, S. K (1979). "Ammonia photolysis and the greenhouse effect in the primordial atmosphere of the earth". Icarus. 37 (1): 207–213. Bibcode:1979Icar...37..207K. doi:10.1016/0019-1035(79)90126-X. hdl:2027.42/23696.
9. ^ Sagan, Carl; Chyba, Christopher (23 May 1997). "The early faint sun paradox: organic shielding of ultraviolet-labile greenhouse gases". Science. 276 (5316): 1217–1221. Bibcode:1997Sci...276.1217S. doi:10.1126/science.276.5316.1217. PMID 11536805.
10. ^ Pavlov, Alexander; Brown, Lisa; Kasting, James (October 2001). "UV shielding of NH3 and O2 by organic hazes in the Archean atmosphere". Journal of Geophysical Research: Planets. 106 (E10): 26267–23287. Bibcode:2001JGR...10623267P. doi:10.1029/2000JE001448.
11. ^ Hart, M. H. (1978). "The evolution of the atmosphere of the EArth". Icarus. 33 (1): 23–39. Bibcode:1978Icar...33...23H. doi:10.1016/0019-1035(78)90021-0.
12. ^ a b Walker, James C. G. (June 1985). "Carbon dioxide on the early earth" (PDF). Origins of Life and Evolution of the Biosphere. 16 (2): 117–127. Bibcode:1985OrLi...16..117W. doi:10.1007/BF01809466. hdl:2027.42/43349. PMID 11542014. S2CID 206804461. Retrieved 2010-01-30.
13. ^ Pavlov, Alexander A.; Kasting, James F.; Brown, Lisa L.; Rages, Kathy A.; Freedman, Richard (May 2000). "Greenhouse warming by CH4 in the atmosphere of early Earth". Journal of Geophysical Research. 105 (E5): 11981–11990. Bibcode:2000JGR...10511981P. doi:10.1029/1999JE001134. PMID 11543544.
14. ^ Berner, Robert; Lasaga, Antonio; Garrels, Robert (1983). "The Carbonate-Silicate Geochemical Cycle and its Effect on Atmospheric Carbon Dioxide over the Past 100 Million Years". American Journal of Science. 283 (7): 641–683. Bibcode:1983AmJS..283..641B. doi:10.2475/ajs.283.7.641.
15. ^ Kasting, J. F.; Ackerman, T. P. (1986). "Climate consequences of very high CO2 levels in the Earth's early atmosphere". Science. 234 (4782): 1383–1385. Bibcode:1986Sci...234.1383K. doi:10.1126/science.11539665. PMID 11539665.
16. ^ Sleep, N.H.; Zahnle, K (2001). "Carbon dioxide cycling and implications for climate on ancient Earth". Journal of Geophysical Research: Planets. 106 (E1): 1373–1399. Bibcode:2001JGR...106.1373S. doi:10.1029/2000JE001247.
17. ^ Rosing, Minik; Bird, Dennis K; Sleep, Norman; Bjerrum, Christian J. (2010). "No climate paradox under the faint early Sun". Nature. 464 (7289): 744–747. Bibcode:2010Natur.464..744R. doi:10.1038/nature08955. PMID 20360739. S2CID 205220182.
18. ^ Kasting, James (2010). "Faint young Sun redux". Nature. 464 (7289): 687–9. doi:10.1038/464687a. PMID 20360727. S2CID 4395659.
19. ^ Shaviv, N. J. (2003). "Toward a solution to the early faint Sun paradox: A lower cosmic ray flux from a stronger solar wind". Journal of Geophysical Research. 108 (A12): 1437. arXiv:astro-ph/0306477. Bibcode:2003JGRA..108.1437S. doi:10.1029/2003JA009997. S2CID 11148141.
20. ^ Caffe, M. W.; Hohenberg, C. M.; Swindle, T. D.; Goswami, J. N. (February 1, 1987). "Evidence in meteorites for an active early sun". The Astrophysical Journal. 313: L31–L35. Bibcode:1987ApJ...313L..31C. doi:10.1086/184826. hdl:2060/19850018239.
21. ^ Minton, David; Malhotra, Renu (2007). "Assessing the Massive Young Sun Hypothesis to Solve the Warm Young Earth Puzzle". The Astrophysical Journal. 660 (2): 1700–1706. arXiv:astro-ph/0612321. Bibcode:2007ApJ...660.1700M. doi:10.1086/514331. S2CID 14526617.
