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Brightness of Saturn's Rings with Decreasing Solar Elevation

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Brightness of Saturn's Rings with Decreasing Solar Elevation Planetary and Space Science 58 (2010) 1758–1765 Contents lists available at ScienceDirect Planetary and Space Science journal homepage: www.elsevier.com/locate/pss Brightness of Saturn’s rings with decreasing solar elevation Alberto Flandes a,Ã, Linda Spilker a, Ryuji Morishima a, Stuart Pilorz b,Ce´dric Leyrat c, Nicolas Altobelli d, Shawn Brooks a, Scott G. Edgington a a Jet Propulsion Laboratory/California Institute of Technology, Pasadena, USA b SETI Institute, Mountain View, USA c Observatoire de Paris-LESIA, France d European Space and Astronomy Center, European Space Agency (ESAC/ESA), Madrid, Spain article info abstract Article history: Early ground-based and spacecraft observations suggested that the temperature of Saturn’s main rings Received 5 January 2010 (A, B and C) varied with the solar elevation angle, B0. Data from the composite infrared spectrometer Received in revised form (CIRS) on board Cassini, which has been in orbit around Saturn for more than five years, confirm this 31 March 2010 variation and have been used to derive the temperature of the main rings from a wide variety of Accepted 6 April 2010 geometries while B0 varied from near À243 to 03 (Saturn’s equinox). Available online 18 April 2010 Still, an unresolved issue in fully explaining this variation relates to how the ring particles are Keywords: organized and whether even a simple mono-layer or multi-layer approximation describes this best. We Planetary rings present a set of temperature data of the main rings of Saturn that cover the 233Frange of B0 angles Rings of Saturn 3 3 obtained with CIRS at low (a 30 ) and high (aZ120 ) phase angles. We focus on particular regions of Thermal studies each ring with a radial extent 5000 km on their lit and unlit sides. In this broad range of B0, the data Saturn r show that the A, B and C rings’ temperatures vary as much as 29–38, 22–34 and 18–23 K, respectively. Interestingly the unlit sides of the rings show important temperature variations with the decrease of B0 as well. We introduce a simple analytical model based on the well known Froidevaux monolayer approximation and use the ring particles’ albedo as the only free parameter in order to fit and analyze this data and estimate the ring particle’s albedo. The model considers that every particle of the ring behaves as a black body and warms up due to the direct energy coming from the Sun as well as the solar energy reflected from the atmosphere of Saturn and on its neighboring particles. Two types of shadowing functions are used. One analytical that is used in the latter model in the case of the three rings and another, numerical, that is applied in the case of the C ring alone. The model lit side albedo values at low phase are 0.59, 0.50 and 0.35–0.38 for the A, B and C rings, respectively. Published by Elsevier Ltd. 1. Introduction 136 775 km, respectively. The A ring seems to be the most dyna- mic of the main rings as its many density waves and clumpiness The main rings of Saturn (A, B and C) can be understood as a created by self gravitational wakes show. vertically thin disk composed of colliding particles covered with Since the first detection of the thermal emission of the rings of an almost pure water ice regolith. Their particle sizes range from Saturn at 10 mm in 1969 (Allen and Murdock, 1971), numerous centimeters to meters following a power-law size distribution infrared observations have been made and, with them, significant (q¼3, French and Nicholson, 2000). The densest and widest of steps in the understanding of the properties and dynamics of the the three main rings, the B ring, sits in the middle of this system rings have been achieved. Some of the early measurements of from 92 000 to 117 580 km from the center of Saturn. The C ring is the lit side of the rings showed that the rings had temperatures on much more transparent and narrower than the B ring and spans the order of those of the planet itself, 94 K (Ingersoll et al., from 74 658 to 92 000 km, which is divided into an innermost 1980), but also suggested that the rings’ observed temperatures homogenous region and an outermost heterogeneous region could vary with the solar elevation angle B0 (Murphy, 1973; Nolt (the Plateaus). Beyond the B ring, the Cassini division and the et al., 1980) (positive on the north side of the rings and negative A ring extend radially from 117 516 to 122 170 km and 122 170 to otherwise). Although these observations covered different values of B0 (6.5–261), since they were ground-based observations, Ã they were restricted to phase angles (a, Sun-rings-observer Corresponding author. Tel.: +1 818 392 0837. 3 E-mail addresses: flandes@geofisica.unam.mx, afl[email protected] angle) r6 , thus no temperature variations with a could be (A. Flandes). determined. 