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. We computed high-precision solar evolutionary models with slightly increased initial masses of M_i = 1.01 to 1.07 M_sun; 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. We find that all of our mass-losing solar models are consistent with the helioseismic observations. 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 about 3 for the observed solar surface composition, and a factor of 2 for the solar interior opacities, the pp nuclear reaction rate, and the diffusion constants for gravitational settling.Comment: LaTeX, 30 pages (including 13 figures); ApJ, in press. Added figures/color figures are available at http://www.cita.utoronto.ca/~boothroy/sun5.htm

Hot bottom burning in asymptotic giant branch stars and its effect on oxygen isotopic abundances

A self-consistent calculation of asymptotic giant branch (AGB) evolution was carried out, including nucleosynthesis at the base of the convective envelope (hot bottom burning). Hot bottom burning was found to occur for stars between ~4.5 and ~7 M_☉, producing envelopes with ^(18)O/^(16)O ≾ 10^(-6) and 10^(-3) ≾ ^(17)O/^(l6)O ≾ 10^(-1). The ^(17)O abundance depends sensitively on the nuclear ^(17)O-destruction rate; this rate is only loosely constrained by the requirement that first and second dredge-up models match O-isotope observations of red giant branch (RGB) stars (Boothroyd, Sackmann, & Wasserburg 1994). In some cases, high mass-loss rates can terminate hot bottom burning before further ^(17)O enrichment takes place or even before all ^(18)O is destroyed. These predictions are in accord with the very limited stellar observations of J type carbon stars on the AGB and with some of the circumstellar Al_2O_3 grains from meteorites. In contrast, precise data from a number of grains and data from most low-mass Sand C AGB stars (≾ 1.7 M_☉) lie in a region of the ^(18)O/^(l6)O versus ^(17)O/^(16)O diagram that is not accessible by first and second dredge-up or by hot bottom burning. We conclude that for AGB stars, the standard models of stellar evolution are not in accord with these observations. We surmise that an additional mixing mechanism must exist that transports material from the cool bottom of the stellar convective envelope to a depth at which ^(18)O is destroyed. This "cool bottom processing" mechanism on the AGB is similar to extra mixing mechanisms proposed to explain the excess ^(13)C (and depleted ^(12)C) observed in the earlier RGB stage of evolution and the large ^7Li depletion observed in low-mass main-sequence stars

Predictions of oxygen isotope ratios in stars and of oxygen-rich interstellar grains in meteorites

We carried out detailed, self-consistent calculations for stars from 1 to 9 M_☉ over a wide range of metallicities, following the evolution and nucleosynthesis from the pre-main sequence to the asymptotic giant branch (AGB), in order to provide a self-consistent grid for evaluating stellar oxygen isotopic variations. These were calculated for first and second dredge-up, and for some masses also for third dredge-up and "hot bottom" convective envelope burning on the AGB. We demonstrate that ^(16)O/^(17)O in red giant envelopes is primarily a function of the star's mass, while ^(16)O/^(18)O is primarily a function of the initial composition. Uncertainties in the ^(17)O-destruction rate have no effect on the ^(16)O/^(17)O ratio for stars from 1 to 2.5 M_☉, but do affect the ratios for higher masses: the stellar ^(16)O/^(17)O observations are consistent with the Landré et al. (1990) rates using ƒ = 0.2 for ^(17)O(p, y)^(18)F and ^(17)O(p, ɑ)^(14)N, and with the Caughlan & Fowler (1988) rates using ƒ ~ 1. The stellar ^(16)O/^(18)O observations require ƒ ~ 0 in the Caughlan & Fowler ^(18)O(p, ɑ)^(15)N rate. First dredge-up has the largest effect on the oxygen isotope ratios, decreasing ^(16)O/^(17)O significantly from the initial value and increasing ^(16)O/^(18)O slightly. Second and third dredge-up have only minor effects for solar metallicity stars. The absence of very low observed ^(16)O/^(18)O ratios is consistent with a major increase in the ^(18)O(ɑ, y)^(22)Ne rate over the Caughlan & Fowler (1988) value. Hot bottom burning in stars above about 5 M_☉ can cause a huge increase in ^(16)O/^(18)O (to ≳10^6), and possibly a significant decrease in ^(16)O/^(17)O; these are accompanied by a huge increase in ^7Li and a value of ^(12)C/^(13)C ≈ 3. The oxygen isotope ratios in the Al_2O_3 grains (Orgueil grain B, the Murchison 83-5 grain, and the new Bishunpur B39 grain) can be accounted for if they originated in stars that did NOT have the same initial ^(16)O/^(18)O ratio. Thus one cannot assume uniform isotope ratios, even for stars of nearly solar composition. The grains' ^(16)O/^(17)O ratios, together with the ^(26)Mg excesses that indicate grain formation in a ^(26)Al-rich environment, indicate that the Orgueil grain B and Murchison 83-5 grain originated in stars of roughly 1.5 M_☉, during third dredge-up on the AGB. The new Bishunpur B39 grain originated in a star of either 2 or of 4-7 M_☉

Deep Circulation in Red Giant Stars: A Solution to the Carbon and Oxygen Isotope Puzzles?

