Abstract
Given a solar luminosity L_Ar = 0.75 L_0 at the beginning of the Archean 3.8 Gyr ago, where L_0 is the present-day one, if the heliocentric distance r of the Earth was r_Ar = 0.956 r_0, the solar irradiance would have been as large as I_Ar = 0.82 I_0. It would allowed for a liquid ocean on the terrestrial surface which, otherwise, would have been frozen, contrary to the empirical evidence. By further assuming that some physical mechanism subsequently displaced the Earth towards its current distance in such a way that the irradiance stayed substantially constant over the entire Archean from 3.8 Gyr to 2.5 Gyr ago, a relative recession rate as large as \dot r/r \simeq 3.4 x 10^-11 yr^-1 would have been required. Although such a figure is roughly of the same order of magnitude of the value of the Hubble parameter 3.8 Gyr ago H_Ar = 1.192 H_0 = 8.2 x 10^-11 yr^-1, standard general relativity rules out cosmological explanations for the hypothesized Earth' s recession rate. Instead, a class of modified theories of gravitation with nonminimal coupling between the matter and the metric naturally predicts a secular variation of the relative distance of a localized two-body system, thus yielding a potentially viable candidate to explain the putative recession of the Earth' s orbit. Another competing mechanism of classical origin which could, in principle, allow for the desired effect is the mass loss which either the Sun or the Earth itself may have experienced during the Archean. On the one hand, this implies that our planet should have lost 2% of its present mass in the form of eroded/evaporated hydrosphere which, thus, should have been two orders of magnitude larger than now. On the other hand, it is widely believed that the Sun could have lost mass at an enhanced rate due to a stronger solar wind in the past for not more than \sim 0.2-0.3 Gyr.
Highlights
The so-called “Faint Young Sun Paradox” (FYSP) [1] consists of the fact that, according to consolidated models of the Sun’s evolution history, the energy output of our star during the Archean, from 3.8 to 2.5 Ga ago, would have been too low to keep liquid water on the Earth’s surface
We assumed that, given a solar luminosity as little as 75% of its current value at the beginning of the Archean 3.8 Ga ago, the Earth was closer to the Sun than by 4.4% in order to allow for an irradiance large enough to keep a vast liquid ocean on the terrestrial surface
Under the assumption that non-climatic effects can solve the Faint Young Sun paradox, some physical mechanism should have subsequently moved our planet to its present-day heliocentric distance in such a way that the solar irradiance stayed substantially constant during the entire Archean eon, i.e., from 3.8 to
Summary
The so-called “Faint Young Sun Paradox” (FYSP) [1] consists of the fact that, according to consolidated models of the Sun’s evolution history, the energy output of our star during the Archean, from 3.8 to 2.5 Ga ago, would have been too low to keep liquid water on the Earth’s surface. As extensively reviewed in [2], there is ample and compelling evidence that the Earth hosted liquid water, and even life, during the entire Archean eon spanning about 1.3 Ga. our planet could not be entirely frozen during such a remote eon, as, instead, it would have necessarily been if it really received only ≈75% of the current solar irradiance, as results from Equation (4). In the view of some recent studies This is not to claim that climatic solutions are nowadays ruled out [15,16], especially those involving a carbon-dioxide greenhouse in the early Archean and a carbon dioxide-methane greenhouse at later times [8,17,18]; we feel that it is worthwhile to pursue different lines of research.
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