Cross Sections for Planetary Systems Interacting with Passing Stars and Binaries

TL;DR

This study uses extensive numerical simulations to calculate interaction cross sections between planetary systems and passing stars or binaries in stellar clusters, revealing universal formulas for various initial conditions and parameters.

Contribution

It provides a comprehensive set of cross sections for planetary system interactions with passing stars, including a universal formula accounting for host mass, velocity dispersion, and orbital parameters.

Findings

Over 2 million scattering simulations performed.

Universal formula for cross sections derived.

Constraints on Solar System's birth environment revisited.

Abstract

Most planetary systems are formed within stellar clusters, and these environments can shape their properties. This paper considers scattering encounters between solar systems and passing cluster members, and calculates the corresponding interaction cross sections. The target solar systems are generally assumed to have four giant planets, with a variety of starting states, including circular orbits with the semimajor axes of our planets, a more compact configuration, an ultra-compact state with multiple mean motion resonances, and systems with massive planets. We then consider the effects of varying the cluster velocity dispersion, the relative importance of binaries versus single stars, different stellar host masses, and finite starting eccentricities of the planetary orbits. For each state of the initial system, we perform an ensemble of numerical scattering experiments and determine the cross sections for eccentricity increase, inclination angle increase, planet ejection, and capture. This paper reports results from over 2 million individual scattering simulations. Using supporting analytic considerations, and fitting functions to the numerical results, we find a universal formula that gives the cross sections as a function of stellar host mass, cluster velocity dispersion, starting planetary orbital radius, and final eccentricity. The resulting cross sections can be used in a wide variety of applications. As one example, we revisit constraints on the birth aggregate of our Solar System due to dynamical scattering and find $N<10^4$ (consistent with previous estimates).