Planetary Torque Research Articles

Three-dimensional Interaction between a Planet and an Isothermal Gaseous Disk. III. Locally Isothermal Cases

We performed linear calculations to determine the Type I planetary migration rate for 3D locally isothermal disks with radial temperature gradients. For 3D disks with radial temperature gradients, the linear wave equation has a divergent term of the third pole, which makes corotation a nonremoval singularity. We suppressed the divergence with the Landau prescription to obtain the wave solutions. Despite the singularity at corotation, we derived a definite torque on the planet because the divergent term amplifies the waves only in the neighborhood of corotation and has little effect on the planetary torque. Consequently, we derived the formulas for the total, Lindblad, and corotation torques for locally isothermal disks. The resulting torque term due to the disk temperature gradient agrees well with the results of previous 3D hydrodynamical simulations for locally isothermal disks. Our linear calculation also provides the 3D horseshoe torque, which is close to the results of previous 3D hydrodynamical simulations.

Study on vibration characteristics of hydraulic planetary transmission considering engine and torque converter excitation

Large-size vehicle loaders are mainly used in various construction projects with complex working environment, which has a serious impact on the internal vibration of the whole system. In this study, the vibration characteristics of hydraulic planetary transmission of vehicle loader considering the influence of the external excitation are evaluated theoretically and experimentally. The output torque of the four-stroke six-cylinder diesel engine is obtained by force calculation of crank and connecting rod mechanism. The equivalent stiffness and damping of the torque converter are solved according to the torsional dynamic equation of the torque converter. The trapped oil area, oil pressure, and flow rate of gear meshing part are extracted to obtain the trapped oil pressure of variable-speed pump. Then, the multi-degree-of-freedom gear system dynamic model is established to calculate the meshing force, which is applied to vibration response analysis model by using mode superposition method. Lastly, the vibration response test is performed on the experimental prototype to verify the calculation method. The conclusion shows that the generation principle of external excitation and its calculation method in this paper are feasible in the analysis of dynamic characteristics of hydraulic planetary torque converter.

Planetary Torque in 3D Isentropic Disks

Abstract Planetary migration is inherently a three-dimensional (3D) problem, because Earth-size planetary cores are deeply embedded in protoplanetary disks. Simulations of these 3D disks remain challenging due to the steep resolution requirements. Using two different hydrodynamics codes, FARGO3D and PEnGUIn, we simulate disk–planet interaction for a one to five Earth-mass planet embedded in an isentropic disk. We measure the torque on the planet and ensure that the measurements are converged both in resolution and between the two codes. We find that the torque is independent of the smoothing length of the planet’s potential (r s), and that it has a weak dependence on the adiabatic index of the gaseous disk (γ). The torque values correspond to an inward migration rate qualitatively similar to previous linear calculations. We perform additional simulations with explicit radiative transfer using FARGOCA, and again find agreement between 3D simulations and existing torque formulae. We also present the flow pattern around the planets that show active flow is present within the planet’s Hill sphere, and meridional vortices are shed downstream. The vertical flow speed near the planet is faster for a smaller r s or γ, up to supersonic speeds for the smallest r s and γ in our study.

On planetary torque signals and sub-decadal frequencies in the discharges of large rivers

We explore the arguments presented in the past linking changes in the angular momentum modulus,|L|, of the Sun’s barycentric orbit, with the discharges of Po River in Europe and Paraná River in South America, looking for any evidence regarding to a possible underlying physical mechanism. We clarify the planetary effect on solar torque presenting new analyses and results; we also improve prior results on Paraná River’s cycles finding significant spectral lines around 6.5yr, 7.6yr, 8.7yr, and 10.4yr. We show that the truly important dynamical parameter in this issue is the vectorial planetary torque. Moreover, following the variations of L respect to the Sun’s spin axis of rotation (i.e., a LS relationship), we found virtually the same Paraná River discharge peaks: 6.3yr, 7.7yr, 8.6yr and 9.9yr. An analysis based on Magnitude Squared Coherence and Wavelet Coherence between Paraná River discharge and our LS relationship shows significant, although intermittently, coherence near 8-yr periodicities. Wavelet Coherence also shows big and significant regions of coherence inside 12–19yr band. Our results ruled out classical tidal effects in this problem; but suggest that, if these rivers are trully related to solar barycentric motion, the physical origin of this connection might be related to a working solar spin–orbit interaction.

