Formation of Free-Floating Planets via Ejection: Population Synthesis with a Realistic IMF and Comparison to Microlensing Observations

TL;DR

This study models the formation of free-floating planets through ejection from planetary systems using population synthesis with a realistic initial mass function, and compares the results with microlensing observations.

Contribution

It introduces a comprehensive population synthesis model incorporating a realistic stellar IMF to predict free-floating planet distributions and compares these predictions with observational data.

Findings

Predicted FFP mass function aligns with observations at high masses.

Low-mass planets tend to remain bound, while Neptune-like planets are often ejected.

Approximately 1.20 ejected planets per star are predicted in the specified mass range.

Abstract

Microlensing observations suggest that the mass distribution of free-floating planets (FFPs) follows a declining power-law with increasing mass. The origin of such distribution is unclear. Using a population synthesis framework, we investigate the formation channel and properties of FFPs, and compare the predicted mass function with observations. Assuming FFPs originate from planet-planet scattering and ejection in single star systems, we model their mass function using a Monte Carlo based planet population synthesis model combined with N-body simulations. We adopt a realistic stellar initial mass function, which naturally results in a large fraction of planetary systems orbiting low-mass stars. The predicted FFP mass function is broadly consistent with observation: it follows the observed power-law at higher masses ($10 \lesssim m/M_\oplus < 10^4$), while at lower masses ($0.1 < m/M_\oplus \lesssim 10$) it flattens, remaining marginally consistent with the lower bound of the observational uncertainties. Low-mass, close-in planets tend to remain bound, while Neptune-like planets at wide orbits dominate the ejected population due to their large Hill radii and shallow gravitational binding. We also compare the mass distribution of bound planets with microlensing observations and find reasonably good agreement with both surveys. Our model predicts $\simeq 1.20$ ejected planets per star in the mass range of $0.33 < m/M_\oplus < 6660$, with a total FFP mass of $\simeq 17.98~M_\oplus$ per star. Upcoming surveys will be crucial in testing these predictions and constraining the true nature of FFP populations.