2.1 Geological Background of Iapetus
So far, most data and images of Iapetus are observed by the 2007 flyby of Cassini orbiter. Several models have been mentioned to construct the geologic inferences of Iapetus. These models are usually classified into different topics:
shape and rotation, inner structure, age, albedo dichotomy of exosphere, and equatorial ridge. All topics will be described next except the origin models of the equatorial ridge, which will be discussed in section 2.3.
2.1.1 Shape and Rotation
Iapetus is a satellite that has a shape of oblate spheroid (746×746×712 km, from Table 1), and its rotation period is tidally synchronized with a 79-day orbiting period (Porco et al., 2005). The highly flattened shape of Iapetus is possibly caused by rotational flattening since the amount of a-c axis difference is large enough to ignore the effect of crater modifying. But 79-day rotation period is too slow to form an oblate spheroid. Consider an equilibrium of gravitational field and centrifugal acceleration due to rotation, the flattening coefficient, f, is given by
𝑓 =
𝑅𝑒−𝑅𝑝𝑅
=
54 𝜔2𝑅3
𝐺𝑀 (2-1)
where R is the mean radius of the satellite, Re and Rp stand for the equatorial and polar radius (a and c axis) of the satellite, ω and M are the angular velocity and the
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mass of the satellite, and G is the gravitational constant. The parameters listed in Table 1 are adopted to calculate the status of hydrostatic equilibrium for the current rotation period. If Iapetus is homogeneous, the estimated a-c difference (Re – Rp) is only 2.53 m. It doesn’t match with the current shape of Iapetus. Thus, Iapetus doesn’t have an equilibrated shape nowadays, and must possess a despinning history.
In the meantime, the hydrostatic equilibrium of the shape of Iapetus yields a predicted period of 16.5 h (from Eq. 2-1). If there was a silicate core inside Iapetus, it would be required a spin period of 15.2 h to form this oblate spheroid
(Castillo-Rogez et al., 2007). So, Iapetus has a fossil shape that formed in the early age of Iapetus. When the rock strength of Iapetus increased due to cooling, Iapetus fixed its outline.
Another issue is that how long did Iapetus despin to the synchronization? In fact, all satellites of Saturn, except Hyperion, are tidally locked by Saturn. However,
synchronous spin on Iapetus is less possible than the other Saturnian satellites since Iapetus has both large mass and semi-major axis (Peale, 1986). Ip (2006) and
Matson et al. (2009) also suggested that Iapetus need much time that possibly more than the age of the Solar System, except that the interior are mostly molten. To describe more precisely, we uses the following formula to calculate the damping time of tidal locking (Gladman et al., 1996; Peale, 1977):
𝑡
𝑙𝑜𝑐𝑘≈
3𝐺𝑀𝜔𝑖𝑎6𝐼𝑄𝑝2𝑘2𝑅5 (2-2)
where ωi is the initial angular velocity of the satellite (1.06×10-4 radian/sec) , a is the
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semi-major axis of the satellite, I is the moment of inertia (≈ 0.4M𝑅2) of the satellite, Q is the dissipation function of the satellite, Mp is the mass of the planet (which is Saturn in this case, 5.6846×1026 kg (Willians, 2012)), k2 is the tidal Love number of the satellite. In general,
𝑘
2≈
1.51+2𝜌𝑔𝑅19𝜇 (2-3)
where μ is the rigidity of the satellite (usually 4×109 Nm-2 for icy satellites), ρ is the mean density of the satellite, g is the surface gravity of the satellite. Set a generic Q of solid bodies = 100, Eq. 2-2 and 2-3 yield a tidal-locking time of 277 My. Since Q has a high uncertainty which ranged from 10-500 for solid icy satellites (Dobrovolskis et al., 1997), Iapetus may have a tidal dissipation timescale of 28-1400 My. Based on the
calculation, we can conclude that it requires the existence of partial melting on the early stage of Iapetus inner core to synchronize its spin, or Iapetus may have spent long time (roughly 100-1000 My) to do so.
2.1.2 Age
Porco et al. (2005) reported that Cassini ISS images showed the heavily cratered surface of Cassini Regio. The whole surface except the equatorial ridge area is controlled by the cratering, with over 3 large ones whose diameters are larger than 350 km. The study of size distribution of craters (Kirchoff & Schenk, 2010) suggests that the terrain age of both dark side and bright side are the same. The high density of craters on Iapetus implies that Iapetus may be geologically old.
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A quantitative value of the age of Iapetus is predicted by Castillo-Rogez et al.
