Spontaneous generation of inertial waves from boundary turbulence in a librating sphere

In this work, we report the excitation of inertial waves in a librating sphere even for libration frequencies where these waves are not directly forced. This spontaneous generation comes from the localized turbulence induced by the centrifugal instabilities in the Ekman boundary layer near the equator and does not depend on the libration frequency. We characterize the key features of these inertial waves in analogy with previous studies of the generation of internal waves in stratified flows from localized turbulent patterns. In particular, the temporal spectrum exhibits preferred values of excited frequency. This first-order phenomenon is generic to any rotating flow in the presence of localized turbulence and is fully relevant for planetary applications

Libration driven multipolar instabilities

We consider rotating flows in non-axisymmetric enclosures that are driven by libration, i.e. by a small periodic modulation of the rotation rate. Thanks to its simplicity, this model is relevant to various contexts, from industrial containers (with small oscillations of the rotation rate) to fluid layers of terrestial planets (with length-of-day variations). Assuming a multipolar $n$-fold boundary deformation, we first obtain the two-dimensional basic flow. We then perform a short-wavelength local stability analysis of the basic flow, showing that an instability may occur in three dimensions. We christen it the Libration Driven Multipolar Instability (LDMI). The growth rates of the LDMI are computed by a Floquet analysis in a systematic way, and compared to analytical expressions obtained by perturbation methods. We then focus on the simplest geometry allowing the LDMI, a librating deformed cylinder. To take into account viscous and confinement effects, we perform a global stability analysis, which shows that the LDMI results from a parametric resonance of inertial modes. Performing numerical simulations of this librating cylinder, we confirm that the basic flow is indeed established and report the first numerical evidence of the LDMI. Numerical results, in excellent agreement with the stability results, are used to explore the non-linear regime of the instability (amplitude and viscous dissipation of the driven flow). We finally provide an example of LDMI in a deformed spherical container to show that the instability mechanism is generic. Our results show that the previously studied libration driven elliptical instability simply corresponds to the particular case $n=2$ of a wider class of instabilities. Summarizing, this work shows that any oscillating non-axisymmetric container in rotation may excite intermittent, space-filling LDMI flows, and this instability should thus be easy to observe experimentally

Mercury's resonant rotation from secular orbital elements

We used recently produced Solar System ephemerides, which incorporate two years of ranging observations to the MESSENGER spacecraft, to extract the secular orbital elements for Mercury and associated uncertainties. As Mercury is in a stable 3:2 spin-orbit resonance these values constitute an important reference for the planet's measured rotational parameters, which in turn strongly bear on physical interpretation of Mercury's interior structure. In particular, we derive a mean orbital period of 87.96934962 $\pm$ 0.00000037 days and (assuming a perfect resonance) a spin rate of 6.138506839 $\pm$ 0.000000028 degree/day. The difference between this rotation rate and the currently adopted rotation rate (Archinal et al, 2011) corresponds to a longitudinal displacement of approx. 67 m per year at the equator. Moreover, we present a basic approach for the calculation of the orientation of the instantaneous Laplace and Cassini planes of Mercury. The analysis allows us to assess the uncertainties in physical parameters of the planet when derived from observations of Mercury's rotation

Significance of Off-Center Rattling for Emerging Low-lying THz Modes in type-I Clathrates

We show that the distinct differences of low-lying THz-frequency dynamics between type-I clathrates with on-center and off-center guest ions naturally follow from a theoretical model taking into account essential features of the dynamics of rattling guest ions. Our model analysis demonstrates the drastic change from the conventional dynamics shown by on-center systems to the peculiar dynamics of off-center systems in a unified manner. We claim that glass-like plateau thermal conductivities observed for off-center systems stem from the flattening of acoustic phonon dispersion in the regime |k|<|G|/4. The mechanism is applicable to other systems such as glasses or relaxers

Spin-orbit coupling and chaotic rotation for coorbital bodies in quasi-circular orbits

