A formation mechanism for narrow rings around minor bodies

TL;DR

The paper tackles why narrow rings around certain minor bodies align with spin-orbit resonances, especially the $1/3$ SOR, and can lie outside the classical Roche radius. It develops a proof-of-concept mechanism where a particle disk evolves under a non-spherical central mass, radial collisional damping, and angular-momentum conservation that couples disk migration to a spin-down of the central body, potentially enabling resonant capture. Key results show that an outward migration driven by an $e_{ m eq}(a)$ gradient can trap disk material into a narrow ring, and a central spin-down can shift resonances outward to permit capture into the $1/3$ SOR for plausible parameter ranges (e.g., $oldsymbol{bc}=0.05$, $oldsymbol{ eta} o 10^{-3}$, $ au_s o 10^{5}$ yr) with a disk mass around $m_{ m disk} ear 8 imes 10^{-3} M_0$. This mechanism provides a plausible formation pathway for rings around Centaurs and TNOs without shepherd moons, including cases where rings lie beyond the Roche limit, though it requires a relatively massive initial debris disk and simplifications such as neglecting disk self-gravity.

Abstract

The recent discovery of narrow rings around minor bodies has raised many questions regarding their origin and current dynamics. Sharp ring boundaries seem indicative of shepherding moonlets, but none have been found. All rings lie close to spin-orbit resonances (SORs) with the central body, particularly the 1/3, even though it is not clear how these may be related. Furthermore, in at least one case the location of the ring is exterior to the Roche radius, adding to the striking differences with respect to giant planets. We study the dynamical evolution of a particle disk around a minor body, perturbed by the non-spherical component of the gravity field, particle collisions, and spin changes of the central mass linked to angular momentum conservation. By varying key parameters, we search for cases where the combined effects may lead to resonance capture and orbital configurations similar to those that have been observed. We performed N-body simulations of massless particles orbiting a central spherical body with a co-rotating mass anomaly. Collisions were modeled by adopting a simple radial damping force. Angular momentum conservation links the body spin to the disk orbital evolution. Since the gravitational effect of the test particles is neglected, this back-reaction is introduced externally assuming ad hoc spin-down rates and disk mass. Interaction between non-sphericity and collisions leads to the formation of a narrow ring that slowly recedes from the central mass. Spin-down of the minor planet shifts the SORs outward, enabling resonant capture. For suitable parameters, a portion -or all- of the initial disk can become trapped in the 1/3 SOR with the mass anomaly, in dynamically stable low-eccentricity orbits. Although the required disk mass is high ($\ge 1\%$ of the central body), long-term collisional erosion could reduce it to values that are consistent with observed ringlets.

Figures (3)

• Figure 1: Orbital evolution of two disk particles under the effects of gravitational perturbations and collisional drag ($\eta = 10^{-3}$). The central body was defined by $\mu = 0.05$, $R_0 = 115$ km and $\Omega_0/n_1 = 0.46$. Top: Eccentricity versus semimajor axis. Initial conditions are indicated in filled circles, while arrows show the direction of flow. The equilibrium eccentricity $e_{\rm eq}$, is highlighted in orange. Bottom: Semimajor axes as a function of time. Notice that the semimajor axes of the particles converge over time.
• Figure 2: Three sets of simulations of the dynamical evolution of particle disks considering different values for the collisional coefficient, $\eta$. In all cases, the mass anomaly was taken to be equal to $\mu = M_1/M_0 = 0.05$, while a spin-down rate with e-folding time $\tau_s = 10^5$ years was adopted for the rotational frequency. The blue curves show the semimajor axes associated with the 1/3 and 1/2 SORs. The vertical lines indicate the times at which the spin-down reached values of $\Omega_0$ equal to $90\%$ and $80\%$ of the initial rotation frequency.
• Figure 3: Schematic view of the different interactions acting on the initial particle disk. Curves of constant angular momentum (per unit mass) are shown in gray, with arrows indicating evolutionary routes due to a radial drag term. Red and orange curves highlight the equilibrium eccentricities of initial conditions undergoing both collisions and gravitational perturbations (assuming $\mu = 0.05$ and $R_0 = 115$ km). Both differ in the assumed angular frequency $\dot{\theta}_1$ of $M_1$ around the center of mass of $M_c$. The red curve shows results assuming $\dot \theta_1$ equal to the keplerian mean-motion ($n_1$). Conversely, the orange curve was calculated considering a sub-keplerian orbital frequency equal to the spin rate of $M_0$, i.e. $\dot \theta_1 = \Omega_0 = 0.46 \, n_1$. For comparison, the black dashed curve shows the semi-secular equilibrium eccentricity $e_{\rm ff}$, as given by equation (\ref{['eq2']}).