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15 - Thermal Properties of Rings and Ring Particles

from III - Ring Systems by Type and Topic

Published online by Cambridge University Press:  26 February 2018

By
L. J. Spilker ,
C. Ferrari ,
N. Altobelli ,
S. Pilorz  and
R. Morishima
Edited by
Matthew S. Tiscareno  and
Carl D. Murray
L. J. Spilker
Affiliation:
NASA Jet Propulsion Laboratory Pasadena, California, USA
C. Ferrari
Affiliation:
Université Paris-Diderot Paris, FRANCE
N. Altobelli
Affiliation:
European Space Agency Madrid, SPAIN
S. Pilorz
Affiliation:
SETI Institute Mountain View, California, USA
R. Morishima
Affiliation:
University of California, Los Angeles Los Angeles, California, USA
Matthew S. Tiscareno
Affiliation:
SETI Institute, California
Carl D. Murray
Affiliation:
Queen Mary University of London
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Summary

INTRODUCTION

Our view of planetary ring particles and the characteristics of their thermal emission has undergone a major paradigm shift since the arrival of Cassini at Saturn. Our understanding of the microstructure and microphysics of the rings has evolved from rings randomly filled with individual particles to Saturn's A and B rings containing particles that tend to clump into transient structures of characteristic sizes and orientations. The dynamics and evolution of rings strongly depend on the outcome of interparticle collisions and on the self-gravity of the rings. Energy loss, mass transfer, and sticking probability for relevant impact velocities will favor either aggregation or disruption and erosion of particles, modifying the size distribution and velocity dispersion, and thus the dynamics and structure of the rings.

The thermal response of a ring is determined by absorbed and emitted radiation or conducted heat within the particles. The radiation source functions depend upon the ring structure. Energy sources include direct, reflected and scattered solar light, mutual heating by neighboring ring particles, and thermal and visible radiation from Saturn. Because of mutual shading and heating between particles, the thermal emission is determined not only by the physical properties of the ring particles, but also by the structural and dynamical properties of the ring disk itself. Friction in mutual dissipative collisions between particles, due to their irregular surfaces, transforms orbital kinetic energy into spin. The particle surface temperature and its thermal emission are expected to vary on the surface along the rotation axis and azimuthally. Ring particles, as they collide into one another, are tumbling around the ring mid-plane with a vertical excursion governed by the local ring dynamics. The thermal history of a particle along its orbit is then an indicator of vertical dynamics. The particle is conditioned by the time it spends in sunlight and in the planetary shadow. At the exit of the shadow, its ability to warm up is a function of the thermal inertia. Any difference in the heating curves between the lit and unlit sides should reveal the time each particle spends on each side.

Type
Chapter
Information
Planetary Ring Systems
Properties, Structure, and Evolution
 , pp. 399 - 433
Publisher: Cambridge University Press
Print publication year: 2018

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References

Allen, D. A., and Murdock, T. L. 1971. Infrared photometry of Saturn, Titan, and the rings. Icarus, 14, 1-2.CrossRefGoogle Scholar
Altobelli, N., Spilker, L., Pilorz, S., et al. 2007. C ring fine structures revealed in the thermal infrared. Icarus, 191, 691—701.CrossRefGoogle Scholar
Altobelli, N., Spilker, L., Leyrat, C., and Pilorz, S. 2008. Thermal observations of Saturn's main rings by Cassini CIRS: Phase, emission and solar elevation dependence. Planet. Space Sci., 56, 134-146.CrossRefGoogle Scholar
