Title: Dynamics of planetary rings under thermal forces
Authors: Zhou, Wen-Han; Kokubo, Eiichiro; Agrusa, Harrison; Ricerchi, Gregorio; Crida, Aurelien; Vokrouhlicky, David; Zhang, Yun; Ballouz, Ronald-Louis
First Author’s Institution: Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan
Status: Published in The Astrophysical Journal Letters [open access]
If you ask anyone what their favourite planet is, the answer you’ll most likely hear is Saturn. Why? Why else than the beautiful and intricate ring system surrounding the gas giant. The other gas and ice giants in our solar system – Jupiter, Uranus, and Neptune – have ring systems themselves but none quite as striking as Saturn. Would it surprise you to learn that astronomers’ best models have not yet totally explained why Saturn’s rings look the way they do?
In contrast, it may not surprise you to hear that people have been trying to explain the rings for as long as we have seen them with telescopes. We now know that planetary rings are collections of relatively small particles (think micrometre up to metre sized), most likely having once been the material of a larger body that was disrupted either by collisions or tidal forces. This material, due to the gravity of its local planet, is sculpted into a flat disc where more subtle interactions then lead to substructure forming within the disc such as gaps and ringlets. Many of these substructures are explained by well understood physics – for example gaps being carved by embedded moonlets, or resonances sculpting ring edges – though there remain some outstanding problems in our understanding.
The authors of today’s paper set their sights on the problematic inner edge of Saturn’s A ring (Figure 1). They describe some mechanisms – namely the collisions of micrometeoroids within the rings – by which a sharp ring edge can be maintained, but there exists a gap in the understanding of how such an edge can form in the first place. All hope is not lost, though, as today’s authors reintroduce a physical process they call the ‘eclipse-Yarkovsky’ (EY) effect which seems to explain these phenomena.
Figure 1: A horizontally sliced image of Saturn’s rings shows the rich substructure and gaps within the various rings. Saturn, which is not shown here, would be to the left of the image. The authors of today’s paper are particularly concerned with the bright and sharp inner (left side) edges of the A and B rings. Source: NASA/JPL/Space Science Institute
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The idea behind this process revolves entirely around light. Non-absorbed sunlight imparts a little ‘bump’ onto each of the particles within a planetary ring when it hits it, ever so slightly altering its trajectory. At the same time, some of the sunlight is absorbed into the particle which heats it up; light is soon re-emitted via thermal radiation which, again, can slightly change the trajectory of these tiny particles. From a point on the surface of each ring particle (see rightmost side of Figure 2), the photons from this thermal radiation are all emitted in random directions; however, across the whole surface of the particle there is a net force! These tiny particles are spinning, and so the side just near ‘sunset’ is hottest and emitting the most thermal photons. In this way, the pressure from the sunlight plus the thermal radiation of each particle imparts a net torque on the ring itself which changes the angular momentum of the ring.
What we described just then is essentially solar radiation pressure plus the Yarkovsky effect. It turns out that the net force from this process typically averages out to zero as the ring particles orbit around the planet. This assumes, though, that the sunlight is constantly shining on the ring. Stunning imagery of Saturn tells us that this isn’t the case, so what happens when we take into account the shadow cast on the ring from the planet? Today’s authors find that the net effect induces a positive change in angular momentum of the ring particles which they call the eclipse-Yarkovsky (EY) effect.
Figure 2: Starlight is the main source of light onto the particles that make up a planetary ring (right panel) though reflected light from the planet’s surface hits it too. This light ‘heats up’ the ring, and forms an asymmetry as the ring is eclipsed by the planet which produces a net force. Source: Adapted from Figure 1 in today’s paper.
After today’s authors detailed all of the math involved in this process (and there is a lot), they put it into practice to try to help explain Saturn’s curious rings. Including the EY effect together with other known effects that drive ring evolution allowed them to reproduce the optical depth profile (how thick the ring looks) of Saturn’s A ring better than ever before (notably the sharp inner edge in Figure 3). On top of this, the EY effect provides another avenue for moonlet formation in the outer edges of ring systems as the positive torque from the effect drives material out towards and away from the Roche limit.
Figure 3: The authors try to explain the current structure of Saturn’s A ring by initialising it with a Gaussian profile of optical thickness versus radius (black dot-dashed line) and evolving it for 81 million years under different effects. When viscous effects are included (blue dashed line), the ring spreads out but it’s only when the EY effect is included (red line) that the model closely matches the observed data (grey line). Source: Adapted from Figure 6 in today’s paper.
Undeniably useful for Saturn, the EY effect may also explain some other conundra in the Solar System. Mars may have once had rings, which are thought to have eventually clumped together to form the inner moon Phobos. This idea is problematic, though, in that current models suggest there should still be some residual ring system around Mars even after Phobos formed. Enter the EY effect: being 100 times stronger for Mars than Saturn (due to its more intense incident sunlight), the effect may have driven out and dispersed that residual ring altogether. While the authors are currently looking into this possibility, the reintroduction of the EY effect has already shown great promise for our most beautiful ringed planetary neighbour.
Astrobite edited by Wasi Naqvi
Featured image credit: NASA/ESA/SSI/Cassini Imaging Team, edited by Ryan White
