Our Sun. V. A bright young Sun consistent with helioseismology and warm temperatures on ancient Earth and Mars

The relatively warm temperatures required on early Earth and Mars have been difficult to account for via warming from greenhouse gases. We tested whether this problem can be resolved for both Earth and Mars by a young Sun that is brighter than predicted by the standard solar model (SSM). We computed high-precision solar evolutionary models with slightly increased initial masses of M-i = 1.01-1.07 M.; for each mass, we considered three different mass-loss scenarios. We then tested whether these models were consistent with the current high-precision helioseismic observations. The relatively modest mass-loss rates in these models are consistent with observational limits from young stars and estimates of the past solar wind obtained from lunar rocks and do not significantly affect the solar lithium depletion. For appropriate initial masses, all three mass-loss scenarios are capable of yielding a solar flux 3.8 Gyr ago high enough to be consistent with water on ancient Mars. The higher flux at the planets is due partly to the fact that a more massive young Sun would be intrinsically more luminous and partly to the fact that the planets would be closer to the more massive young Sun. At birth on the main sequence, our preferred initial mass M-i = 1.07 M. would produce a solar flux at the planets 50% higher than that of the SSM, namely, a flux 5% higher than the present value (rather than 30% lower, which the SSM predicts). At first (for 1-2 Gyr), the solar flux would decrease; subsequently, it would behave more like the flux in the SSM, increasing until the present. We find that all of our mass-losing solar models are consistent with the helioseismic observations; in fact, our preferred mass-losing case with M-i = 1.07 M. is in marginally (although insignificantly) better agreement with the helioseismology than is the SSM. The early solar mass loss of a few percent does indeed leave a small fingerprint on the Sun's internal structure. However, for helioseismology to significantly constrain early solar mass loss would require higher accuracy in the observed solar parameters and input physics, namely, by a factor of similar to3 for the observed solar surface composition and a factor of similar to2 for the solar interior opacities, the p-p nuclear reaction rate, and the diffusion constants for gravitational settling.