Altobelli, N., Spilker, L., Pilorz, S., et al. 2009. Thermal phase curves observed in Saturn's main rings by Cassini-CIRS: Detection of an opposition effect? Geophys. Res. Lett, 36, L10105.CrossRefGoogle Scholar
Altobelli, N., et al. 2014. Two numerical models designed to reproduce Saturn ring temperatures as measured by Cassini-CIRS. Icarus, 238, 205-220.CrossRefGoogle Scholar
Araki, S. 1991. The dynamics of particle disks. III. Dense and spinning particle disks. Icarus, 90, 139-171.CrossRefGoogle Scholar
Aumann, H. H., and Kieffer, H. H. 1973. Determination of particle sizes in Saturn's rings from their eclipse cooling and heating curves. Astrophys. J., 186, 305-311.CrossRefGoogle Scholar
Baillie, K., Colwell, J. E., Lissauer, J. J., Esposito, L. W., and Sremčević, M. 2011. Waves in Cassini UVIS stellar occultations. 2. The C ring. Icarus, 216, 292-308.CrossRefGoogle Scholar
Bohren, C. F., and Hoffman, D. R. 1983. Absorption and Scattering of Light by Small Particles. New York: Wiley.Google Scholar
Bradley, E. T., Colwell, J. E., Esposito, L. W., etal. 2010. Far ultraviolet spectra properties of Saturn's rings from Cassini UVIS. Icarus, 206, 458-466.Google Scholar
Bradley, E. T., Colwell, J. E., and Esposito, L. W. 2013. Scattering properties of Saturn's rings in far ultraviolet from Cassini UVIS spectra. Icarus, 225, 726-739. Chandrasekhar, S. 1960. Radiative Transfer. New York: Dover.Google Scholar
Charnoz, S., Salmon, J., and Crida, A. 2010. The recent formation of Saturn's moonlets from viscous spreading of the main rings. Nature, 465, 752-754.CrossRefGoogle ScholarPubMed
Ciarniello, M., Capaccioni, F., and Filacchione, G. 2014. A test of Hapke's model by means of Monte Carlo ray-tracing. Icarus, 237, 293-305.CrossRefGoogle Scholar
Colwell, J. E., Esposito, L. W., and Sremčević, M. 2006. Self-gravity wakes in Saturn's A ring measured by stellar occultations from Cassini. Geophys. Res. Lett, 33, L07201.CrossRefGoogle Scholar
Colwell, J. E., Esposito, L. W., Sremčević, M., Stewart, G. R., and McClintock, W. E. 2007. Self-gravity wakes and radial structure of Saturn's Bring. Icarus, 190, 127-144.CrossRefGoogle Scholar
Colwell, J. E., Cooney, J. H., Esposito, L. W., and Sremčević, M. 2009. Density waves in Cassini UVIS stellar occulations. 1. The Cassini division. Icarus, 200, 574-580.CrossRefGoogle Scholar
Cooke, M. L. 1991. Saturn's rings: Photometric studies of the C ring and radial variation in the Keeler gap. Ph. D. Thesis, Cornell University.Google Scholar
Courtin, R., Lena, P., de Muizon, M., et al. 1979. Far-infrared photometry of planets —Saturn and Venus. Icarus, 38, 411—419.CrossRefGoogle Scholar
Cunningham, C. T., Ade, P. A. R., Robson, E. I., Nolt, I. G., and Radostitz, J. V. 1981. The submillimeter spectra of the planets: Narrow-band photometry. Icarus, 48, 127-139.CrossRefGoogle Scholar
Cuzzi, J. N., and Estrada, P. R. 1998. Compositional evolution of Saturn's rings due to meteoroid bombardment. Icarus, 132, 1—35.CrossRefGoogle Scholar
Cuzzi, J. N., Lissauer, J. J., Esposito, L. W., et al. 1984. Saturn's rings - Properties and processes. Pages 73-199 of: Greenberg, R., and Brahic, A. (eds.), Planetary Rings. Tucson, AZ: University of Arizona Press.Google Scholar
Cuzzi, J. N., et al. 2009. Ring particle composition and size distribution. Pages 459-509 of: Dougherty, M. K., Esposito, L. W., and Krimingis, S. M. (eds.), Saturn from Cassini-Huygens. Berlin: Springer.Google Scholar
Deau, E. 2015. The opposition effect in Saturn's main rings as seen by Cassini ISS: 2. Constraints on the ring particles and their regolith with analytical radiative transfer models. Icarus, 253, 311-345.CrossRefGoogle Scholar
Dunn, D. E., de Pater, I., and Nolnar, L. A. 2007. Examining the wake structure in Saturn's rings from microwave observations over varying ring opening angles and wavelengths. Icarus, 191, 56-76.Google Scholar
