Comparative study on opposition effect of icy solar system objects

Abstract

Opposition effect is a nonlinear increase in the brightness of an object close to astronomical opposition. We present a comparison and summary of the phase curves of some icy solar system objects, and terrestrial ice. We have constructed a method of approximating the height and width of the opposition peak and evaluating the practicality of the method in each case, with the aid of a four-parameter fit to a linear-exponential function and computing the a posteriori probability distribution of the height and width of the opposition peak. The procedure described is most applicable in finding a realistic fit and evaluating the suitability of data, even with moderate inaccuracy. We have studied the effect of the number of data points to the feasibility of the fit, in order to estimate the minimum amount of data required for a desired accuracy. Furthermore, we present an interpretation of the phase curves by means of two scattering mechanisms with important applications to the recent study of the opposition effect: shadowing and coherent backscattering.

Introduction

The nonlinear increase in the brightness of an object close to astronomical opposition (i.e. close to zero phase angle), the opposition effect, is observed for numerous atmosphereless solar system objects, including the Moon and other planetary satellites, planetary rings, and asteroids. Numerous earth-based phase curves have been observed, combined and analyzed, e.g., for the Galilean satellites of Jupiter and the icy satellites of Saturn, having later been supplemented by space observations and more detailed photometric modelling. The effect has also been produced in the laboratory for various materials. Despite the certain differences in the structures of planetary and terrestrial regoliths, the laboratory study provides an important means of determining in situ the properties crucial to the opposition effect.

The space missions, such as the NASA Cassini Mission to Saturn and the ESA SMART-1 to the Moon, will provide a vital improvement in our knowledge of both the surfaces of these satellites and their scattering properties, including the opposition effect. NASA's Galileo Spacecraft flybys of Io, Europa, and Ganymede have quite recently produced new images. Spectral observations of Europa's surface composition have also been carried out by the instruments of Galileo [1]. Some of these observations have been made at small phase angles.

The traditional way of explaining the opposition effect has been shadow hiding in a porous surface layer. Recently, coherent backscattering has gained more acceptance as an explanation for the phenomenon [2], [3], [4]. The recent modelling of the opposition effect is built on these two mechanisms (e.g. [5], [6]). Coherent backscattering has also been applied in the case of the polarization opposition effect of, e.g., the Galilean satellites [7] and Saturn's rings, ([8] and references therein), for which the opposition peak is too narrow to be explained by shadowing. The polarization opposition effect requires the vector approach, for which the Monte Carlo simulation has proven practical [9], [10], [11].

The earth-based photometry of the Galilean and Saturnian satellites and rings started a little after the introduction of the photometric equipment in the first decades of the 19th century. In the 1970s, a multitude of lightcurves of the Galilean satellites at different wavelength ranges were published [12], [13], [14], [15]. In 1992, Thompson and Lockwood [16] presented phase curves of Europa and Callisto, observed during a period long enough to yield a reasonable number of points for theoretical analyses. An equal interest was paid to the photometric study of Saturn's satellites in the 1970s.

The opposition effect is also clearly visible for Saturnian [17] and Uranian [18] rings. An extensive summary of the opposition effect of 33 asteroids is given in [19], with comparison to the phase curves of atmosphereless satellites and meteorites, coinciding in amplitude and width with asteroids of similar type. It has been suggested, that the surface porosity and structure play a key role in the backscattering characteristics of an object. The surface of, e.g., Europa has been observed to be very smooth, with high porosity [20], [21]. Geological activity is evident in all the Galilean satellites except Callisto. Due to the diversity of terrains on the surfaces, different hemispheres of these satellites lead to different phase curves of each side.

During the last two decades, many of the disk-integrated telescopic phase curves have been accompanied by spacecraft observations providing disk-resolved data and high resolution imaging. The Voyager spacecraft started to produce photometry of various Jovian and Saturnian satellites in the late 1970s, including phase curves. More information was derived on the surface microstructure and the spectral and photometric properties of Europa and other Galilean satellites, as well as several icy satellites of Saturn [22], [23], [24]. The Voyager phase curves combined with the earth-based data have been analyzed widely [25], [26], with photometric modelling. Voyager photometry of the Uranian satellites [27] also exists.

The most recent disk-resolved phase curves of Europa and Callisto have been obtained from the images by the Galileo spacecraft. These images show an area of a satellite at small phase angles, where the opposition brightening appears as a brighter diffuse spot, enabling a brand new method of obtaining a phase curve of a satellite, with local variations [28], [29]. Furthermore, the Hubble Space Telescope offers a wide range of new data on these objects.

In 1952, Knowles Middleton and Mungall [30] carried out a set of profound experiments to measure the bidirectional reflectances for six different samples of natural snow surfaces. There were one of the first in situ measurements of terrestrial snow, including classification of the snow and comparison to theoretical results. Small phase angles relevant to opposition effect were not reached. Since then, terrestrial snow and ice have been studied from ultraviolet to infrared, in both spectroscopic and photometric means, with comparisons to icy satellite photometry [31], [32]. Differences have arisen between the photometric properties of terrestrial snows and icy satellite regoliths, which are not yet properly understood.

Many of the field studies of snow and ice have a rather glaciological viewpoint, and hence only a little opposition photometry has been published of the terrestrial snow samples until very recently. Among the first field measurements of opposition photometry of terrestrial snow were those carried out by Piironen in 1979–81 [33], who discovered a strong backscattering peak for terrestrial snow.

The present article summarizes the study of disk-integrated phase curves of the Galilean satellites, Uranian and Saturnian rings, as well as a sample of terrestrial ice. The mechanisms dominating the opposition effect, coherent backscattering and shadowing, are also studied here in order to interpret qualitatively the phase curves. A linear-exponential function, combined with the computations of coherent backscattering and shadowing, is fitted to the observed phase curves of some icy objects: Galilean satellites, Saturnian and Uranian rings, and terrestrial ice. The technique is an indirect way of parameter estimation in the case of a complicated function with no possibility of an analytical approach, in this case the radiative transfer functions with coherent backscattering and shadowing taken into account, obtained via Monte Carlo and ray tracing methods, respectively, and described in Section 2. Results are provided in Section 3. All the data are presented in Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10, Fig. 11, Fig. 12, along with the simulations described in the next section.