The Faint Young Sun and Faint Young Stars Paradox (1706.01016v1)

Abstract: The purpose of this paper is to explore a resolution for the Faint Young Sun Paradox that has been mostly rejected by the community, namely the possibility of a somewhat more massive young Sun with a large mass loss rate sustained for two to three billion years. This would make the young Sun bright enough to keep both the terrestrial and Martian oceans from freezing, and thus resolve the paradox. It is found that a large and sustained mass loss is consistent with the well observed spin-down rate of Sun-like stars, and indeed may be required for it. It is concluded that a more massive young Sun must be considered a plausible hypothesis.

• The paper introduces a hypothesis that an early higher solar mass and sustained mass loss resolved the Faint Young Sun Paradox by maintaining sufficient luminosity for liquid oceans.
• Methodologies include analyzing stellar spin-down rates and wind torque models to connect solar mass loss with angular momentum evolution.
• Implications extend to reinterpreting early planetary climates and habitability criteria for Earth, Mars, and other exoplanetary systems.

An Examination of the Faint Young Sun and Faint Young Stars Paradox

The paper "The Faint Young Sun and Faint Young Stars Paradox" by Petrus C. Martens addresses the longstanding enigma known as the Faint Young Sun Paradox. This paradox raises the question of how early Earth and Mars maintained liquid oceans under a Sun that was less luminous than it is today. Conventional stellar evolution theory posits that the young Sun emitted about 70% of its current luminosity. Despite this, geological evidence indicates that early Earth had warm oceans, which were crucial for the emergence of life. The paradox is profound for Mars as well, considering its greater distance from the Sun and presumably lower energy influx.

Hypothesis and Methodology

The paper explores a less conventional hypothesis to resolve this paradox by proposing that the young Sun was initially more massive and subsequently lost significant mass over the first few billion years. This hypothesis suggests that a more massive Sun would have been sufficiently luminous to prevent the freezing of Earth's and Mars' oceans. The paper scrutinizes whether an increased mass loss rate, consistent with observed spin-down rates of Sun-like stars, could make this scenario plausible.

Mass Loss and Solar Luminosity

The relationship between solar mass and luminosity is nonlinear, following the mass-luminosity relation where luminosity scales with the fourth to fifth power of the mass. Thus, an increase in the Sun's initial mass would result in a substantial increase in luminosity. The paper argues that a mass loss rate of approximately $10^{-11} M_{\odot} \, \text{yr}^{-1}$ sustained over two to three billion years could facilitate a more luminous young Sun, sufficient to address the Faint Young Sun Paradox.

Stellar Spin-Down Analysis

A critical aspect of the paper is correlating the proposed mass loss rates with the angular momentum loss required for the observed spin-down rates of solar analogs. The torque applied by stellar winds plays a pivotal role in the spin-down of stars as they evolve from rapid rotation periods at the zero-age main sequence (ZAMS) to slower rotations in middle age. The paper employs the models of Weber and Davis (1967), which link angular momentum loss to wind torque, while considering the influence of magnetic field topology as modeled by Keppens and Goedbloed (2000).

Implications

The findings suggest that a sustained, higher mass loss rate is a tenable solution for the Faint Young Sun Paradox. The proposal that a massive solar wind could have consistently affected both Earth and Mars supports a unified solution under Occam's Razor. Furthermore, should observations in stellar mass loss rates in young solar analogs support this hypothesis, it could redefine our understanding of star-planet interactions in early solar system environments.

Future Prospects

Continued investigation into the mass loss rates of young G stars via methods such as astroseismology or X-ray calibration could yield insights into the veracity of this hypothesis. The resolution of the Faint Young Sun Paradox not only has implications for understanding early solar system development but also for astrobiological prospects in G star systems. This research opens pathways for future studies on the longevity of habitable zones and the development of life in varying stellar environments.

In conclusion, the paper presents a scientifically grounded hypothesis that could challenge prevailing notions of early solar evolution while aligning with observed stellar behaviors. Further empirical validation through stellar observations would be instrumental in resolving this paradox and enriching our comprehension of stellar and planetary evolution.