Esposito, L. W., O'Callaghan, M., Simmons, K. E., Hord, C. W., and West, R. A. 1983. Voyager photopolarimeter stellar occultations of Saturn's rings. J. Geophys. Res., 88, 8643-8649.CrossRefGoogle Scholar
Esposito, L. W., Cuzzi, J. N., Holberg, J. B., et al. 1984. Saturn's rings - Structure, dynamics, and particle properties. Pages 463—545 of: Gehrels, T., and Matthews, M. S. (eds.), Saturn. Tucson, AZ: University of Arizona Press.Google Scholar
Ferrari, C. 2006. Cassini-CIRS observations of Saturn's rings. Asia Oceania Geosciences Society 3rd Annual Meeting. Ferrari, C., and Leyrat, C. 2006. Thermal emission of spherical spinning ring particles. Astron. Astrophys., 447, 745—760.Google Scholar
Ferrari, C., and Reffet, E. 2013. The dark side of Saturn's Bring: Seasons as clues to its structure. Icarus, 223, 28-39.CrossRefGoogle Scholar
Ferrari, C., Galdemard, P., Lagage, P. O., and Pantin, E. 1999. Thermal inertia of Saturn's ring particles. Bull. A. A. S., 31, 1588—1588.Google Scholar
Ferrari, C., Galdemard, P., Lagage, P. O., Pantin, E., and Quorin, C. 2005. Imaging Saturn's rings with CAMIRAS: thermal inertia of B and C rings. Astron. Astrophys., 441, 379-389.CrossRefGoogle Scholar
Ferrari, C., Brooks, S., Edgington, S., et al. 2009. Structure of self-gravity wakes in Saturn's A ring as measured by Cassini CIRS. Icarus, 199, 145-153.CrossRefGoogle Scholar
Filacchione, G., et al. 2012. Saturn's icy satellites and rings investigated by Cassini-VIMS: III —Radial compositional variability. Icarus, 220, 1064-1096.CrossRefGoogle Scholar
Flandes, A., et al. 2010. Brightness of Saturn's rings with decreasing solar elevation. Planet. Space Sci, 58, 1758-1765.CrossRefGoogle Scholar
Flasar, F. M., et al. 2004. Exploring the Saturn system in the thermal infrared: The composite infrared spectrometer. Space Sci. Rev., 115, 169-297.CrossRefGoogle Scholar
French, R. G., and Nicholson, P. D. 2000. Saturn's rings. II. Particle sizes inferred from stellar occultation data. Icarus, 145, 502-523.CrossRefGoogle Scholar
French, R. G., Salo, H., McGhee, C. A., and Dones, L. 2007. HST observations of azimuthal asymmetry in Saturn's rings. Icarus, 189, 493-522.CrossRefGoogle Scholar
Froidevaux, L. 1981. Saturn's rings: Infrared brightness variation with solar elevation. Icarus, 46, 4-17.CrossRefGoogle Scholar
Froidevaux, L., and Ingersoll, A. P. 1980. Temperatures and optical depths of Saturn's rings and a brightness temperature for Titan. J. Geophys. Res., 85, 5929-5936.CrossRefGoogle Scholar
Froidevaux, L., Matthews, K., and Neugebauer, G. 1981. Thermal response of Saturn's ring particles during and after eclipse. Icarus, 46, 18-26.CrossRefGoogle Scholar
Haas, M. R., Erickson, E. F., McKibbin, D. D., Goorvitch, D., and Caroff, L. J. 1982. Far-infrared spectrophotometry of Saturn and its rings. Icarus, 51, 476-190.CrossRefGoogle Scholar
Hanel, R., et al. 1981. Infrared observation of the Saturnian system from Voyager 1. Science, 212, 192-200.CrossRefGoogle Scholar
Hanel, R., et al. 1982. Infrared observation of the Saturnian system from Voyager 2. Science, 215, 544—548.CrossRefGoogle Scholar
Hapke, B. 1993. Theory of Reflectance and Emittance Spectroscopy. New York: Cambridge University Press.CrossRefGoogle Scholar
Hedman, M. M., et al. 2007. Self-gravity wake structures in Saturn's A ring revealed by Cassini VIMS. Astron. J., 133, 2624-2629.CrossRefGoogle Scholar
Hedman, M. M., Burt, J. A., Burns, J. A., and Tiscareno, M. S. 2010. The shape and dynamics of a heliotropic dusty ringlet in the Cassini division. Icarus, 210, 284-297.CrossRefGoogle Scholar
Hedman, M. M., Nicholson, P. D., Cuzzi, J. N., etal. 2013. Connections between spectra and structure in Saturn's main rings based on Cassini VIMS data. Icarus, 223, 105-130.CrossRefGoogle Scholar
