Saturn's rings age I.: Reconsideration of the exposure age

Abstract

At the end of the Cassini mission, Saturn's rings have been claimed to be spectacularly young compared to the age of the Solar System: their unusual ice-rich composition corresponds to initially pure ice rings polluted by interplanetary dust particles for 100 to 400 Myr. Since then, this exposure age has been commonly accepted as the real age of the rings. In this paper, we review the processes that are involved in determining the exposure age. We aim to see how the exposure age depends on various parameters and how relevant it is to define the real rings age. First, a new expression for the gravitational focusing onto planar rings, important parameter but crudely defined in the literature, is derived. Then, an analytical formula describing how the dust fraction varies with time in static or viscously evolving rings is provided, including possible vaporisation at impact. Finally, we introduce a cleaning process from space weathering to possibly alter dust and reduce its amount to make rings look younger than they are. We first found that the gravitational focusing is 5 times less important than previously thought, which automatically increases the exposure age from 0.5 to 2 Gyr. Moreover, depending on the impact properties (vaporisation rate, space weathering efficiency), several billion years can easily be reached. Finally, we find that the dust fraction in the rings converges towards a finite value which, in particular with an efficient space weathering mechanism, can be close to the observed one in the current rings. In this case, neither the age nor the initial composition of the rings can be derived, and the measure of the dust fraction and bombardment rate only constrains the physical parameters of the impacts and the efficiency of the space weathering. As long as the latter parameters are not known, the exposure age argument in favour of young rings is completely undercut.

Figures (19)

• Figure 1: Plain lines: Effective cross sections to hit the rings at distance $r\leqslant r_{\rm Roche}=140\ 000$ km, for different values of the angle $\theta$ between the incoming trajectory and the rings plane and with a velocity of $v_\infty=6.8$ km/s. The 'mushroom' shapes show when we change the face of the rings the particles strike (first constraint of Appendix \ref{['sec: final exp dFg rings']}). The geometrical cross section of the rings inclined by an angle $\theta$ is represented by the different ellipses and circle, with the same colour code for the effective cross sections. The segment of the rings in the $x>0$ is dashed while the $x\leqslant0$ segment is dotted. Finally, the gray dash-dotted line is the cross section to hit a sphere of radius $r=140\ 000$ km.
• Figure 2: Blue: Distribution of the velocity at infinity of the dust particles detected by Cassini, where $v_\infty$ has been obtained with our approximation of Eq. \ref{['eq:vrel at saturn']} and with the data of kempf_micrometeoroid_2023. The histogram is similar to theirs (see main text for details). Red: Debiased distribution of the velocity at infinity of the particles as they enter Saturn's Hill sphere. Since they are more focussed by Saturn's gravity, slow particles represent a larger fraction of the Cassini sample than of the unfocussed distribution.
• Figure 3: Semi-log plot of different gravitational focusing expressions. Solid and dashed blue: Eq. \ref{['eq:fg_sphere full']} and \ref{['eq:fg_sphere local']} (respectively $F_g$ and $F_g^*$ for a sphere), with $v_\infty=4.3$ km/s. Dotted green: estrada_constraints_2023. Dash-dotted red: local gravitational focusing for rings with $v_\infty=4.3$ km/s (Eq. \ref{['eq:fg_generalised rings']}). Bottom magenta curve: same as the red one with $v_\infty=6.8$ km/s. The vertical dashed line corresponds to the distance $r_B=1.8$$R_S$.
• Figure 4: Semi-log plot comparing the expression of kempf_micrometeoroid_2023 (solid thick black curve), the global (solid red curve) and local gravitational focusing (dash-dotted red curve, same as in Fig. \ref{['fig:new dFg rings new vinfty']}) we found for the rings, using $v_\infty=4.3$ km/s. The dashed black curve accounts for the gravitational focusing of the mentioned article when removing the factor $2$ in their equation 12 of their supplementary material.
• Figure 5: Colormaps of the exposure age (in Gyr) to reach a fraction of dust $f_m$ depending on $(\eta, \zeta)$. The three dots represent the values of $t_{\rm exp}$ for the three reference cases of $(\eta, \zeta)$: 1. estrada_constraints_2023, 2. doyle_radiative_1989, 3. hyodo_pollution_2025 (for $\zeta$ only). Top panel: B ring where $f_m=0.93\%$. Bottom panel: C ring case with $f_m=6\%$. The different ages are 1: 0.58 Gyr, 2: 0.56 Gyr, 3: 19.4 Gyr for the B ring. For the C ring we have 1: 0.73 Gyr, 2: 0.50 Gyr, 3: 24.43 Gyr. Here the rings do not evolve viscously. The black dotted level curve is the one of $4.5$ Gyr for the other ring.