scholarly journals The Origin of Commensurabilities in the Satellite Systems

1974 ◽  
Vol 62 ◽  
pp. 57-58
Author(s):  
S. F. Dermott
Keyword(s):  
Formation Process ◽  
Orbital Evolution ◽  
Dissipation Function ◽  
Chemical Compositions ◽  
Tidal Evolution ◽  
Tidal Dissipation ◽  
Satellite Formation ◽  
Satellite Systems ◽  
Tidal Forces ◽  
Frequency Independent

The distribution of orbits in the satellite systems of the major planets is definitely nonrandom as there is a marked preference for commensurability among pairs of mean motions in these systems. If this preference is not the result of a formation process then it follows that since the time of satellite formation dynamical evolution has occurred. In this paper (a full version of which is to be submitted to another journal) I show that there is a bulk of evidence in favour of the hypothesis that orbital evolution has occurred as the result of tidal dissipation in the planets. This evidence can be listed as follows:(i) In a tidally evolved satellite system there should be a linear correlation between log (orbital radius) and log (satellite mass). The expected correlation is observed among the inner satellites of Saturn and Uranus, the slope of the log-log plots being consistent with an amplitude and frequency independent Q (the tidal dissipation function). The correlation in Saturn's system must be largely due to either a formation process or possibly an early amplitude and frequency dependent tidal process, but certainly the present satellite distribution is completely consistent with the tidal hypothesis.(ii) If Q is amplitude- and frequency-independent then the Mimas-Tethys and Enceladus-Dione resonances are stable under the action of tidal forces. This is an important result as it indicates that the necessary tidal dissipation occurred in the solid parts of the planets. Whether or not these planets have any solid parts at present is a matter of dispute.(iii) The tidal hypothesis can account for the formation (capture into libration) of the Mimas-Tethys and Enceladus-Dione resonances.(iv) If it is allowed that the age of the Mimas-Tethys resonance is not small (> 108 yr) in comparison with that of the solar system and that orbital evolution since the time of satellite formation has been appreciable then it can be shown that tidal forces (with Q amplitude- and frequency-independent) can account for the present large amplitude of libration of this resonance.(v) If tidal evolution in the satellite systems of Jupiter and Saturn has been appreciable then from the present orbits of Io and Mimas it can be deduced that Q (Jupiter) ~1.1 × 105 and Q (Saturn) ~1.2 × 105. As the masses of the two satellites differ by a factor ~2000 and the amplitudes of the tides they raise on their respective planets differ by a factor ~ 5000 this agreement in the Q-values is somewhat remarkable. But as the stability of the Mimas-Tethys and Enceladus-Dione resonances demands that Q is amplitude- and frequency-independent and as the chemical compositions and structures of Jupiter and Saturn are probably similar then one should expect the Q's of these planets to be similar and thus the result supports the tidal hypothesis.(vi) Finally, as the values of Q are so very high it would be remarkable if tidal evolution had not taken place.

scholarly journals Formation of single-moon systems around gas giants

2020 ◽  
Vol 635 ◽  
pp. L4 ◽  
Author(s):  
Yuri I. Fujii ◽  
Masahiro Ogihara
Keyword(s):  
Giant Planet ◽  
Orbital Evolution ◽  
Effect Of Temperature ◽  
Temperature Structure ◽  
Satellite Formation ◽  
Satellite Systems ◽  
Evolution Stage ◽  
First Time ◽  
Final Evolution ◽  
Orbital Migration

