Statistical Emulators for Inferring Planet Formation Conditions

Music City Center 

Exploring the full parameter space of planet formation conditions and processes is computationally impractical as each simulation can take weeks to complete, and the parameter space remains vast. In this work, we propose a framework to infer planet formation conditions while reducing computational costs. Our approach accounts for intrinsic variations in conditions and the stochastic nature of outcomes within a given set of conditions. We employ statistical emulators to model the relationship between planet formation parameters - such as solid normalization, radial distribution of solids, and gas disk depletion - and key observables, including period ratio, transit multiplicity, transit ratio, and hill spacing. Since these observables are inherently stochastic and represented by probability distributions, we first map the stochastic outputs to a reduced-dimensional space. We then use Gaussian processes (GP) to model the relationships within this reduced space. Once the emulators are trained on existing simulation data, we apply a Bayesian modular approach to infer the underlying parameters. Fast GP predictions within the likelihood ensure computationally feasible inference.

Emulators

Gaussian Process

Stochastic Simulator

Astrostatistics

Planet formation 

Section on Physical and Engineering Sciences