# Constraining the initial planetary population in the gravitational instability model

## TL;DR

This study combines planet formation models with observational data to constrain how often gravitational instability leads to planet formation, emphasizing the importance of migration efficiency in matching observed exoplanet populations.

## Contribution

It introduces a comprehensive approach integrating planet contraction models and population synthesis to evaluate GI planet formation scenarios against multiple observational constraints.

## Key findings

- GI formation occurs in at least tens of percent of systems with super migration.
- Efficient migration is necessary to explain the population of massive giants inside 5 AU.
- GI formation at wide orbits is less likely if migration is quenched by gap opening.

## Abstract

Direct imaging (DI) surveys suggest that gas giants beyond 20 AU are rare around FGK stars. However, it is not clear what this means for the formation frequency of Gravitational Instability (GI) protoplanets due to uncertainties in gap opening and migration efficiency. Here we combine state-of-the-art calculations of homogeneous planet contraction with a population synthesis code. We find DI constraints to be satisfied if protoplanet formation by GI occurs in tens of percent of systems if protoplanets `super migrate' to small separations. In contrast, GI may occur in only a few percent of systems if protoplanets remain stranded at wide orbits because their migration is `quenched' by efficient gap opening. We then use the frequency of massive giants in radial velocity surveys inside 5 AU to break this degeneracy - observations recently showed that this population does not correlate with the host star metallicity and is therefore suspected to have formed via GI followed by inward migration. We find that only the super-migration scenario can sufficiently explain this population whilst simultaneously satisfying the DI constraints and producing the right mass spectrum of planets inside 5 AU. If massive gas-giants inside 5 AU formed via GI, then our models imply that migration must be efficient and that the formation of GI protoplanets occurs in at least a tens of percent of systems.