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

TL;DR

The paper investigates whether free-floating planets (FFPs) can arise predominantly from planet–planet scattering in single-star systems by employing a physically motivated population synthesis with a realistic stellar IMF and validating instability prescriptions against N-body simulations. The IL PPS model simulates disk evolution, core growth, migration, and post-disk dynamics, while a trimmed IMF ensures consistency with microlensing target demographics; results show Neptune-like planets at wide separations dominantly populate the ejected pool, with low-mass planets more often remaining bound. Comparisons to microlensing data indicate broad agreement for bound and ejected populations, especially for $m\gtrsim10~M_\oplus$, and yield quantified expectations: ~1.20 ejected planets per star in $0.33<m/M_\oplus<6660$ with total ejected mass ~$17.98~M_\oplus$ per star, reducing tensions at higher masses when contrasted with observational power-laws. The findings imply FFP demographics are shaped by wide-separation, Neptune-like planets rather than abundant Earth-mass bodies and provide a testable benchmark for future surveys like the Roman Space Telescope.

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.

Figures (5)

• Figure 1: Left: normalized probability distribution functions (PDFs) of the stellar IMF used in Sumi_2023 (red) and in our simulations (blue). Right: corresponding cumulative distribution functions (CDFs). Our simulations adopt a trimmed IMF over the range $-1.1 < \log{(M_*/M_\odot)}<0.9$, covering $\simeq 66\%$ of the stellar sample in Sumi_2023.
• Figure 2: Results of MC simulations for 3000 stars (set A). (a): scatter plot of all bound planets in the 3000 systems at the end of simulation ($t_{\rm{MC,end}} = 10^9$ yr) on the $(a,m)$ plane. Red, blue, and green points represent gaseous, icy, and rocky planets, respectively. (b): 2D KDE of the data points in (a). The color scale represents the KDE values. (c): Mass histograms of the ejected planets (red), bound planets (green), and both population combined (blue). (d): Semi-major axes and masses of ejected planets prior to the moment of ejection. Colors distinguish the causes of ejection of the planets. Purple dots represent small planets (defined as those with $e_{\rm{esc}} < 1$) that are considered removed by enhanced secular perturbations when giant planets become unstable to acquire time-dependent large eccentricities ("secular removal"). Blue dots mark non-giant planets with $m<30~M_\oplus$ (embryos) that are ejected by another embryo during close scattering ("embryo-embryo"). Red dots show embryos that are ejected by giant planets ("embryo-giant"). Green dots indicate giant planets that are ejected by other giant planets ("giant-giant"). Yellow dots show the planets that are ejected during the migration of a giant planet ("secular removal"). (e) Same as (b) but for data points in (c). (f): A pie chart demonstrating the fraction of different ejection channels shown in panel (d).
• Figure 3: (a)-(c): Same as panels (a), (c), and (e) in Figure \ref{['fig:MC_population']} but for simulation set B (300 stars). The total simulation time is $t_{\rm{MC,end}}=10^8$ yr. (d)-(e): distribution of planets at $t \simeq t_{\rm{dep}}$, as initial conditions for N-body simulations. The planets that undergo collisions and ejections are highlighted in yellow and red filled circles (d) and (c), respectively. (f): Final planets in REBOUND simulations (at the end of integration $t_{\rm{REB,end}} = 10^8$ yr).
• Figure 4: Comparison of the mass distributions of bound planets (left) and ejected planets (right) in MC (solid, set B) and N-body simulations (dashed, set C).
• Figure 5: Comparison of MC simulation results with microlensing observations. Left: Mass distribution of bound planets (selected from 0.5 to 2 times the Einstein radius $R_E$) from MC simulations. Blue and green data points with error bars show microlensing observation data extracted from Zang_2025 and Suzuki_2016, respectively. Right: Mass distribution of ejected planets from MC simulations. The blue dashed line shows the power-law fit from Sumi_2023. To cover the larger uncertainties of observational data (especially in the low-mass regime), we plot the $1\sigma$ confidence interval of their broken power-law fit with the blue shaded region. The red and yellow histograms show the planets ejected through orbital instability and migration, respectively. The gray histogram shows the mass distribution of all the ejected planets combining those from orbital instability and migration of giant planets.