Context. Several mechanisms have been proposed to explain the formation process of satellite systems, and relatively large moons are thought to be born in circumplanetary disks. Making a single-moon system is known to be more difficult than multiple-moon or moonless systems. Aims. We aim to find a way to form a system with a single large moon, such as Titan around Saturn. We examine the orbital migration of moons, which change their direction and speed depending on the properties of circumplanetary disks. Methods. We modeled dissipating circumplanetary disks with taking the effect of temperature structures into account and calculated the orbital evolution of Titan-mass satellites in the final evolution stage of various circumplanetary disks. We also performed N-body simulations of systems that initially had multiple satellites to see whether single-moon systems remained at the end. Results. The radial slope of the disk-temperature structure characterized by the dust opacity produces a patch of orbits in which the Titan-mass moons cease inward migration and even migrate outward in a certain range of the disk viscosity. The patch assists moons initially located in the outer orbits to remain in the disk, while those in the inner orbits fall onto the planet. Conclusions. We demonstrate for the first time that systems can form that have only one large moon around giant planet. Our N-body simulations suggest satellite formation was not efficient in the outer radii of circumplanetary disks.

Tidal parameters and habitability of the TRAPPIST-1 planets

2020 ◽  
Author(s):  
Vera Dobos ◽  
Amy Barr ◽  
Ramon Brasser
Keyword(s):  
Liquid Water ◽  
Planetary System ◽  
Weighted Average ◽  
Orbital Evolution ◽  
Heat Fluxes ◽  
The Body ◽  
Interior Structure ◽  
Tidal Dissipation ◽  
Tidal Forces ◽  
Tidal Heating

<p>The discovery of seven Earth-sized planets around the ultracool dwarf star TRAPPIST-1 in 2017 brought a new type of planetary system to our attention. Modelling the planets of this system and considering new physical processes may result in a more realistic description of those exoplanets that are considered to be the most habitable ones. Similar planetary systems to the TRAPPIST-1 are expected to be discovered with current and upcoming missions, and in fact, recently, two Earth-sized planet candidates were announced around the ultracool Teegarden's Star (Zechmeister et al. 2019). Detailed modelling of similar exoplanetary systems will be an important task to reveal their astrobiological potential. Until new discoveries, the TRAPPIST-1 system serves as a prototype of an ultracool M dwarf with a planetary system of Earthlike planets. For this reason, studying the TRAPPIST-1 planetary system is a pioneering work that will help in the characterization of similar systems that are yet to be discovered.</p> <p><br />The habitability of Earth-like exoplanets around M dwarfs is becoming the forefront of exoplanetary research as the TRAPPIST-1 system is recently in the centre of attention. Tidal heating may be an important effect influencing habitability, especially for close-in planets or moons. Close-in bodies quickly become tidally locked, but if their eccentricities are excited by periodic perturbing effects of other planets or moons in the system, then varying tidal forces keep causing friction inside the body that leads to continuous heat generation (Peale et al. 1979). Some studies suggest that tidal heating may enable the emergence of life in otherwise too cold environments (Scharf 2006, Dobos & Turner 2015, Forgan & Dobos 2016, Dobos et al. 2017).</p> <p><br />Using a Maxwell viscoelastic rheology, we computed the tidal response of the planets using the volume-weighted average of the viscosities and rigidities of the metal, rock, high-pressure ice, and liquid water/ice I layers. After determining the possible interior structures, we computed the heat flux due to stellar irradiation and tidal heating for the inner four planets (Barr et al. 2018, Dobos et al. 2019). We found that planet e is the most likely to support a habitable environment, with Earth-like surface temperatures and possibly liquid water oceans. Planet d also avoids a runaway greenhouse state (in which it would irreversibly lose all of its surface water content), if its surface reflectance is at least as high as that of the Earth. Planets b and c have heat fluxes high enough to trigger a runaway greenhouse and to support volcanism on the surfaces of their rock layers. Planets f, g, and h do not experience significant tidal heating arising from the star, and likely have solid ice surfaces with possible subsurface liquid water oceans.</p> <p><br />We also connected dynamic evolution of planetary orbits with interior structure considerations for the inner two TRAPPIST-1 planets (Brasser et al., 2019). Based on stability considerations, and with the assumption that orbital resonances are lasting for planets b and c, lower limits can be determined for their k<sub>2</sub>/Q tidal parameter. This parameter can further be constrained by the planets' interior structure which determines their tidal dissipation. Although the two approaches gave different results, well-constrained tidal parameters will improve the realism of orbital evolution simulations including tidal effects.</p>

