SIMBAD references

In recent years, analysing 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 dlogR_p/dlogP ≃ -0.11 even for stars as small as 0.1 M_⊙, as observed in latest studies. Furthermore, we find that the slope of the radius valley in the planet size-stellar mass space is dlogR_p/dlogM_* ≃ (3ζ - 2)/36 where ζ is given by the stellar mass-luminosity relation $L_\ast \propto M_\ast ^\zeta$. Because ζ is ≳ 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 ζ with stellar mass. While around 1.0 M_⊙ stars the slope is dlogR_p/dlogM_* ∼ 0.37, it is as low as ∼0.13 around 0.1 M_⊙ 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.