Tidal Orbital Evolution Research Articles

The Origin of Neptune’s Unusual Satellites from a Planetary Encounter

Abstract The Neptunian satellite system is unusual, comprising Triton, a large (∼2700 km) moon on a close-in, circular, yet retrograde orbit, flanked by Nereid, the largest irregular satellite (∼300 km) on a highly eccentric orbit. Capture origins have been previously suggested for both moons. Here we explore an alternative in situ formation model where the two satellites accreted in the circum-Neptunian disk and are imparted irregular and eccentric orbits by a deep planetary encounter with an ice giant (IG), like that predicted in the Nice scenario of early solar system development. We use N-body simulations of an IG approaching Neptune to 20 Neptunian radii (R Nep), through a belt of circular prograde regular satellites at 10–30 R Nep. We find that half of these primordial satellites remain bound to Neptune and that 0.4%–3% are scattered directly onto wide and eccentric orbits resembling that of Nereid. With better matches to the observed orbit, our model has a success rate comparable to or higher than capture of large Nereid-sized irregular satellites from heliocentric orbit. At the same time, the IG encounter injects a large primordial moon onto a retrograde orbit with specific angular momentum similar to Triton’s in 0.3%–3% of our runs. While less efficient than capture scenarios, our model does indicate that an in situ origin for Triton is dynamically possible. We also simulate the post-encounter collisional and tidal orbital evolution of Triton analog satellites and find they are decoupled from Nereid on timescales of ∼104 yr, in agreement with Cuk & Gladman.

Orbital evolution of Saturn’s mid-sized moons and the tidal heating of Enceladus

The formation and orbital evolution of Saturn’s inner mid-sized moons – Rhea, Dione, Tethys, Enceladus, and Mimas – are still debated. The most puzzling aspects are 1) how the Tethys–Dione pair and the Mimas–Enceladus pair passed through their strong 3:2 mean-motion resonances during the tidal orbital evolution, and 2) the current strong heat flow from Enceladus, which is a few orders of magnitude higher than the tidal energy dissipation caused by the present orbital eccentricity of Enceladus. Here we perform N-body simulations of the moons’ orbital evolution from various initial conditions – assuming that the moons were formed from Saturn’s hypothetical massive ring – and investigate possible paths to solve the above difficulties. If the moons remain on nearly circular orbits and the influence of the rings is neglected, we find that the Tethys–Dione pair cannot avoid becoming trapped in the 2:1 and 3:2 mean-motion resonances as they recede from Saturn, and that the Tethys–Enceladus pair cannot avoid collisions after the resonance trapping, in case Saturn’s quality factor is smaller than 15,000. These findings are inconsistent with the current orbital configuration. However, taking into account both the eccentricity excitation and the orbital expansion caused by the ring torque, we find that these resonance captures are avoided. With the relatively high eccentricity pumped up by the torque, Enceladus passes through all the mean-motion resonances with Tethys, and the Dione–Tethys pair passes through their 2:1 resonance and possibly the 3:2 resonance as well. After Enceladus resides beyond the 2:1 resonance with the outer ring edge, the eccentricity can be tidally damped. While this is a promising path of evolution, in most runs, Enceladus collides with Tethys by the excited eccentricity. There is a hint that a ring mass decrease (possibly due to Mimas formation) could avoid the collision between Enceladus and Tethys. The parameter survey taking into account detailed ring evolution and Mimas is left for future study. The heat that was tidally dissipated due to the eccentricity excitation by the ring torque in the past is stored in the moons and slowly radiated away through conductive transfer. The stored heat in Enceladus may account for the current anomalously high heat flow.

WTS-2 b: Too close for comfort?

We report the discovery of WTS-2 b, a typical hot Jupiter in an unusually close 1.02-day orbit to a K-dwarf star. This is the second planet to be discovered in the infrared light curves of the WFCAM Transit Survey (WTS) and is only one-and-a-half times the separation from its host star at which is would be destroyed by Roche lobe overflow. The predicted remaining lifetime of the planet is just 38 Myrs, assuming a tidal dissipation quality factor of Q'* = 106. The magnitude of Q'* is largely unconstrained by observations, thus WTS-2 b provides a useful calibration point for theories describing how frictional processes within a host star affect the tidal orbital evolution of its companion giant planets. It is expected that stars with large convective envelopes are more efficient at dissipating the orbital energy of the planet, and WTS-2 b provides an observational constraint in the sparsely populated K-dwarf regime. In addition, despite its relatively faint magnitude, the favourable size ratio of the WTS-2 star-planet system and the predicted hot equilibrium temperature of the planet will make it possible to characterise the planet's atmosphere via secondary eclipse measurements using existing ground-based instrumentation.

