Ringed versus Ringless Worlds: How Poynting-Robertson Drag Shapes Rings across the Solar System

TL;DR

This study investigates the Solar System's ringed-vs-ringless dichotomy by testing whether solar Poynting-Robertson (PR) drag on isolated ring particles can regulate ring survival over gigayear timescales. It uses the analytic PR-drag formulation from Lia23, including planetary shadow and obliquity, to derive a secular decay rate $\left\langle \frac{da_{\mathrm{par}}}{dt} \right\rangle$ and a lifetime formula $\tau_{\mathrm{decay}} = \frac{8 \pi c^{2} \rho_{\mathrm{par}} r_{\mathrm{par}} a_{\mathrm{pla}}^{2}}{3 Q L_{\odot}}$, showing $\tau_{\mathrm{decay}} \propto a_{\mathrm{pla}}^{2} r_{\mathrm{par}}$. The key finding is a robust bimodal architecture: outer planets and distant small bodies can retain rings for gigayears, while inner bodies lose rings on shorter times, largely independent of $Q$ within realistic ranges. The framework yields testable predictions for future surveys, constrains debris-size distributions from past giant impacts, and explains why more rings are expected to be found in the outer Solar System, with Lucy testing Trojan-ring scenarios.

Abstract

Planetary rings are not only ubiquitous around the giant planets in the outer Solar System, but have also been discovered around several small distant bodies. In contrast, no rings have been observed around any inner Solar System objects. To constrain the dynamical origin of this ringed-versus-ringless dichotomy, we employ a numerically cross-checked analytical model of gigayear-scale Poynting-Robertson (PR) drag due to the solar flux acting on an isolated particle, expressed as a function of the host body's heliocentric distance \(\,a_{\mathrm{pla}}\) and the particle radius \(\,r_{\mathrm{par}}\). Here we show that, in the absence of additional perturbations, PR drag alone can explain the observed ring architecture of the Solar System: outer planets and Centaurs/TNOs are able to retain rings for the age of the Solar System, whereas any rings around the inner planets are removed on much shorter timescales. Because the PR-drag lifetime scales steeply with heliocentric distance \(\bigl(τ_{\mathrm{decay}}\propto a_{\mathrm{pla}}^{2} \,r_{\mathrm{par}}\bigr)\), we predict that forthcoming surveys will reveal an ever-growing population of ring-bearing bodies in the distant Solar System.

Figures (2)

• Figure 1: Time evolution of the orbital distance of a particle around a central body, initially starting from $a_{\rm par} = 5R_{\rm pla}$. For reference, $a_{\rm par} \sim 3R_{\rm pla}$ is the Roche limit of Earth and Mars. The red, black, and blue curves corresponds to a particle radius of $r_{\rm par}=1$ cm, $10$ cm, and $1$ m, respectively. Both the planetary obliquity and the particle's orbital inclination are set to zero. In these calculations, the central body is assumed to be spherical. The calculations here include the perturbations from the planet's shadow (the $\phi$ term given in Table \ref{['table_1']})
• Figure 2: Parameter space of the decay timescale as a function of the central body's semi-major axis and ring particle radius (Eq. \ref{['eq_decay']}). The top and bottom panels correspond to cases with $\rho_{\rm par} = 3.0,{\rm g,cm^{-3}}$ and $\rho_{\rm par} = 1.0,{\rm g,cm^{-3}}$, corresponding to densities typical of rocky and icy ring particles, respectively. Regions with $\tau_{\mathrm{decay}} > 4\times10^{9}$ yr are shaded light blue, whereas those with $\tau_{\mathrm{decay}} < 4\times10^{9}$ yr are shaded light red. Contours indicate constant timescales of $\tau_{\mathrm{decay}} = 10^{9}$, $10^{8}$, $10^{7}$, and $10^{6}$ yr. $Q=1$ is assumed. Vertical lines indicate the reference semi-major axes of selected planetary bodies.