7.1 The Faint Young Sun Paradox: Greenhouse or deep freeze?

Standard solar models imply that the Sun’s bolometric luminosity has monotonically increased during the past 4.6 Gyr. At its ZAMS stage (t = –4.6 Gyr), the solar luminosity was only 70 – 75% its present-day level. In the absence of an atmosphere, the Earth’s surface equilibrium temperature would then have amounted to 355 K (Sagan and Chyba, 1997Jump To The Next Citation Point). Assuming an albedo and an atmospheric composition equal to values of the present-day Earth, the mean surface temperature would have been below the freezing point of seawater until ≈ 2 Gyr ago (Sagan and Mullen, 1972Jump To The Next Citation Point). The increase of the surface temperature in the presence of an atmosphere is due to the greenhouse effect, i.e., the property of the atmospheric mixture to be transparent to incoming optical and near-infrared light but to absorb mid-infrared emission that has been re-emitted from the surface. The present-day atmosphere of the Earth rises the surface temperature by only 33 K compared to the atmosphere-free equilibrium value (Sagan and Mullen 1972Jump To The Next Citation PointKasting and Catling 2003Jump To The Next Citation Point, see Figure 37View Image).
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Figure 37: Illustration of the greenhouse and the Faint Young Sun Paradox for the Earth. The solid line indicates the solar luminosity relative to the present value (right y axis); the lower dashed curve is the effective radiating temperature of the Earth (i.e., its surface being treated as a blackbody radiator); the upper dashed curve shows the calculated, mean global surface temperature affected by the greenhouse (CO2 mixing ratio and relative humidity have been kept fixed; from Kasting and Catling 2003,  2003 by Annual Reviews, reprinted with permission).

On the other hand, there is clear geologic evidence for a warm climate in the early Earth’s history, with average temperatures perhaps even significantly above present-day values (Kasting and Toon 1989Jump To The Next Citation PointKasting 1989Karhu and Epstein 1986, see also summary of further evidence in Sackmann and Boothroyd 2003Jump To The Next Citation Point). Sedimentary rocks (Bowring et al., 1989) and indirect evidence of microbial life in rock dated to 3.8 Gyr ago (Mojzsis et al. 1996; see also summaries by Nisbet 2000 and Nisbet and Sleep 2001) clearly suggest the presence of liquid water (see also Kasting and Toon, 1989Jump To The Next Citation Point).

There is similar geological evidence for a warmer young Mars, as seen in particular in extensive channels formed by massive streams of liquid water. But again, the mean Martian surface temperature is too low for the presence of liquid water, and the less intense photospheric light from the younger Sun would obviously have aggravated this problem.

The apparent contradiction between implications from the standard solar model and the geologic evidence for a warm early climate on the Earth and Mars is known as the “Faint Young Sun Paradox” (Kasting and Toon, 1989Jump To The Next Citation PointKasting and Grinspoon, 1991). This problem has been addressed along two major lines of argumentation of which one (assuming a higher mass loss rate for the young Sun) indirectly relates to the magnetic activity of the young Sun; the other (arguing with greenhouse gases) may be related in as of yet unknown ways to magnetic activity as well (via atmospheric chemistry, see Section 7.2.1), although other processes in no ways related to solar magnetic fields may be relevant. After reviewing these two approaches, I will discuss model calculations that specifically address the influence of magnetic activity on planetary atmospheres (Section 7.2).

7.1.1 The relevance of greenhouse gases

Today’s modest greenhouse effect is due to atmospheric CO2 and H2O (see, e.g., Kasting and Toon, 1989Jump To The Next Citation Point, for a summary). A stronger greenhouse could have been effective in a different atmosphere of the young Earth:

1) A higher content of atmospheric gaseous CO2 might increase the greenhouse effect (Owen et al., 1979Jump To The Next Citation PointCess et al., 1980) as in the present-day atmosphere of Venus, but a 100fold increase compared to present-day levels would be required (Kasting and Toon, 1989Jump To The Next Citation Point); such levels of CO2 are plausible because the carbonate-silicate geochemical cycle (which binds CO2 dissolved in rainwater to silicate minerals in the soil) operates in such a way that removal of atmospheric CO2 increases with increasing temperature, thus inducing a negative feedback loop between CO2 greenhouse warming and CO2 removal (Kasting and Toon, 1989Jump To The Next Citation Point). However, the absence of siderite in old soils argues against the required high levels of CO2 (Rye et al., 1995). For Mars, high levels of CO2 in a higher-pressure atmosphere would condense in clouds. The resulting increased global albedo would in fact lead to a net cooling (Kasting, 1991). Although the same clouds may also back-scatter radiation and therefore support the greenhouse (Forget and Pierrehumbert, 1997), experiments suggest that this mechanism is too small to rise the temperatures above the freezing point (Glandorf et al., 2002).

