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Investigating the Origin of the Iapetus Ridge Emily Dahlberg Julie Rathbun University of Redlands Abstract Since the discovery of the ridge on Iapetus in January 2005, there have been three theories on the origin of this system. These include formation by ring accretion (Ip, 2005), despin and surface relaxation (Porco et al., 2005), and convection (Czechowski and Leliwa- Kopystyński, 2008). These theories have been thoroughly analyzed in this research, with the main focus convection. This analysis has displayed substantial evidence against all three theories, implying that the origin of the Iapetus ridge remains a mystery. Ridge Characteristics The ridge extends along a third of the circumference in the leading hemisphere with a length of 1600 km. A typical cross-section is 18 km in height, and 200 km across the base. Crater analysis indicates age comparable to surrounding terrain, ~4.5 Ga. (Giese at al., 2008) 1. Ring Accretion (Ip, 2005): The ridge formed from accretion of a former ring system. Since Iapetus is an outer moon of Saturn, it has an abnormally large Hill sphere, which increases the probability of Iapetus supporting a ring despite its small size. Evidence against Ring Accretion [4]: Fails to explain why ridge only covers a third of the circumference. Morphology of the ridge is very complex, which does not agree with a simple accretion model. An atmosphere is necessary to pull down the particles in the ring. An atmosphere on Iapetus at any point is very unlikely. The angle of the slope of the ridge in many locations is greater than the angle of repose. These four reasons indicate that the ridge was not formed by ring accretion. 2. Despin/Relaxation (Porco et al., 2005): Iapetus has a large bulge. The equatorial radius is 35 km larger than the polar radius, corresponding to a spin period of 16 hr. Its current spin period is 79 days. Iapetus is believed to have despun and only partially relaxed. It is possible that the ridge was erected during the partial relaxation. Evidence against Despin/Relaxation : According to the work done by Melosh (1977), despinning causes one of two tectonic features: strike-slip faulting diagonal to the equator or thrust faulting perpendicular to the equator. Neither of these systems could account for the ridge, so depending on Meloshs work, it is unlikely that it was formed as a result of despinning. 3. Convection Theory (Czechowski et al., 2008): The convection theory proposes that Iapetus has two cells of convection, allowing upward currents at the equator, which could form a ridge similar to the ocean ridges on Earth. The characteristics of these two types of ridges are similar (see images 4-7). Due to the symmetry of the tidal heating which supposedly induced convection, the moon would have needed to reorient itself by 90°. Iapetus ridge Image 7 Iapetus ridge Image 6 Present equator Present pole Topographical image of ocean ridge on Earth Ridge Height Ridges are formed on the surface above upward currents because of isostacy. The height of the ridge can be calculated. The height, y, can be expressed as Coefficient of thermal expansion, [7] Temperature difference between surface and mantle, [8] Thermal diffusivity, [7,8] Horizontal distance from the ridge crest, x, varies from x=0km to x=100km Horizontal velocity of the lithosphere, [3] [6] This equation yields the results displayed in Plot 1 (inverted with crest at y=0). As shown, the maximum possible height for the ridge relative to half a width away is ~2km. This is significantly less than the average height of 18km. depth, b length, λ/2 v u Image 8 Two-cell Convection In order for the convection theory by [3] to be true, Iapetus would need two cells of convection, one in each hemisphere. According to [6] a number of variables affect the possible convection cell size. The downward velocity of the convection cell (v in Image 4) can be determined by balancing the downward, gravitational force and the upward viscous friction (method 1). This order of magnitude estimate was then compared to the downward velocity specified by fluid conservation (method 2). Assuming steady convection, the gravitational force on the plume must be balanced by the viscous friction from the surrounding material. The total downward force is calculated from the temperature profile of the plume, and the negative buoyancy, F b over the depth of the cell. The equation and values used are presented below. where ρ is density, g is gravitational acceleration, b is depth of the cell, u is horizontal velocity, v is vertical velocity, κ is thermal diffusivity, and λ is wavelength of the convection system [6]. Along the boundaries of the plume, there is horizontal and vertical stresses, τ h and τ v, respectively: Equating the rate at which work is done by both forces, we have Substituting and solving for v, Resulting in 2. This result can be compared to another calculation of downward velocity: fluid conservation. By simple geometry, the following equation can be derived from image 8: Resulting in These calculations produced significantly different values for the downward velocity based on a convection cell of this size. Since the size of the convection cell is crucial to [3]s theory, this result greatly reduces the probability of convection forming the ridge. Additional Tectonic Features If there is convection producing a ridge at the equator, then the lithosphere must be subducted elsewhere. [3] suggests the subduction zone is near the pole, and preliminary observations show no indication of a significant subduction zone. The remaining surface also fails to reveal any tectonic patterns indicating subduction. Although these are preliminary observations, they also indicate a weak link in the convection theory. Upward convection patterns Extensive analysis has been done on three-dimensional convection [9]. Although this study mainly focused on tetrahedral and cubic patterns, the general result was that upward currents tend to form in cylindrical shapes to reduce surface area. A long, linear pattern of upward currents as seen on Iapetus is highly unlikely, and is an unstable configuration [9]. Further programming and numerical analysis is necessary to determine conclusive evidence for Iapetus. Reorientation Czechowski et al. (2008) propose either tidal forces or radiogenic decay to be the source of heat that induced convection on Iapetus. Regardless of the source, the current orientation of the ridge is not preferred by any system [3]. If the convection was the result of tidal heating, 90° reorientation is necessary. Very basic calculations were done for 90° [10]. Ultimately, it was found that reorientation produces two points of symmetry. These two points are the leading and trailing side for 90°. The preliminary observations show no indications of symmetric tectonic features around any two points. Additionally, the source for such a massive reorientation is non-obvious. Again, more extensive analysis is necessary to reach a conclusion, but the preliminary results indicate reorientation is unlikely. Since reorientation is crucial to the theory, these results also indicate the ridge forming by convection to be unlikely. Conclusion The three current theories on the formation of the mysterious ridge on Iapetus present significant flaws. Specifically, five analyses were conducted on the convection theory, all of which returned evidence against the theory. Although more extensive analysis should be done, at this point, I submit that the convection theory is implausible. The Three Theories: Image 1 Image 2 Image 4 Image 5 Testing the Convection Theory Reference Key: 1. (Ip, 2006), 2. (Porco et al., 2005), 3. (Czechowski et al., 2008), 4. (Giese et al., 2008), 5. (Melosh, 1977), 6. (Turcotte, 1982), 7. (Turney, 2004), 8. (Castillo-Rogez et al., 2007), 9. (Bercovici et al., 1989), 10. (Matsuyama at al., 2008) Viscosity, [8] Density, [8] Gravitational acceleration, [8] Wavelength of cell, [3] Depth of cell, [8] Downward velocity, [3] 0°0° -30 ° 90 ° 30 ° 60 ° -90 ° -60 ° 0°0° 180 ° 120 ° 60 ° 180 ° 240 ° 300 ° Longitude Latitude Image 3 Due to the large discrepancy in the calculated and actual height, it is highly unlikely the ridge was formed by isostacy. 1.

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