Planetary Tides Research Articles

Tidal dissipation in rotating and evolving giant planets with application to exoplanet systems

ABSTRACT We study tidal dissipation in models of rotating giant planets with masses in the range 0.1–10MJ throughout their evolution. Our models incorporate a frequency-dependent turbulent effective viscosity acting on equilibrium tides (including its modification by rapid rotation consistent with hydrodynamical simulations) and inertial waves in convection zones, and internal gravity waves in the thin radiative atmospheres. We consider a range of planetary evolutionary models for various masses and strengths of stellar instellation. Dissipation of inertial waves is computed using a frequency-averaged formalism fully accounting for planetary structures. Dissipation of gravity waves in the radiation zone is computed assuming these waves are launched adiabatically and are subsequently fully damped (by wave breaking/radiative damping). We compute modified tidal quality factors Q′ and evolutionary time-scales for these planets as a function of their ages. We find inertial waves to be the dominant mechanism of tidal dissipation in giant planets whenever they are excited. Their excitation requires the tidal period (Ptide) to be longer than half the planetary rotation (Prot/2), and we predict inertial waves to provide a typical Q′ ∼ 103(Prot/1d)2, with values between 105 and 106 for a 10-d period. We show correlations of observed exoplanet eccentricities with tidal circularization time-scale predictions, highlighting the key role of planetary tides. A major uncertainty in planetary models is the role of stably-stratified layers resulting from compositional gradients, which we do not account for here, but which could modify predictions for tidal dissipation rates.

Constraints on planetary tidal dissipation from a detailed study of Kepler 91b

Context. With the detection of thousands of exoplanets, characterising their dynamical evolution in detail represents a key step in the understanding of their formation. Studying the dissipation of tides occurring both in the host star and in the planets is of great relevance in order to investigate the distribution of the angular momentum occurring among the objects populating the system and to studying the evolution of the orbital parameters. From a theoretical point of view, the dissipation of tides throughout a body may be studied by relying on the so-called phase or time-lag equilibrium tides model in which the reduced tidal quality factor Q′p, or equivalently the product between the love number and the time lag (k2,pΔtp), describe how efficiently tides are dissipated within the perturbed body. Constraining these factors by looking at the current configuration of the exoplanetary system is extremely challenging, and simulations accounting for the evolution of the system as a whole might help to shed some light on the mechanisms governing this process. Aims. We aim to constrain the tidal dissipation factors of hot-Jupiter-like planets by studying the orbital evolution of Kepler-91b. Methods. We firstly carried out a detailed asteroseismc characterisation of Kepler-91 and computed a dedicated stellar model using both classical and astereoseismic constraints. We then coupled the evolution of the star to the one of the planets by means of our orbital evolution code and studied the evolution of the system by accounting for tides dissipated both in the planet and in the host star. Results. We found that the maximum value for k2,pΔtp (or equivalently the minimum value for Q′p) determining the efficiency of equilibrium tides dissipation occurring within Kepler-91b is 0.4 ± 0.25 s (4.5−1.5+5.8 × 105). We constrained these factors by computing the evolution of the planetary orbit and by reproducing the current properties of the Kepler-91 system. Conclusions. We developed a new method to constrain the tidal dissipation factors using the observed eccentricity of a given planet. Our new approach showed that Kepler 91b has dissipation coefficients compatible with colder Jupiter-like planets. When applied to other targets, our new method could potentially give more precise boundary values to the tidal dissipation factors, and determine whether planetary tides dominate the dissipation during the stellar main sequence.

Can the Uranian Satellites Form from a Debris Disk Generated by a Giant Impact?

Abstract Hydrodynamic simulations of a giant impact to proto-Uranus indicated that such an impact could tilt its rotational axis and produce a circumplanetary debris disk beyond the corotation radius of Uranus. However, whether Uranian satellites can actually be formed from such a wide disk remains unclear. Herein, we modeled a wide debris disk of solids with several initial conditions inferred from the hydrodynamic simulations and performed N-body simulations to investigate in situ satellite formation from the debris disk. We also took account of orbital evolutions of satellites due to the planetary tides after the growth of satellites. We found that, in any case, the orbital distribution of the five major satellites could not be reproduced from the disk as long as the power index of its surface density is similar to that of the disk generated just after the giant impact. Satellites in the middle region obtained much larger masses than Ariel or Umbriel, while the outermost satellites did not grow to the mass of Oberon. Our results indicate that we should consider the thermal and viscous evolution of the evaporated disk after the giant impact to form the five major satellites through the in situ formation scenario. On the other hand, the small inner satellites would be formed from the rings produced by the disrupted satellites that migrated from around the corotation radius of Uranus due to the planetary tides.

