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Register a new userThe Origin of Kepler-419b: A Path to Tidal Migration Via Four-body Secular Interactions
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We test the high-eccentricity tidal migration scenario for Kepler-419b, a member of the eccentric warm Jupiter class of planets whose origin is debated. Kepler-419 hosts two known planets (b,c). However, in its current configuration, planet c cannot excite the eccentricity of planet b enough to undergo high-eccentricity tidal migration. We investigate whether the presence of an undiscovered fourth body could explain the orbit of Kepler-419b. We explore the parameter space of this potential third giant planet using a suite of N-body simulations with a range of initial conditions. From the results of these simulations, coupled with observational constraints, we can rule out this mechanism for much of the parameter space of initial object d conditions. However, for a small range of parameters (masses between 0.5 and 7 $m_{rm{Jup}}$, semi-major axes between 4 and 7.5 AU, eccentricities between 0.18 and 0.35, and mutual inclinations near 0$^{circ}$) an undiscovered object d could periodically excite the eccentricity of Kepler-419b without destabilizing the system over 1 Gyr while producing currently undetectable radial velocity and transit timing variation signals.
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The (yet-to-be confirmed) discovery of a Neptune-sized moon around the ~3.2 Jupiter-mass planet in Kepler 1625 puts interesting constraints on the formation of the system. In particular, the relatively wide orbit of the moon around the planet, at ~40 planetary radii, is hard to reconcile with planet formation theories. We demonstrate that the observed characteristics of the system can be explained from the tidal capture of a secondary planet in the young system. After a quick phase of tidal circularization, the lunar orbit, initially much tighter than 40 planetary radii, subsequently gradually widened due to tidal synchronization of the spin of the planet with the orbit, resulting in a synchronous planet-moon system. Interestingly, in our scenario the captured object was originally a Neptune-like planet, turned into a moon by its capture.
In Efroimsky & Makarov (2014), we derived from the first principles a formula for the tidal heating rate in a tidally perturbed homogeneous sphere. We compared it with the formulae used in the literature, and pointed out the differences. Using this result, we now present three case studies - Mercury, Kepler-10b, and a triaxial Io. A very sharp frequency-dependence of k2/Q near spin-orbit resonances yields a similarly sharp dependence of k2/Q on the spin rate. This indicates that physical libration may play a major role in tidal heating of synchronously rotating bodies. The magnitude of libration in the spin rate being defined by the planets triaxiality, the latter should be a factor determining the dissipation rate. Other parameters equal, a synchronously rotating body with a stronger triaxiality should generate more heat than a similar body of a more symmetrical shape. Further in the paper, we discuss scenarios where initially triaxial objects melt and lose their triaxiality. Thereafter, dissipation in them becomes less intensive; so the bodies freeze. The tidal bulge becomes a new permanent figure, with a new triaxiality lower than the original. In the paper, we also derive simplified, approximate expressions for dissipation rate in a rocky planet of the Maxwell rheology, with a not too small Maxwell time. The three expressions derived pertain to the cases of a synchronous spin, a 3:2 resonance, and a nonresonant rotation; so they can be applied to most close-in super-Earth exoplanets detected thus far. In such bodies, the rate of tidal heating outside of synchronous rotation is weakly dependent on the eccentricity and obliquity, provided both these parameters are small or moderate. According to our calculation, Kepler-10b could hardly survive the great amount of tidal heating without being synchronised, circularised and also reshaped through a complete or partial melt-down.
The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could have both resonance angles associated with the resonance librating if the orbital eccentricities are sufficiently small, because the width of first-order resonances diverges in the limit of vanishingly small eccentricity. We consider a widely-held scenario in which pairs of planets were captured into first-order resonances by migration due to planet-disk interactions, and subsequently became detached from the resonances, due to tidal dissipation in the planets. In the context of this scenario, we find a constraint on the ratio of the planets tidal dissipation function and Love number that implies that some of the Kepler planets are likely solid. However, tides are not strong enough to move many of the planet pairs to the observed separations, suggesting that additional dissipative processes are at play.
Planetary transits provide a unique opportunity to investigate the surface distributions of star spots. Our aim is to determine if, with continuous observation (such as the data that will be provided by the Kepler mission), we can in addition measure the rate of drift of the spot belts. We begin by simulating magnetic cycles suitable for the Sun and more active stars, incorporating both flux emergence and surface transport. This provides the radial magnetic field distribution on the stellar surface as a function of time. We then model the transit of a planet whose orbital axis is misaligned with the stellar rotation axis. Such a planet could occult spots at a range of latitudes. This allows us to complete the forward modelling of the shape of the transit lightcurve. We then attempt the inverse problem of recovering spot locations from the transit alone. From this we determine if transit lightcurves can be used to measure spot belt locations as a function of time. We find that for low-activity stars such as the Sun, the 3.5 year Kepler window is insufficient to determine this drift rate. For more active stars, it may be difficult to distinguish subtle differences in the nature of flux emergence, such as the degree of overlap of the butterfly wings. The rate and direction of drift of the spot belts can however be determined for these stars. This would provide a critical test of dynamo theory.
The planets with a radius $<$ 4 $R$$_oplus$ observed by the Kepler mission exhibit a unique feature, and propose a challenge for current planetary formation models. The tidal effect between a planet and its host star plays an essential role in reconfiguring the final orbits of the short-period planets. In this work, based on various initial Rayleigh distributions of the orbital elements, the final semi-major axis distributions of the planets with a radius $<$ 4 $R_oplus$ after suffering tidal evolutions are investigated. Our simulations have qualitatively revealed some statistical properties: the semi-major axis and its peak value all increase with the increase of the initial semi-major axis and eccentricity. For the case that the initial mean semi-major axis is less than 0.1 au and the mean eccentricity is larger than 0.25, the results of numerical simulation are approximately consistent with the observation. In addition, the effects of other parameters, such as the tidal dissipation coefficient, stellar mass and planetary mass, etc., on the final semi-major axis distribution after tidal evolution are all relatively small. Based on the simulation results, we have tried to find some clues for the formation mechanism of low-mass planets. We speculate that these low-mass planets probably form in the far place of protoplanetary disk with a moderate eccentricity via the type I migration, and it is also possible to form in situ.
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