AGU Fall 2006

(Abstract of presentation for AGU December 14, 2006)

The “Faint Young Sun” has been a paradox of astrophysics. Standard models of the Sun’s evolution predict that 4 billion years ago Earth was too cold to support life. Geology and the fossil record contradict this prediction. The paradox and theoretical solution are a fascinating combination of astrophysics, relativity and Earth sciences.

Models predict that 4.5 billion years ago the Sun shone with approximately 70% of its present luminosity. Since power P is related to temperature T by the Stefan-Boltzmann law P ~ T^4, Earth’s temperature would have been only 91% of its present value. Today's temperature is approximately 283K, so temperature in the past would have been only 258K. Earth’s surface would have frozen solid, making evolution of life very unlikely.

Geology shows evidence of sedimentation 4 billion years ago, indicating the presence of rivers and seas. Other geological markers corroborate the presence of liquid water on Earth during this period. Paleontology dates the earliest organisms at least 3.4 billion years old. Clearly liquid water and life both existed when the model predicts Earth was frozen solid. This conflict with observations is the Faint Young Sun paradox.

Fortunately, Relativity and Space/Time can help save the standard solar model. The Sun converts fuel to energy according to E = mc^2. Unified Space/Time predicts that c is given by:

GM = tc^3

Where t is age of the Universe, GM combines its mass and gravitational constant. Solving, we have c(t) = (GM)^{1/3} t^{-1/3}. Billions of years ago, solar output and temperature were therefore higher than originally estimated.

Earth is estimated to be 4.6 billion years and the Universe 13.7 billion years old, 1.5 times its age at the time of Earth’s formation. Energy E = mc^2 is adjusted by: (1.5)^{2/3} = 1.31 times the initial estimate. Multiplying by that estimate of 70%, the Sun’s actual output was 91.7% of the present value. Temperature was then (0.917)^{1/4} = 98% of today's value. If we start with an estimate of 76%, solar luminosity was exactly the present value. The “paradox” leads to an extraordinary confirmation of Theory. The solar constant may indeed be constant, allowing life to have evolved on Earth for billions of years.

Prediction of a changing c can be more precisely corroborated using observations of Type Ia supernovae. Earth’s temperature provides additional data points to supplement supernova data from a more distant past. This corroborating data distinguishes Theory from “accelerating universe” ideas. Theory may also help determine whether CO2 warmed Earth's temperature in the past.

CONCLUSION: The “Faint Young Sun” is not a problem but a window from the Earth sciences to astrophysics and cosmology. Geology and the fossil record can help verify “fossil” values of fundamental measurements, determining whether they are indeed constant.