Interior structures and tidal heating in the TRAPPIST-1 planets

Context. With seven planets, the TRAPPIST-1 system has among the largest number of exoplanets discovered in a single system so far. The system is of astrobiological interest, because three of its planets orbit in the habitable zone of the ultracool M dwarf. Aims. We aim to determine interior structures for each planet and estimate the temperatures of their rock mantles due to a balance between tidal heating and convective heat transport to assess their habitability. We also aim to determine the precision in mass and radius necessary to determine the planets’ compositions. Methods. Assuming the planets are composed of uniform-density noncompressible materials (iron, rock, H2O), we determine possible compositional models and interior structures for each planet. We also construct a tidal heat generation model using a single uniform viscosity and rigidity based on each planet’s composition. Results. The compositions for planets b, c, d, and e remain uncertain given the error bars on mass and radius. With the exception of TRAPPIST-1c, all have densities low enough to indicate the presence of significant H2O. Planets b and c experience enough heating from planetary tides to maintain magma oceans in their rock mantles; planet c may have surface eruptions of silicate magma, potentially detectable with next-generation instrumentation. Tidal heat fluxes on planets d, e, and f are twenty times higher than Earth’s mean heat flow. Conclusions. Planets d and e are the most likely to be habitable. Planet d avoids the runaway greenhouse state if its albedo is ≳0.3. Determining the planet’s masses within ~0.1–0.5 Earth masses would confirm or rule out the presence of H2O and/or iron. Understanding the geodynamics of ice-rich planets f, g, and h requires more sophisticated modeling that can self-consistently balance heat production and transport in both rock and ice layers.

Formation of Massive Rocky Exomoons by Giant Impact

The formation of satellites is thought to be a natural by-product of planet formation in our Solar System, and thus, moons of extrasolar planets (exomoons) may be abundant in extrasolar planetary systems, as well. Exomoons have yet to be discovered. However, moons larger than 0.1 Earth masses can be detected and characterized using current transit techniques. Here, we show that collisions between rocky planets with masses between a quarter to ten Earth masses can create impact-generated debris disks that could accrete into moons. Collisions between like-sized objects, at oblique impact angles, and velocities near escape speed create disks massive enough to form satellites that are dynamically stable against planetary tides. Impacts of this type onto a superearth between 2 to 7 Earth masses can launch into orbit enough mass to create a satellite large enough to be detected in Kepler transit data. Impact velocity is a crucial controlling factor on disk mass, which has been overlooked in all prior studies of moon formation via planetary collision.

Synchronized Helicity Oscillations: A Link Between Planetary Tides and the Solar Cycle?

Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we ask for a possible physical mechanism that might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by some m=2 perturbation that reflects a tidal oscillation. Specifically, we speculate that the 11.07 years tidal oscillation induced by the Venus--Earth--Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the alpha-effect. Finally, in the framework of a reduced, zero-dimensional alpha--Omega dynamo model we recover a 22.14-year cycle of the solar dynamo.

DIFFICULTY IN THE FORMATION OF COUNTER-ORBITING HOT JUPITERS FROM NEAR-COPLANAR HIERARCHICAL TRIPLE SYSTEMS: A SUB-STELLAR PERTURBER

ABSTRACT Among 100 transiting planets with a measured projected spin–orbit angle λ, several systems are suggested to be counter-orbiting. While these cases may be due to the projection effect, the mechanism that produces a counter-orbiting planet has not been established. A promising scenario for counter-orbiting planets is the extreme eccentricity evolution in near-coplanar hierarchical triple systems with eccentric inner and outer orbits. We examine this scenario in detail by performing a series of systematic numerical simulations, and consider the possibility of forming hot Jupiters (HJs), especially a counter-orbiting one under this mechanism with a distant sub-stellar perturber. We incorporate quadrupole and octupole secular gravitational interaction between the two orbits, and also short-range forces (correction for general relativity, star and inner planetary tide, and rotational distortion) simultaneously. We find that most systems are tidally disrupted and that a small fraction of the surviving planets turn out to be prograde. The formation of counter-orbiting HJs in this scenario is possible only in a very restricted parameter region, and thus is very unlikely in practice.

