Self-gravity and viscous overstability: Dynamical and photometric modelling of the fine structure in Saturn’s rings
Mondino-Llermanos, Annabella Elizabeth (2025-05-23)
© University of Oulu, 2025. This publication is copyrighted. You may download, display and print it for your own personal use. Commercial use is prohibited. © Oulun yliopisto, 2025. Julkaisu on tekijänoikeussäännösten alainen. Teosta voi lukea ja tulostaa henkilökohtaista käyttöä varten. Käyttö kaupallisiin tarkoituksiin on kielletty.
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https://urn.fi/URN:NBN:fi:oulu-202505233862
Kuvaus
Tiivistelmä
This thesis examines the local dynamics of dense planetary rings using numerical modelling. The focus is on the interplay between two intrinsic mechanisms influencing ring fine structure: self-gravity wakes and viscous overstabilities. Self-gravity wakes are temporary density enhancements caused by the mutual gravitational attraction between particles, leading to filament-like structures that trail behind orbital motion due to interaction with orbital shear. Viscous overstability, on the other hand, is an oscillatory instability that occurs when viscosity sharply increases with density, causing growing density disturbances to be amplified due to energy transferred from the background motion. This study specifically targets axisymmetric overstability. The dynamical models are also combined with photometric modelling of Saturn’s A and B rings, helping to determine the distribution and physical properties of the particles that constitute these rings.
A dynamical N-body simulation tool called SOFTIS (SOFT-sphere Impact Simulator) has been developed to study the collisional and gravitational dynamics of planetary rings. This numerical tool incorporates a soft-sphere particle collision method into the publicly available tree-based gravity code, REBOUND. Collisions are modelled using a linear visco-elastic approach for inter-particle contact forces, allowing for the simulation of dense and strongly self-gravitating systems, where describing the evolution of the system as a series of independent binary impacts becomes challenging. To efficiently explore a wide range of values for various dynamical parameters, an MPI library is used to parallelize the execution of each simulation across distributed memory computing systems.
The numerical simulations presented in this study have identified the parameter range where self-gravity wakes and overstable oscillations can coexist. A key finding is that in regions with moderate self-gravity, there is a critical optical depth beyond which self-gravity wakes suppress overstability. Additionally, the simulations reveal a strong inverse correlation between the strength of these patterns over time, suggesting that this interaction could be responsible for the eventual suppression of overstability in systems with strong self-gravitating dominated by prominent wakes. Conversely, in systems with weak self-gravity with virtually no wakes, the conditions for the onset of overstability match those predicted by kinetic theory analysis of linear stability, written in terms of the ring’s central-plane filling factor.
The photometric effects of small-scale structures in planetary rings are analysed using synthetic observations generated by Monte Carlo ray tracing of the simulated particle fields, which are then compared with ground base and space-probe observations of Saturn’s outer main rings. This analysis includes Hubble Space Telescope observations of the rings’ azimuthal brightness asymmetry and opacity measurements obtained by Cassini. The findings highlight the critical role of incorporating particle size distribution to achieve a close match between simulation models and actual observations. The presence of overstabilities throughout the B-ring and in the inner A-ring suggests moderate self-gravity strength, implying a relatively low internal density of particles. However, there is still a possibility that particles are significantly influenced by adhesion forces, which could allow for internal densities approaching that of solid ice.
Original papers
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Mondino-Llermanos, A. E., & Salo, H. (2022). An implementation of viscous pressure-force (‘Soft-sphere’) model in REBOUND for local ring simulations. Monthly Notices of the Royal Astronomical Society, 513(4), 4711–4728. https://doi.org/10.1093/mnras/stac1179 https://doi.org/10.1093/mnras/stac1179
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Mondino-Llermanos, A. E., & Salo, H. (2023). Axisymmetric viscous overstability in fully self-gravitating systems. Conditions for the onset of overstable oscillations. Monthly Notices of the Royal Astronomical Society, 521(1), 638–661. https://doi.org/10.1093/mnras/stad500 https://doi.org/10.1093/mnras/stad500
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Salo, H., & Mondino-Llermanos, A. E. (2025). Photometric modelling of self-gravity wakes and overstable oscillations in Saturn’s rings. Astronomy & Astrophysics, 695, A37. https://doi.org/10.1051/0004-6361/202452328 https://doi.org/10.1051/0004-6361/202452328
Osajulkaisut
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Mondino-Llermanos, A. E., & Salo, H. (2022). An implementation of viscous pressure-force (‘Soft-sphere’) model in REBOUND for local ring simulations. Monthly Notices of the Royal Astronomical Society, 513(4), 4711–4728. https://doi.org/10.1093/mnras/stac1179 https://doi.org/10.1093/mnras/stac1179
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Mondino-Llermanos, A. E., & Salo, H. (2023). Axisymmetric viscous overstability in fully self-gravitating systems. Conditions for the onset of overstable oscillations. Monthly Notices of the Royal Astronomical Society, 521(1), 638–661. https://doi.org/10.1093/mnras/stad500 https://doi.org/10.1093/mnras/stad500
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Salo, H., & Mondino-Llermanos, A. E. (2025). Photometric modelling of self-gravity wakes and overstable oscillations in Saturn’s rings. Astronomy & Astrophysics, 695, A37. https://doi.org/10.1051/0004-6361/202452328 https://doi.org/10.1051/0004-6361/202452328
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