The long-standing puzzle of low ^(12)C/^(13)C in low-mass red giant branch (RGB) stars, and the more recent puzzle of low ^(18)O/^(16)O ratios in asymptotic giant branch (AGB) stars and in circumstellar Al_2O_3 grains preserved in meteorites, can be resolved by deep circulation currents below the bottom of the standard convective envelope. These currents transport matter from the nonburning bottom of the convective envelope down to regions where some CNO processing can take place ("cool bottom processing"). Modeling circulation with separate downward and upward streams, we found that, to resolve both discrepancies, the base of the extra mixing had to reach a temperature TP close to that of the H-burning shell, namely, Δ log T ≈ 0.17 from the base of the H-shell for both RGB and AGB stars. While the envelope composition depends sensitively on TP, it is insensitive to the speed or geometry of mixing. This indicates that our stream circulation model is generic, so that more sophisticated mixing models with the same TP would yield similar results. On the AGB, our models predict that stars with low ^(18)O/^(16)O can be either S or C stars but must have low ^(12)C/^(13)C (~4) and elevated ^(14)N. Cool bottom processing also destroys ^3He, so that galactic (D + ^3He) decreases with time; this removes the strongest lower limit on the baryon density Ω_b from big bang nucleosynthesis models

Our Sun. IV. The Standard Model and Helioseismology: Consequences of Uncertainties in Input Physics and in Observed Solar Parameters

Helioseismology provides a powerful tool to explore the deep interior of the Sun: for example, the adiabatic sound speed can be inferred with an accuracy of a few parts in 10,000. This has become a serious challenge to theoretical models of the Sun. Therefore, we have undertaken a self-consistent, systematic study of sources of uncertainties in the standard solar model, which must be understood before the helioseismic observations can be used as constraints on theory. We find that the largest uncertainty in the sound speed in the solar interior, namely, 3 parts in 1000, arises from uncertainties in the observed photospheric abundances of the elements; uncertainties of 1 part in 1000 arise from (1) the 4% uncertainty in the OPAL opacities, (2) the 5% uncertainty in the basic pp nuclear reaction rate, (3) the 15% uncertainty in the diffusion constants for the gravitational settling of helium, and (4) the 50% uncertainties in diffusion constants for the heavier elements. (Other investigators have shown that similar uncertainties arise from uncertainties in the interior equation of state and in rotation-induced turbulent mixing.) The predicted pre-main-sequence solar lithium depletion is a factor of order 20 (an order of magnitude larger than that predicted by earlier models that neglected gravitational settling and used older opacities), and is uncertain by a factor of 2. The predicted neutrino capture rate is uncertain by 30% for the Cl-37 experiment and by 3% for the Ga-71 experiments (not including uncertainties in the capture cross sections), while the B-8 neutrino flux is uncertain by 30%.Comment: LaTeX, 38 pages (including 8 figures); ApJ, in press. Added figures/color figurea available at http://www.cita.utoronto.ca/~boothroy/sun4.htm

Higher Flux from the Young Sun as an Explanation for Warm Temperatures for Early Earth and Mars

Observations indicate that the Earth was at least warm enough for liquid water to exist as far back as 4 Gyr ago, namely, as early as half a billion years after the formation of the Earth; in fact, there is evidence suggesting that Earth may have been even warmer then than it is now. These relatively warm temperatures required on early Earth are in apparent contradiction to the dimness of the early Sun predicted by the standard solar models. This problem has generally been explained by assuming that Earth's early atmosphere contained huge amounts of carbon dioxide (CO2), resulting in a large enough greenhouse effect to counteract the effect of a dimmer Sun. However, recent work places an upper limit of 0.04 bar on the partial pressure of CO2 in the period from 2.75 to 2.2 Gyr ago, based on the absence of siderite in paleosols; this casts doubt on the viability of a strong CO2 greenhouse effect on early Earth. The existence of liquid water on early Mars has been even more of a puzzle; even the maximum possible CO2 greenhouse effect cannot yield warm enough Martian surface temperatures. These problems can be resolved simultaneously for both Earth and Mars, if the early Sun was brighter than predicted by the standard solar models. This could be accomplished if the early Sun was slightly more massive than it is now, i.e., if the solar wind was considerably stronger in the past than at present. A slightly more massive young Sun would have left fingerprints on the internal structure of the present Sun. Today, helioseismic observations exist that can measure the internal structure of the Sun with very high precision. The task undertaken here was to compute solar models with the highest precision possible at this time, starting with slightly greater initial masses. These were evolved to the present solar age, where comparisons with the helioseismic observations could be made. Our computations also yielded the time evolution of the solar flux at the planets - a key input to the climates of early Earth and Mars. Early solar mass loss is not the only influence that can alter the internal structure of the present Sun. There are minor uncertainties in the physics of the solar models and in the key observed solar parameters that also affect the present Sun's internal structure. It was therefore imperative to obtain an understanding of the effects of these other uncertainties, in order to disentangle them from the fingerprints that might be left by early solar mass loss. From these considerations, our work was divided into two parts: (1) We first computed the evolution of standard solar models with input parameters varied within their uncertainties, to determine their effect on the observable helioseismic quantities; (2) We then computed non-standard solar models with higher initial masses to test against the helioseismological observations