Photometric modelling of self-gravity wakes and overstable oscillations in Saturn’s rings

Space Physics and Astronomy Research unit, University of Oulu, 90014 Oulu, Finland

^★ Corresponding author; heikki.salo@oulu.fi

Received: 20 September 2024
Accepted: 23 December 2024

Abstract

Context. We present a detailed survey of the effect of various dynamical parameters on the photometric properties of Saturn’s rings. Our numerical simulations include the mutual impacts and self-gravity of particles and cover the range of parameters leading to axisymmetric viscous overstabilities and/or trailing self-gravity wake structures.

Aims. Our goal is to place constraints on the physical parameters of ring particles (internal density, ρ, elasticity, ϵ_n, size distribution width, W), based on a comparison with Hubble Space Telescope observations of the ring’s azimuthal brightness asymmetry. The best fit models are also compared to B and A ring opacity and viscosity measurements.

Methods. Photometric modelling uses Monte Carlo (MC) ray tracing of simulated particle fields. Dynamical simulations are performed in a message passage interface (MPI) environment with the novel SoftIS code, which incorporates the treatment of impacts in terms of visco-elastic forces with a Rebound code using tree-based gravity calculation. Besides fully self-gravitating simulations, we performed simulations in which self-consistent planar gravity was combined with an enhanced frequency of vertical oscillations, Ω_z/Ω > 1. Such ‘hybrid’ simulations mimic additional sticking forces in the sense that they lead to vertically more flattened self-gravity wake structures.

Results. Our models demonstrate the close correspondence between the strength of wake structures, measured by gravitational viscosity, and the amplitude of azimuthal variations in brightness, I/F, and optical depth, τ_phot. Trailing self-gravity wakes connect to I/F and τ_phot minima ~20° before the ansae, where the wakes are viewed along their long axis. No abrupt change in asymmetry amplitude is seen between overstability- or wake-dominated systems. The clearest sign of axisymmetric overstability is the shift in the longitude of minimum towards ring ansae. In the weak gravity regime, the simulated minimum can occur even after the ring ansa, due to the presence of shear-induced leading density enhancements; however, the associated amplitude is a few percents at most and is thus hidden if wakes or overstabilities are present. Our models emphasise the importance of size distribution: in the weak gravity regime, the inclusion of an extended size distribution shifts an overstable system to a wake-dominated one, as self-gravity becomes more effective due to the increased filling factor inside the wakes. In the case of strong gravity, size distribution reduces the asymmetry amplitude, the more uniformly distributed small particles partially hiding the wakes, which however remain dynamically strong among large particles. The best overall match to various observations is obtained with extended size distribution models, for ρ ~ 250 kg m⁻³; however, hybrid models leading to flatter and thus weaker wakes can match larger ρ better.

Conclusions. Size distribution models with self-gravity and inelastic collisions can match the constraints set by azimuthal brightness asymmetry, and reproduce well the A and B ring opacity versus elevation profiles. However, models that include only self-gravity forces indicate very low internal density of particles. Additional sticking forces, in this study mimicked as extra vertical compression, are thus likely to be important, allowing for an internal density closer to the solid ice density. Photometric comparisons similar to the ones in the current study but based on simulations including realistic sticking forces are clearly needed.