Coorbital bodies are observed around the Sun sharing their orbits with the planets, but also in some pairs of satellites around Saturn. The existence of coorbital planets around other stars has also been proposed. For close-in planets and satellites, the rotation slowly evolves due to dissipative tidal effects until some kind of equilibrium is reached. When the orbits are nearly circular, the rotation period is believed to always end synchronous with the orbital period. Here we demonstrate that for coorbital bodies in quasi-circular orbits, stable non-synchronous rotation is possible for a wide range of mass ratios and body shapes. We show the existence of an entirely new family of spin-orbit resonances at the frequencies $n\pm k\nu/2$, where $n$ is the orbital mean motion, $\nu$ the orbital libration frequency, and $k$ an integer. In addition, when the natural rotational libration frequency due to the axial asymmetry, $\sigma$, has the same magnitude as $\nu$, the rotation becomes chaotic. Saturn coorbital satellites are synchronous since $\nu\ll\sigma$, but coorbital exoplanets may present non-synchronous or chaotic rotation. Our results prove that the spin dynamics of a body cannot be dissociated from its orbital environment. We further anticipate that a similar mechanism may affect the rotation of bodies in any mean-motion resonance.Comment: 6 pages. Astrophysical Journal (2013) 6p

Long-term Evolution and Stability of Saturnian Small Satellites: Aegaeon, Methone, Anthe, and Pallene

Aegaeon, Methone, Anthe, and Pallene are four Saturnian small moons, discovered by the Cassini spacecraft. Although their orbital characterization has been carried on by a number of authors, their long-term evolution has not been studied in detail so far. In this work, we numerically explore the long-term evolution, up to $10^5$ yr, of the small moons in a system formed by an oblate Saturn and the five largest moons close to the region: Janus, Epimetheus, Mimas, Enceladus, and Tethys. By using frequency analysis we determined the stability of the small moons and characterize, through diffusion maps, the dynamical behavior of a wide region of geometric phase space, $a$ vs $e$, surrounding them. Those maps could shed light on the possible initial number of small bodies close to Mimas, and help to better understand the dynamical origin of the small satellites. We found that the four small moons are long-term stable and no mark of chaos is found for them. Aegaeon, Methone, and Anthe could remain unaltered for at least $\sim0.5$Myr, given the current configuration of the system. They remain well-trapped in the corotation eccentricity resonances with Mimas in which they currently librate. However, perturbations from nearby resonances, such as Lindblad eccentricity resonances with Mimas, seem responsible for largest variations observed for Methone and Anthe. Pallene remains in a non-resonant orbit and it is the more stable, at least for 64 Myr. Nonetheless, it is affected by a quasi-resonance with Mimas, which induces long-term orbital oscillations of its eccentricity and inclination.Comment: 17 pages, 12 figures, 5 tables. Accepted for publication in MNRA

Spin-Cooling of the Motion of a Trapped Diamond

Observing and controlling macroscopic quantum systems has long been a driving force in research on quantum physics. In this endeavor, strong coupling between individual quantum systems and mechanical oscillators is being actively pursued. While both read-out of mechanical motion using coherent control of spin systems and single spin read-out using pristine oscillators have been demonstrated, temperature control of the motion of a macroscopic object using long-lived electronic spins has not been reported. Here, we observe both a spin-dependent torque and spin-cooling of the motion of a trapped microdiamond. Using a combination of microwave and laser excitation enables the spin of nitrogen-vacancy centers to act on the diamond orientation and to cool the diamond libration via a dynamical back-action. Further, driving the system in the non-linear regime, we demonstrate bistability and self-sustained coherent oscillations stimulated by the spin-mechanical coupling, which offers prospects for spin-driven generation of non-classical states of motion. Such a levitating diamond operated as a compass with controlled dissipation has implications in high-precision torque sensing, emulation of the spin-boson problem and probing of quantum phase transitions. In the single spin limit and employing ultra-pure nano-diamonds, it will allow quantum non-demolition read-out of the spin of nitrogen-vacancy centers under ambient conditions, deterministic entanglement between distant individual spins and matter-wave interferometry.Comment: New version with a calibration of angular resolution and sensitivity. Fig. 1 is also replaced to show an ODMR when the diamond is static to avoid spin-torque induced distortion