(2009, 2007). They set a model considering the shape, despinning and the thermal history of Iapetus, and the best-fit age value is between ~3.4-5.4 Myr after the formation of calcium-aluminum inclusions (CAIs). The age of CAIs was measured by Amelin et al. (2002), who proposed an age of 4567.2±0.6 Myr from Pb-Pb dating method. Thus the age of Iapetus is 4563.8 to 4561.8 My. Since all the surface features on Iapetus appear old, they might form on the early stage of Iapetus. The crater frequencies analyzing result (Neukum et al., 2005) also implied an over 4-billion-year surface on Iapetus. Based on lunar crater studies, the age of the surface of Iapetus is probably close to 4400-4500 Myr.
2.1.3 Inner Structure and Composition
As previous mentioned, Iapetus has 2 possible internal structures: 1) Iapetus has large portion of low-density materials; 2) Iapetus has a porous inner core. If Iapetus is composed of low-density materials, then water ice is the most likely matters since ice has a low density (0.9 g/cm3) similar to the density of Iapetus. In the model proposed by Leliwa-Kopystyhski et al. (1994), Iapetus is set to have an icy mantle of 418-km thickness and an silicate inner core (whose density is 3.361 g/cm3) of 328-km radius. But the radius of the inner core decreases when mantle is mixed with
ammonia (NH3) and methane (CH4), which are the bulk compounds in the Jovian planets. In the other hand, Owen et al. (2001) analyzed the infrared spectrum of 0.3-3.8 μm to get the information of the surface composition of Iapetus. They found that the surface of Cassini Regio is deposited by the mixed matters of water ice, amorphous carbon, and nitrogen-rich compounds. After Cassini orbiter’s
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observation, Buratti et al. (2005) obtained the VIMS data for Iapetus, and concluded that the bright side is ice-rich so that it appears the high albedo; and that the
detection of carbon dioxide (CO2) in the dark side implies the removal of the regolith. Cruikshank et al. (2010) even noted that the CO2 on Iapetus is native, enclathrated in water ice, and then released due to the exposure of the solar wind.
Therefore, an acceptable model is that the bulk composition of Iapetus is H2O, and that there are compounds which are rich in carbon, nitrogen inside the water ice.
A porous inner core may exist, but is less possible due to a lack of gravitational data. Sandwell and Schubert (2010) used this hypothesis to construct a model of the formation of the equatorial ridge, which will be discussed later.
2.1.4 Thermal History
Thermal history is the key to the chronology of Iapetus. If the tidal-dissipating time is relatively short, sufficient heat is needed for the partial melting of the inner core. Furthermore, the fossil 16-h shape implies a core which generated large amount of heat but lost it quickly. Castillo-Rogez et al. (2007) noted that 26Al could play a significant role on the early stage of Iapetus. 26Al is one of short-lived
radioactive isotopes (SLRI), which include the common radioactive isotopes with the half-life of under several million years. 26Al is also abundant in CAIs, but quickly decay to 26Mg with a half-life of 0.716-0.73 Myr (Kita et al., 2005). Castillo-Rogez et al.
(2009) also pointed out that the abundance of 26Al dominated the age, the porosity changes, and the shape evolution. Their modeling result shows a possible 26Al-rich scene: after Iapetus formed (with the age mentioned in section 2.1.2), the heating from radioactive nuclides lowered the strength of the material of Iapetus, shaped
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an oblate spheroid. When Iapetus synchronized its spin within 200-1000 Myr, no more 26Al radioactive heat was generated so that the satellite was cooling down, remaining a 16-h fossil shape.
2.1.5 Albedo Dichotomy
Iapetus’ albedo dichotomy can be easily recognized in Fig. 1.4. The Cassini Regio (dark side) distributes over low to mid-latitude regions, and is constrained in 0-210 degrees of longitude. Squyres and Sagan (1983) first noted that there is a
one-magnitude difference of albedo between the dark side and the bright side. The VIMS survey mentioned in 2.1.3 offered a possible composition of these 2 sides (Buratti et al., 2005; Cruikshank et al., 2010): The bulk composition of the bright side is water ice, however the matters on the dark side mixed with several compounds including H2O, CO2, and N-rich organic compounds which are often called tholins.
Because we observed that CO2 emited from ice clathrates, it is accepted that the dark side is regolith-depleted; in other words, the deep rock of Iapetus is exposed to the surface because of the removal of the weathering soil.
Dozens of hypotheses were proposed to explain the origin of the dichotomy.
