http://arxiv.org/abs/1811.03202
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 $\text{d log} R_p/ \text{d log} P \simeq 1/(3(1-\beta)) \simeq -0.11$, where $M_c \propto R_c^{\beta}$ is the mass-radius relation of the core. $\beta \simeq 4$ yields good agreement with observations, attesting to the significance of internal compression for planetary cores more massive than Earth. We further find that the location of the valley scales with the uncompressed core density 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.
A. Gupta and H. Schlichting
Fri, 9 Nov 18
10/64
Comments: 9 pages and 5 figures. Submitted to MNRAS