Evidence that Core-Powered Mass-Loss Dominates Over Photoevaporation in Shaping the Kepler Radius Valley

Abstract

The dearth of planets with sizes around 1.8 ${\mathrm{R}}_{\oplus }$ is a key demographic feature discovered by the $Kepler$ mission. Two theories have emerged as potential explanations for this valley: photoevaporation and core-powered mass-loss. However, Rogers et al. (2021) shows that differentiating between the two theories is possible using the three-dimensional parameter space of planet radius, incident flux, and stellar mass. We use homogeneously-derived stellar and planetary parameters to measure the $Kepler$ exoplanet radius gap in this three-dimensional space. We compute the slope of the gap as a function of incident flux at constant stellar mass ($\hat{I}\pm$ $\equiv$ ${\left(\partial \log R_{\mathrm{gap}}/\partial \log S\right)}_{M_{\star }}$) and the slope of the gap as a function of stellar mass at constant incident flux (${\hat{I}}^2$ $\equiv$ ${\left(\partial \log R_{\mathrm{gap}}/\partial \log M_{\star }\right)}_S$) and find $\hat{I}\pm$ = 0.069${}_{-0.023}^{+0.019}$ and ${\hat{I}}^2$ = $-$0.046${}_{-0.117}^{+0.125}$. Given that Rogers et al. (2021) shows that core-powered mass-loss predicts $\hat{I}\pm$ $\approx$ 0.08 and ${\hat{I}}^2$ $\approx$ 0.00 while photoevaporation predicts $\hat{I}\pm$ $\approx$ 0.12 and ${\hat{I}}^2$ $\approx$ --0.17, our measurements are more consistent with core-powered mass-loss than photoevaporation. However, we caution that different gap-determination methods can produce systematic offsets in both $\hat{I}\pm$ and ${\hat{I}}^2$; therefore, we motivate a comprehensive re-analysis of $Kepler$ light curves with modern, updated priors on eccentricity and mean stellar density to improve both the accuracy and precision of planet radii and subsequent measurements of the gap.

10 pages, 4 figures. Submitted to ApJL