Hauke Hussmann

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin’s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

Hydrothermal systems in small ocean planets.

We examine means for driving hydrothermal activity in extraterrestrial oceans on planets and satellites of less than one Earth mass, with implications for sustaining a low level of biological activity over geological timescales. Assuming ocean planets have olivine-dominated lithospheres, a model for cooling-induced thermal cracking shows how variation in planet size and internal thermal energy may drive variation in the dominant type of hydrothermal system-for example, high or low temperature system or chemically driven system. As radiogenic heating diminishes over time, progressive exposure of new rock continues to the current epoch. Where fluid-rock interactions propagate slowly into a deep brittle layer, thermal energy from serpentinization may be the primary cause of hydrothermal activity in small ocean planets. We show that the time-varying hydrostatic head of a tidally forced ice shell may drive hydrothermal fluid flow through the seafloor, which can generate moderate but potentially important heat through viscous interaction with the matrix of porous seafloor rock. Considering all presently known potential ocean planets-Mars, a number of icy satellites, Pluto, and other trans-neptunian objects-and applying Earth-like material properties and cooling rates, we find depths of circulation are more than an order of magnitude greater than in Earth. In Europa and Enceladus, tidal flexing may drive hydrothermal circulation and, in Europa, may generate heat on the same order as present-day radiogenic heat flux at Earths surface. In all objects, progressive serpentinization generates heat on a globally averaged basis at a fraction of a percent of present-day radiogenic heating and hydrogen is produced at rates between 10(9) and 10(10) molecules cm(2) s(1).

Spin-orbit coupling for tidally evolving super-Earths

We investigate the spin behaviour of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyse the possibility of temporary captures in spin–orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rotation follows the so-called pseudo-synchronization. Analytical results obtained through the averaged equations of the spin–orbit problem show a good agreement with the numerical simulations. We apply the analysis to the cases of the recently discovered hot super-Earths Kepler-10 b, GJ 3634 b and 55 Cnc e. The simulated dynamical history of these systems indicates the possibility of capture in several spin–orbit resonances; particularly, GJ 3634 b and 55 Cnc e can currently evolve under a non-synchronous resonant motion for suitable values of the parameters. Moreover, 55 Cnc e may avoid a chaotic rotation behaviour by evolving towards synchronization through successive temporary resonant trappings.

Interiors and Evolution of Icy Satellites

Since the discovery of the four largest moons of Jupiter by Galileo Galilei in 1610, the satellite systems of the outer planets have intensely been investigated, which culminated in the images and data obtained by the Voyager 1 and 2 spacecraft (flybys at the four giant planets and their moons between 1979 and 1989) and recently by Galileo (Jupiter orbiter 1995–2003), Cassini (Saturn orbiter since 2004), and the Huygens probe (landed on Titan, January 2005). The Galileo and Cassini / Huygens missions have immensely improved our knowledge of the Jupiter and Saturn system, with respect to the giant planets, their ring systems, magnetospheres, and satellite systems. Our current knowledge on the satellites of Uranus and Neptune is mainly based on the Voyager 2 flybys in 1986 and 1989, respectively.

Structural and tidal models of Titan and inferences on cryovolcanism

Titan, Saturns largest satellite, is subject to solid body tides exerted by Saturn on the timescale of its orbital period. The tide-induced internal redistribution of mass results in tidal stress variations, which could play a major role for Titans geologic surface record. We construct models of Titans interior that are consistent with the satellites mean density, polar moment-of-inertia factor, obliquity, and tidal potential Love number k2 as derived from Cassini observations of Titans low-degree gravity field and rotational state. In the presence of a global liquid reservoir, the tidal gravity field is found to be consistent with a subsurface water-ammonia ocean more than 180 km thick and overlain by an outer ice shell of less than 110 km thickness. The model calculations suggest comparatively low ocean ammonia contents of less than 5 wt % and ocean temperatures in excess of 255 K, i.e., higher than previously thought, thereby substantially increasing Titans potential for habitable locations. The calculated diurnal tidal stresses at Titans surface amount to 20 kPa, almost comparable to those expected at Enceladus and Europa. Tidal shear stresses are concentrated in the polar areas, while tensile stresses predominate in the near-equatorial, midlatitude areas of the sub- and anti-Saturnian hemispheres. The characteristic pattern of maximum diurnal tidal stresses is largely compliant with the distribution of active regions such as cryovolcanic candidate areas. The latter could be important for Titans habitability since those may provide possible pathways for liquid water-ammonia outbursts on the surface and the release of methane in the satellites atmosphere.

Interior structure models of terrestrial exoplanets and application to CoRoT-7 b

In this study, we model the internal structure of CoRoT-7b as a type example for a terrestrial extrasolar planet using mass and energy balance constraints. Our results suggest that the deep interior is predominantly composed of dry silicate rock, similar to the Earth’s Moon. A central iron core, if present, would be relatively small and less massive (< 15 wt.% of the planet’s total mass) as compared to the Earth’s (core mass fraction 32.6 wt.%). Furthermore, a partly molten near-surface magma ocean could be maintained, provided surface temperatures were sufficiently high and the rock component was mainly composed of Earth-like mineral phase assemblages.

Tidal friction in close-in planets

We use Darwins theory (Darwin, 1880) to derive the main results on the orbital and rotational evolution of a close-in companion (exoplanet or planetary satellite) due to tidal friction. The given results do not depend on any assumption linking the tidal lags to the frequen- cies of the corresponding tide harmonics (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the study of the synchronization of the planetary rotation in the two possible final states for a non-zero eccentricity : (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) the capture into a 1:1 spin-orbit resonance (true synchronization), which is only possible if an additional torque exists acting in opposition to the tidal torque. Results are given under the assumption that this additional torque is produced by a non-tidal permanent equatorial asymmetry of the planet. The indirect tidal effects and some non-tidal effects due to that asymmetry are considered. For sake of comparison with other works, the results obtained when tidal lags are assumed proportional to the corresponding tidal wave frequencies are also given.

The reference frames of Mercury after the MESSENGER mission

We report on recent refinements and the current status for the rotational state models and the reference frames of the planet Mercury. We summarize the performed measurements of Mercury rotation based on terrestrial radar observations as well as data from the Mariner 10 and the MESSENGER missions. Further, we describe the different available definitions of reference systems for Mercury and obtain the corresponding reference frame using data provided by instruments on board MESSENGER. In particular, we discuss the dynamical frame, the principal-axes frame, the ellipsoid frame, as well as the cartographic frame. We also describe the reference frame adopted by the MESSENGER science team for the release of their cartographic products, and we provide expressions for transformations from this frame to the other reference frames.

Optical/mechanical design of the focal plane receiver of the Ganymede Laser Altimeter (GALA) for the Jupiter Icy Moons Explorer (JUICE) mission

The Jupiter Icy Moons Explorer (JUICE) mission of the European Space Agency to be launched in 2022 will provide an opportunity for a dedicated exploration of the Jovian system including its icy moons. The Ganymede Laser Altimeter (GALA) has been selected as one of the ten payloads of JUICE. GALA will enable unique studies of the topography and shape, tidal and rotational state, and geology of primarily Ganymede but also Europa and Callisto. The GALA project is an ongoing international collaboration led by Germany, together with Switzerland, Spain, and Japan. This paper presents the optical and mechanical design of the focal plane receiver, the Japanese part of GALA.