Rings around irregular bodies - I. Structure of the resonance mesh, and applications to Chariklo, Haumea, and Quaoar

Open Access

Table 1

Resonance widths, maximum eccentricities, and resonant excitation time.

Resonance	W/ao	e_peak	T_res / T_cor
First-order	3\|(m−1)\|\|2ϵ′\|^2/3	\|16ϵ′\|^1/3	2/\|3πm(m − 1)(2ϵ′²)^1/3\|
Second-order	\|(m − 2)ϵ′\|	\|4ϵ′\|^1/2	4/\|3πm(m − 2)ϵ′\|
Third-order	0	(4/3)\|ϵ′\|	NA

Dependence on µ and C₂₂

First-order	$\propto μ^{2 / 3}, \propto C_{22}^{\| m \| / 3}$ $\propto {\mu ^{2/3}},\, \propto C_{22}^{\left\| m \right\|/3}$	$\propto μ^{1 / 3}, \propto C_{22}^{\| m \| / 6}$ $\propto {\mu ^{1/3}},\, \propto C_{22}^{\left\| m \right\|/6}$	$\propto μ^{- 2 / 3}, \propto C_{22}^{\| m \| / 3}$ $\propto {\mu ^{ - 2/3}},\, \propto C_{22}^{\left\| m \right\|/3}$
Second-order	$\propto μ, \propto C_{22}^{\| m \| / 2}$ $\propto \mu ,\, \propto C_{22}^{\left\| m \right\|/2}$	$\propto μ^{1 / 2}, \propto C_{22}^{\| m \| / 4}$ $\propto {\mu ^{1/2}},\, \propto C_{22}^{\left\| m \right\|/4}$	$\propto μ^{- 1}, \propto C_{22}^{\| m \| / 2}$ $\propto {\mu ^{ - 1}},\, \propto C_{22}^{\left\| m \right\|/2}$
Third-order	NA	$\propto μ, \propto C_{22}^{\| m \| / 2}$ $\propto \mu ,\, \propto C_{22}^{\left\| m \right\|/2}$	NA

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.