2) Greenhouse gases such as NH3 (Sagan and Mullen, 1972Jump To The Next Citation Point) and CH4 (Sagan and Chyba, 1997Jump To The Next Citation Point) could have been present in appreciable amounts in the young atmospheres, in analogy to the present-day atmosphere of Titan. However, NH3 dissociates rapidly due to solar UV radiation (Kuhn and Atreya 1979; see also Owen et al. 1979). While CH4 is subject to UV dissociation as well, its lifetime is much longer, and biological activity could regenerate it at sufficiently high levels (Pavlov et al., 2000). Moreover, its photolysis may produce a high-altitude haze of organic solids that shields ammonia sufficiently from UV dissociation (Sagan and Chyba, 1997).

How the changes in the atmospheres came about is not entirely clear but may partly be related to the past solar activity (apart from, e.g., weathering, plate tectonics, volcanism, and biological activity). Although enhanced levels of solar EUV and X-ray emission will not directly alter the lower planetary atmospheres but only affect the higher thermosphere (where this radiation is absorbed) and the exosphere (see Section 7.2 below), the complex chemistry induced by photoionization, photodissociation, and heating through enhanced high-energy irradiation may be a key factor in determining what greenhouse gases were available in the young planetary atmospheres, as speculated by Ribas et al. (2005Jump To The Next Citation Point). For example, enhanced photodissociation may have influenced the abundances of ammonia and methane. Also, photochemistry and subsequent production of UV-shielding O3 (Canuto et al., 1982Jump To The Next Citation Point1983Jump To The Next Citation Point) was important for the formation and evolution of life, and life itself eventually altered the composition of the young terrestrial atmosphere very significantly.

7.1.2 A bright young Sun?

A more radical remedy of the Faint Young Sun Paradox would be a Sun that was in fact not faint, i.e., did not follow the standard solar model calculations (see Sackmann and Boothroyd, 2003Jump To The Next Citation Point, for a discussion on controversies related to possible greenhouse effects, or their need, in the early atmospheres of Earth and Mars). Such would be possible if the ZAMS Sun had been more massive, having lost its mass in a wind at rates considerably higher than the present-day solar wind. The latter results in a mass loss of (2 – 3) × 10–14 M ⊙ yr–1 (Wood, 2004, and references therein), and the radiative losses of energy transformed in thermonuclear reactions amount to about 3 times this rate. If the Sun had been subject to these present-day losses for its entire lifetime, its ZAMS mass would have been only 0.05% higher than the present-day value (Minton and Malhotra, 2007Jump To The Next Citation Point). This would change the young Sun’s bolometric luminosity negligibly (recall the mass-luminosity relation for MS stars, which requires approximately Lbol ∝ M3; based on Siess et al. 2000 ZAMS calculations for low-mass stars).

Higher wind mass-loss rates would be an interesting alternative (Graedel et al., 1991). Willson et al. (1987) hypothesized that intermediate-mass stars may lose appreciable amounts of mass during their MS life, in particular in the pulsation-instability strip; early G-type stars would then be descendants of A-type stars. Hobbs et al. (1989Jump To The Next Citation Point) concluded that a wind mass loss of 0.041 M ⊙ since the Sun’s arrival on the ZAMS would suffice to explain the low Li values observed in the present-day photosphere (because Li would be diluted when the wind-driving surface layer is progressively mixed with Li-free material entering from lower, hotter layers; see also Schramm et al. 1990; note, however, that there are other, and more important, processes that deplete Li, see Sackmann and Boothroyd 2003Jump To The Next Citation Point). A higher mass loss rate for the young Sun is in fact supported by meteoritic and lunar evidence, suggesting that 2.5 – 3.5 Gyr ago (solar age of 1 – 2 Gyr), the wind mass loss was on average 10 times higher than at present (Geiss and Bochsler, 1991). This would, however, result in a solar mass still only ≈ 0.1% higher at t = –3 Gyr than now (Sackmann and Boothroyd, 2003Jump To The Next Citation Point). To simultaneously fulfill therequirement of liquid water on young Mars, the initial solar mass would have to be > ∼ 1.03 M ⊙ (Sackmann and Boothroyd, 2003Jump To The Next Citation Point).

Gaidos et al. (2000Jump To The Next Citation Point) used radio observations of three solar analogs at ages of a few 100 Myr to set upper limits to their present mass-loss rate. Because the spin rates of solar analogs reveal a power-law decay in time, Ω ∝ t–0.6 (Equation 8View Equation, also Skumanich 1972 who gave an exponent of –0.5), Gaidos et al. (2000Jump To The Next Citation Point) argued for a power-law decay of the mass-loss rate as well (Equation 6View Equation), which, together with the radio upper limits, results in a maximum cumulative mass loss of 6% of the solar mass during the past 4 Gyr. This is close to the suggested mass losses to dilute Li (Hobbs et al. 1989, but note other Li depletion processes), is in agreement with the minimum loss of 3% required to explain liquid water on Mars (Sackmann and Boothroyd, 2003Jump To The Next Citation Point), and is also slightly lower than the upper limit of 7% of M ⊙ to avoid runaway greenhouse on Earth (Whitmire et al., 1995Kasting, 1988Jump To The Next Citation Point) (the runaway greenhouse would evaporate the entire water ocean so that all water would be present in the atmosphere as steam; photodissociation and rapid loss of hydrogen by hydrodynamic escape [see Section 7.2.3 below] would lead to a dry planet – analogous to present-day Venus; see Ingersoll 1969Jump To The Next Citation Point).

