TY - JOUR
T1 - The fine-scale spiral structure of low and moderately high optical depth regions of Saturn's main rings
T2 - Surfaces and Atmospheres of the Outher Planets their Satellites
AU - Griv, Evgeny
AU - Gedalin, Michael
N1 - Funding Information:
This work was supported in part by the Israel Science Foundation and the Israeli Ministry of Immigrant Absorption in the framework of the program “Kamea”. The authors thank Tzi-Hong Chiueh, David Eichler, Edward Livertz, Yury Lyubarsky, Shlommi Pistiner, Frank Shu, Irina Shuster, Raphael Steinitz, and Chi Yuan for valuable discussions. We also thank the first anonymous referee for constructive criticism and the second anonymous referee for a very thorough report that led to an improvement of the paper. This work was initiated at the Academia Sinica Institute of Astronomy and Astrophysics (ASIAA) in Taiwan while one of the authors (E.G.) was a Senior Postdoctoral Fellow at the ASIAA, and we appreciate the hospitality of the ASIAA.
PY - 2003/12/1
Y1 - 2003/12/1
N2 - This article reviews recent studies of morphology and dynamics of low and moderately high optical depth regions of the Saturnian ring system of discrete mutually gravitating particles with special emphasis on its fine-scale spiral structure (irregular cylindric structures of the order of 100 m or so). We explain the very existence and the value of the critical wavelength λcrit ∼ 100 m of the fine structure, arising due to classical Jeans instability of gravity perturbations, in a local version of kinetic stability theory. The same interpretation is suggested to explain the gravitational wakes in simplified N-body computer simulations in Hill's equations context of an orbiting patch of the ring. A self-consistent system of the Boltzmann kinetic equation with a Krook phenomenological integral of collisions and the Poisson equation is used to study the phenomenon. The simplified case of relatively rare collisions between identical particles is examined, when the collision frequency is smaller than (compared to) the orbital frequency. It is shown that there is a dominant Fourier mode of maximum instability of Jeans-type collective oscillations in Saturn's rings (and the associated number of spiral arms and the pitch angle). We again argue that sufficient velocity dispersion prevents the Jeans instability from occurring but inelastic interparticle collisions reduce the relative particle velocities so that the Jeans instability may be an effective generating mechanism for the recurrent fine structure of the ring system. The stability analysis presented here and N-body simulations in Hill's approximation by Salo (Nature 359 (1992) 619), Richardson (Monthly Notices Roy. Astron. Soc. 269 (1994) 493), Osterbart and Willerding (Planet. Space Sci. 43 (1995) 289), Sterzik et al. (Planet. Space Sci. 43 (1995) 259), and others, would have to be regarded as a prediction of the long-term recurrent, tightly wound spiral structure in the range of few tens to few hundreds meters in regions of Saturn's main A, B, and C rings with optical depth τ≲1 that could be compared to forthcoming in 2004 Cassini spacecraft high-resolution measurements.
AB - This article reviews recent studies of morphology and dynamics of low and moderately high optical depth regions of the Saturnian ring system of discrete mutually gravitating particles with special emphasis on its fine-scale spiral structure (irregular cylindric structures of the order of 100 m or so). We explain the very existence and the value of the critical wavelength λcrit ∼ 100 m of the fine structure, arising due to classical Jeans instability of gravity perturbations, in a local version of kinetic stability theory. The same interpretation is suggested to explain the gravitational wakes in simplified N-body computer simulations in Hill's equations context of an orbiting patch of the ring. A self-consistent system of the Boltzmann kinetic equation with a Krook phenomenological integral of collisions and the Poisson equation is used to study the phenomenon. The simplified case of relatively rare collisions between identical particles is examined, when the collision frequency is smaller than (compared to) the orbital frequency. It is shown that there is a dominant Fourier mode of maximum instability of Jeans-type collective oscillations in Saturn's rings (and the associated number of spiral arms and the pitch angle). We again argue that sufficient velocity dispersion prevents the Jeans instability from occurring but inelastic interparticle collisions reduce the relative particle velocities so that the Jeans instability may be an effective generating mechanism for the recurrent fine structure of the ring system. The stability analysis presented here and N-body simulations in Hill's approximation by Salo (Nature 359 (1992) 619), Richardson (Monthly Notices Roy. Astron. Soc. 269 (1994) 493), Osterbart and Willerding (Planet. Space Sci. 43 (1995) 289), Sterzik et al. (Planet. Space Sci. 43 (1995) 259), and others, would have to be regarded as a prediction of the long-term recurrent, tightly wound spiral structure in the range of few tens to few hundreds meters in regions of Saturn's main A, B, and C rings with optical depth τ≲1 that could be compared to forthcoming in 2004 Cassini spacecraft high-resolution measurements.
KW - Instabilities
KW - Planets
KW - Satellites
KW - Waves
UR - http://www.scopus.com/inward/record.url?scp=0242691688&partnerID=8YFLogxK
U2 - 10.1016/j.pss.2003.05.003
DO - 10.1016/j.pss.2003.05.003
M3 - Conference article
AN - SCOPUS:0242691688
SN - 0032-0633
VL - 51
SP - 899
EP - 927
JO - Planetary and Space Science
JF - Planetary and Space Science
IS - 14-15
Y2 - 22 April 2002 through 26 April 2002
ER -