HOT JUPITERS AND COOL STARS

Close-in planets are in jeopardy as their host stars evolve off the main sequence to the subgiant and red giant phases. In this paper, we explore the influences of the stellar mass (in the range 1.5--2\Mso ), mass-loss prescription, planet mass (from Neptune up to 10 Jupiter masses), and eccentricity, on the orbital evolution of planets as their parent stars evolve to become subgiants and Red Giants. We find that planet engulfment during the Red Giant Branch is not very sensitive to the stellar mass or mass-loss rates adopted in the calculations, but quite sensitive to the planetary mass. The range of initial separations for planet engulfment increases with decreasing mass-loss rates or stellar mass and increasing planetary masses. Regarding the planet's orbital eccentricity, we find that as the star evolves into the red giant phase, stellar tides start to dominate over planetary tides. As a consequence, a transient population of moderately eccentric close-in Jovian planets is created, that otherwise would have been expected to be absent from main sequence stars. We find that very eccentric and distant planets do not experience much eccentricity decay, and that planet engulfment is primarily determined by the pericenter distance and the maximum stellar radius.

The tides of Mercury and possible implications for its interior structure

The combination of the radio tracking of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft and Earth‐based radar measurements of the planet's spin state gives three fundamental quantities for the determination of the interior structure of Mercury: mean density ρ, moment of inertia C, and moment of inertia of the outer solid shell Cm. This work focuses on the additional information that can be gained by a determination of the change in gravitational potential due to planetary tides, as parameterized by the tidal potential Love number k2. We investigate the tidal response for sets of interior models that are compatible with the available constraints (ρ, C, and Cm). We show that the tidal response correlates with the size of the liquid core and the mean density of material below the outer solid shell and that it is affected by the rheology of the outer solid shell of the planet, which depends on its temperature and mineralogy. For a mantle grain size of 1 cm, we calculate that the tidal k2 of Mercury is in the range 0.45 to 0.52. Some of the current models for the interior structure of Mercury are compatible with the existence of a solid FeS layer at the top of the core. Such a layer, if present, would increase the tidal response of the planet.

Are Planetary Tides on the Sun and the Birthplace of Sunspots Related?

We study whether the birthplaces of sunspots (defined as the location of first appearance in the photosphere) are related to the planetary tides on the Sun. The heliocentric longitudes of newly emerging sunspots are statistically compared to the longitudes of tidal peaks caused by the tidal planets Mercury, Venus, Earth, and Jupiter. The longitude differences between new sunspots and tidal planets (and their conjugate locations) as well as the magnitudes of the vertical and horizontal tidal forces at the birthplace of new sunspots are calculated. The statistical distributions are compared with simulation results calculated using a random sunspot distribution. The results suggest that the birthplaces of sunspots (in the photosphere) are independent of the positions of tidal planets and the strength of tidal forces caused by them. However, since the sunspots actually originate near the tachocline (well below the photosphere) and it takes considerable time for the disturbances to reach photosphere, we hesitate to conclude that the formation of sunspots are not related to planetary positions.

Does the Sun work as a nuclear fusion amplifier of planetary tidal forcing? A proposal for a physical mechanism based on the mass-luminosity relation