The mass, orbit, and tidal evolution of the Quaoar–Weywot system

Here we present new adaptive optics observations of the Quaoar–Weywot system. With these new observations we determine an improved system orbit. Due to a 0.39day alias that exists in available observations, four possible orbital solutions are available with periods of ∼11.6, ∼12.0, ∼12.4, and ∼12.8days. From the possible orbital solutions, system masses of 1.3–1.5±0.1×1021kg are found. These observations provide an updated density for Quaoar of 2.7–5.0gcm−3. In all cases, Weywot’s orbit is eccentric, with possible values ∼0.13–0.16. We present a reanalysis of the tidal orbital evolution of the Quaoar–Weywot system. We have found that Weywot has probably evolved to a state of synchronous rotation, and has likely preserved its initial inclination over the age of the Solar System. We find that for plausible values of the effective tidal dissipation factor tides produce a very slow evolution of Weywot’s eccentricity and semi-major axis. Accordingly, it appears that Weywot’s eccentricity likely did not tidally evolve to its current value from an initially circular orbit. Rather, it seems that some other mechanism has raised its eccentricity post-formation, or Weywot formed with a non-negligible eccentricity.

Observational constraints on tidal effects using orbital eccentricities★

We have analysed radial velocity measurements for known transiting exoplanets to study the empirical signature of tidal orbital evolution for close-in planets. Compared to standard eccentricity determination, our approach is modified to focus on the rejection of the null hypothesis of a circular orbit. We are using a MCMC analysis of radial velocity measurements and photometric constraints, including a component of correlated noise, as well as Bayesian model selection to check if the data justifies the additional complexity of an eccentric orbit. We find that among planets with non-zero eccentricity values quoted in the literature, there is no evidence for an eccentricity detection for the 7 planets CoRoT-5b, WASP-5b, WASP-6b, WASP-10b, WASP-12b, WASP-17b, and WASP-18b. In contrast, we confirm the eccentricity of HAT-P-16b, e=0.034\pm0.003, the smallest eccentricity that is reliably measured so far for an exoplanet as well as that of WASP-14b, which is the planet at the shortest period (P=2.24 d), with a confirmed eccentricity, e= 0.088\pm0.003. As part of the study, we present new radial velocity data using the HARPS spectrograph for CoRoT-1, CoRoT-3, WASP-2, WASP-4, WASP-5 and WASP-7 as well as the SOPHIE spectrograph for HAT-P-4, HAT-P-7, TrES-2 and XO-2. We show that the dissipative effect of tides raised in the planet by the star and vice-versa explain all the eccentricity and spin-orbit alignment measurements available for transiting planets. We revisit the mass-period relation (Mazeh et al. 2005, Pont 2011) and consider its relation to the stopping mechanism of orbital migration for hot Jupiters. In addition to CoRoT-2 and HD 189733 (Pont 2009), we find evidence for excess rotation of the star in the systems CoRoT-18, HAT-P-20, WASP-19 and WASP-43.

THE FATE OF MOONS OF CLOSE-IN GIANT EXOPLANETS

We show that the fate of moons of a close-in giant planet is mainly determined by the migration history of the planet in the protoplanetary disk. As the planet migrates in the disk from beyond the snow line towards a multi-day period orbit, the formed and forming moons become unstable as the planet's sphere of influence shrinks. Disk-driven migration is faster than the moons' tidal orbital evolution. Moons are eventually ejected from around close-in exoplanets or forced into collision with them before tides from the star affect their orbits. If moons are detected around close-in exoplanets, they are unlikely to have been formed in situ, instead they were captured from the protoplanetary disk on retrograde orbits around the planets.

Constraints on the Orbital Evolution of Triton

We present simulations of Triton's postcapture orbit that confirm the importance of Kozai-type oscillations in its orbital elements. In the context of the tidal orbital evolution model, these variations require average pericenter distances much higher than previously published, and the timescale for the tidal orbital evolution of Triton becomes longer than the age of the solar system. Recently discovered irregular satellites present a new constraint on Triton's orbital history. Our numerical integrations of test particles indicate a timescale for Triton's orbital evolution to be less than 105 yr for a reasonable number of distant satellites to survive Triton's passage. This timescale is inconsistent with the exclusively tidal evolution (timescale of over 108 yr), but consistent with the interaction with the debris from satellite-satellite collisions. Any major regular satellites will quickly collide among themselves after being perturbed by Triton, and the resulting debris disk would eventually be swept up by Triton; given that the total mass of the Uranian satellite system is 40% of that of Triton, large-scale evolution is possible. This scenario could have followed either collisional capture or the recently discussed capture based on three-body interactions.