Sculpting the valley in the radius distribution of small exoplanets as a by-product of planet formation: the core-powered mass-loss mechanism

Abstract

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 ⊕ . 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 d logR p /d logP 1/ (3(1 − β)) which evaluates to −0.11 for β 4, where M c /M ⊕ = (R c /R ⊕ ) β (ρ c * /ρ ⊕ ) β/3 is the massradius relation of the core. This choice for β 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 ρ −4/9 c * and that the observed planet population must have predominantly rocky cores with typical water-ice fractions of less than ∼ 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.

Architectures of exoplanetary systems – I. A clustered forward model for exoplanetary systems around Kepler’s FGK stars

“…While this model allows for more similar sizes of planets within the same system, the fit to the observed radius ratio distribution is not significantly improved in terms of the KS or AD distances, suggesting that additional features in this distribution are still inadequately reproduced by any of our current models. Most notably, the observed radius ratio distribution appears to be quite asymmetric, which is likely a signature of stripped planetary atmospheres due to photo-evaporation (Lopez, Fortney, & Miller 2012;Owen & Wu 2017) or core-powered mass loss (Gupta & Schlichting 2018). Weiss et al (2018a) find a very similar effect of clustering and asymmetry in the radius ratio distribution and also a slight positive correlation between radius ratio and the difference in effective temperatures between adjacent plan-ets.…”

“…In addition, planet sizes appear to be highly correlated, as evidenced by the peaked nature of the adjacent radii ratio distribution (Weiss et al 2018a), and this clustering extends to planet masses (Millholland, Wang, & Laughlin 2017). While the mechanisms of photo-evaporation (Owen & Wu 2013;Fulton et al 2017;Owen & Wu 2017;Van Eylen et al 2017;Carrera et al 2018) or core-powered mass-loss from formation Gupta & Schlichting 2018) have been proposed to explain these features in the distributions of radii and radii ratios, complex observational biases limit our ability to distinguish models or understand the relative contribution of physical and observational effects. To further illustrate this point, most recently Zhu (2019) has challenged the statistical significance of the correlations reported by Ciardi et al (2013) and Weiss et al (2018a).…”

Oxygen fugacities of extrasolar rocks: Evidence for an Earth-like geochemistry of exoplanets

“…, (1) where xi k are mole fractions of the species i in phase k, γi k are activity coefficients for the species, and thermodynamic activities are ai k = xi k γi k . To facilitate comparison, we set the uncertain activity coefficients to unity, so the second term on the right-hand side of Equation (1) vanishes.…”

Breaking Resonant Chains: Destabilization of Resonant Planets Due to Long-term Mass Evolution

“…Close-in planets that grow in the gas disk would accrete H/He atmospheres that come from the protoplanetary disk (Ikoma & Hori 2012). These atmospheres escape from planets by the photoevaporation (e.g., Valencia et al 2010;Lopez & Fortney 2013;Owen 2019;Hori & Ogihara 2020), core-powered mass loss (Ginzburg et al 2016;Gupta & Schlichting 2019), and Parker wind (Owen & Wu 2016). Planets can lose 10% of their masses through the atmospheric escape.…”