A Robust Launching Mechanism for Freely-Floating Planets from Host Stars with Close-in Planets

TL;DR

This study identifies a robust channel for forming free-floating planets through dynamical energy exchange between close-in planets and distant, highly eccentric intruders after the gas disk phase. It combines analytic energy-exchange criteria with high-precision N-body simulations (REBOUND/REBOUNDx) to show that close encounters can eject outer planets, while tides and collisions shape the retained population. The results indicate that inner planet mass and orbit strongly control ejection timescales and probabilities, and that the channel can produce a measurable fraction of FFPs, potentially extending to Neptune- to Jovian-mass objects depending on the mass distribution. The findings imply significant dynamical coupling between inner planetary systems and distant companions, with observable consequences for planetary architectures, spin-orbit misalignments, and the overall census of FFPs.

Abstract

Secular perturbations from binary stars and distant massive planets can drive cold planets onto nearly parabolic orbits with pericenter passages extremely close to their host stars. Meanwhile, short-period super-Earths are frequently observed around nearby stars. Gravitational scattering between these two distinct populations can lead to substantial orbital energy exchange, liberating some intruders from the gravitational confinement of their host systems. This process offers a robust formation channel for a subset of the abundant freely floating planet population. It may also significantly perturb the original orbits of close-in planets, induce collisional trajectories between close-in planets and their host stars, and disrupt the dynamical evolution of cold planets toward close stellar encounters.

Figures (9)

• Figure 1: The basic physical mechanism for producing free-floating planets through two-body scattering, depicted across three panels. Panel (a) shows an intruding cold planet ($m_{\rm in}$), characterized by an extremely eccentric orbit ($a_{\rm out}$, $e_{\rm out}$), as it intercepts a short-period super Earth ($m_{\rm in}$) with a nearly circular orbit ($a_{\rm in}$, $e_{\rm in}$). Panel (b) captures the outcome of their close gravitational encounter, where the intruding planet ($m_{\rm out}$) may gain sufficient energy to transition into a more loosely bound orbit. Panel (c) demonstrates the culmination of this process, where, after several orbital crossings, the intruding planet ($m_{\rm out}$) undergoes ejection from the system due to the cumulative energy changes from repeated interactions, ultimately becoming a free-floating object.
• Figure 2: (a) Duty cycle fraction (the cumulative duration of extreme eccentricity excitation ($e > 0.99$) fraction) driven by the von Zeipel-Lidov-Kozai mechanism was quantified in a hierarchical triple system containing a Sun-like primary, a $M_\odot$ stellar companion ($a_{\rm pert} = 10^3$ au, $e_{\rm pert} = 0.5$), and a Jupiter-mass planet ($a_{\rm out} = 10$ au, $e_{\rm out}$ is sampled from a Rayleigh distribution, characterized by the probability density function: $f(e; \sigma) = e/\sigma^2 \exp\left(-e^2/(2\sigma^2)\right)$, where the scale parameter $\sigma \approx 0.3$. Numerical integrations over $3 \times 10^8$ years (neglecting tidal effects) demonstrate repeated eccentricity surges reaching $e_{\rm out} > 0.99$. (b) Distribution of the theoretical maximum $e_{\rm out}$ attainable by the systems. 12% of the systems can reach $e_{\rm out} = 0.99$, and 49% can reach $e_{\rm out} = 0.9$.
• Figure 3: Evolution of the orbital elements $r_{\rm peri}=a(1-e)$, $a$, and $r_{\rm apo}=a(1+e)$ for a representative two-planet system over $10^7$ years. The outer planet is represented by blue lines (dark line: semi-major axes $a$; light lines: pericenter $q$ and apocenter $Q$), while the close-in planet is shown in orange. Parameters in (a) are $m_{\rm in} = m_{\rm out} = m_{\rm J}$, $R_{\rm out} = R_{\rm in} = R_{\rm J}$, $e_{\rm out} = 0.99$, $e_{\rm in} = 0$, $a_{\rm out} = 20$ au, $a_{\rm in} = 0.25$ au. Parameters in (b) are $m_{\rm in} = m_{\rm out} = m_{\rm J}$, $R_{\rm out} = R_{\rm in} = R_{\rm J}$, $e_{\rm out} = 0.9$, $e_{\rm out} = 0.99$, $a_{\rm out} = 20$ au, $a_{\rm in} = 2$ au. Parameters in (c) are $m_{\rm in} = 10 M_{\oplus}$, $R_{\rm in} = R_{\oplus}(m_{\rm in}/M_{\oplus})^{1/3}$, $m_{\rm out} = M_{\rm J}$, $R_{\rm out} = R_{\rm J}$, $e_{\rm out} = 0.99$, $e_{\rm out} = 0.99$, $a_{\rm out} = 20$ au, $a_{\rm in} = 0.25$ au.
• Figure 4: The distribution of ejection timescale ($t_{\rm eje}$) of the outer planet. The fiducial settings are: $a_{\rm out} = 10$ au, $e_{\rm out} = 0.99$, $a_{\rm in} = 0.1$ au, $e_{\rm in} = 0$. The ejection fraction is defined as $f_{\rm eje} = dN_{\rm eje}/ d\log_{10}(\tau_{\rm eje}/{\rm yr}) / N_{\rm tot}$, where $N_{\rm tot} = 1000$ is the total number of simulated systems (identical for all three cases). The masses of the close-in planet and the outer planet are compared with various cases. We simply test three mass configurations: $m_{\rm out} = m_{\rm in} = 10 M_{\oplus}$ (blue steps), $m_{\rm out} = m_{\rm in} = M_{\rm J}$ (orange steps), and $m_{\rm out} = M_{\rm J}$, $m_{\rm in} = 10 M_{\oplus}$ (green steps).
• Figure 5: The image illustrates how the escape timescale of the outer planet varies with the mass ($m_{\rm in}$) and initial semi-major axis ($a_{\rm in}$) of the inner planet. Both quantities are generated with a uniform logarithmic distribution. In the top panels, the outer planet is assigned a fixed mass of 10 Earth masses ($10 M_{\oplus}$), whereas in the bottom panels, it assumes a Jupiter mass ($M_{\rm J}$). Across the three panels, distinct orbital parameters of the outer planet are employed. Left panels: $a_{\rm out} = 10$ au, $e_{\rm out} = 0.999$; Middle panels: $a_{\rm out} = 10$ au, $e_{\rm out} = 0.99$; Right panels: $a_{\rm out} = 20$ au, $e_{\rm out} = 0.99$. The color bar indicates the escape timescale of the outer planet. Additionally, contours of the escaping occurrence timescale, based on Equation (\ref{['eq:tc']}), are plotted for comparison.