Please note! This essay has been submitted by a student.
In 2017 the famous NASA’s Cassini Spacecraft made its final approach to Saturn and crushed on its surface, therefore ending its 13-years long mission, that included a collaboration with some other international space agencies. The mission allowed scientists to gather a big amount of important data about Saturn rings, atmosphere and moons. At the meant time, Voyagers spacecrafts help exploring other gas giants: Uranus, Jupiter and Neptune, which also have ring planetary system, which was a surprise for me. Due to these missions, a mysterious world of rings of the planets. Although now mass, width and some other properties of rings are known, their origins and process of appearing and evolving are still a topic of numerous debates.
Since I am interested in astronomy and astrophysics, I decided to choose a topic relatable to those areas of science. The Grande Finale of the Cassini Mission made me look into the world of enormous gaseous planets, especially their amazing rings. In this way I came up with my research question: « How does the opacity of the rings of gas giants depend on the distance between a ring and its center mass? » Thereby, physical properties and structures of ring systems will be discussed in this essay, alongside with the goal of determining, whether they obey uniform or unique laws. Thereby, the possible factors and processes, affecting the properties of rings are also to be explored, such as an impact of gravitational forces produced by the center mass and its moons, or inner processes like collisions between particles.
This research question is worthy of investigation, because it doesn’t only relate to a field of contemporary research, but also may shed light on other areas or issues of the same field of science. The planetary ring systems show scientist a big variety of structures and processes, taking place inside or outside of it, affecting its behavior and form. Moreover, some of these processes in planetary rings can be found operating in other astrophysical systems, such as spiral galaxies, protoplanetary or accretion disks. Thus, the results and conclusions based on studies of the rings of gas giants can be put to use in exploring the dynamics of other astronomical phenomena. This section includes the discussion of structure of each of planetary rings system separately and together, supported with graphs, tables and needed calculations.
Saturn is a planet famous for its rich planetary ring system with a big diversity of structures. The particles, that make the rings, mostly consist of water ice or rock, where the latter is said to be similar to the material of Saturn’s nearby moons. A feature, that drastically differs Saturn rings from those of other gas giants, is the number of dense rings. That being said, rings can be divided in two main groups: A, B, C Rings, which are the densest in the system, and D, E, G Rings, that are much more tenuous than the previous ones. There is also F Ring, that should be payed attention to, as it shares some of characteristics of both of those ring groups — although it is located on the outskirts of the system, it is dense and has sharp edges like B and A Rings. The biggest and broadest ring, located far away from the planet, is called Phoebe Ring.
On the diagram we should note two areas of rather high optical den. First one is located near the planet, then the ring becomes fainter. Afterwards we can see a peak value of optical density, that corresponds to B Ring, followed by a sudden decrease in opacity, which indicates Cassini division. The next rise in opacity is due to A Ring. The two following intervals of decrease in opacity are caused by the presence of Encle and Keeler Gaps, that are embedded by the moons Pan and Daphnis respectively.
Then, at the point where ~ 0.1, F Ring starts. The ring is often considered as an exception in scientific papers, as it keeps its form and sharp edges (which is a feature of dense rings) while being located rather far from Saturn, with the help of moons Pandora and Prometheus orbiting Saturn along with the ring. To be more precise, there is also Janus/Epimetheus Ring that follows after F Ring, but no information about its properties was found.
The rest of the curve indicates the faintest and broadest rings: G, E and Phoebe Rings. The former ring is a dusty ring, isolated from its neighbors, which can’t be seen on the diagram. The following ring includes three narrow and very faint rings called after the moons that occupy their regions: Methone, Anthe and Pallene Rings. E Ring is broad, dusty and faint, like G Ring, but it gets denser near the orbit of Enceladus. The last and broadest ring is Phoebe Ring, that also has rather big vertical extent, and is named after the moon Phoebe, which orbits near its outer edge.
Although Saturn is unique in its rich planetary ring system, after it we can reasonably place Uranus. It is worth noting, that since the planet almost lays on its side, the rings and moons still orbit around its equator, which differs Uranus’ ring system from the others.
This planet possesses the most substantial rings, which generally consists of narrow and dense rings, such as 4, 5, 6 Rings and Rings. The latter is a bit different from the others, as it has the highest opacity and biggest width. The rings are, in their turn, covered in dusty material, which also contains narrow and dusty ringlets, such as ring.
On the outer edges of Uranus’ ring system there are two more dusty rings, which are very wide and tenuous, named and (respectively to their distance from the planet). The former is bounded by moons Portia and Rosalind, but still has diffuse edges. Ring also represents a certain connection with the nearby moon Mab, as its width peaks at the orbit of the satellite, but still it remains faint, without any sharp edges. Those rings were discovered rather recently, so there isn’t a lot of scientific work done now due to lack of information and understanding.