Tidal dissipation in the oceans: astronomical, geophysical and oceanographic consequences

1977 ◽  
Vol 287 (1347) ◽  
pp. 545-594 ◽  
Keyword(s):  
Energy Dissipation ◽  
Solid Earth ◽  
Global Ocean ◽  
Ocean Tide ◽  
The Moon ◽  
Tidal Dissipation ◽  
Tidal Forces ◽  
Degree Harmonic ◽  
Tidal Acceleration ◽  
Second Degree

The most precise way of estimating the dissipation of tidal energy in the oceans is by evaluating the rate at which work is done by the tidal forces and this quantity is completely described by the fundamental harmonic in the ocean tide expansion that has the same degree and order as the forcing function. The contribution of all other harmonics to the work integral must vanish. These harmonics have been estimated for the principal M 2 tide using several available numerical models and despite the often significant difference in the detail of the models, in the treatment of the boundary conditions and in the way dissipating forces are introduced, the results for the rate at which energy is dissipated are in good agreement. Equivalent phase lags, representing the global ocean-solid Earth response to the tidal forces and the rates of energy dissipation have been computed for other tidal frequencies, including the atmospheric tide, by using available tide models, age of tide observations and equilibrium theory. Orbits of close Earth satellites are periodically perturbed by the combined solid Earth and ocean tide and the delay of these perturbations compared with the tide potential defines the same terms as enter into the tidal dissipation problem. They provide, therefore, an independent estimate of dissipation. The results agree with the tide calculations and with the astronomical estimates. The satellite results are independent of dissipation in the Moon and a comparison of astronomical, satellite and tidal estimates of dissipation permits a separation of energy sinks in the solid Earth, the Moon and in the oceans. A precise separation is not yet possible since dissipation in the oceans dominates the other two sinks: dissipation occurs almost exclusively in the oceans and neither the solid Earth nor the Moon are important energy sinks. Lower limits to the Q of the solid Earth can be estimated by comparing the satellite results with the ocean calculations and by comparing the astronomical results with the latter. They result in Q > 120. The lunar acceleration n , the Earth’s tidal acceleration O T and the total rate of energy dissipation E estimated by the three methods give astronomical based estimate —1.36 —28±3 —7.2 ± 0.7 4.1±0.4 satellite based estimate —1.03 —24 ±5 — 6.4 ± 1.5 3.6±0.8 numerical tide model — 1.49 —30 ±3 —7.5± 0.8 4.5±0.5 The mean value for O T corresponds to an increase in the length of day of 2.7 ms cy -1 . The non-tidal acceleration of the Earth is (1.8 ± 1.0) 10 -22 s ~2 , resulting in a decrease in the length of day of 0.7 ± 0.4 ms cy -1 and is barely significant. This quantity remains the most unsatisfactory of the accelerations. The nature of the dissipating mechanism remains unclear but whatever it is it must also control the phase of the second degree harmonic in the ocean expansion. It is this harmonic that permits the transfer of angular momentum from the Earth to the Moon but the energy dissipation occurs at frequencies at the other end of the tide’s spatial spectrum. The efficacity of the break-up of the second degree term into the higher modes governs the amount of energy that is eventually dissipated. It appears that the break-up is controlled by global ocean characteristics such as the ocean­-continent geometry and sea floor topography. Friction in a few shallow seas does not appear to be as important as previously thought: New estimates for dissipation in the Bering Sea being almost an order of magnitude smaller than earlier estimates. If bottom friction is important then it must be more uniformly distributed over the world's continental shelves. Likewise, if turbulence provides an important dissipation mechanism it must be fairly uniformly distributed along, for example, coastlines or along continental margins. Such a global distribution of the dissipation makes it improbable that there has been a change in the rate of dissipation during the last few millennium as there is no evidence of changes in ocean volume, or ocean geometry or sea level beyond a few metres. It also suggests that the time scale problem can be resolved if past ocean-continent geometries led to a less efficient breakdown of the second degree harmonic into higher degree harmonics.

