Recent observations revealed a bimodal radius distribution of small , short-period exoplanets with a paucity in their occurrence , a radius ‘ valley ’ , around 1.5 - 2.0 R _ { \oplus } .
In this work , we investigate the effect of a planet ’ s own cooling luminosity on its thermal evolution and atmospheric mass-loss ( core-powered mass-loss ) and determine its observational consequences for the radius distribution of small , close-in exoplanets .
Using simple analytical descriptions and numerical simulations , we demonstrate that planetary evolution based on the core-powered mass-loss mechanism alone ( i.e. , without any photoevaporation ) can produce the observed valley in the radius distribution .
Our results match the valley ’ s location , shape and slope in planet radius-orbital period parameter space , and the relative magnitudes of the planet occurrence rate above and below the valley .
We find that the slope of the valley is , to first order , dictated by the atmospheric mass-loss timescale at the Bondi radius and given by \text { d log } R _ { p } / \text { d log } P \simeq 1 / ( 3 ( 1 - \beta ) ) which evaluates to -0.11 for \beta \simeq 4 , where M _ { c } / M _ { \oplus } = ( R _ { c } / R _ { \oplus } ) ^ { \beta } ( \rho _ { c* } / \rho _ { \oplus } ) ^ { \beta / 3 } is the mass-radius relation of the core .
This choice for \beta yields good agreement with observations and attests to the significance of internal compression for massive planetary cores .
We further find that the location of the valley scales as \rho _ { c* } ^ { -4 / 9 } and that the observed planet population must have predominantly rocky cores with typical water-ice fractions of less than \sim 20 \% .
Furthermore , we show that the relative magnitude of the planet occurrence rate above and below the valley is sensitive to the details of the planet-mass distribution but that the location of the valley is not .