Question

What was the value of Energyout from the Earth's surface during the Faint Young Sun era? Give your answer in W/m2, but don't write the W/m2 part.

Answer 1

By the 1950s, stellar astrophysicists had worked

out the physical principles governing the structure

and evolution of stars [Kippenhahn and Weigert ,

1994]. This allowed the construction of theoretical

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

that the luminosity of the Sun had to change over

time, with the young Sun being considerably less.

According to standard solar models, when nu-

clear fusion ignited in the core of the Sun at the

time of its arrival on what is called the zero-age

main sequence (ZAMS) 4.57 Ga (1 Ga = 109years

ago), the bolometric luminosity of the Sun (the so-

lar luminosity integrated over all wavelengths) was

about 30% lower as compared to the present epoch

[Newman and Rood, 1977]. The long-term evolu-

tion of the bolometric solar luminosity L(t) as a

function of time tcan be approximated by a simple formula

-

where L⊙ = 3.85 × 1026 W is the present‐day solar luminosity and t⊙ = 4.57 Gyr (1 Gyr = 109 years) is the age of the Sun. Except for the first ∼0.2 Gyr in the life of the young Sun, this approximation agrees very well with the time evolution calculated with more recent standard solar models [e.g., Bahcall et al., 2001]; see the comparison in Figure 1.

Note that solar models had been under intense scrutiny for a long time in the context of the “solar neutrino problem,” an apparent deficiency of neutrinos observed in terrestrial neutrino detectors. That is now considered to be resolved by a modification of the standard model of particle physics rather than to be an indication of problems with solar models. Furthermore, the time evolution of the Sun's luminosity has been shown to be a very robust feature of solar models. Thus it appears highly unlikely that the prediction of low luminosity for the early Sun is due to fundamental problems with solar models. (Slightly modified solar models involving a larger mass loss in the past) In a way the robustness of the luminosity evolution of stellar models is not surprising, since the gradual rise in solar luminosity is a simple physical consequence of the way the Sun generates energy by nuclear fusion of hydrogen to helium in its core. Over time, helium nuclei accumulate, increasing the mean molecular weight within the core. For a stable, spherical distribution of mass, twice the total kinetic energy is equal to the absolute value of the potential energy. According to this virial theorem, the Sun's core contracts and heats up to keep the star stable, resulting in a higher energy conversion rate and hence a higher luminosity. There seems no possibility for escape . “The gradual increase in luminosity during the core hydrogen burning phase of evolution of a star is an inevitable consequence of Newtonian physics and the functional dependence of the thermonuclear reaction rates on density, temperature and composition.”In addition to this slow evolution of the bolometric solar luminosity over timescales of ∼109 years, the Sun exhibits variability on shorter timescales of up to ∼103 years . This variability in solar radiation is a manifestation of changes in its magnetic activity related to the solar magnetic field created by a magnetohydrodynamic dynamo within the Sun . The bolometric solar luminosity is dominated by radiation in the visible spectral range originating from the Sun's lower atmosphere that shows very little variation with solar activity. For the present‐day Sun, for example, total solar irradiance varies by only ≃0.1% over the 11 year sunspot cycle.The Sun's ultraviolet radiation, on the other hand, is predominantly emitted by the hotter upper layers of the solar atmosphere that are subject to much larger variability. Solar variability (and thus ultraviolet luminosity) was higher in the past due to a steady decrease in magnetic activity over time caused by the gradual slowing of the Sun's rotation that ultimately drives the magnetohydrodynamic dynamo. From observations of young stars similar to the Sun one can infer a decrease in rotation rate Ω⊙ of the Sun with time t that follows a power law [Güdel, 2007]

For the same reason, the solar wind was stronger for the young Sun, with consequences for the early Earth's magnetosphere and the loss of volatiles and water from the early atmosphere, especially considering the fact that the strength of Earth's magnetic field was estimated to be ∼50–70% of the present‐day field strength 3.4–3.45 Ga. The effects of these changes in ultraviolet radiation and solar wind will be briefly discussed later on.Coming back to the lower bolometric luminosity of the Sun, an estimate of the amount of radiative forcing of the climate system this reduction corresponds to is given by ΔF = ΔS0 (1 − A)/4 (the change in incoming solar radiation corrected for geometry and Earth's albedo A). Using the present‐day solar constant S0 ≃ 1361 W m−2 [Kopp and Lean, 2011] and Earth's current albedo A ≃ 0.3 yields values of ΔF ≈ 60 W m−2 and ΔF ≈ 40 W m−2 at times 3.8 Ga and 2.5 Ga, respectively. For comparison, the net anthropogenic radiative forcing in 2005 is estimated to be ≃1.6 Wm−2.