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

Abstract: Free-floating planets (FFPs) may retain dynamical signatures of the mechanisms that eject them from their host systems. We integrate $10^6$ collisionless FFP test particles for $10^8$~yr in a static, phenomenological Galactic potential, comparing a mass-independent kick model with a mass-coupled prescription ($σ<em>{\rm CB}\propto M<sup>{-0.15}$, $v</em>{\rm PL}\propto M<sup>{-0.5}$) against a matched no-kick control. The imposed mass dependence is recovered at injection, with the combined-channel median coupled kick decreasing from $10.716$ to $0.708~{\rm km\,s<sup>{-1}}$ across five mass bins---a factor of $\sim15.1$. A mass-dependent trend remains visible after $100$~Myr of Galactic propagation in the matched kicked-versus-control displacement, whose median decreases from $0.7001$ to $0.0539$~kpc across the same bins. The remaining numerical distinction is concentrated in this mass-resolved differential displacement rather than in the bulk phase-space moments: the final velocity dispersions of the null and coupled kicked populations are nearly identical, only a few percent of particles leave the adopted disk region, and the fraction of particles satisfying the formal Galactic-unbound criterion ($E_i&gt;0$) remains negligible in every diagnostic we report. Comparing each kicked population against its matched no-kick control shows that much of the overall kinematic heating arises from the evolution of the initially warm, nonequilibrium disk rather than from the ejection kick itself, isolating the kick's smaller contribution.