For instances, Owen et al. (2001) interpreted the dark side as debris deposits, which were originated from Titan. On the other hand, Marchi et al. (2002) regarded the dichotomy as a result of Iapetus-Hyperion collision event. Wilson and Sagan (1996) also suggested that there is a removal of ice on the dark side, and then the dark matters were exposed; the trigger of the removal of ice is numerous impact events from interplanetary dust particles. Most of these hypotheses are related to
exogenic procedures. In the recent study, a new model is illustrated by Spencer and
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Denk (2010), who plausibly explained the albedo dichotomy as a global thermal migration of water ice. In this model, a slight albedo difference is given in the beginning. Since Iapetus has an unusual synchronous spin, the day temperature is high enough to sublimate water ice. If there is a slight albedo dichotomy on Iapetus, water ice in the dark side will be sublimated during daytime. The gaseous H2O will migrate and deposit in the bright side, and then increase the albedo of the bright side. This positive feedback enlarges the difference of the two sides, and finally depletes the water ice in the dark side. The process costs 2400 Myr to form the nowadays condition of Iapetus. Because Iapetus need ~109 years to be synchronized, the albedo dichotomy may be a “new” structure on the Iapetus, or still in
development.
Fig. 2-1 Portion of image N1483174398. From Porco et al. (2005).
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2.2 Geomorphological Data of Iapetus’ Equatorial Ridge
The earliest mosaic images of Iapetus are published by Porco et al. (2005). Fig.
2-1 is one of the images of the peculiar equatorial ridge. The ridge in Fig. 2-1 shows 2 features: 1) several parallel linear structures aligning the ridge; and 2) heavily
cratered surface with some parts which is devastated (the lower left corner of the ridge in Fig. 2-1).
To obtain more detailed morphological data of Iapetus, Thomas et al. (2007) employed the limb coordinates and stereogrammetric control points which were measured by the Cassini ISS. They treated Iapetus as an oblate spheroid with
747.4×747.4×712.4 km. And the next, the limb area (especially in the equatorial bulge) of each image is located and measured. Finally, Thomas et al. gathered 31 limb
profiles of the equatorial bulge area. However, Giese, Denk et al. (2008) pointed out that the limb profile may be over-estimating on the height of the equatorial ridge.
They used another way to construct the Digital Terrain Model (DTM) data of Iapetus.
Their simple idea is to superimpose multiple images which have control points and picture at the same area of Iapetus. The shadowed area that is caused by the highlands of Iapetus varies when the position of the orbiter changes, so the height of the surface is obtained by superimposing images taken by Cassini ISS from different places. Giese, Denk et al. utilized their method to icy satellites including Enceladus (Giese, Wagner et al., 2008), Phoebe (Giese et al., 2006), and of course Iapetus. Fig. 2-2 displays the calculated DTM data of leading side (dark side). (Giese, Denk et al. also noted that the DTM height of the ridge is 10-20 km, which a width of 100-200 km and an average slope of 4-10 degrees. The DTM data shows a lower
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ridge than previous suggestion by Thomas et al. (2007), but the precision of the surface profile is enhanced. For example, the A-A’ profile in Fig. 2-2 cuts through a crater, the ridge, a depression area and a plateau area; this profile distinguishes them respectively. The resolution of DTM data is kilometer-scale, but the small structure of such this scale may be ignored when modeling; that is, DTM data is useful on large-scale structures like big craters or the ridge, but it is not so precise for the small structures.
Fig. 2-2 Digital Terrain Model (DTM) of Iapetus. Reference shape is a 748×748×713
oblate spheroid. A-A’ profile cuts though the depression area, the ridge and crater No. 5. Modified from Giese, Denk et al. (2008).
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2.3 The Origin Models and Flexural Implications of Iapetus’ Equatorial Ridge
The equatorial ridge is also an old structure since the crater density is similar to the other areas of Iapetus. If we accept the crater-frequency dating proposed by Neukum et al. (2005), the ridge has remained its shape for over 4 billion years.
Although there is a fossil 16-h equatorial bulge, the ridge seems to be excluded from the bulge and superimposes on it. Obviously, the ridge was not formed simply by despinning, and the other scene is needed to explain the origin of the ridge.
Until 2012, the ridge has been interpreted into several different origins, which can be divided into two main classes: endogenic model and exogenic model. Due to the lack of in situ survey, it is still under debate that which one is more correct. The brief descriptions of these models are listed in Table 2 for the detailed discussion in the next section.
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Table 2 Origin Models of Iapetus’ Equatorial Ridge
Author(s) and year Model Class Description
Ip (2006) Exogenic The collapse of the ring system, which originated during Iapetus’ formation Castillo-Rogez et al.
(2007); Porco et al.
(2005)
Enodogenic Tectonic activity triggered by the despinning
Dombard et al. (2012);
Levison et al. (2011)
Exogenic The collapse of the ring system, which originated from an impact event Giese, Denk, et al.
