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 with warming from greenhouse gases. A slightly more massive young Sun would be brighter than predicted by the standard solar model, simultaneously resolving this problem for both Earth and Mars. We computed high-precision solar models with seven initial masses, from Mi = 1.01 to 1.07 solar mass - the latter being the maximum permitted if the early Earth is not to lose its water via a moist greenhouse effect. The relatively modest early mass loss that is required remains consistent with observational limits on mass loss from young stars and with estimates of the past solar wind obtained from lunar rocks. We considered three types of mass loss rates: (1) a reasonable choice of a simple exponential decline, (2) an extreme step-function case that gives the maximum effect consistent with observations, and (3) the radical case of a linear decline which is inconsistent with the solar wind mass loss estimates from lunar rocks. Our computations demonstrated that mass loss leaves a fingerprint oil the Sun's internal structure large enough to be detectable with helioseismic observations. All of our mass-losing solar models were consistent with the helioseismic observations; in fact, our preferred mass-losing cases were in marginally better agreement with the helioseismology than the standard solar model was, although this difference was smaller than the effects of other uncertainties in the input physics and in the solar composition. Mass loss has only a relatively minor effect on the predicted lithium depletion; the major portion of the solar lithium depletion must still be due to rotational mixing. Thus the modest mass loss cases considered here cannot be ruled out by observed lithium depletions. For the three mass loss types considered, the preferred initial masses were 1.07 solar mass for the exponential case and 1.04 solar mass for the step-function and linear cases; all of these provided high enough solar fluxes at Mars 3.8 Gyr ago to be consistent with the existence of liquid water. For a more massive early Sun, the planets would have had to be closer to the young Sun in order to end up in their present orbits; the orbital radii of the planets would vary inversely with the solar mass. Both of these effects contribute to the fact that the early solar flux at the planets would have been considerably higher than that of the standard solar model at that time. In fact, the 1.07 solar mass exponential case has a flux at birth 5% higher than the present solar flux, while the radical 1.04 solar mass linear case has a nearly constant flux over the first 3 Gyr only about 10% lower than at present. The early solar evolution would be in the opposite direction in the H-R diagram to that of the standard Sun.