Properties of the radius valley around low mass stars: Predictions from the core-powered mass-loss mechanism

Abstract

In recent years, analyzing the bimodality in the size distribution of small planets, i.e., the `radius valley', has given us unprecedented insight into the planet formation process. Here we explore the properties of the radius valley for low mass stars, assuming that the core-powered mass-loss is the dominant process shaping the small exoplanet population. We show that the slope of radius valley in the planet size-orbital period space, to first-order, does not vary with stellar mass and has a negative slope of $\text{d log}{R}_p/\text{d log}P\simeq -0.11$ even for stars as small as 0.1 $M_{\odot }$, as observed in latest studies. Furthermore, we find that the slope of the radius valley in the planet size-stellar mass space is $\text{d log}{R}_p/\text{d log}{M}_{\ast }\simeq (3\hat{I}\P -2)/36$ where $\hat{I}\P$ is given by the stellar mass-luminosity relation $L_{\ast }\propto M_{\ast }^{\hat{I}}\P$. Because $\hat{I}\P$ is $\gtrsim$ 2 and increases with stellar mass, we predict that the radius valley has a positive slope in the planet size-stellar mass space across FGKM dwarfs. This slope, however, decreases (increases) in magnitude towards lower (higher) mass stars, due to the variation of $\hat{I}\P$ with stellar mass. While around 1.0 $M_{\odot }$ stars the slope is $\text{d log}{R}_p/\text{d log}{M}_{\ast }\sim 0.37$, it is as low as $\sim 0.13$ around 0.1 $M_{\odot }$ stars. In addition, we find that the radius valley is narrower and less empty around lower mass stars. Finally, we show that predictions for the radius valley for core-powered mass-loss and photoevaporation become increasingly distinct for lower mass stars.

9 pages, 5 figures and 1 table. Accepted for publication in MNRAS