Ingersoll, A. P., Orton, G. S., Munch, G., Neugebauer, G., and Chase, S. C. 1980. Pioneer Saturn infrared radiometer -Preliminary results. Science, 207, 439-443.CrossRefGoogle ScholarPubMed
Joseph, J. H., Wiscomne, W. J., and Weinman, J. A. 1976. The delta-Eddington approximation for radiative flux transfer. J. Atmos. Sci., 33, 2452-2459.2.0.CO;2>CrossRefGoogle Scholar
Karjalainen, R. 2007. Aggregate impacts in Saturn's rings. Icarus, 189, 523-537.CrossRefGoogle Scholar
Karjalainen, R., and Salo, H. 2004. Gravitational accretion of particles in Saturn's rings. Icarus, 172, 328-348.CrossRefGoogle Scholar
Kawata, Y. 1983. Infrared brightness temperature of Saturn's rings based on the inhomogeneous multilayer assumption. Icarus, 56, 453-64.CrossRefGoogle Scholar
Kawata, Y., and Irvine, W. M. 1983. Thermal emission from a multiple scattering model of Saturn's rings. Icarus, 56, 453-464. Kunde, V. G., et al. 1996. Cassini infrared Fourier spectroscopic investigation. Pages 162-177 of: Horn, L. (ed.), Proc. SPIE Vol. 2803, Cassini/Huygens: A Mission to the Saturnian Systems. Bellinsham: SPIE.Google Scholar
Leyrat, C., Spilker, L. J., Altobelli, N., Pilorz, S., and Ferrari, C. 2008a. Infrared observations of Saturn's rings by Cassini CIRS: Phase angle and local time dependence. Planet. Space Sci., 56, 117—133.CrossRefGoogle Scholar
Leyrat, C., Ferrari, C., Charnoz, S., et al. 2008b. Spinning particles in Saturn's C ring from mid-infrared observations: Pre-Cassini mission results. Icarus, 196, 625-641.CrossRefGoogle Scholar
Li, L., et al. 2010. Saturn's emitted power. J. Geophys. Res., 115, El 1002.CrossRefGoogle Scholar
Lumme, K., and Bowell, E. 1981a. Radiative transfer in the surfaces of atmosphereless bodies. I. Theory. Astron. J., 86, 1694—1704.Google Scholar
Lumme, K., and Bowell, E. 1981b. Radiative transfer in the surfaces of atmosphereless bodies. II. Interpretation of phase curves. Astron. J., 86, 1705-1721.Google Scholar
Lumme, K., and Irvine, W. M. 1976. Photometry of Saturn's rings. Astron. J., 81, 863-893. Mie, G. 1908. Contributions to the optics of turbid media, particularly colloidal metal suspensions (in German). Ann. Phys., 25, 377-445.CrossRefGoogle Scholar
Mishchenko, M. I., and Dlugach, J. M. 2009. Radar polarimetry of Saturn's rings: Modeling ring particles as fractal aggregates built of small ice monomers. J. Quant. Spectros. Radiat. Trans., 110, 1706-1712.Google Scholar
Modest, F. M. 2003. Radiative Heat Transfer. Academic Press. Morel, C. 2013. Detectabilite d'anneauxplanetaires autour de super-Terres en imagerie directe infrarouge. These de l'Universite Paris Diderot.
Morishima, R., and Salo, H. 2004. Spin rates of small moonlets embedded in planetary rings. I. Three-body calculations. Icarus, 167, 330-346.CrossRefGoogle Scholar
Morishima, R., and Salo, H. 2006. Simulations of dense planetary rings IV Spinning self-gravitating particles with size distribution. Icarus, 181, 272-291.CrossRefGoogle Scholar
Morishima, R., Salo, H., and Ohtsuki, K. 2009. A multilayer model for thermal infrared emission of Saturn's rings: Basic formulation and implications for Earth-based observations. Icarus, 201, 634-654.CrossRefGoogle Scholar
Morishima, R., Spilker, L., Salo, H., et al. 2010. A multilayer model for thermal infrared emission of Saturn's rings II: Albedo, spins, and vertical mixing of ring particles inferred from Cassini CIRS. Icarus, 210, 330-345.CrossRefGoogle Scholar
Morishima, R., Spilker, L., and Ohtsuki, K. 2011. A multilayer model for thermal infrared emission of Saturn's rings III: Thermal inertia inferred from Cassini CIRS. Icarus, 215, 107-127.CrossRefGoogle Scholar
Morishima, R., G., Edgington S., and Spilker, L. 2012. Regolith grain sizes of Saturn's rings inferred from Cassini-CIRS far-infrared spectra. Icarus, 221, 888-899.CrossRefGoogle Scholar
