Long term evolution and chaotic diffusion of the insolation quantities of Mars

As the obliquity of Mars is strongly chaotic, it is not possible to give a solution for its evolution over more than a few million years. Using the most recent data for the rotational state of Mars, and a new numerical integration of the Solar System, we provide here a precise solution for the evolution of Mars' spin over 10 to 20 Myr. Over 250 Myr, we present a statistical study of its possible evolution, when considering the uncertainties in the present rotational state. Over much longer time span, reaching 5 Gyr, chaotic diffusion prevails, and we have performed an extensive statistical analysis of the orbital and rotational evolution of Mars, relying on Laskar's secular solution of the Solar System, based on more than 600 orbital and 200,000 obliquity solutions over 5 Gyr. The density functions of the eccentricity and obliquity are specified with simple analytical formulas. We found an averaged eccentricity of Mars over 5 Gyr of 0.0690 with standard deviation 0.0299, while the averaged value of the obliquity is 37.62° with a standard deviation of 13.82°, and a maximal value of 82.035°. We find that the probability for Mars' obliquity to have reached more than 60° in the past 1 Gyr is 63.0%, and 89.3% in 3 Gyr. Over 4 Gyr, the position of Mars' axis is given by a uniform distribution on a spherical cap limited by the obliquity 58.62°, with the addition of a random noise allowing a slow diffusion beyond this limit. We can also define a standard model of Mars' insolation parameters over 4 Gyr with the most probable values 0.068 for the eccentricity and 41.80° for the obliquity.     

Generalized YORP evolution: Onset of tumbling and new asymptotic states

Asteroids have a wide range of rotation states. While the majority spin a few times to several times each day in principal axis rotation, a small number spin so slowly that they have somehow managed to enter into a tumbling rotation state. Here we investigate whether the Yarkovsky-Radzievskii-O'Keefe-Paddack (YORP) thermal radiation effect could have produced these unusual spin states. To do this, we developed a Lie-Poisson integrator of the orbital and rotational motion of a model asteroid. Solar torques, YORP, and internal energy dissipation were included in our model. Using this code, we found that YORP can no longer drive the spin rates of bodies toward values infinitely close to zero. Instead, bodies losing too much rotation angular momentum fall into chaotic tumbling rotation states where the spin axis wanders randomly for some interval of time. Eventually, our model asteroids reach rotation states that approach regular motion of the spin axis in the body frame. An analytical model designed to describe this behavior does a good job of predicting how and when the onset of tumbling motion should take place. The question of whether a given asteroid will fall into a tumbling rotation state depends on the efficiency of its internal energy dissipation and on the precise way YORP modifies the spin rates of small bodies.     

A Teleseismic Delay Time Study Across the Central African Shear Zone In the Adamawa Region of Cameroon, West Africa

Summary. P -wave relative teleseismic residuals were measured for a network of seismological stations along a 300 km profile across the Adamawa Plateau and the Central African Shear Zone of central Cameroon, to determine the variation in crust and upper mantle velocity associated with these structures. A plot of the mean relative residuals for the stations shows a long wavelength (> 300 km) variation of amplitude 0.45 s. the slowest arrivals are located over and just to the north, of the faulted northern margin of the Adamawa Plateau. the residuals do not correlate with topography, surface geology or the previously determined crustal structure, in any simple way.
The Aki inversion technique has been used to invert the relative residuals into a 3-D model of velocity perturbations from a mean earth model. the results show the region is divided roughly into three blocks by two subvertical boundaries, striking ENE and traversing both the crust and upper mantle down to depths greater than 190km. the central block, which is 2 per cent slower than the adjacent blocks, roughly corresponds to the Central African Shear Zone. the Adamawa Plateau, as an individual uplifted area, is explained by the interaction of a regional anomalous upper mantle associated with the West African Rift System, and the Central African Shear Zone, which provided a conduit for heat flow to the surface.     

Volcanic and Scientific Activity at Kick ’em Jenny Submarine Volcano 2001–2002: Implications for Volcanic Hazard in the Southern Grenadines,Lesser Antilles

Kick em Jenny submarine volcano, ~8 km north of Grenada, has erupted at least 12 times since it was first discovered in 1939, making it the most frequently active volcano in the Lesser Antilles arc. The volcano lies in shallow water close to significant population centres and directly beneath a major shipping route, and as a consequence an understanding of the eruptive behaviour and potential hazards at the volcano is critical. The most recent eruption at Kick em Jenny occurred on December 4 2001, and differed significantly from past eruptions in that it was preceded by an intensive volcanic earthquake swarm. In March 2002 a multi-beam bathymetric survey of the volcano and its surroundings was carried out by the NOAA ship Ronald H Brown. This survey provided detailed three-dimensional images of the volcano, revealing the detailed morphology of the summit area. The volcano is capped by a summit crater which is breached to the northeast and which varies in diameter from 300 to 370 m. The depth to the summit (highest point on the crater rim) is 185 m and the depth to the lowest point inside the crater is 264 m. No dome is present within the crater. The crater and summit region of Kick em Jenny are located at the top of an asymmetrical cone which is about 1300 m from top to bottom on its western side. It lies within what appear to be the remnants of a much larger arcuate collapse structure. An evaluation of the morphology, bathymetry and eruptive history of the volcano indicates that the threat of eruption-generated tsunamis is considerably lower than previously thought, mainly because the volcano is no longer thought to be growing towards the surface. Of more major and immediate concern are the direct hazards associated with the volcano, such as ballistic ejecta, water disturbances and lowered water density due to degassing.     

Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids

Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study — for static and dynamical situations — the equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes are compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material with a Drucker-Prager yield criterion. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. We first collapse our dynamical approach to its statical limit to derive regions in spin-shape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the Drucker-Prager failure law is available [Sharma, I., Jenkins, J.T., Burns, J.A., 2005a. Bull. Am. Astron. Soc. 37, 643; Sharma, I., Jenkins, J.T., Burns, J.A., 2005b. Equilibrium shapes of ellipsoidal soil asteroids. In: García-Rojo, R., Hermann, H.J., McNamara, S. (Eds.), Proceedings of the 5th International Conference on Micromechanics of Granular Media, vol. 1. A.A. Balkema, UK; Holsapple, K.A., 2007. Icarus 187, 500-509]. Here, we obtain the equilibrium landscapes for general triaxial ellipsoids, as well as provide the requisite governing formulae. In addition, we demonstrate that it may be possible to better interpret the results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361] within the context of a Drucker-Prager material. The graphical result for prolate ellipsoids in the static limit is the same as those of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] because, when worked out, his final equations will match ours. This is because, though the formalisms to reach these expressions differ, in statics, at the lowest level of approximation, volume-averaging and the approach of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] coincide. We note that the approach applied here was obtained independently [Sharma, I., Jenkins, J.T., Burns, J.A., 2003. Bull. Am. Astron. Soc. 35, 1034; Sharma, I., 2004. Rotational Dynamics of Deformable Ellipsoids with Applications to Asteroids. Ph.D. thesis, Cornell University] and it provides a general, though approximate, framework that is amenable to systematic improvements and is flexible enough to incorporate the dynamical effects of a changing shape, different rheologies and complex rotational histories. To demonstrate our technique, we investigate the non-equilibrium dynamics of rigid-plastic, spinning, prolate asteroids to examine the simultaneous histories of shape and spin rate for rubble piles. We have succeeded in recovering most results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361], who obtained equilibrium shapes by studying numerically the passage into equilibrium of aggregates containing discrete, interacting, frictionless, spherical particles. Our mainly analytical approach aids in understanding and quantifying previous numerical simulations.     

The influence of obliquity on europan cycloid formation

Tectonic patterns on Europa are influenced by tidal stress. An important well-recognized component is associated with the orbital eccentricity, which produces a diurnally varying stress as Jupiter's apparent position in Europa's sky oscillates in longitude. Cycloidal lineaments seem to have formed as cracks propagated in this diurnally varying stress field. Maps of theoretical cycloid patterns capture many of the characteristics of the observed distribution on Europa. However, a few details of the observed cycloid distribution have not been reproduced by previous models. Recently, it has been shown that Europa has a finite forced obliquity, so Jupiter's apparent position in Europa's sky will also oscillate in latitude. We explore this new type of diurnal effect on cycloid formation. We find that stress from obliquity may be the key to explaining several characteristics of observed cycloids such as the shape of equator-crossing cycloids and the shift in the crack patterns in the Argadnel Regio region. All of these improvements of the fit between observation and theory seem to require Jupiter crossing Europa's equatorial plane 45° to 180° after perijove passage, suggestive of complex orbital dynamics that locks the direction of Europa's pericenter with the direction of the ascending node at the time these cycloids were formed.     

Computing the effects of YORP on the spin rate distribution of the NEO population

The overall change of NEO spin rate due to planetary encounters and YORP is evaluated by using a Monte Carlo model. A large sample of test objects mimicking a source population is evolved over a timescale comparable with the Solar System age until they reach a steady state spin distribution that should reproduce the current NEO distribution. The spin change due to YORP is computed for each body according to a simplified model based on Scheeres [Scheeres, D.J., 2007a. Icarus 188, 430-450].The steady state cumulative distribution of NEO spin rates obtained from our simulation nicely reproduces the observed one, once our results are biased to match the diameter distribution of the sample of objects included in the observational database. The excellent agreement strongly suggests that YORP is responsible for the concentration of spin at low rotation rates. In fact, in the absence of YORP the steady state population significantly deviates from the observed one. The spin evolution due to YORP is also so rapid for NEOs that the initial rotation rate distribution of any source population is quickly relaxed to that of the observed population. This has profound consequences for the study of NEO origin since we cannot trace the sources of NEOs from their rotation rate only.     

Origin of ice diapirism, true polar wander, subsurface ocean, and tiger stripes of Enceladus driven by compositional convection

We consider the scenario in which the presence of ammonia in the bulk composition of Enceladus plays a pivotal role in its thermochemical evolution. Because ammonia reduces the melting temperature of the ice shell by 100 K below that of pure water ice, small amounts of tidal dissipation can power an “ammonia feedback” mechanism that leads to secondary differentiation of Enceladus within the ice shell. This leads to compositionally distinct zones at the base of the ice shell arranged such that a layer of lower density (and compositionally buoyant) pure water ice underlies the undifferentiated ammonia-dihydrate ice layer above. We then consider a large scale instability arising from the pure water ice layer, and use a numerical model to explore the dynamics of compositional convection within the ice shell of Enceladus. The instability of the layer can easily account for a diapir that is hemispherical in scale. As it rises to the surface, it co-advects the warm internal temperatures towards the outer layers of the satellite. This advected heat facilitates the generation of a subsurface ocean within the ice shell of Enceladus. This scenario can simultaneously account for the origin of asymmetry in surface deformation observed on Enceladus as well as two global features inferred to exist: a large density anomaly within the interior and a subsurface ocean underneath the south polar region.