Do planets remember how they formed?

TL;DR

This study introduces an entropy-based model to analyze the size-ordering of multi-planet systems, revealing that Kepler systems retain memory of their formation processes despite dynamical evolution.

Contribution

The paper develops a novel entropy measure for planetary size-ordering and demonstrates its effectiveness in detecting formation memory in Kepler multi-planet systems.

Findings

Kepler systems show significantly lower entropy than random populations.

Entropy increases with system age proxy, indicating dynamical evolution effects.

Results are robust even when accounting for missing planets.

Abstract

One of the most directly observable features of a transiting multi-planet system is their size-ordering when ranked in orbital separation. Kepler has revealed a rich diversity of outcomes, from perfectly ordered systems, like Kepler-80, to ostensibly disordered systems, like Kepler-20. Under the hypothesis that systems are born via preferred formation pathways, one might reasonably expect non-random size-orderings reflecting these processes. However, subsequent dynamical evolution, often chaotic and turbulent in nature, may erode this information and so here we ask - do systems remember how they formed? To address this, we devise a model to define the entropy of a planetary system's size-ordering, by first comparing differences between neighboring planets and then extending to accommodate differences across the chain. We derive closed-form solutions for many of the micro state occupancies and provide public code with look-up tables to compute entropy for up to ten-planet systems. All three proposed entropy definitions exhibit the expected property that their credible interval increases with respect to a proxy for time. We find that the observed Kepler multis display a highly significant deficit in entropy compared to a randomly generated population. Incorporating a filter for systems deemed likely to be dynamically packed, we show that this result is robust against the possibility of missing planets too. Put together, our work establishes that Kepler systems do indeed remember something of their younger years and highlights the value of information theory for exoplanetary science.