(2008)
Endogenic Endogenic tectonic unwarping (fold)
Czechowski and Leliwa-Kopystyński (2008)
Endogenic The rising point in the two-cell convection
Melosh and Nimmo (2009)
Endogenic Igneous dike intruded in a thin lithosphere
Sandwell and Schubert (2010)
Endogenic Lithosphere was applied by the contraction stress, which originated from a porous core
23 2.3.1 Exogenic Models
Porco et al. (2005) first noted that the equatorial ridge may originate from the same process that formed the equatorial bulge. Castillo-Rogez et al. (2007)
expanded this idea and developed a model to evaluate the possibility of a despinning scenario. In this model, the ridge is interpreted to what was buckled when Iapetus started to slow down its rotation from a high initial spin rate. Set the thickness of lithosphere is 15 km, and then a 5-h initial spin rate is adequate to redistribute enough amount of material (~3.5×106 km3) that reaches the volume of the ridge (~3×106 km3). Although there’s a high uncertainty affected by the
lithospheric thickness, the initial spin rate is so close to the 3.8-h Roche limit that it hardly maintain a shape of oblate spheroid.
Therefore, the dispinning scenario is doubtful. Ip (2006) computed that the despinning has not likely finished for limited age of the Solar System, just as discussed in section 2.1.1. He also suggested a new exogenic model that describes the ridge as deposits of a ring system remnant. Just like Saturn or the other gaseous planets, satellites may have their ring system during the formation stage. Iapetus’
dust particles in the ring system might collide and drag with each other, making a dissipation of energy. This condition resulted in the decay of the ring orbit, and that numerous particles impacted on the equator of Iapetus, accumulating an equatorial ridge. Similar phenomenon was recently discovered on another Saturian satellite, Rhea, which has a completed equatorial linear trace that was soon interpreted as a ring remnant, although the total mass is much lesser than the equatorial ridge (Schenk et al., 2011). Ip also proved that the possible volume of the Iapetus ring is sufficient to accrete the nowadays equatorial ridge. Fig. 2-3 simply describes the
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process he proposed, and it makes sence that why the ridge lies precisely on the equator.
Based on the previous idea, the exogenic model has been developed by Levison et al. (2011) and Dombard et al. (2012). These two studies suggested that an ancient
giant impact created Iapetus’ ring system. Dombard et al. noted that if both Iapetus and its ring system have formed from the Saturian subnebula, it would have not been explained why the equatorial ridge was only found in Iapetus. Alternatively, they proposed the model that the ring formation may be posterior to the formation of Iapetus due to a unique catastrophic incident on Iapetus. Levison et al. (2011)
Fig. 2-3 Illustration for a ring-collapsing scenario, modified from Ip (2006). Top:
Iapetus owned its ring system. Middle: The ring system gradually decayed its orbital radius due to the tidal dissipation. Bottom: The remnant of the ring deposited on the equator of Iapetus, building the ridge. Dombard et al. (2012) and Levison et al. (2011) used similar process to explain the transformation from an impact event to the equatorial ridge.
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presented a scenario that the impact debris built the ring straightly; while Dombard et al. (2012) proposed that the impact may form a subsatellite first, and then this
subsatellite decayed its orbit, eventually entering the Roche limit of Iapetus, torn into pieces, building the ring indirectly. After the ring formed, the accumulation scene is similar to Fig. 2-3.
2.3.2 Endogenic Models
Some researchers preferred endogenic models which need some special structural conditions. Giese, Denk et al. (2008) first pointed out that the ring remnant deposits should build a steep hill and a sharp peak, whose angle of
response is up to 30-40 degrees. However, the average slope of the equatorial ridge is only 8-15 degrees (Giese, Denk et al., 2008), and the topography of the peak revealed by their DTM model is really flat. Therefore, they argued that the ridge may not be formed by an exogenic process, but an ancient tectonic activity. Steep slopes and top-flatted peaks can be simply attributed to tectonic upwarping. They also figured out that there are some depressions aligned with the equatorial ridge; these depressions may stand for the flexural signals.
Next, Sandwell and Schubert (2010) expanded their study for the equatorial ridge. They suggested an innovative model describing a porous inner core (where porosity is over 10%) and a solid outer shell in Iapetus’ early stage. When the inner core was heated and reached about 200K, the core began shrinking and lost the support force to the outer shell. Then the shell must deform its shape to match the volume with the inner core. The equatorial ridge is such a product of this buckling process. If the ridge was buckled, the flexure model can be used to construct a
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relation between the thickness of the outer shell and the buckling type. This model in the spheroid case is suggested by the following formula (Beuthe, 2008; Sandwell
& Schubert, 2010):
where W is the vertical deformation (flexure value) in terms or Legendre
polynomials, q0 is the vertical load, D is flexural rigidity which will be mentioned in Chapter 3, R is the radius of the satellite, E and ν are Young’s modulus and Poisson ratio of the material, F is the end load, h is the thickness of the lithospheric outer
polynomials, q0 is the vertical load, D is flexural rigidity which will be mentioned in Chapter 3, R is the radius of the satellite, E and ν are Young’s modulus and Poisson ratio of the material, F is the end load, h is the thickness of the lithospheric outer