THE FAINT YOUNG SUN PROBLEM 1 Georg Feulner For more than four decades, scientists have been on higher concentrations of atmospheric greenhouse trying to find an answer to one of the most fundamen- gases like carbon dioxide, methane or ammonia. All tal questions in paleoclimatology, the ‘faint young of these solutions present considerable difficulties, Sun problem’. For the early Earth, models of stellar however, so the faint young Sun problem cannot be evolution predict a solar energy input to the climate regarded as solved. Here I review research on the system which is about 25% lower than today. This subject, including the latest suggestions for solutions would result in a completely frozen world over the of the faint young Sun problem and recent geochem- first two billion years in the history of our planet, if ical constraints on the composition of Earth’s early all other parameters controlling Earth’s climate had atmosphere. Furthermore, I will outline the most been the same. Yet there is ample evidence for the promising directions for future research. In partic- presence of liquid surface water and even life in the ular I would argue that both improved geochemical Archean (3.8 to 2.5 billion years before present), so constraints on the state of the Archean climate sys- some effect (or effects) must have been compensat- tem and numerical experiments with state-of-the-art ing for the faint young Sun. A wide range of possible climate models are required to finally assess what solutions have been suggested and explored during kept the oceans on the Archean Earth from freezing the last four decades, with most studies focussing over completely. 1. INTRODUCTION faint young Sun problem could be solved in prin- ciple before the options are discussed in detail in The faint young Sun problem for Earth’s early the following sections. Section 4 looks at modifi- climate has been briefly reviewed a few times in the cations of the standard solar model, in particular past, for example in the general context of climate the possibility of a strong mass-loss of the young change on geological timescales [Crowley, 1983; Sun. The most likely solution of the faint young Barron, 1984], the formation and early history of Sun problem in terms of an enhanced greenhouse Earth [Zahnle et al., 2007], the evolution of Earth’s effect is discussed in Section 5, the main Section of atmosphere and climate [Pollack, 1991; Kasting, this review paper. Then the effects of clouds (Sec- 1993; Shaw, 2008; Nisbet and Fowler, 2011], life tion 6) and differences in rotation rate and conti- on the early Earth [Nisbet and Sleep, 2001], evo- nental configuration (Section 7) will be explored, lution of the terrestrial planets and considerations before the review is concluded by a summary and of planetary habitability [Pollack, 1979; Rampino suggestions for future research in Section 8. and Caldeira, 1994; Kasting and Catling, 2003] or the evolution of the Sun [Kasting and Grinspoon, 2. THE FAINT YOUNG SUN PROBLEM 1991; G¨udel, 2007]. The more comprehensive re- views of this topic are somewhat dated by now, In this Section, the faint young Sun problem is however, and most look at the issue from the point introduced, beginning with a discussion of the evo- of view of the global energy balance without ex- arXiv:1204.4449v1 [astro-ph.EP] 19 Apr 2012 lution of the Sun on long timescales. ploring important internal aspects of the climate system like the transport of heat. 2.1. A Fainter Sun in the Past This paper presents a new and detailed review By the 1950s, stellar astrophysicists had worked of the faint young Sun problem and is organized as out the physical principles governing the structure follows. Section 2 describes the evidence for a faint and evolution of stars [Kippenhahn and Weigert, young Sun and for the existence of liquid water on 1994]. This allowed the construction of theoretical early Earth. Section 3 explores in what ways the models for the stellar interior and the evolutionary changes occurring during the lifetime of a star. Ap- plying these principles to the Sun, it became clear 1Earth System Analysis, Potsdam Institute for that the luminosity of the Sun had to change over Climate Impact Research, Potsdam, Germany time, with the young Sun being considerably less Copyright 2012 by the American Geophysical Union. Reviews of Geophysics, ???, / pages 1–32 8755-1209/12/£15.00 Paper number • 1 • 2 • FEULNER: THE FAINT YOUNG SUN PROBLEM luminous than today [Hoyle, 1958; Schwarzschild, the core hydrogen burning phase of evolution of 1958]. a star is an inevitable consequence of Newtonian According to standard solar models, when nu- physics and the functional dependence of the ther- clear fusion ignited