Velocities of Free Floaters in a Sea of Stars

TL;DR

This paper studies the velocity evolution of free-floating planets and interstellar objects, revealing how gravitational interactions influence their velocities and distributions over time.

Contribution

It introduces a new equilibrium velocity scaling for free floaters and shows how their velocity distributions evolve differently from Maxwellian expectations.

Findings

Equilibrium velocity scales as σ√(2ln(m/m_p))

Slow floaters double their velocities within a few relaxation times

Low-mass free floaters may retain signatures of their origins

Abstract

We investigate the velocity evolution of free-floating planets and interstellar objects (``free floaters'') through gravitational scatterings by field stars (with the stellar mass $m$ much larger than the mass of the floater, $m_p$). We show that the equilibrium velocity -- where dynamical friction balances stochastic acceleration -- is given by $\sigma \sqrt{2\ln(m/m_p)}$ (where $\sigma$ is the velocity disperson of the field stars), diverging from the standard energy equipartition scaling. While the timescale to reach this equilibrium is prohibitively long, we find that slow floaters ($v \lesssim \sigma$) undergo mass-independent acceleration, doubling their velocities within a few relaxation times. Consequently, free floaters initially following the Maxwellian distribution of their parent stars develop distinctly non-Maxwellian velocity distributions on a relaxation timescale. Since the relaxation time of the Galactic disk is longer than the age, our results suggest that the kinematics of low-mass free floaters in the disk may preserve signatures of their parent stars and ejection history.