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The Galactic Dynamics of Free-Floating Planets: From Ejection Kicks to Microlensing

This study demonstrates that while mass-dependent ejection kicks leave a detectable signature in the differential displacement of free-floating planets after 100 million years of Galactic propagation, the overall kinematic heating of these populations is primarily driven by the evolution of the initial nonequilibrium disk rather than the ejection mechanism itself.

Original authors: Zara Sayed, Stefano Profumo, Nolan Smyth

Published 2026-09-21

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CC BY 4.0

Original authors: Zara Sayed, Stefano Profumo, Nolan Smyth

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the crowded streets of our Milky Way galaxy, a hidden population of travelers wanders alone. These are free-floating planets, worlds that have been cast out from their home star systems to drift through the cold darkness of interstellar space. For decades, astronomers have debated how common these exiles are and how they move. While some are likely born from the chaotic collisions of planets within a system, others may be flung out by the gravitational tug-of-war between binary stars. The big question is whether the speed at which a planet is ejected depends on its size. Does a massive Jupiter-like world get kicked harder than a small Earth-like one, or do they all receive a similar shove? If the speed of the kick changes with the planet's mass, that difference should leave a lasting fingerprint on where these planets end up after millions of years of traveling through the galaxy.

A team of researchers set out to test this idea using a massive computer simulation. They did not observe real planets directly; instead, they built a virtual model of the Milky Way and populated it with one million digital test particles, each representing a free-floating planet. They gave these planets a starting point in a warm, rotating disk of stars and then applied a single, sudden push to each one, mimicking the moment of ejection. Crucially, they ran two different versions of the experiment. In one version, every planet, regardless of its mass, received a kick that followed a standard, unchanging rule. In the other version, the researchers programmed the kick to depend on the planet's mass, specifically making lighter planets receive a stronger push and heavier planets a weaker one, based on theories about how planetary systems break apart. To ensure their results were accurate, they also ran a control group where the planets received no kick at all, allowing them to separate the effects of the ejection from the natural movement of the galaxy itself.

The simulation tracked these virtual worlds for one hundred million years, a blink of an eye in cosmic time but enough to see how the initial push changed their paths. The researchers found that the mass-dependent rule they programmed worked exactly as intended at the very beginning: the lighter planets did indeed receive significantly larger kicks than the heavy ones. However, as time passed and the planets traveled through the complex gravitational field of the galaxy, the story became more subtle. The massive, chaotic motion of the galaxy itself, combined with the fact that the starting population was already moving with some speed, tended to wash out the distinct differences between the groups. By the end of the simulation, the overall speed and spread of the planets looked almost identical whether they had been kicked or not, and whether the kick had depended on their mass.

Despite this blurring effect, a clear signal remained when the researchers looked closely at how far the planets had moved from their starting points. The planets that had received the mass-dependent kicks showed a distinct pattern: the lighter planets, which had been pushed harder, traveled significantly farther away from their birthplaces than the heavier planets. This difference was measurable even after one hundred million years, proving that the initial mass-dependent kick left a permanent mark on the spatial distribution of the population. The study also revealed that much of the movement observed in the simulation was not caused by the ejection kick itself, but rather by the natural evolution of the starting population as it settled into the galaxy's gravitational flow. This distinction is vital, as it shows that to understand the history of free-floating planets, one must carefully separate the initial event from the long-term journey.

The researchers then used their final map of where these virtual planets ended up to predict what a future telescope might see. They calculated how often these planets would pass in front of distant stars and briefly brighten them, an effect known as microlensing. Because the simulation did not assume a specific total number of planets in the galaxy, the results were not a prediction of exactly how many events would occur. Instead, they provided a shape-level forecast, showing the relative likelihood of detecting different sizes of planets. The model suggested that the distribution of detection times would vary depending on the mass of the planet, offering a specific signature that future observations could look for. While the study confirms that mass-dependent ejection leaves a detectable trace in the galaxy's structure, it also highlights that the galaxy's own dynamics are powerful enough to obscure the details of the initial event, requiring careful analysis to uncover the true history of these wandering worlds.

Technical Summary: The Galactic Dynamics of Free-Floating Planets: From Ejection Kicks to Microlensing

Problem Statement
Free-floating planets (FFPs) are planetary-mass objects unbound to any host star, potentially produced by mechanisms such as planet-planet scattering, stellar flybys, or circumbinary instabilities. These ejection channels imprint distinct initial velocity distributions, often exhibiting mass-dependent characteristics (e.g., lower-mass planets receiving larger kicks). A central dynamical question is whether these initial mass-dependent ejection signatures survive subsequent propagation through the Galactic potential over timescales of $10^8$ years. Furthermore, it is necessary to distinguish the kinematic heating caused by the ejection kick itself from the evolution of the initial non-equilibrium "warm" disk population. Observationally, the Nancy Grace Roman Space Telescope is expected to detect FFPs via microlensing; accurately predicting the relative timescale distribution of these events requires a robust theoretical framework for the FFP phase-space distribution.

