The opposition and tilt effects of Saturn's rings from HST observations

The two major factors contributing to the opposition brightening of Saturn's rings are i) the intrinsic brightening of particles due to coherent backscattering and/or shadow-hiding on their surfaces, and ii) the reduced interparticle shadowing. We utilize the Hubble Space Telescope observations for different elevation angles B to disentangle these contributions. We assume that the intrinsic contribution is independent of B, so that any B dependence of the phase curves is due to interparticle shadowing, which must also act similarly for all colors. We construct a grid of dynamical/photometric simulation models to fit the elevation-dependent part of opposition brightening. Eliminating the modeled interparticle component yields the intrinsic contribution to the opposition effect: for the B and A rings it is almost entirely due to coherent backscattering; for the C ring, an intraparticle shadow hiding contribution may also be present. Based on our simulations, the width of the interparticle shadowing effect is roughly proportional to B. This follows from the observation that as B decreases, the scattering is primarily from the rarefied low filling factor upper ring layers, whereas at larger $B$'s the dense inner parts are visible. The elevation angle dependence of interparticle shadowing also explains most of the B ring tilt effect (the increase of brightness with elevation). From comparison of the magnitude of the tilt effect at different filters, we show that multiple scattering can account for at most a 10% brightness increase as B -> 26^o, whereas the remaining 20% brightening is due to a variable degree of interparticle shadowing. The negative tilt effect of the middle A ring is well explained by the the same self-gravity wake models that account for the observed A ring azimuthal brightness asymmetry.