TY - JOUR
T1 - A gas-kinetic stability analysis of self-gravitating and collisional participate disks with application to Saturn's rings
AU - Griv, Evgeny
AU - Gedalin, Michael
AU - Eichler, David
AU - Yuan, Chi
N1 - Funding Information:
The authors wish to thank numerous colleagues for many discussions, especially Kai-Wing Chen, Tzihong Chiueh, Alexei M. Fridman, Peter Goldreich, Edward Liverts, Muzafar N. Maksumov, William Peter, Shlomi Pistinner, Frank H. Shu, and Raphael Steinitz. We are grateful to the first referee of the paper, R. H. Durisen, for very useful comments and constructive criticism that improved our understanding of the problems under consideration. This research was sponsored in part by the Ministry of Science and the Science Foundation founded by the Academy of Sciences and Humanities in Israel, and the Academia Sinica in Taiwan. One of us (E.G.) was financially supported by the Israeli Ministry of Immigrant Absorption in the framework of the program “Giladi”.
PY - 2000/6/1
Y1 - 2000/6/1
N2 - Linear theory is used to determine the stability of the self-gravitating, rapidly (and nonuniformly) rotating, two-dimensional, and collisional particulate disk against small-amplitude gravity perturbations. A gas-kinetic theory approach is used by exploring the combined system of the Boltzmann and the Poisson equations. The effects of physical collisions between particles are taken into account by using in the Boltzmann kinetic equation a Krook model integral of collisions modified to allow collisions to be inelastic. It is shown that as a direct result of the classical Jeans instability and a secular dissipative-type instability of small-amplitude gravity disturbances (e.g. those produced by a spontaneous perturbation and/or a companion system) the disk is subdivided into numerous irregular ringlets, with size and spacing of the order of 4πρ ≈ 2πh, where ρ ≈ cr/κ is the mean epicyclic radius, cr is the radial dispersion of random velocities of particles, κ is the local epicyclic frequency, and h ≈ 2ρ is the typical thickness of the system. The present research is aimed above all at explaining the origin of various structures in highly flattened, rapidly rotating systems of mutually gravitating particles. In particular, it is suggested that forthcoming Cassini spacecraft high-resolution images may reveal this kind of hyperfine ∼2πh ≲ 100 m structure in the main rings A, B, and C of the Saturnian ring system.
AB - Linear theory is used to determine the stability of the self-gravitating, rapidly (and nonuniformly) rotating, two-dimensional, and collisional particulate disk against small-amplitude gravity perturbations. A gas-kinetic theory approach is used by exploring the combined system of the Boltzmann and the Poisson equations. The effects of physical collisions between particles are taken into account by using in the Boltzmann kinetic equation a Krook model integral of collisions modified to allow collisions to be inelastic. It is shown that as a direct result of the classical Jeans instability and a secular dissipative-type instability of small-amplitude gravity disturbances (e.g. those produced by a spontaneous perturbation and/or a companion system) the disk is subdivided into numerous irregular ringlets, with size and spacing of the order of 4πρ ≈ 2πh, where ρ ≈ cr/κ is the mean epicyclic radius, cr is the radial dispersion of random velocities of particles, κ is the local epicyclic frequency, and h ≈ 2ρ is the typical thickness of the system. The present research is aimed above all at explaining the origin of various structures in highly flattened, rapidly rotating systems of mutually gravitating particles. In particular, it is suggested that forthcoming Cassini spacecraft high-resolution images may reveal this kind of hyperfine ∼2πh ≲ 100 m structure in the main rings A, B, and C of the Saturnian ring system.
UR - http://www.scopus.com/inward/record.url?scp=0012326783&partnerID=8YFLogxK
U2 - 10.1016/s0032-0633(00)00037-4
DO - 10.1016/s0032-0633(00)00037-4
M3 - Article
AN - SCOPUS:0012326783
SN - 0032-0633
VL - 48
SP - 679
EP - 698
JO - Planetary and Space Science
JF - Planetary and Space Science
IS - 7-8
ER -