- Open Access
Spatial structure and coherent motion in dense planetary rings induced by self-gravitational instability
Earth, Planets and Space volume 51, pages1195–1213(1999)
We investigate the formation of spatial structure in dense, self-gravitating particle systems such as Saturn’s B-ring through local N-body simulations to clarify the intrinsic physics based on individual particle motion. In such a system, Salo (1995) showed that the formation of spatial structure such as wake-like structure and particle grouping (clump) arises spontaneously due to gravitational instability and the radial velocity dispersion increases as the formation of the wake structure. However, intrinsic physics of the phenomena has not been clarified. We performed local N-body simulations including mutual gravitational forces between ring particles as well as direct (inelastic) collisions with identical (up to N ∼ 40000) particles. In the wake structure particles no longer move randomly but coherently. We found that particle motion was similar to Keplerian motion even in the wake structure and that the coherent motion was produced since the particles in a clump had similar eccentricity and longitude of perihelion. This coherent motion causes the increase and oscillation in the radial velocity dispersion. The mean velocity dispersion is rather larger in a more dissipative case with a smaller restitution coefficient and/or a larger surface density since the coherence is stronger in the more dissipative case. Our simulations showed that the wavelength of the wake structure was approximately given by the longest wavelength λcr = 4π2GΣ/κ2in the linear theory of axisymmetric gravitational instability in a thin disk, where G, Σ, and κ are the gravitational constant, surface density, and a epicyclic frequency.
Araki, S., The dynamics of particles disks. II. Effects of spin degrees of freedom, Icarus, 65, 83–109, 1988.
Araki, S., The dynamics of particles disks. III. Dense and spinning particle disks, Icarus, 90, 139–171, 1991.
Araki, S. and S. Tremaine, The dynamics of dense particle disks, Icarus, 65, 83–109, 1986.
Binney, J. and S. Tremaine, Galactic Dynamics, 283 pp., Princeton Univ. Press, Princeton, NJ, 1987.
Bridges, F. G., A. Hatzes, and D. N. C. Lin, Structure, stability and evolution of Saturn’s rings, Nature, 309, 333–335, 1984.
Cameron, A. G. W. and W. R. Ward, The origin of the Moon, Proc. Lunar Planet Sci. Conf., 7, 120–122, 1976.
Dilley, J. P., Energy loss in collisions of icy spheres: Loss mechanism and size-mass dependence, Icarus, 105, 225–234, 1993.
Dones, L., J. N. Cuzzi, and M. R. Showalter, Voyager photometry of Saturn’s A ring, Icarus, 105, 184–215, 1993.
Esposito, L. W., Understanding planetary rings, Annu. Rev. Earth Planet. Sci., 21, 487–523, 1993.
Esposito, L. W., M. O’Callaghan, and R. A. West, The structure of Saturn’s rings: Implications from the Voyager stellar occultation, Icarus, 56, 439–452, 1983a.
Esposito, L. W., M. O’Callaghan, K. E. Simmons, C. W. Hord, R. A. West, A. L. Lane, R. B. Pomphery, D. L. Coffeen, and M. Sato, Voyager photopolarimeter stellar occultation of Saturn’s rings, J. Geophys. Res., 88, 8643–8649, 1983b.
Goldreich, P. and S. Tremaine, The velocity dispersion in Saturn’s rings, Icarus, 34, 227–239, 1978.
Goldreich, P. and S. Tremaine, Precession of the ∈ ring of Uranus, Astron. J., 84, 1638–1641, 1979.
Goldreich, P. and S. Tremaine, The dynamics of planetary rings, Annu. Rev. Astron. Astrophys., 20, 249–283, 1982.
Griv, E., Local stability criterion for the Saturnian ring system, Planet. Space Sci., 46, 615–628, 1998.
Hartmann, W. K. and D. R. Davis, Satellite-sized planetesimals and lunar origin, Icarus, 24, 504–515, 1975.
Hatzes, A. P., F. G. Bridges, and D. N. C. Lin, Collision properties of ice spheres at low impact velocities, Mon. Not. R. Astron. Soc., 231, 1091–1115, 1988.
Hill, G. W., Researches in the lunar theory, Amer J. Math., 1, 5–26, 129–147, 245–260, 1878.
Ida, S, Stirring and dynamical friction rates of planetesimals in the solar gravitational field, Icarus, 88, 129–145, 1990.