22. ^ Gaidos, Eric J.; Güdel, Manuel; Blake, Geoffrey A. (2000). "The faint young Sun paradox: An observational test of an alternative solar model" (PDF). Geophysical Research Letters. 27 (4): 501–504. Bibcode:2000GeoRL..27..501G. CiteSeerX 10.1.1.613.1511. doi:10.1029/1999GL010740. PMID 11543273.
23. ^ Wood, Bernard (2005). "New mass-loss measurements from astrospheric Ly alpha absorption". The Astrophysical Journal. 628 (2): L143–L146. arXiv:astro-ph/0506401. Bibcode:2005ApJ...628L.143W. doi:10.1086/432716. S2CID 7137741.
24. ^ Wood, Bernard (2002). "Measured mass loss rates of solar-like stars as a function of age and activity". The Astrophysical Journal. 574 (1): 412–425. arXiv:astro-ph/0203437. Bibcode:2002ApJ...574..412W. doi:10.1086/340797. S2CID 1500425.
25. ^ Goldblatt, C.; Zahnle, K. J. (2011). "Clouds and the Faint Young Sun Paradox". Climate of the Past. 6 (1): 203–220. arXiv:1102.3209. Bibcode:2011CliPa...7..203G. doi:10.5194/cp-7-203-2011. S2CID 54959670.
26. ^ Svensmark, Henrik (2007). "Cosmoclimatology: a new theory emerges". Astronomy & Geophysics. 48 (1): 14–28. Bibcode:2007A&G....48a..18S. doi:10.1111/j.1468-4004.2007.48118.x.
27. ^ Krissansen-Totton, J.; Davies, R. (2013). "Investigation of cosmic ray–cloud connections using MISR". Geophysical Research Letters. 40 (19): 5240–5245. arXiv:1311.1308. Bibcode:2013GeoRL..40.5240K. doi:10.1002/grl.50996. S2CID 119299932.
28. ^ a b c Catling, David C.; Kasting, James F. (2017). Atmospheric Evolution on Inhabited and Lifeless Worlds. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-84412-3.
29. ^ Irwin, R. P.; Howard, Alan; Craddock, Robert; Moore, Jeffrey (2005). "An Intense Terminal Epoch of Widespread Fluvial Activity on Early Mars: 2. Increased Runoff and Paleolake Development". Journal of Geophysical Research. 110 (E12): E12S15. Bibcode:2005JGRE..11012S15I. doi:10.1029/2005JE002460.
30. ^ Howard, Alan D.; Moore, Jeffrey M. (2005). "An intense terminal epoch of widespread fluvial activity on early Mars: 1. Valley network incision and associated deposits". Journal of Geophysical Research. 110 (E12): E12S14. Bibcode:2005JGRE..11012S14H. doi:10.1029/2005JE002459.
31. ^ a b c Wordsworth, Robin D. (2016). "The Climate of Early Mars". Annual Review of Earth and Planetary Sciences. 44: 381–408. arXiv:1606.02813. Bibcode:2016AREPS..44..381W. doi:10.1146/annurev-earth-060115-012355. S2CID 55266519.
32. ^ a b c Ramirez, Ramirez R.; Craddock, Robert A. (2018). "The geological and climatological case for a warmer and wetter early Mars". Nature Geoscience. 11 (4): 230–237. arXiv:1810.01974. Bibcode:2018NatGe..11..230R. doi:10.1038/s41561-018-0093-9. S2CID 118915357.
33. ^ Haberle, R.; Catling, D.; Carr, M; Zahnle, K (2017). "The Early Mars Climate System". The Atmosphere and Climate of Mars. The Atmosphere and Climate of Mars. Cambridge, UK: Cambridge University Press. pp. 526–568. doi:10.1017/9781139060172.017. ISBN 9781139060172. S2CID 92991460.
34. ^ Ramirez, R. M.; Kopparapu, R.; Zugger, M. E.; Robinson, T. D.; Freedman, R.; Kasting, J. F. (2014). "Warming early Mars with CO2 and H2". Nature Geoscience. 7 (1): 59–63. arXiv:1405.6701. doi:10.1038/ngeo2000. S2CID 118520121.
35. ^ Wordsworth, Y.Kalugina; Lokshtanov, A.Vigasin; Ehlmann, J.Head; Sanders, H.Wang (2017). "Transient reducing greenhouse warming on early Mars". Geophysical Research Letters. 44 (2): 665–671. doi:10.1002/2016GL071766. S2CID 5295225.
36. ^ Kasting, J. F. (1988). "Runaway and moist greenhouse atmospheres and the evolution of Earth and Venus". Icarus. 74 (3): 472–494. Bibcode:1988Icar...74..472K. doi:10.1016/0019-1035(88)90116-9. PMID 11538226.