Numerous empirical evidences suggest that planetary tides may influence solar activity. In particular, it has been shown that: (1) the well-known 11-year Schwabe sunspot number cycle is constrained between the spring tidal period of Jupiter and Saturn, ∼9.93 year, and the tidal orbital period of Jupiter, ∼11.86 year, and a model based on these cycles can reconstruct solar dynamics at multiple time scales (Scafetta, in press); (2) a measure of the alignment of Venus, Earth and Jupiter reveals quasi 11.07-year cycles that are well correlated to the 11-year Schwabe solar cycles; and (3) there exists a 11.08 year cyclical recurrence in the solar jerk-shock vector, which is induced mostly by Mercury and Venus. However, Newtonian classical physics has failed to explain the phenomenon. Only by means of a significant nuclear fusion amplification of the tidal gravitational potential energy dissipated in the Sun, may planetary tides produce irradiance output oscillations with a sufficient magnitude to influence solar dynamo processes. Here we explain how a first order magnification factor can be roughly calculated using an adaptation of the well-known mass-luminosity relation for main-sequence stars similar to the Sun. This strategy yields a conversion factor between the solar luminosity and the potential gravitational power associated to the mass lost by nuclear fusion: the average estimated amplification factor is A≈4.25×106. We use this magnification factor to evaluate the theoretical luminosity oscillations that planetary tides may potentially stimulate inside the solar core by making its nuclear fusion rate oscillate. By converting the power related to this energy into solar irradiance units at 1 AU we find that the tidal oscillations may be able to theoretically induce an oscillating luminosity increase from 0.05–0.65W/m2 to 0.25–1.63W/m2, which is a range compatible with the ACRIM satellite observed total solar irradiance fluctuations. In conclusion, the Sun, by means of its nuclear active core, may be working as a great amplifier of the small planetary tidal energy dissipated in it. The amplified signal should be sufficiently energetic to synchronize solar dynamics with the planetary frequencies and activate internal resonance mechanisms, which then generate and interfere with the solar dynamo cycle to shape solar dynamics, as further explained in Scafetta (in press). A section is devoted to explain how the traditional objections to the planetary theory of solar variation can be rebutted.

Variability of parameters of the F2-layer maximum in the quiet midlatitude ionosphere under low solar activity: 2. Strong fluctuations of critical frequency

This paper presents a qualitative analysis of the properties and particular examples of strong (10% 30%) fluctuations in the critical frequency of the F2 layer (foF2) of the quiet ionosphere at midlatitudes under low solar activity according to the Irkutsk station data for 2007–2008. It is found that strong day-to-day fluctuations in foF2 are mainly related to changes in thermospheric parameters, which have a nature of planetary waves and tides. Evidently, very strong day-to-day fluctuations in foF2 are caused by superposition of the effects in the ionosphere caused by changes in the thermospheric parameters and those related to a complex of processes of solar wind interaction with the magnetosphere, including the effects caused by the reversal of the vertical component of the solar wind magnetic field southwards. The increase in foF2 during nighttime hours in winter up to values typical for the daytime maximum in foF2 is the brightest example of very strong changes in foF2 in the quiet ionosphere.

Tidal decay and circularization of the orbits of short-period planets

We analyze the long-term tidal evolution of a single-planet system through the use of numerical simulations and averaged equations giving the variations of the semi-major axis and eccentricity of the relative orbit. For different types of planets, we compute the variations due to the planetary and stellar tides. We then calculate the critical value of the eccentricity for which the stellar tide becomes dominant over the planetary tide. The timescales for orbital decay and circularization are also discussed and compared.

Regarding the Putative Eccentricity of Charon's Orbit

Based on astrometry from an orbit derived by Hubble Space Telescope imagery, Charon's orbital eccentricity has been reported to be in the range of 0.003–0.008. Solar and planetary tides are orders of magnitude too small to induce the reported eccentricity. This nonzero value, if correct, therefore indicates some significant forcing against the two-body tidal equilibrium value, which should formally be zero. Here we follow up on a preliminary study to investigate whether the reported eccentricity of Charon's orbit could be due to gravitational perturbations by Kuiper belt object (KBO) flybys through the Pluto-Charon system and KBO impacts directly onto Pluto and Charon. We find it is unlikely that Charon's reported eccentricity could be caused by this effect. Although we cannot rule out some additional source of eccentricity excitation (e.g., an undiscovered satellite in the system, or a Kozai resonance), our analysis indicates it is plausible that Charon's actual orbital eccentricity is substantially smaller than the 0.003 lower limit reported previously.

Resonant nonlinear interactions between atmospheric waves in the polar summer mesopause region

