Signatures of the Core-Powered Mass-Loss Mechanism in the Exoplanet Population: Dependence on Stellar Properties and Observational Predictions

Abstract: Recent studies have shown that atmospheric mass-loss powered by the cooling luminosity of a planet's core can explain the observed radius valley separating super-Earths and sub-Neptunes, even without photoevaporation. In this work, we investigate the dependence of this core-powered mass-loss mechanism on stellar mass ($M_\ast$), metallicity ($Z_\ast$) and age ($\tau_\ast$). Without making any changes to the underlying planet population, we find that the core-powered mass-loss model yields a shift in the radius valley to larger planet sizes around more massive stars with a slope given by $\text{d log}R_p/\text{d log}M_\ast \simeq 0.35$, in agreement with observations. To first order, this slope is driven by the dependence of core-powered mass-loss on the bolometric luminosity of the host star and is given by $\text{d log}R_p/\text{d log}M_\ast \simeq (3\alpha-2)/36 \simeq 0.33$, where $(L_\ast/L_\odot) = (M_\ast/M_\odot)^\alpha$ is the stellar mass-luminosity relation and $\alpha\simeq 4.6$ for the CKS dataset. We therefore find, in contrast to photoevaporation models, no evidence for a linear correlation between planet and stellar mass, but can't rule it out either. In addition, we show that the location of the radius valley is, to first order, independent of stellar age and metallicity. Since core-powered mass-loss proceeds over Gyr timescales, the abundance of super-Earths relative to sub-Neptunes increases with age but decreases with stellar metallicity. Finally, due the dependence of the envelope's cooling timescale on metallicity, we find that the radii of sub-Neptunes increase with metallicity and decrease with age with slopes given by $\text{d log}R_p/\text{d log}Z_\ast \simeq 0.1$ and $\text{d log}R_p/\text{d log}\tau_\ast \simeq -0.1$, respectively. We conclude with a series of observational tests that can differentiate between core-powered mass-loss and photoevaporation models.

• The paper demonstrates how core-powered mass loss explains the exoplanet radius valley with a stellar mass-dependent slope of 0.35 in log-log space.
• It combines numerical simulations using the CKS dataset with analytical models to reveal metallicity and age effects on atmospheric evolution.
• The research offers observational predictions to distinguish between core-powered mass loss and photoevaporation, guiding future exoplanet studies.

Signatures of the Core-Powered Mass-Loss Mechanism in the Exoplanet Population: Dependence on Stellar Properties and Observational Predictions

The study conducted by Gupta and Schlichting makes significant progress in understanding the core-powered mass-loss mechanism for exoplanet atmospheres and its dependence on stellar properties. This research provides an in-depth analysis of how this mechanism can explain the observed radius valley separating super-Earths and sub-Neptunes, exploring variations in its effectiveness due to host stellar characteristics like mass, metallicity, and age. The paper offers both numerical and analytical insight, aligning theoretical predictions with observed exoplanet data.

Numerical Results and Observational Correlations

The researchers utilize the California-Kepler Survey (CKS) dataset to model host star properties. They reveal that the core-powered mass-loss mechanism results in a radius valley that increases with stellar mass, demonstrating a slope of about 0.35 in log-log space. This slope is corroborated through observations and attributed to the bolometric luminosity dependence, which scales with stellar mass, where the stellar mass-luminosity relation assumes a critical role. The results align well with observational data showing a proportional relationship between the radius valley and stellar mass variations.

Their numeric simulations extend to showcase the relative abundance of planetary types and the drift toward greater planet size in higher stellar mass environments. The study similarly illustrates that stellar ages largely influence the observable exoplanet population, predicting a steady depletion of sub-Neptunes over gigayear timescales due to thermal contraction and core-powered mass-loss. Metallicity finds its influence in modulating thermal contraction rates where sub-Neptunes are larger with increased stellar metallicity.

Analytical Insights and Theoretical Predictions

Gupta and Schlichting develop analytical frameworks to predict slope changes in the radius valley correlated to stellar parameters. The dependence on stellar mass is primarily explained by energy available from cooling, which dictates atmospheric loss. Their mathematical derivations capture the expected adjustments in planet radii due to metallicity and age, predicting trends that are consistent with numerical results. For instance, their models show sub-Neptunes enlarging with metallicities owing to slower cooling rates related to increased opacities, agreeing with empirical measurements.

The paper meticulously approaches the implications of assumed correlations between planet and stellar mass distributions. While evidence for a linear correlation between these distributions is not stringent within their findings, they explore the potential shifts that could be introduced by postulating such relationships, particularly in photoevaporative models that rely on altered initial conditions.

Conclusion and Speculative Paths Forward

The research provides ample observational tests to distinguish between core-powered mass-loss and photoevaporation. With replica possibilities like predicted trends in stellar age correlations manifesting significantly beyond 500 million years—a direct contradiction to the photoevaporation timeline—the manuscript lays a foundation for the differential diagnosis of atmospheric stripping processes. Planets found within the radius valley may further serve as live evidence of ongoing atmospheric loss, potentially observable by modern astrophysical instruments.

Future work envisaged by Gupta and Schlichting could amalgamate models incorporating both mass-loss mechanisms, offering comprehensive insights into the configurational dynamics of close-in exoplanets. The long-term objective focuses on refining our grasp of exoplanetary cores’ compositions and atmospheres by deeply intertwining theoretical propositions with observational confirmations, broadening the investigative scope of planetary sciences.