FORMATION of NARROW PLANETARY RINGS by SATELLITE DIS- RUPTION; Joshua E

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FORMATION OF NARROW PLANETARY RINGS BY SATELLITE DIS- RUPTION; Joshua E. Colwell, and Larry W. Esposit o, Laboratory for Atmospheric and Space Physics, University of Colorado, Box 392, Boulder, CO 80309 The small moons of Jupiter, Saturn, Uranus, and Neptune (R - 10 to 100 km) are subject to impacts by meteoroids and comets, some of which may be sufficiently energetic to catastrophically fragment the moons. These satellites orbit close to their respective planets, often within the observed ring system of the planet. When catastrophically fragmented the debris either reaccretes or disperses to form a new planetary ring, depending on the size of the initial satellite, its distance from the planet, and the velocity imparted to the fragments by the disruption event. Since the processes that alter and destroy narrow rings operate on timescales of a few million to a few hundred million years (e.g. 1) it is tempting to see if the observed rings are part of a collisionally derived size distribution with the small satellites at the largest sizes. In this collisional cascade model of planetary rings the moons supply a reservoir of mass for the creation of new rings as the old ones are ground into dust or collisionally evolve to the point where they are no longer observable as planetary rings. We have performed stochastic simulations of the catastrophic fragmentation of small planetary satellites using estimates of the cometary flux in the outer so- lar system, results of fragmenation experiments, and scaling arguments (2). We use a combination of Monte Carlo and Markov chain simulations which provide complimentary pictures of the stochastic nature of satellite fragmentation (Fig. 1). These simulations show that small moons cannot have survived intact since the end of planet formation unless we have grossly overestimated the flux of impacting comets. As the moons are disrupted, a large number of hitherto unseen ringmoons

(R N 1 to 10 km) are created in addition to observable planetary rings. These moons are necessary to explain many observed phenomena in the ring systems of the outer planets including density waves (3) and the shepherding of narrow ring edges (4). They arise as a natural consequence of the collisional cascade model. The velocity distribution of the fragments is critical in determining the fate of catastrophically disrupted planetary satellites. We extend our initial model to include the effects of a realistic fragment velocity distribution. We use a power-law form for the velocity distribution of the fragments of mass m: f (> v) = I v) is the mass fraction with velocities exceeding v, and K cx. loglo(m1/3)as a first estimate of the velocity distribution. The velocity distribution is normalized to median fragment velocities derived from scaling arguments (5). With this simple model we find that narrow rings are a natural outcome of the disruption of a R - 10 km moon. We derive two-dimensional optical depth and surface mass density profiles of newly formed rings in the absence of collisions. Thus, we have assumed that no reaccretion occurs. With this simplification, the debris spreads in azimuth on a timescale of about 10 years to form an azimuthally uniform ring with exponentially sharp edges and a width of a few tens of kilometers. Our initial results indicate that the model of ring and moonlet belt formation from the catastrophic disruption of

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PLANETARY RING FORMATION: Colwell, J. E., and Esposito, L. W. small moons is viable. However, further work where the effects of collisions and the possible reaccretion of the fragments are included is necessary. Depending on the total mass of the nascent ring and the kinetic energy of the particles the satellite fragments may reaccrete to form a gravitationally bound rubble pile. Indeed, the narrow planetary rings around the four giant planets have masses u-hich indicate a progenitor satellite with R < 10 km which is approximately the onset of the regime where gravity plays an important role in disruption and fragmentation. Thus, it may be that the absence of rings more massive than the E ring is due to the increased difficulty in catastrophically disrupting moons much larger than 10 km radius and avoiding siginificant reaccretion of the fragments.

3 '5 2; Z - V) f .-3 0 o:....1....P....p....1.e.4-0 Ir" 0 5.0~10' 1.0x108 1.5~1o8 2.0~1o8 2.5~1o8 Time (yeors) Fig. 1: The mean (solid), median (asterisks), and modal (squares) sizes of the largest surviving fragment of the moon Cordelia (Uranus VI) assuming no reaccretion based on Monte Carlo simulations of the collisional cascade (2). (1) Dermott, S. F. (1984) Dynamics of Narrow Rings. In Planetary Rings pp. 589-637. (R. Greenberg, A. Brahic, Eds.). University of Arizona Press: Tucson. (2) Colwell, J. E., and L. W. Esposito (1992) Origins of the Rings of Uranus and Neptune: I. Statistics of Satellite Disruptions. (submitted to JGR Planets). (3) Horn, L. J., P. A. Yanamandra-Fisher, L. W. Esposito, and A. L. Lane (1988) Physical Properties of the Uranian 6 Ring from a Possible Density Wave. Icarw 76, 485492. (4) Murray, C. D., and R. P. Thompson (1990) Orbits of Shepherd Satellites Deduced from the Structure of the Rings of Uranus. Nature 348,499-502. (5) Housen, K. R., and K. A. Holsapple (1990) On the Ragmentation of As- teroids and Planetary Satellites. Icarw 84, 226-253.

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