Critical Analysis of a Hypothesis of the Planetary Tidal Influence on Solar Activity

The present work is a critical revision of the hypothesis of the planetary tidal influence on solar activity published by Abreu et al. (Astron. Astrophys. 548, A88, 2012; called A12 here). A12 describes the hypothesis that planets can have an impact on the solar tachocline and therefore on solar activity. We checked the procedure and results of A12, namely the algorithm of planetary tidal torque calculation and the wavelet coherence between torque and heliospheric modulation potential. We found that the claimed peaks in long-period range of the torque spectrum are artefacts caused by the calculation algorithm (viz. aliasing effect). Also the statistical significance of the results of the wavelet coherence is found to be overestimated by an incorrect choice of the background assumption of red noise. Using a more conservative non-parametric random-phase method, we found that the long-period coherence between planetary torque and heliospheric modulation potential becomes insignificant. Thus we conclude that the considered hypothesis of planetary tidal influence on solar activity is not based on a solid ground.

LOW-MASS PLANETS IN PROTOPLANETARY DISKS WITH NET VERTICAL MAGNETIC FIELDS: THE PLANETARY WAKE AND GAP OPENING

We study wakes and gap opening by low mass planets in gaseous protoplanetary disks threaded by net vertical magnetic fields which drive magnetohydrodynamical (MHD) turbulence through the magnetorotational instabilty (MRI), using three dimensional simulations in the unstratified local shearing box approximation. The wakes, which are excited by the planets, are damped by shocks similar to the wake damping in inviscid hydrodynamic (HD) disks. Angular momentum deposition by shock damping opens gaps in both MHD turbulent disks and inviscid HD disks even for low mass planets, in contradiction to the "thermal criterion" for gap opening. To test the "viscous criterion", we compared gap properties in MRI-turbulent disks to those in viscous HD disks having the same stress, and found that the same mass planet opens a significantly deeper and wider gap in net vertical flux MHD disks than in viscous HD disks. This difference arises due to the efficient magnetic field transport into the gap region in MRI disks, leading to a larger effective \alpha within the gap. Thus, across the gap, the Maxwell stress profile is smoother than the gap density profile, and a deeper gap is needed for the Maxwell stress gradient to balance the planetary torque density. We also confirmed the large excess torque close to the planet in MHD disks, and found that long-lived density features (termed zonal flows) produced by the MRI can affect planet migration. The comparison with previous results from net toroidal flux/zero flux MHD simulations indicates that the magnetic field geometry plays an important role in the gap opening process. Overall, our results suggest that gaps can be commonly produced by low mass planets in realistic protoplanetary disks, and caution the use of a constant \alpha-viscosity to model gaps in protoplanetary disks.

Is there a planetary influence on solar activity?

Context. Understanding the Sun’s magnetic activity is important because of its impact on the Earth’s environment. Direct observations of the sunspots since 1610 reveal an irregular activity cycle with an average period of about 11 years, which is modulated on longer timescales. Proxies of solar activity such as 14 C and 10 Be show consistently longer cycles with well-defined periodicities and varying amplitudes. Current models of solar activity assume that the origin and modulation of solar activity lie within the Sun itself; however, correlations between direct solar activity indices and planetary configurations have been reported on many occasions. Since no successful physical mechanism was suggested to explain these correlations, the possible link between planetary motion and solar activity has been largely ignored. Aims. While energy considerations clearly show that the planets cannot be the direct cause of the solar activity, it remains an open question whether the planets can perturb the operation of the solar dynamo. Here we use a 9400 year solar activity reconstruction derived from cosmogenic radionuclides to test this hypothesis.Methods. We developed a simple physical model for describing the time-dependent torque exerted by the planets on a non-spherical tachocline and compared the corresponding power spectrum with that of the reconstructed solar activity record. Results. We find an excellent agreement between the long-term cycles in proxies of solar activity and the periodicities in the planetary torque and also that some periodicities remain phase-locked over 9400 years.Conclusions. Based on these observations we put forward the idea that the long-term solar magnetic activity is modulated by planetary effects. If correct, our hypothesis has important implications for solar physics and the solar-terrestrial connection.

