Dynamical Stability of Polar Circumbinary Orbits and Planet-Formation in Planetary Disc of 99 Herculis

TL;DR

This study investigates the stability of polar circumbinary orbits in the 99 Herculis system, providing empirical formulas for stable regions, and explores implications for planet formation and debris disc characteristics.

Contribution

The paper introduces an empirical formula for stable polar orbit radii in binary systems and analyzes planetesimal collision dynamics in the 99 Herculis debris disc.

Findings

Stable polar orbit radius formula applicable to various binary parameters.

Polar disc has lower accretion efficiency and moderate collision impact.

Collision timescales exceed gas disc dissipation time, hindering planetesimal growth.

Abstract

A possible polar-ring debris disc, the dynamics of which can be described by the outer hierarchical restricted three-body problem, has been detected in 99 Herculis. An empirical formula on the minimum radius beyond which test particles in polar orbits can keep stable within ${10^7}$ binary periods is provided through the numerical fitting, applying to the binary eccentricity $e_{1} \in \left[ {0,0.8} \right)$ and the mass ratio of binary $ \lambda \in \left[ {0.1,1} \right]$, where $ \lambda = m_0/m_1$ (${m_0}$ and ${m_1}$ represent the masses of the two binary stars). The polar planetary disc has the lowerest statistical accretion efficiency and moderate impact frequency of collisions among planetesimals (with a radius of 1-10km) compared to that in the circumbinary coplanar disc and the standard disc around the single host star. Colliding timescales in the circumbinary disk (both polar and coplanar configuration) are longer than $10^7$ yr exceeding the dissipation timescales of the gas disc. The stochastic simulations show that successive collisions cannot make planetesimal grow up which may explain the formation of the debris disc observed in 99 Herculis.