Data obtained from the mobile SOUSY VHF radar at Andoya/Norway in summer 1987 have been used to study the nonlinear interactions between planetary waves, tides and gravity waves in the polar mesosphere, and the instability of background atmosphere above the mesopause. It is observed that 35-h planetary wave, diurnal, semidiurnal and terdiurnal tides are the prominent perturbations in the Lomb-Scargle spectra of the zonal wind component. By inspecting the frequency combinations, several triads are identified. By bispectral analysis it is shown that most bispectral peaks stand for quadratic coupling between tidal harmonics or between tide and planetary or gravity wave, and the height dependence of bispectral peaks reflects the variation of wave-wave interactions. Above the mesopause, the occurrence heights of the maximum L-S power spectral peaks corresponding to the prominent wave components ten to increase with their frequencies. This may result from the process in which two low frequency waves interact to generate a high frequency wave. Intensities of the planetary wave and tides increase gradually, arrive at their maxima, and then decay quickly in turn with increasing height. This kind of scene correlates with a “chain” of wave-wave resonant interactions that shifts with height from lower frequency segment to higher frequency segment. By instability analysis, it is observed that above the mesopause, theRichardson number becomes smaller and smaller with height, implying that the turbulent motion grows stronger and stronger and accordingly the background atmosphere more and more instable. It is suggested that the wave-wave sum resonant interaction and the wave dissipation due to instability are two dominant dynamical processes that occur in the mesopause region. The former invokes the energy transfer from lower frequency waves to higher frequency waves. The latter results in the heating of the atmosphere and accelerating of the background flow.

1620 Geographos and 433 Eros: Shaped by Planetary Tides?

Until recently, most asteroids were thought to be solid bodies whose shapes were determined largely by collisions with other asteroids. It now seems that many asteroids are little more than rubble piles, held together by self-gravity; this means that their shapes may be strongly distorted by tides during close encounters with planets. Here we report on numerical simulations of encounters between a ellipsoid-shaped rubble-pile asteroid and the Earth. After an encounter, many of the simulated asteroids develop the same rotation rate and distinctive shape (i.e., highly elongated with a single convex side, tapered ends, and small protuberances swept back against the rotation direction) as 1620 Geographos. Since our numerical studies show that these events occur with some frequency, we suggest that Geographos may be a tidally distorted object. In addition, our work shows that 433 Eros, which will be visited by the NEAR spacecraft in 1999, is much like Geographos, which suggests that it too may have been molded by tides in the past.

Variability and anisotropy of mesospheric wind spectra

The winter mesosphere over Japan was observed with the new MF radars at Wakkanai (45.4°N, 141.7°E) and Yamagawa (31.2°N, 130.6°E). The wind spectra show dominance of different tidal waves at the two sites at the same time. The temporal evolution of the wind spectra is suggestive of resonant nonlinear interactions between planetary waves, tides, and gravity waves. At Wakkanai, the decay of the 24‐h and 12‐h waves was observed in the spectra of the zonal wind component. It is remarkable that the 12‐h wave of the meridional wind component remained strong while the zonal 12‐h wave disappeared. Further anisotropies of the meridional and zonal frequency spectra are described, as well as the slopes of the wind power spectra.

Can Tidal Disruption of Asteroids Make Crater Chains on the Earth and Moon?

Crater chains, presumably formed by weak asteroids or comets stretched apart by planetary tides, have been tentatively identified on both the Earth and Moon. By modeling tidal disruption by the Earth and Moon of “rubble-pile” bodies, we find that the Earth disrupts enough objects over the last 3.8 billion years to account for one or two lunar crater chains, but that the reciprocal production rate of terrestrial crater chains is too low to make any in observable geological history.

Testing for the influence of planetary tides on solar flares: Dong Shi-lunBeijing Astronomical Observatory, Beijing 100080

Testing for the influence of planetary tides on solar flares: Dong Shi-lunBeijing Astronomical Observatory, Beijing 100080

On the origin of solar cycle periodicity

Recently, the origin of the solar cycle is considered to be rooted in the dynamics of the solar core (Grandpierre, 1996). The dynamic solar core model requires macroscopic flow and magnetic field as basic inputs. The macroscopic flow cannot be generated by the quasistatic solar structure and it has to reach a larger than critical size (Grandpierre, 1984) in order to survive dissipation. Therefore the flow must be generated by outer agents. The most significant outer agents to the Sun are the planets of the Solar System. These theoretical arguments are supported by observations showing that planetary tides follow a pattern correlating with the solar cycle in the last three and a half centuries (Wood, 1972; Desmoulins, 1995). Therefore the pulsating-ejecting solar core model gives a firm theoretical basis for the interpretation of these largely ignored observations. In this paper a new and simple calculation is presented which enlightens the planetary origin of the eleven-year period and gives a physical basis for a detailed modelling of the dynamo and the solar cycle.