Architectures of Exoplanetary Systems. IV: A Multi-planet Model for Reproducing the Radius Valley and Intra-system Size Similarity of Planets around Kepler's FGK Dwarfs

TL;DR

Kepler's radius valley and intra-system size similarity pose a joint constraint on exoplanet demographics. The authors present a hybrid SysSim population model that merges AMD-stability–driven architectures with a mass–radius–period framework including envelope loss from photoevaporation, enabling simultaneous reproduction of the radius valley and peas-in-a-pod patterns. The model emphasizes strongly clustered initial planet masses (HM-C) and uses a forward ABC inference pipeline with differential evolution optimization and Gaussian-process emulation to fit Kepler FGK dwarfs, yielding Earth- and Venus-like planet occurrences that are 2–4 times lower than in non-clustered scenarios and predicting a radius cliff beyond roughly $2.5\,R_\oplus$. This approach provides a cohesive, forward-modeling framework to jointly constrain multiple size-patterns in multi-planet systems and informs the physical processes shaping exoplanet architectures.

Abstract

The Kepler-observed distribution of planet sizes have revealed two distinct patterns: (1) a radius valley separating super-Earths and sub-Neptunes and (2) a preference for intra-system size similarity. We present a new model for the exoplanet population observed by Kepler, which is a "hybrid" of a clustered multi-planet model in which the orbital architectures are set by the angular momentum deficit (AMD) stability (He et al. 2020; arXiv:2007.14473) and a joint mass-radius-period model involving envelope mass-loss driven by photoevaporation (Neil & Rogers 2020; arXiv:1911.03582). We find that the models that produce the deepest radius valleys have a primordial population of planets with initial radii peaking at $\sim 2.1 R_\oplus$, which is subsequently sculpted by photoevaporation into a bimodal distribution of final planet radii. The hybrid model requires strongly clustered initial planet masses in order to match the distributions of the size similarity metrics. Thus, the preference for intra-system radius similarity is well explained by a clustering in the primordial mass distribution. The hybrid model also naturally reproduces the observed radius cliff (steep drop-off beyond $\sim 2.5 R_\oplus$). Our hybrid model is the latest installment of the SysSim forward models, and is the first multi-planet model capable of simultaneously reproducing the observed radius valley and the intra-system size similarity patterns. We compute occurrence rates and fractions of stars with planets for a variety of planet types, and find that the occurrence of Venus and Earth-like planets drops by a factor of $\sim 2$-4 for the hybrid models compared to previous clustered models in which there is no envelope mass-loss.

Figures (2)

• Figure 1: Radius-mass relationships of various models. The H20 model is shown as the black dashed line (median prediction) and the gray shaded region (16-84% quantiles), for reference. The initial radius-mass relation from the 2020ApJ...891...12N models is shown in cyan (solid line for the median prediction and shaded region for the 16-84% quantiles). It is a power-law with two break points, smoothed by logistic functions, as also described in §\ref{['sec:methods:new_model:initialMR']}; for illustrative purposes, here we have adopted the best-fit parameters from "Model 2" of 2020ApJ...891...12N (the upper break occurs at $>10 R_\oplus$ and is thus off the axes). The brown curve shows the pure-silicate relation from 2007ApJ...669.1279S (equation \ref{['eq:radius_mass_pure_silicate']}), where the shaded region denotes a 5% scatter as adopted by 2020ApJ...891...12N for drawing final planet radii from their core masses for the planets that have lost their envelopes. The top panel shows the initial planet mass distribution from 2020ApJ...891...12N model 2.
• Figure 2: Cartoon illustration of the hybrid models. The difference between HM-U and HM-C is in the first step, where the initial planet masses and radii are drawn (HM-C draws clustered initial masses as in §\ref{['sec:methods:new_model:clustered']}, while HM-U does not). The planets are also assigned envelope masses in this step. The planets are then subject to photoevaporation and some lose their gaseous envelopes, resulting in the final masses and radii (§\ref{['sec:methods:new_model:photoevap']}). Finally, the critical AMD of the system is computed and distributed among the individual planets to draw their orbital eccentricities and mutual inclinations, as in the H20 model.