PLANET-DISK INTERACTION IN THREE DIMENSIONS: THE IMPORTANCE OF BUOYANCY WAVES

We carry out local three dimensional (3D) hydrodynamic simulations of planet-disk interaction in stratified disks with varied thermodynamic properties. We find that whenever the Brunt-Vaisala frequency (N) in the disk is nonzero, the planet exerts a strong torque on the disk in the vicinity of the planet, with a reduction in the traditional "torque cutoff". In particular, this is true for adiabatic perturbations in disks with isothermal density structure, as should be typical for centrally irradiated protoplanetary disks. We identify this torque with buoyancy waves, which are excited (when N is non-zero) close to the planet, within one disk scale height from its orbit. These waves give rise to density perturbations with a characteristic 3D spatial pattern which is in close agreement with the linear dispersion relation for buoyancy waves. The torque due to these waves can amount to as much as several tens of per cent of the total planetary torque, which is not expected based on analytical calculations limited to axisymmetric or low-m modes. Buoyancy waves should be ubiquitous around planets in the inner, dense regions of protoplanetary disks, where they might possibly affect planet migration.

Dynamical characterization of the last prolonged solar minima

The planetary hypothesis of the solar cycle is an old idea in which the gravitational influence of the planets has a non-negligible effect on the causes of the solar magnetic cycle. The advance of this hypothesis is based on phenomenological correlations between dynamical parameters of the Sun’s movement around the barycentre of the Solar System and sunspots time series; and more especially, identifying relationships linking solar barycentric dynamics with prolonged minima (especially Grand Minima events). However, at present there is no clear physical mechanism relating these phenomena. The possible celestial influence on solar cycle modulation is of great importance not only in solar physics but also in Earth sciences, because prolonged solar minima have associated important climatic and telluric variations, in particular, during the Maunder and Dalton Minimum. In this work we looked for a possible causal link in relation with solar barycentric dynamics and prolonged minima events. We searched for particular changes in the Sun’s acceleration and concentrated on long-term variations of the solar cycle. We show how the orbital angular momentum of the Sun evolves and how the inclination of the solar barycentric orbit varies during the epochs of orbital retrogressions. In particular, at these moments, the radial component of the Sun’s acceleration (i.e., in the barycentre-Sun direction) had an exceptional magnitude. These radial impulses occurred at the very beginning of the Maunder Minimum, during the Dalton Minimum and also at the maximum of cycle 22 before the present extended minimum. We also found a strong correlation between the planetary torque and the observed sunspots international number around that maximum. We apply our results in a novel theory of Sun–planets interaction that it is sensitive to Sun barycentric dynamics and found a very important effect on the Sun’s capability of storing hypothetical reservoirs of potential energy that could be released by internal flows and might be related to the solar cycle. This process begins about 40years before the solar angular momentum inversions, i.e., before Maunder Minimum, Dalton Minimum, and before the present extended minimum. Our conclusions suggest a dynamical characterization of peculiar prolonged solar minima. We discuss the possible implications of these results for the solar cycle including the present extended minimum.

The role of angular momentum in the splitting of isolated eddies

The question of which oceanic eddies can split and break up is addressed with the aid of two simplified analytical models which rely on the conservation of integrated angular momentum. First, an inviscid barotropic model with an initial round vortex is considered. The conditions necessary for the breakup of the vortex without exchanging angular momentum with its environment are examined. A solution for the final state is obtained without solving for the highly nonlinear transient splitting process. It is found that only cyclonic eddies meet the necessary condition for splitting — anticyclonic eddies can never split, no matter what their structure is . The cyclones are subject to a critical intensity above which breaking is possible and below which splitting is impossible. Specifically, cyclones with relative vorticity higher than f (where f is the (uniform) Coriolis parameter) can split into 2 eddies, whereas cyclones with a vorticity higher than f /3 can split into 3 or 4 vortices. The peculiar asymmetry between anticyclones and cyclones is a result of the conservation of integrated angular momentum. This can be demonstrated by noting that during the splitting process, the newly formed eddies are pushed away from their original center of rotation acquiring planetary torque. Therefore, in order for splitting to occur, the torque of the parent eddy must be large enough to accommodate for this addition of planetary torque. It turns out that only cyclones, which typically have more absolute angular momentum than their anticyclonic counterparts (because they rotate in the same sense as the spin of the earth), have enough torque to allow splitting. The above analysis is also applied to the splitting of a fully nonlinear zero potential vorticity lens. As in the barotropic anticyclonic cases, splitting is strictly impossible because the parent eddy does not have enough angular momentum. DOI: 10.1034/j.1600-0870.1990.t01-2-00006.x