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

TL;DR

This study predicts the properties of the radius valley in small exoplanets around low-mass stars, emphasizing how the core-powered mass-loss mechanism explains observed trends and differs from photoevaporation predictions.

Contribution

It provides theoretical predictions for the radius valley's slope and width around low-mass stars based on the core-powered mass-loss model, extending understanding to stars as small as 0.1 solar masses.

Findings

Radius valley slope in size-period space is approximately -0.11, consistent across stellar masses.

The slope in size-stellar mass space varies with stellar mass, from 0.13 to 0.37.

Radius valley is narrower and less empty around lower mass stars.

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 $\text{d log}R_p/\text{d log}M_\ast \simeq (3 \zeta - 2)/36$ where $\zeta$ is given by the stellar mass-luminosity relation $L_\ast \propto M_\ast^\zeta$. Because $\zeta$ 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 $\zeta$ 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.