... Saturn

This work is dedicated to late Paolo Farinella (1953-2000) who was prompting one of us (D.V.) to analyse orbital effects of thermal forces on ring particles back in 1998. Flooded with many other ideas, Paolo never came to analyse this problem in detail.

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...

Appendices are only available in electronic form at http://www.aanda.org

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... Saturn

The absorptivities $\alpha$ are assumed here to be the effective values, spectrally integrated about the peak of the source emissivity. In the optical, the ring particle albedo increases toward larger wavelengths becoming then flat enough up to $\sim$$1.5~\mu$m (e.g., Poulet & Cuzzi 2002; Porco et al. 2005) so that $\alpha _{\rm V}$ is about the value in the green filter. The situation is much less known in the mid-infrared where Saturn's emissivity is maximum. Measurements of optical parameters for polluted ices by Hudgins et al. (1993) in the relevant temperature and spectral range reveal several absorption features. Generally, though the mid-infrared absorptivity $\alpha _{\rm I}$ is assumed to be close to unity for the inferred composition (e.g., Irvine & Pollack 1968; Kawata & Irvine 1975; Hudgins et al. 1993; Poulet & Cuzzi 2002; Poulet et al. 2003).

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... acceleration

This is a part of a more general formula giving orbital mean values of both the radial $f_{\rm r}$ and transverse $f_\tau$ acceleration components: $\left[f_{\rm r}+{\rm i} f_\tau\right]_1 = -{4\over 3} \sqrt{2\over 3\pi}~\omega^{3/4}~ \Phi~s_+\varphi^+$.

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... mid-infrared

Cassini observations reported by Spilker et al. (2005) provide empiric values of ring emissivities. While no detailed attempt to translate these values into the Bond albedo of the individual particles was done using a radiative transfer theory, we may consider them to provide an upper bound on $A_{\rm I}$, namely: (i) $A_{\rm I}\leq 0.14$ for the B ring, (ii) $A_{\rm I}\leq 0.19$ for the A ring, and (iii) $A_{\rm I}\leq 0.25$ for the C ring. We re-ran simulations presented in the main text with these upper bound values of $A_{\rm I}$ and found no significant change in results.

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