Morishima, R., Spilker, L., and Truner, N. 2014. Azimuthal temperature modulations of Saturns A ring caused by self-gravity wakes. Icarus, 228, 247-259.CrossRefGoogle Scholar
Morishima, R., Spilker, L., Brooks, S., Deau, E., and Pilorz, S. 2016. Incomplete cooling down of Saturn's A ring at solar equinox: Implication for seasonal thermal inertia and internal structure of ring particles. Icarus, 279, 2—19.CrossRefGoogle Scholar
Morrison, D. 1974. Infrared radiometry of the rings of Saturn. Icarus, 22, 57-65.CrossRefGoogle Scholar
Murphy, R. E. 1973. Temperatures of Saturn's rings. Astrophys. J., 181, L87-L90.CrossRefGoogle Scholar
Murphy, R. E., Cruikshank, D. P., and Morrison, D. 1972. Limb darkening of Saturn and thermal properties of the rings from 10 and 20 micron radiometry. Bull. A. A. S., 4, 358-359.Google Scholar
Nicholson, P. D., and Hedman, M. M. 2010. Self-gravity wake parameters in Saturn's A and Brings. Icarus, 206, 410—423.CrossRefGoogle Scholar
Nicholson, P. D., French, R. G., Campbell, D. B., et al. 2005. Radar imaging of Saturn's rings. Icarus, 111, 32—62.Google Scholar
Nicholson, P. D., et al. 2008. A close look at Saturn's rings with Cassini VIMS. Icarus, 193, 182-212.CrossRefGoogle Scholar
Nixon, C. A., et al. 2009. Infrared limb sounding of Titan with the Cassini Composite InfraRed Spectrometer: effects of the mid-IR detector spatial responses. Appl. Opt, 48, 1912—1925.CrossRefGoogle ScholarPubMed
Nolt, I. G., Tokunaga, A. T., Gillett, F. C., and Caldwell, J. 1978. The 22. 7 micron brightness of Saturn's rings versus declination of the Sun. Astrophys. J. Lett., 219, L63-L66.CrossRefGoogle Scholar
Nolt, I. G., Barrett, E. W., Caldwell, J., et al. 1980. IR brightness and eclipse cooling of Saturn's rings. Nature, 283, 842—843.CrossRefGoogle Scholar
Ohtsuki, K. 1993. Capture probability of colliding planetesimals -Dynamical constraints on accretion of planets, satellites, and ring particles. Icarus, 106, 228-246.CrossRefGoogle Scholar
Ohtsuki, K. 2006. Rotation rate and velocity dispersion of planetary ring particles with size distribution. II. Numerical simulation for gravitating particles. Icarus, 183, 384-395.Google Scholar
Ohtsuki, K., and Toyama, D. 2005. Local A–body simulations for the rotation rates of particles in planetary rings. Astrophys. J., 130, 1302-1310.Google Scholar
Pilorz, S., Altobelli, N., Col well, J., and Sho waiter, M. 2015. Thermal transport in Saturn's Bring inferred from Cassini CIRS. Icarus, 254, 157-177.CrossRefGoogle Scholar
Pilorz, S., Showalter, M., and Edgington, S. 2016. Occultations of the star Eta Carinae observed with Cassini CIRS. Icarus, in preparation.
Pilorz, S., et al. 2017b. Thermal emissivity. Icarus, in preparation.
Pollack, J. B. 1975. The rings of Saturn. Space Sci. Rev., 18, 3-93.CrossRefGoogle Scholar
Porco, C. C., et al. 2005. Initial results on Saturn's rings and small satellites. Science, 307, 1226-1236.CrossRefGoogle ScholarPubMed
Porco, C. C., Weiss, J., Richardson, D. C., et al. 2008. Simulations of the dynamical and light-scattering behaviour of Saturn's rings and the derivation of ring particle and disk properties. Astron. J., 136, 2172-2200.CrossRefGoogle Scholar
Poulet, E., Cruikshank, D. P., Cuzzi, J. N., Roush, T. L., and French, R. G. 2003. Composition of Saturn's rings A, B, and C from high resolution near-infrared spectroscopic observations. Astron. Astrophys., 412, 305-316.CrossRefGoogle Scholar
Reffet, E., Verdier, M., and Ferrari, C. 2015. Thickness of Saturn's Bring as derived from seasonal temperature variations measured by Cassini CIRS. Icarus, 254, 276-286.CrossRefGoogle Scholar
Richardson, D. C. 1994. Tree code simulations of planetary rings. Mon. Not. R. Astron. Soc, 269, 493-511.Google Scholar