scholarly journals Tidal interactions in rotating multiple stars and their impact on their evolution

2014 ◽  
Vol 9 (S307) ◽  
pp. 208-210
Author(s):  
P. Auclair-Desrotour ◽  
S. Mathis ◽  
C. Le Poncin-Lafitte
Keyword(s):  
Fluid Model ◽  
Orbital Evolution ◽  
Tidal Dissipation ◽  
Tidal Waves ◽  
Physical Mechanisms ◽  
Tidal Interactions ◽  
The Earth ◽  
Half Height ◽  
Multiple Stars ◽  
Stellar Interiors

AbstractTidal dissipation in stars is one of the key physical mechanisms that drive the evolution of binary and multiple stars. As in the Earth oceans, it corresponds to the resonant excitation of their eigenmodes of oscillation and their damping. Therefore, it strongly depends on the internal structure, rotation, and dissipative mechanisms in each component. In this work, we present a local analytical modeling of tidal gravito-inertial waves excited in stellar convective and radiative regions respectively. This model allows us to understand in details the properties of the resonant tidal dissipation as a function of the excitation frequencies, the rotation, the stratification, and the viscous and thermal properties of the studied fluid regions. Then, the frequencies, height, width at half-height, and number of resonances as well as the non-resonant equilibrium tide are derived analytically in asymptotic regimes that are relevant in stellar interiors. Finally, we demonstrate how viscous dissipation of tidal waves leads to a strongly erratic orbital evolution in the case of a coplanar binary system. We characterize such a non-regular dynamics as a function of the height and width of resonances, which have been previously characterized thanks to our local fluid model.

scholarly journals Tidal dissipation in rotating low-mass stars and implications for the orbital evolution of close-in planets

2017 ◽  
Vol 604 ◽  
pp. A112 ◽  
Author(s):  
F. Gallet ◽  
E. Bolmont ◽  
S. Mathis ◽  
C. Charbonnel ◽  
L. Amard
Keyword(s):  
Orbital Evolution ◽  
Low Mass Stars ◽  
Tidal Dissipation ◽  
Low Mass

scholarly journals Survival of planets around shrinking stellar binaries

2015 ◽  
Vol 112 (30) ◽  
pp. 9264-9269 ◽  
Author(s):  
Diego J. Muñoz ◽  
Dong Lai
Keyword(s):  
Binary Stars ◽  
Orbital Evolution ◽  
Eclipsing Binaries ◽  
Target List ◽  
Tidal Dissipation ◽  
Compact Binaries ◽  
Kepler Mission ◽  
Orbital Decay ◽  
Erratic Behavior ◽  
Circumbinary Planets

The discovery of transiting circumbinary planets by the Kepler mission suggests that planets can form efficiently around binary stars. None of the stellar binaries currently known to host planets has a period shorter than 7 d, despite the large number of eclipsing binaries found in the Kepler target list with periods shorter than a few days. These compact binaries are believed to have evolved from wider orbits into their current configurations via the so-called Lidov–Kozai migration mechanism, in which gravitational perturbations from a distant tertiary companion induce large-amplitude eccentricity oscillations in the binary, followed by orbital decay and circularization due to tidal dissipation in the stars. Here we explore the orbital evolution of planets around binaries undergoing orbital decay by this mechanism. We show that planets may survive and become misaligned from their host binary, or may develop erratic behavior in eccentricity, resulting in their consumption by the stars or ejection from the system as the binary decays. Our results suggest that circumbinary planets around compact binaries could still exist, and we offer predictions as to what their orbital configurations should be like.

