Capture of interstellar objects I: the capture cross-section

TL;DR

This paper analyzes the capture cross-section of interstellar objects by planet-star binaries, providing analytical and numerical insights into different encounter regimes and their dependence on system parameters.

Contribution

It offers a novel analytical framework for understanding ISO capture cross-sections across various encounter types in planet-star systems.

Findings

Capture cross-sections follow specific power-law dependencies on incoming velocity.

Wide interactions have limited energy transfer, affecting capture likelihood.

Close interactions are necessary for higher energy changes, influencing capture probability.

Abstract

We study the capture of interstellar objects (ISOs) by a planet-star binary with mass ratio $q\ll1$, semi-major axis $a_p$, orbital speed $v_c$, and eccentricity $e_p$. Very close (slingshot) and wide encounters with the planet are amenable to analytic treatment, while numerically obtained capture cross-sections $\sigma$ closely follow the analytical results even in the intermediate regime. Wide interactions can only generate energy changes $\Delta E\lesssim qv_c^2$, when $\sigma\propto v_\infty^{-2} |\ln\Delta E|^{2/3}$ (with $v_\infty$ the ISO's incoming speed far away from the binary), which is slightly enhanced for $e_p>0$. Energy changes $\Delta E\gtrsim qv_c^2$, on the other hand, require close interactions when $\sigma\propto (v_\infty \Delta E)^{-2}$ hardly depending on $e_p$. Finally, at $\Delta E\gtrsim v_c^2$, the cross-section drops to zero, depending on the planet's radius $R_p$ through the Safronov number $\Theta=qa_p/R_p$. We also derive the cross-sections for collisions of ISOs with planets or moons.