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

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. Vertical segregation of particle sizes further enhances this effect. 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°, 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 (Salo, H., Karjalainen, R., French, R.G. [2004]. Icarus 170, 70-90; French, R.G., Salo, H., McGhee, C.A., Dones, L. [2007]. Icarus 189, 493-522).