scholarly journals Tidal evolution of circumbinary systems with arbitrary eccentricities: applications for Kepler systems

2020 ◽  
Vol 634 ◽  
pp. A12
Author(s):  
F. A. Zoppetti ◽  
A. M. Leiva ◽  
C. Beaugé
Keyword(s):  
Time Lag ◽  
Semimajor Axis ◽  
Tidal Flow ◽  
Orbital Evolution ◽  
Axis Ratio ◽  
Tidal Evolution ◽  
Tidal Interactions ◽  
Orbital Instability ◽  
Outward Migration ◽  
Circumbinary Planets

We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between pairs are computed, regardless of their size. We derive analytical expressions for the variational equations governing the spin and orbital evolution, which are expressed as high-order elliptical expansions in the semimajor axis ratio but retain closed form in terms of the binary and planetary eccentricities. These are found to reproduce the results of the numerical simulations with arbitrary eccentricities very well, as well as reducing to our previous results in the low-eccentric case. Our model is then applied to the well-characterised Kepler circumbinary systems by analysing the tidal timescales and unveiling the tidal flow around each different system. In all cases we find that the spins reach stationary values much faster than the characteristic timescale of the orbital evolution, indicating that all Kepler circumbinary planets are expected to be in a sub-synchronous state. On the other hand, all systems are located in a tidal flow leading to outward migration; thus the proximity of the planets to the orbital instability limit may have been even greater in the past. Additionally, Kepler systems may have suffered a significant tidally induced eccentricity damping, which may be related to their proximity to the capture eccentricity. To help understand the predictions of our model, we also offer a simple geometrical interpretation of our results.

scholarly journals Orbital Evolution of Planetary Systems

2004 ◽  
Vol 202 ◽  
pp. 175-177
Author(s):  
Tapan K. Chatterjee ◽  
V. B. Magalinsky
Keyword(s):  
Solar System ◽  
Ground State ◽  
Minimum Energy ◽  
Orbital Stability ◽  
Planetary Systems ◽  
Active Role ◽  
Orbital Evolution ◽  
Circular Orbits ◽  
Tidal Forces

It is significant that the orbits of the planets in the solar system are very nearly circular, except for Mercury and Pluto where, conceivably, due to their comparatively small sizes, the tidal forces have played a less active role. Most of the suspected planets orbiting pulsars have nearly circular orbits. These systems tend to have minimum energy and are subjected to tidal forces. We find that a planet circularizes its orbit, in an effort to attain orbital stability and the ground state. Details can be found in Magalinsky & Chatterjee, 1997, and Magalinsky and Chatterjee, 2000.

scholarly journals SPH Simulations of Early and Late Superhumps

2004 ◽  
Vol 194 ◽  
pp. 130-131
Author(s):  
S. Kunze
Keyword(s):  
Accretion Disk ◽  
Early Stage ◽  
Hot Spot ◽  
Type Systems ◽  
Tidal Dissipation ◽  
Tidal Forces ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Low Mass ◽  
Low Mass Ratio

AbstractSmoothed particle hydrodynamics is a Lagrangian method for the solution of the hydrodynamic equations. Here this method is used to simulate the accretion disk in dwarf novae with very low mass ratio, q < 0.25, typical for SU UMa-type systems where the accretion disk can become eccentric and precessing during a superoutburst, leading to periodic brightness variations, so-called superhumps. Two phenomena are examined. First the late superhumps, i.e., the occasional persistence of superhumps well after the return to quiescence, seen e.g. in OY Car and IY UMa. This is due to a varying brightness of the hot spot region, as the eccentric disk continues to precess in quisecence. Second, the occurence of early superhumps in the superoutburst of WZ Sge. Tidal forces compress the rim of the disk, the tidal dissipation leads to a double-peaked strucure in the orbital light curve during the early stage of the superoutburst.

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