Diamonds are Not Forever: Dynamical Evolution of Saturn&#8217;sRings Driven by Micrometeoroid Bombardment
Authors: Estrada Paul , Durisen Richard H. 
Published: July 2021

. IntroductionAfter more than a dozen years in orbit about Saturn,&#160;the Cassini mission provided key measurements that&#160;are important for determining the age of Saturn&#8217;s rings.&#160;These include the extrinsic micrometeoroid flux at Saturn&#160;[1], the volume fraction of non-icy pollutants in&#160;the rings [e.g., 2], and the total ring mass [3]. These&#160;factors help to constrain the ring age to be no more&#160;than a few 100 Myr [1]. The Cassini Grand Finale&#160;also provided a suite of observations that demonstrate&#160;that the rings are losing mass to the planet at a surprising&#160;rate. Some of the mass flux falls as &#8220;ring rain&#8221; at&#160;higher latitudes consistent with the H+3&#160;infrared emission&#160;pattern thought to be produced by an influx of&#160;charged water products from the rings [e.g., 4]. The&#160;contribution needed to account for the ring rain phenomenon&#160;though is considerably less than the total&#160;equatorial measured mass influx of 4800 &#8211; 45000 kg/s [5]. Taken together, these observations imply that&#160;the rings are not only young, but also ephemeral. Here&#160;we argue that bombardment by micrometeoroids can&#160;account for these observations.2. What&#8217;s Driving the Mass Inflow?It has been recently argued that the above age estimate&#160;for the rings derived from exposure to micrometeoroids&#160;is not the same as their formation age, and&#160;that the rings could look young but still be quite old&#160;[6]. At their current mass, the observed mass inflow&#160;is orders of magnitude more than what viscous evolution&#160;can currently produce [7,8]. However, recall that&#160;micrometeoroid bombardment (MB) not only leads to&#160;pollution of the rings over time (as well as a catalyst&#160;for ring rain), but also to exchange of mass and angular&#160;momentum throughout the rings due to ballistic&#160;transport (BT) of their impact ejecta. As a result of&#160;this fundamental feature of BT, the rings act like an&#160;accretion disk with outward angular momentum transport&#160;leading to a steady inward drift of material to the&#160;planet.&#160;In [8], we quantify this radial drift rate in the context&#160;of a quasi-steady uniform ring using an accretion&#160;disk analog to show that for plausible choices of the&#160;ejecta yield Y , that direct deposition (mass loading,&#160;ML) of micrometeoroids and BT can produce the observed&#160;mass inflow rates (Fig. 1). More importantly it&#160;means that as ring mass decreases and viscosity can no&#160;longer effectively drive their evolution, the rings can&#160;continue to dynamically evolve driven by MB. This&#160;has implications not only for the formation age and&#160;initial mass of Saturn&#8217;s current rings, but also for the&#160;long-term evolutionary state of planetary rings.3. Evolution Under ML &amp; BTIn [9] we have modeled the dynamical evolution of&#160;rings with initial disk masses ranging from 1-100&#160;Mimas under the effects of viscosity and ML (Fig. 2,&#160;upper panel). For comparison, we show (blue dashed&#160;curve) the evolution due to viscosity alone for an initial&#160;disk mass of 100 Mimas [see 7]. This occurs because&#160;the evolution of massive rings is driven very&#160;strongly early on by viscosity, but weakens at later&#160;times as the ring spreads. We find though that when&#160;we include just ML (black curves), the rings&#8217; dynamical&#160;evolution is eventually driven more strongly by ML&#160;once a threshold mass is achieved, and the ring mass&#160;continues to decrease. This result suggests, based on&#160;ML alone, that a primordial massive ring would likely&#160;have become low mass much earlier on in Solar System&#160;history, especially if the flux was much higher in&#160;the past. If one also includes BT (shown for 1 Mimas&#160;mass, magenta dotted curve) with Y = 104 for comparison,&#160;evolution (and mass loss) is greatly accelerated&#160;leading to much shorter life times. Figure 2 (bottom)&#160;shows the corresponding pollution rates which all&#160;achieve the observed range of volume fractions (green&#160;dotted lines) of non-icy material in the A/B rings [3] in &#8804;&#160;few 100 Myr timescales independent of initial mass.4. Implications for Ring EvolutionThese results suggest that if the micrometeoroid flux&#160;was relatively constant at least at its current measured&#160;value [1] then the rings cannot be ancient, regardless&#160;of their initial mass. Moreover, given the relatively&#160;short life time of rings subject to the effects of MB, it&#160;is highly unlikely then that they started so massive, so&#160;recently. We argue in [9] using lower initial mass evolutionary&#160;models that the rings appear consistent with&#160;being only &#8764;100 Myr old, and likely had an initial&#160;mass of &#8764;1-4 Mimas masses with a remaining lifetime&#160;of &#8804;200 Myr. In these models, we have ignored&#160;that BT manifests and plays an important role in structural&#160;evolution which imposes additional constraints&#160;strengthening this argument. Such complicated effects&#160;require more detailed models which is the subject of&#160;ooing work. In reality, we expect that rings will&#160;achieve such low mass that BT becomes inefficient at&#160;further transport, and speculate that even initially massive&#160;rings will evolve to a highly polluted, low density&#160;tenuous state similar to the rings of Uranus and&#160;Neptune. This would be in agreement with Crida and&#160;Charnoz [10] who first suggested these ice giants may&#160;have had initially massive rings.Acknowledgements:&#160;This work was supported by a grant from NASA&#8217;s&#160;Cassini Data Analysis Program.References:[1] Kempf, S., et al.: In prep., 2021[2] Zhang, Z., et al.: Icarus 294, 14-42. 2017[3] Iess, L., et al.: Science 364, id.aat2965, 2019[4] O&#8217;Donoghue, J., et al.: Icarus 322, 251-260, 2019[5] Waite, J. H., et al.: Science 362, id.aat2382, 2018[6] Crida, A. et al.: Nature Astronomy 3, 967-970, 2019[7] Salmon, J. et al.: Icarus 209, 771-785, 2010[8] Durisen, R. H. &amp; Estrada, P. R.: Icarus, sub., 2021[9] Estrada, P. R., &amp; Durisen, R. H.: Icarus, sub., 2021[10] Crida, A. &amp; Charnoz, S.: Science 338, 1196, 2012