Robbins, S. J., Stewart, G. R., Lewis, M. C., ColweU, J. E., and Sremčević, M. 2010. Estimating the masses of Saturn's A and Brings from high-optical depth Af-body simulations and stellar occultations. Icarus, 206, 431-445.CrossRefGoogle Scholar
Roellig, T. L., Werner, M. W., and Becklin, E. E. 1988. Thermal emission from Saturn's rings at 380 microns. Icarus, 73, 574-583.CrossRefGoogle Scholar
Rubincam, D. P. 2006. Saturn's rings, the Yarkovsky effects, and the ring of fire. Icarus, 184, 532-542.CrossRefGoogle Scholar
Salmon, J., Charnoz, S., Crida, A., and Brahic, A. 2010. Long-term and large-scale viscous evolution of dense planetary rings. Icarus, 209, 771-785.CrossRefGoogle Scholar
Salo, H. 1987. Numerical simulations of collisions between rotating particles. Icarus, 70, 37—51.CrossRefGoogle Scholar
Salo, H. 1995. Simulations of dense planetary rings. III. Self-gravitating identical particles. Icarus, 111, 287-312.Google Scholar
Salo, H., and French, R. G. 2010. The opposition and tilt effects of Saturn's rings from HST observations. Icarus, 210, 785—816.CrossRefGoogle Scholar
Salo, H., and Karjalainen, R. 2003. Photometric modeling of Saturn's rings. I. Monte Carlo method and the effect of nonzero volume filling factor. Icarus, 164, 428-460.Google Scholar
Seal, D., and Buffington, B. B. 2009. The Cassini extended mission. Page 725 of: Dougherty, M. K., Esposito, L. W., and Krimingis, S. M. (eds.), Saturn from Cassini-Huygens. Berlin: Springer.Google Scholar
Seeliger, H. 1887. Zur Theorie der Beleuchtung der grossen Planeten, insbesondere des Saturn. Abhandl. Bayer. Akad. Wiss. Kl. II, 18, 1-72.Google Scholar
Smith, B. A., and imaging team, Voyager 1. 1981. Encounter with Saturn Voyager 1 imaging science results. Science, 212, 163-191.\Google ScholarPubMed
Spilker, L. J., Ferrari, C., Cuzzi, J. N., et al. 2003a. Saturn's rings in the thermal infrared. Planet. Space Sci., 51, 929-935.CrossRefGoogle Scholar
Spilker, L. J., Pilorz, S., Ferrari, C., Pearl, J., and Wallis, B. 2003b. Thermal and energy balance measurements of Saturn's C ring. Bull. Amer. Astron. Soc, 35, 929.Google Scholar
Spilker, L. J., Pilorz, S. H., Edgington, S. G., et al. 2005. Cassini CIRS observations of a roll-off in Saturn ring spectra at submillimeter wavelengths. Earth Moon Planets, 96, 149—163.Google Scholar
Spilker, L. J., et al. 2006. Cassini thermal observations of Saturn's main rings: Implications for particle rotation and vertical mixing. Planet. Space Sci., 54, 1167-1176.CrossRefGoogle Scholar
Spilker, L. J., Ferrari, C., and Morishima, R. 2013. Saturn's ring temperatures at equinox. Icarus, 226, 316—322.CrossRefGoogle Scholar
Thomson, F. S., Marouf, E. A., Tyler, G. L., French, R. G., and Rappa-port, N. J. 2007. Periodic micro structure in Saturn's rings A and B. Geophys. Res. Lett, 34, L24203.
Tiscareno, M. S., Burns, J. A., Nicholson, P. D., Hedman, M. M., and Porco, C. C. 2007. Cassini imaging of Saturn's rings. II. A wavelet technique for analysis of density waves and other radial structure in the rings. Icarus, 189, 14-34.Google Scholar
Tokunaga, A. T., Caldwell, J., and Nolt, I. G. 1980. The 20-micron brightness temperature of the unilluminated side of Saturn's rings. Nature, 287, 212-214.CrossRefGoogle Scholar
Vokroughlicky, D., Nesvorny, D., Dones, L., and Bottke, W. F. 2007. Thermal forces on planetary ring particles: application to the main system of Saturn. Astron. Astrophys., 471, 717-730.Google Scholar
Whitcomb, S. E., Hildebrand, R. H., and Keene, J. 1980. Brightness temperatures of Saturn's disk and rings at 400 and 700 microns. Science, 210, 788-789.CrossRefGoogle Scholar
Zebker, H. A., Marouf, E. A., and Tyler, G. L. 1985. Saturn's rings -Particle size distributions for thin layer model. Icarus, 64, 531—548.CrossRefGoogle Scholar

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