Methodology
The authors perform a controlled numerical experiment using $10^6$ collisionless test particles integrated for $10^8$ years in a static, phenomenological Galactic potential (comprising a disk, a triaxial bulge, and an NFW-like dark matter halo). The simulation employs a leapfrog kick-drift-kick integration scheme with a timestep of $10^4$ years.

The core of the methodology involves a matched no-kick control population. For every "kicked" particle, a control twin is initialized with identical birth positions, masses, and pre-kick velocities but receives no ejection kick. This allows the authors to isolate the incremental dynamical effect of the kick from the background evolution of the initially warm disk.

Two ejection prescriptions are compared:

Null Model: Mass-independent kick distributions. The circumbinary (CB) channel uses a Gaussian velocity dispersion of $\sigma_{CB} = 10$ km s $^{-1}$ , and the planet-planet scattering (PL) channel uses a narrow Gaussian centered at $v_k = 4$ km s $^{-1}$ .
Coupled Model: Explicitly mass-dependent prescriptions. The CB channel follows $\sigma_{CB} \propto M^{-0.15}$ , and the PL channel follows $v_{PL} \propto M^{-0.5}$ .

The FFPs are sampled across five mass bins ($1 $–$ 317 M_\oplus$) and two channels (CB and PL). The initial spatial distribution follows a warm-disk prescription (gamma distribution for radius, Laplace for height) with Gaussian velocity dispersions, rather than a cold disk on circular orbits.

Key Contributions and Results

Recovery of Mass Dependence at Injection: The simulation successfully recovers the imposed mass-dependent kick scaling at $t=0$ . In the coupled model, the median kick speed decreases by a factor of $\sim 15.1$ across the mass bins (from $10.716$ km s $^{-1}$ for $1 $–$ 3 M_\oplus$ to $0.708$ km s $^{-1}$ for $100 $–$ 317 M_\oplus$).
Survival of Spatial Signatures: After $100$ Myr of propagation, the mass-dependent trend remains visible in the matched kicked-versus-control displacement. In the coupled model, the median displacement decreases from $0.7001$ kpc to $0.0539$ kpc across the mass bins. Notably, the null model also exhibits a mass-dependent displacement trend (decreasing from $0.7687$ to $0.3329$ kpc), indicating that mass-dependent spatial redistribution can arise from the sampled initial conditions and orbital evolution even without an explicit mass-dependent kick. However, the trend is substantially stronger in the coupled case.
Bulk Kinematic Moments: The global velocity dispersions ( $\sigma_R, \sigma_z$ ) of the null and coupled populations are nearly identical at the final snapshot (e.g., $\sigma_R \approx 87.7$ vs. $87.6$ km s $^{-1}$ ). The matched-control comparison reveals that the kick-attributable quadrature excess is modest ( $\sim 9$ km s $^{-1}$ in $\sigma_R$ and $\sim 5$ km s $^{-1}$ in $\sigma_z$ ). The authors conclude that the bulk kinematic heating is dominated by the evolution of the initially warm, non-equilibrium disk rather than the ejection kick itself.
Escape and Disk Departure: The fraction of particles formally unbound from the Galaxy ( $E_i > 0$ ) remains negligible. The fraction of particles departing the thin-disk region ( $|z| > 2$ kpc) is low (a few percent) and shows minimal dependence on the kick prescription or mass.
Microlensing Connection: The authors construct a schematic, shape-level microlensing event-rate calculation for the Roman Space Telescope. Using the final phase-space distribution, they predict the relative timescale distribution ( $d\Gamma/dt_E$ ) for FFPs in different mass bins. The results confirm that peak Einstein timescales increase with mass ( $t_{E,peak} \propto \sqrt{M}$ ), remaining in the sub-day regime.

Significance and Claims
The paper claims to provide a controlled dynamical experiment demonstrating that while mass-dependent ejection kicks produce a clear, measurable signature in the differential spatial displacement (kicked vs. control) after $100$ Myr, this signature is largely washed out in the bulk velocity moments due to the dominant evolution of the initial warm disk population.

The authors explicitly state that their microlensing results are illustrative and shape-level only. They do not claim to predict absolute event yields for Roman, as the calculation lacks an absolute FFP density normalization, a realistic source-star population, and survey selection functions. Instead, the framework establishes the relative contributions of injected kick effects versus background dynamical evolution.

The study concludes that a definitive long-term assessment of mass-dependent signatures (at Gyr timescales) and a physically general prediction for the present-day Galactic FFP population require future work involving higher-resolution integrations, convergence tests, and a dynamically self-consistent initial distribution function, rather than the Jeans-like warm-disk construction used here.

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