Uranus’ rings system differs from that of Saturn, as its rings are eccentric and have inclination in their orbits. Moreover, they are dark, which makes its observation and exploration more difficult. Scientist suppose that the possible cause for such ‘color’ is some organic material that ring particles might contain.
The first one lasts from the start until the first decrease in opacity. It is rather symmetric and represents main dense rings (from 4 Ring to Ring). The reason for not having any sharp decreases in optical depth is possibly the dusty material that covers the (in numerous articles it is regarded as an inwardly directed Ring). The following rise in opacity (in the second part of the diagram) corresponds to the Ring. Actually, this ring can be compared to F Ring of Saturn. Although it is on the outskirts of its ring system, it is dense and narrow (in other words, it has sharp edges, which is usually a feature off rings close to its center mass). In the same way as F, Ring keeps its form likely due to two moons shepherding it: Cordelia and Ophelia.
Jupiter is the biggest planet of our solar system and possesses the most tenouous ring system out of all gas giants observed. The closest ring to the planet is Halo Ring, that consists of debris. Then there is Main Ring, the densest and thickest ring, that extendeds to the moons Metis and Adrastea, which are likely to be suppliers of its material. Exterior to Main Ring there is Gossamer Ring, composed of Rings Amalthea and Thebe, that were named after moons orbiting on their outer edges. Then there is a tenuous outward extension of Thebe Ring, that has the lowest opacity in the ring system.
Jovian Rings have relatively simple form and mostly consist of a very small micron-sized particles, although there are some pieces up to at least centimeter across. This will be takein into account in Section 2, as the forces, that affect mass distribution in rings and hence the optical depth, will be different from that of the other planetary ring systems.
This diagram differs from previous ones. First of all, it can be seen that there is only one peak in optical depth ( = 5 10-6) situated in Main Ring, that follows after Halo. Then opacity value falls quite sharply. The cause for such decrease might be Adrastea and Thebe that orbit around the ring’s outer edge and thus keep debris and particles more or less inside of their ring. Afterwards, curve indicates two components of Gossamer Ring, Amalthea and Thebe Rings, that are similar in the values of optical depth.
Neptune possesses rather tenuous and dusty planetary ring system, which consists of five rings and, most importantly, arcs. In fact, rings of this planet are still poorly understood and researched due to the very limited data.
Nearest to the Neptune is Galle Ring. It is faint and broad, and probably reaches all the way down to the planet. The following ring is Le Verrier Ring, which is narrow and has rather high optical depth, compared to the dusty rings that surround it. The next ring called Lassell is uniform and extends outwards from the previous one, almost reaching Adams Ring. The latter is the most prominent narrow ring out of all and contains unique arcs, that are designated as Courage, Liberté, Egalité 1&2 and Fraternité and appear to be rather stable in their structures. In many scientific articles I also came across Arago Ring, which turned out to be a name for the edge of Lassell Ring. It was named due to the increase in the ring’s brightness at its outer boundary, in order to distinct it from the rest of the ring.
The structure of the curve in Diagram 1.4.1 is a bit similar to that of Uranus. It must be due to the fact that both Neptune and Uranus are ice giants, that in their turn differ from gas giants. The most important difference is the force of their magnetic fields: magnetic field of ice giants is weaker than that of gas giants. Therefore, dense rings with the peak in optical depth are expected to be found further from Neptune and Uranus, than in the Saturn’s and Jupiter’s ring system.
There is an increase in optical depth in the beginning, that indicates Le Verrier Ring. Afterwards it falls in value, which is due to uniform and dusty Lassell Ring. Then it increases in value again, indicating the opaquest ring — Adams Ring, that contains arcs. The latter are believed to be confined by the little moon of Neptune Galatea, particularly by its co-rotation resonance. There is also a presence of dust population outside the rest of the rings, separated by rather big distance. However, there is still little information about this ‘extension’, so we will stop on Adams Ring.
The ring system of Neptune mainly consist of dust and micron-sized particles. In this regard it is similar to the Jovian planetary ring system. Thus, some other processes and forces, different from those we can find in the dense rings, are to be observed influencing structure of the rings. In this section I am going to discuss possible factors influencing the formation and structure of the planetary rings, focusing more on mass distribution as it is directly related to the key parameter of my essay — opacity.
The gravity causes one of the most crucial impacts on the structure of the rings, whether the attraction is produced by the center mass, its moons or rings themselves. Such concept, as Roche limit, or Roche radius, plays important role in our understanding of the rings systems. It is also the reason for the moons not being observed to orbit close to its center planets.
Roche limit is related to the mass distribution and its aggregation in the planetary rings. Inside of this limit the gravitational attraction of a center mass prevails the attraction between particles in a mass (or two smaller masses), that causes them to split up. On the contrary, outside of the Roche radius gravitational force between smaller masses is stronger, hence they can approach each other, or, in a case with a single mass, it stays together.
The effect of Roche limit was seen in 1922 when the Comet Shoemaker-Levy 9 entered the Roche radius of Jupiter and broke apart into pieces due to tidal forces.