in the core of the Sun at the monuclear reaction rates on density, temperature time of its arrival on what is called the zero-age and composition.” main sequence (ZAMS) 4.57 Ga (1 Ga = 109 years In addition to this slow evolution of the bolo- ago), the bolometric luminosity of the Sun (the so- metric solar luminosity over timescales of ∼ 109 yr, lar luminosity integrated over all wavelengths) was the Sun exhibits variability on shorter timescales about 30% lower as compared to the present epoch of up to ∼ 103 yr [Fr¨ohlich and Lean, 2004]. This [Newman and Rood, 1977]. The long-term evolu- variability in solar radiation is a manifestation of tion of the bolometric solar luminosity L(t) as a changes in its magnetic activity related to the solar function of time t can be approximated by a sim- magnetic field created by a magnetohydrodynamic ple formula [Gough, 1981] dynamo within the Sun [Weiss and Tobias, 2000]. The bolometric solar luminosity is dominated by radiation in the visible spectral range originating L (t) 1 = , (1) from the Sun’s lower atmosphere which shows very L⊙ 1+ 2 1 − t little variation with solar activity [Fr¨ohlich and 5 t⊙ Lean, 2004]. For the present-day Sun, for exam- 26 ≃ where L⊙ = 3.85 × 10 W is the present-day ple, total solar irradiance varies by only 0.1% solar luminosity and t⊙ = 4.57 Gyr (1 Gyr = over the 11-year sunspot cycle [Gray et al., 2010]. 109 years) is the age of the Sun. Except for the The Sun’s ultraviolet radiation, on the other first ∼ 0.2 Gyr in the life of the young Sun, this hand, is predominantly emitted by the hotter up- approximation agrees very well with the time evo- per layers of the solar atmosphere which are sub- lution calculated with more recent standard solar ject to much larger variability [Lean, 1987; Fr¨ohlich models [e.g., Bahcall et al., 2001], see the compar- and Lean, 2004]. Solar variability (and thus ultra- ison in Figure 1. violet luminosity) was higher in the past due to Note that solar models had been under intense a steady decrease in magnetic activity over time scrutiny for a long time in the context of the “so- caused by the gradual slowing of the Sun’s rota- lar neutrino problem”, an apparent deficiency of tion which ultimately drives the magnetohydrody- neutrinos observed in terrestrial neutrino detec- namic dynamo [Zahnle and Walker, 1982; Dorren tors [Haxton, 1995] which is now considered to be and Guinan, 1994; G¨udel, 2007]. From observa- resolved by a modification of the standard model tions of young stars similar to the Sun one can in- of particle physics [Mohapatra and Smirnov, 2006] fer a decrease in rotation rate Ω⊙ of the Sun with rather than to be an indication of problems with time t which follows a power law solar models. Furthermore, the time evolution of the Sun’s luminosity has been shown to be a very −0.6 Ω⊙ ∝ t (2) robust feature of solar models [Newman and Rood, 1977; Bahcall et al., 2001]. Thus it appears highly [G¨udel, 2007]. For the same reason, the solar unlikely that the prediction of low luminosity for wind was stronger for the young Sun, with conse- the early Sun is due to fundamental problems with quences for the early Earth’s magnetosphere and solar models. (Slightly modified solar models in- the loss of volatiles and water from the early at- volving a larger mass loss in the past will be dis- mosphere [Sterenborg et al., 2011], especially con- cussed in Section 4.) sidering the fact that the strength of Earth’s mag- In a way the robustness of the luminosity evo- netic field was estimated to be ∼ 50 − 70% of the lution of stellar models is not surprising, since the present-day field strength 3.4 − 3.45 Ga [Tarduno gradual rise in solar luminosity is a simple physical et al., 2010]. The effects of these changes in ul- consequence of the way the Sun generates energy traviolet radiation and solar wind will be briefly by nuclear fusion of hydrogen to helium in its core. discussed later on. Over time, Helium nuclei accumulate, increasing Coming back to the lower bolometric luminosity the mean molecular weight within the core. For of the Sun, an estimate of the amount of radiative a stable, spherical distribution of mass twice the forcing of the climate system this reduction cor- total kinetic energy is equal to the absolute value responds to is given by ∆F = ∆S0(1 − A)/4 (the of the potential energy. According to this virial change in incoming solar radiation corrected for ge- theorem, the Sun’s core contracts and heats up ometry and Earth’s albedo A). Using the present- −2 to keep the star stable, resulting in a higher en- day solar constant S0 ≃ 1361 W m [Kopp and ergy conversion rate and hence a higher luminos- Lean, 2011] and Earth’s current albedo A ≃ 0.3 ity.