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 to 1.07 M _ { \odot } ; 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 _ { \odot } 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 _ { \odot } is in marginally ( though 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 \sim 3 for the observed solar surface composition , and a factor of \sim 2 for the solar interior opacities , the pp nuclear reaction rate , and the diffusion constants for gravitational settling .