So, what does it have to do with planetary rings? First of all, it prevents particles in the rings inside of the limit from aggregating into bigger masses, like moons, bringing the homogeneity feature in mass distribution in rings. It also doesn’t allow particles to escape their rings, as the force again prevails their esc that they can get during their internal collisions. The Roche limit can be found using following formula:
r(R)=χ R(M) ∛(ρ(M)/ρ(m), where R(M) and ρ(M) are radius and density of the center mass respectively, ρ(m) is density of the smaller mass and χ is a coefficient that varies for different types of second mass. In the case, where we have a rigid body (spherical satellite) χ=1,26, and if the smaller body is considered to be a fluid satellite χ=2,44. It is known that most particle in the rings of gas giants are made of ice water and rocks, the latter is likely to be the same as the material of nearby moons. This is why I am going to calculate Roche limit for two types of densities. In case with the rocky material, many articles suggest equaling the density of a center mass to that of a second mass, with which I am going to proceed.
In Saturn planetary ring system, Roche Limit encompasses all dense rings from C Ring to A Ring. Thereby, optical depth is being sustained and doesn’t change (at least on large scales) in dense rings. It is known, that the most particles in the rings consist of water ice, then F Ring and other distant rings stay out of Roche Zone. With making an exception for F Ring (see Section 1-I), we can note, that all the rings outside of Roche Limit (G, E and Phoebe Rings) are dusty and ethereal, thus they tend to aggregate into large, isolated objects. This indicates that there are some other processes and forces involved in keeping them in their present states, hence sustaining their optical depth.
In Uranus planetary ring system, Roche Limit encompasses all rather dense and prominent rings from 6 Ring to Ring. Dusty and diffuse μ and Rings are observed to be out of the limit, similar to Saturn’s ones, but the dusty Ring stays inside of it.
Jupiter planetary ring system is mostly made of dust, that comes from the inner moons and striking meteors, hence for this case we are going to assume that the rock material is the same, so ρ(M)= ρ(m). Then the Roche Limit again encompasses the densest rings from Halo Ring to the Main Ring, adding to it the inner part of Gossamer Ring. The outermost and faintest rings, such as Thebe Extension, are left out of this limit.
Neptune planetary ring system is made mostly from dust and the rest of the material is small rock. In this case we calculate Roche Limit in the same way we did it for Jovian Rings. Thereby, it encompasses narrow rings from Galle Ring to Lassell Ring. Adams Ring lies beyond the limit, but still is rather prominent, possibly due to nearby moon Galatea, compared to an unnamed dusty ring that is located between it and Arago.
Combining observations, it’s easy to see, that Roche Limit contributes a lot for mass distribution and its sustaining in the dense rings, which is directly related to the optical depth. Outside of it, there are mostly dusty and diffuse rings. Surprisingly, they don’t seem to be aggregating into unite bodies. This indicates that dust is subject to a lot of different forces and perturbations.
Drag Forces are one of the forces that have a great impact on the structure of dusty rings. They can also help to bring more material in the rings. The best-known example for this is Jupiter’s two components of Gossamer Ring, Amalthea and Thebe Rings, where two moons are believed to be the sources of debris and dust, knocked off of them (e.g. by meteoroids). Nevertheless, drag forces can also cause the loss of material, due to different processes, such as internal collisions or interactions with plasma. This effect can be seen in G Ring of Saturn, that encompasses the orbit of the small moon Aegaeon. As the ring goes further from the moon, the gravitational force of the latter weakens, which allows the material to drift away and decreases the optical depth. A similar process of mass loss can be also observed in Uranus’ Ring with nearby moon Mab.
Dusty rings are also exposed to inertial perturbing forces, such as solar radiation pressure. Since dusty rings mainly consist of micron-sized particles, the latter can exchange momentum with solar photons. In consequence, as if being kicked out from the ring, particles can form ringlets. Such phenomenon can be observed in Cassinni Division in the form of faint ringlet of low optical depth.
Since there are a lot of rings that encompass the orbits of small moons, the gravitational pull of moons also plays important role in mass distribution. In the beginning of the essay, an assumption about all ring being homogeneous was made. In fact, exactly because of such force, which can also be called resonant perturbation, the rings aren’t uniform. On the images, made by Cassinni Spacecraft, it is possible to see the changes that gravitational pull causes: clumps, self-wakes, density waves etc.
These were some of the forces that impact dusty rings, where the density, hence optical depth, is low. For the particles bigger than micron-sizes it still can take a lot of time to interact. In denser rings, on the contrary, particle collision is more likely to happen, and thus collisions and gravitational interactions between particles cannot be ignored.
The process of evaluating the dynamics of dense rings is complicated. Its behavior depends on the basic parameters of the ring, such as size of particles, their average number etc., and, obviously, on the distance from the planet, since the velocity increases as the body goes nearer to the center mass.