Numerical Determination of the Gravitational Cross Sections of an Accreting Binary

TL;DR

This study numerically calculates the gravitational cross sections of binary systems in accretion streams, revealing complex behaviors influenced by orbital configurations and providing data for future research.

Contribution

It introduces a comprehensive numerical method to determine gravitational cross sections of binaries, highlighting how these vary with system parameters and offering a useful grid for future studies.

Findings

Cross sections are complex and depend on orbital configuration.

Binaries tend to grow towards smaller mass ratios under gravitational focusing.

Provided a grid of cross sections for future modeling.

Abstract

A significant amount of work has been devoted to the study of small binary solar system objects. The majority of these binaries, especially among the near-earth or main belt asteroids have small radius ratios, implying a large difference in size between the primary and its companion. Farther from the sun, the binary fraction increases, with the Kuiper Belt having many known binaries with radius ratios of order unity. In this paper, we consider the runaway growth of a binary system in an accretionary stream of small particles. We perform brute-force integrations, each with 10 million test particles and numerically compute the gravitational cross sections for each member of the binary as a function of the system's separation and mass ratio. We show that the behavior of the cross section is complex, and it can be either diminished or enhanced depending on the orbital configuration. In the regime where gravitational focusing dominates the accretion process, we show that binaries grow towards smaller mass ratios than would be expected given single-body cross sections. Finally, we provide a grid of these cross sections for use in the future study of such systems.