0032-0633/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.pss.2010.04.002 A. Flandes et al. / Planetary and Space Science 58 (2010) 1758–1765 1759 Early ground-based models describing the rings’ temperature their superimposed emission produces a single spectrum. dependence on B0, assumed either that the ring particles are A simple model for the observed intensity, I(k), leads to an spread in a single plane or ‘‘monolayer’’ (Froidevaux, 1981) or that expression in terms of a representative temperature, T, and the rings are a stack of multiple layers of particles or ‘‘multilayer’’ thermal-derived filling factor b, i.e. IðkÞ¼bBðk,TÞ. Here, B(k,T)is (Kawata, 1983). Unlike the monolayer approximation, the multi- the Planck function related to the field of view (FOV) with a layer model deals with the radiative transfer equation and surface area s, that is emitting at a temperature, T and k is the considers the small-sized particle population contributions. To wave number. All CIRS spectra analyzed to date resemble Planck date, the vertical structure of the rings is not well understood, but functions so closely that the two parameter fit works exception- a growing body of evidence suggests that, at least, the bigger ring ally well (Spilker et al., 2005, 2006). The fit temperature is a particles may form a monolayer, even in large parts of the A and B representative temperature within the footprint; the parameter, rings (Salo, 1995; French and Nicholson, 2000). However, the b, is a scaling factor ranging from 0 to 1 that represents the net multilayer model remains applicable for the population of smaller emissivity of the ring structure. It includes the IR emissivity of the particles that may be easily spread along the vertical direction. individual particles surfaces, the geometrical cross section, and a Early models (Froidevaux, 1981; Kawata, 1983) cannot entirely component that is dependent upon the temperature distribution explain the more recent and detailed observations obtained with within the field of view. the Cassini composite infrared spectrometer (CIRS) instrument, in The extensive set of thermal measurements of Saturn’s main particular, because they were defined considering only ground- rings by (CIRS) provides a new information on the rings, since the based observations and therefore they are restricted to near zero temperatures are retrieved for the lit and unlit side of the rings phase angle geometries. On the other hand, recent monolayer over a variety of ring geometries (Spilker et al., 2003) that include (Ferrari et al., 2005; Leyrat et al., 2008) and multilayer (Morishima a , B0, spacecraft elevation B (both with respect to the ring plane) et al., 2009) models, which are applicable to any observational and local hour angle c (noon in the direction of the Sun). Saturn geometry have been able to explain some of the features of the equinox took place in August 2009 which allows us to include Cassini CIRS data. Dones et al. (1993) suggest that the A and B data that cover from near B0 ¼ 233 to 01. With this new set of data rings may be physically thin, such that their multilayer model was we can get a better picture of the thermal behavior of the rings. unable to reproduce the observed ring phase functions at visible It has been observed that, to first order, the largest tempera- wavelengths and particularly the rings’ low reflectivity at large ture changes on the lit face of the rings are driven by variations in phase angles. Nevertheless, the fraction of small particles may be a, while differences in temperature with changing B and c are a small, but non-negligible according to observations (Marouf et al., secondary effect (Altobelli et al., 2009); however, important 1983) and the importance of this fraction could grow with the variations in temperature are observed at different radial elevation of the observer, jBj. The opposition surge seen in distances from the planet rS due to optical depth ðtÞ and albedo photometric observations was explained by the inter-particle variations. These former considerations are taken into account in shadowing effect of packed ring particles in multilayer models order to isolate the effects of B0 on the main rings. (Lumme et al., 1983). However, recent work by Nelson et al. A first general approach to the temperature evolution in the (1998) and Poulet and Cuzzi (2002) suggests that coherent main rings with changing solar elevation can be observed in Fig. 1. backscatter, in addition to shadow hiding, may be responsible Fig. 1a shows 12 radial scans of the lit side of the main rings— for the opposition surge observed at low phase angles in visible outside the planet’s shadow—from À221 to 01 or Saturn’s equinox wavelengths, so that a multilayer model may no longer be needed (see Table 1 for the observation geometry details) where we can to explain the strong ring opposition surge.
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