Corresponding models have been computed by, among others, Boothroyd et al. (1991Jump To The Next Citation Point), Guzik and Cox (1995Jump To The Next Citation Point), and Sackmann and Boothroyd (2003Jump To The Next Citation Point). The upper limit for the ZAMS Sun allowed by the Li depletion purely due to wind-mass loss was found to be 1.1 M ⊙ (Boothroyd et al., 1991Jump To The Next Citation PointGuzik and Cox, 1995Jump To The Next Citation Point). Helioseismology constraints are compatible with model calculations starting with ZAMS solar masses up to (1.07 – 1.10) M ⊙ (Boothroyd et al., 1991Guzik and Cox, 1995Jump To The Next Citation Point) but the consequent enhanced mass loss should be confined to the earliest ≈ 200 Myr of the Sun’s life on the MS, implying loss rates as high as 5 × 10–10 M ⊙ yr–1 (Guzik and Cox, 1995). Somewhat depending on the precise mass-loss law, the solar flux starts at values up to 7% higher than the present-day value (corresponding to mass-loss rates of ≈ 10–11 – 10–10 M ⊙ yr–1 at ZAMS age) to drop to a minimum no less than 80% after 1 – 2 Gyr, and to increase again in agreement with the evolution of the standard solar model (Figure 38View Image). The highest acceptable initial solar mass is 1.07 M ⊙ to ensure that the young Earth would not lose its water via a greenhouse effect, photodissociation and subsequent loss of hydrogen into space (Sackmann and Boothroyd 2003Jump To The Next Citation Point; see also Section 7.2 below).

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Figure 38: Solar flux in time relative to present, for a Sun that was subject to strong mass loss in its past. Different curves show calculations for different initial masses and corresponding mass-loss rates such that the present-day values are obtained. The mass-loss rate declines exponentially in time; the flux increase at later times is due to the luminosity increase of the Sun for nearly constant mass. The double arrow indicates the lower limit for the presence of liquid water on early Mars, the thin arrow an (unrealistic) extreme lower limit (from Sackmann and Boothroyd, 2003Jump To The Next Citation Point, reproduced by permission of AAS).

However, the indirect inferences for the mass-loss rates of the young Sun derived by Wood et al. (2002Jump To The Next Citation Point) and Wood et al. (2005Jump To The Next Citation Point) (see Section 5.1) would again not support a significantly brighter ZAMS Sun. Using the power-law mass-loss decay relation of Wood et al. (2002Jump To The Next Citation Point) back to ZAMS, a total mass-loss of about 0.01 M ⊙ would result (Sackmann and Boothroyd, 2003), with an uncertainty of a factor of a few. Most of the mass loss would occur in the first few 100 Myr. The suppressed mass loss at early times, however (Wood et al., 2005Jump To The Next Citation Point), suggests that no more than 0.003 M ⊙ could be lost during the Sun’s MS life (Minton and Malhotra, 2007Jump To The Next Citation Point).

In summary, the main problem with the “bright young Sun” model remains the disagreement between climatic requirements for the young-Sun mass (i.e., a ZAMS solar mass of [1.03 – 1.07] M ⊙) and the indirectly measured mass-loss rates (Minton and Malhotra, 2007) that tend to be too small (Wood et al. 2005Jump To The Next Citation Point, i.e., resulting in a ZAMS mass of no more than 1.01 M ⊙), although radio upper limits (Gaidos et al., 2000) are still compatible with the required mass-loss rates.

7.1.3 Cosmic rays and a stronger solar wind

Shaviv (2003Jump To The Next Citation Point) suggested a link between the cosmic ray flux and average global temperatures on Earth. Although a physical basis and an accepted proof are still missing, there is suggestive evidence that elevated cosmic-ray fluxes have a cooling effect on the Earth’s atmosphere. In this picture, cosmic rays ionize tropospheric layers, and charged ion clusters lead to condensation nuclei that eventually form clouds. Low-lying clouds have a cooling effect (Shaviv, 2003).

Given that wind of the young Sun was stronger (Section 5.1), the cosmic-ray flux reaching the inner solar system was suppressed compared to present-day fluxes. Cloud formation would thus be suppressed, leading to a warmer climate. Model calculations (also including effects due to variable star-formation rate in the solar vicinity on the cosmic-ray generation, a more rapid rotation of the Earth, and a smaller land mass) suggest that about 2/3 of the temperature reduction associated with the fainter young Sun can be compensated.

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