Ida, S. and J. Makino, N-body simulation of gravitational interaction between planetesimals and a protoplanet I. Velocity distribution of planetesimals, Icarus, 96, 107–120, 1992.
Ida, S., R. M. Canup, and G. R. Stewart, Lunar accretion from an impact-generated disk, Nature, 389, 353–357, 1997.
Julian, W. H. and A. Toomre, Non-axisymmetric responses of differentially rotating disks of starts, Astrophys. J., 146, 810–827, 1966.
Kokubo, E., S. Ida, and J. Makino, Evolution of a circumterrestrial disk and formation of a single moon, Icarus, 1999 (submitted).
Lin, D. N. C. and P. Bodenheimer, On the stability of Saturn’s rings, Astrophys. J. Lett., 248, L83–L86, 1981.
Lukkari, J., Collisional amplification of density fluctuations in Saturn’s rings, Nature, 292, 433–435, 1981.
Makino, J. and S. J. Aarseth, On a Hermite integrator with Ahmad-Cohen scheme for gravitational many-body problems, Publ. Astron. Soc. Japan., 44, 141–151, 1992.
Makino, J., E. Kokubo, and M. Taiji, HARP: A special-purpose computer for N-body problem, Publ. Astron. Soc. Japan., 45, 349–360, 1993.
Nakazawa, K. and S. Ida, Hill’s approximation in the three-body problem, Prog. Theor Phys. Suppl., 96, 167–174, 1988.
Ohtsuki, K., Equilibrium velocities in planetary rings with low optical depth, Icarus, 95, 265–282, 1992.
Ohtsuki, K., Capture probability of colliding planetesimals: Dynamical constraints on accretion of planets, satellites, and ring particles, Icarus, 106, 228–246, 1993.
Ohtsuki, K., Evolution of particle velocity dispersion in a circumplanetary disk due to inelastic collisions and gravitational interactions, Icarus, 137, 152–177, 1999.
Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, 472 pp., Cambridge Univ. Press, London/NewYork, 1986.
Richardson, D. C., Tree code simulations of planetary rings, Mon. Not. R. Astron. Soc., 269, 493–511, 1994.
Salo, H., Numerical simulations of dense collisional systems, Icarus, 90, 254–270, 1991.
Salo, H., Numerical simulations of dense collisional systems. II. Extended distribution of particle sizes, Icarus, 96, 85–106, 1992a.
Salo, H., Gravitational wakes in Saturn’s rings, Nature, 395, 619–621, 1992b.
Salo, H., Simulations of dense planetary rings. III. Self-gravitating identical particles, Icarus, 117, 287–312, 1995.
Smith, B. A., L. Soderblom, R. Batson, P. Bridges, J. Inge, H. Masursky, E. Shoemaker, R. Beebe, J. Boyce, G. Briggs, A. Bunker, S. A. Collins, C. J. Hansen, T. V. Johnson, J. L. Mitchell, R. J. Terrile, A. F. Cook, II, J. Cuzzi, J. B. Pollack, G. E. Danielson, A. P. Ingersoll, M. E. Davies, G. E. Hunt, D. Morrison, T. Owen, C. Sagan, J. Veverka, R. Strom, and V. E. Suomi, A new look at Saturn system: The Voyager 2 images, Science, 215, 504–537, 1982.
Sugimoto, D., Y. Chikada, J. Makino, T. Ito, T. Ebisuzaki, and M. Umemura, A special-purpose computer for gravitational many-body problem, Nature, 345, 33–35, 1990.
Supulver, K. D., F. G. Bridges, and D. N. C. Lin, The coefficient of restitution of ice particles in glancing collisions: Experimental results for unfrosted surfaces, Icarus, 113, 188–199, 1995.
Toomre, A., On the gravitational stability of a disk of stars, Astrophys. J., 139, 1217–1238, 1964.
Ward, W. R., On the radial structure of Saturn’s ring, Geophys. Res. Lett., 8, 641–643, 1981.
Wisdom, J. and S. Tremaine, Local simulations of planetary rings, Astron. J., 95, 925–940, 1988.
About this article
Cite this article
Daisaka, H., Ida, S. Spatial structure and coherent motion in dense planetary rings induced by self-gravitational instability. Earth Planet Sp 51, 1195–1213 (1999). https://doi.org/10.1186/BF03351594
- Velocity Dispersion
- Coherent Motion
- Simulation Region
- Gravitational Instability
- Structure Case