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Register a new userThe Mass, Orbit, and Tidal Evolution of the Quaoar-Weywot System
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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 0.39 day alias that exists in available observations, four possible orbital solutions are available with periods of $sim11.6$, $sim12.0$, $sim12.4$, and $sim12.8$ days. From the possible orbital solutions, system masses of $1.3-1.5pm0.1times10^{21}$ kg are found. These observations provide an updated density for Quaoar of $2.7-5.0{g cm$^{-3}$}$. In all cases, Weywots orbit is eccentric, with possible values $sim0.13-0.16$. We present a reanalysis of the tidal orbital evolution of the Quoaor-Weywot system. We have found that Weywot has probably evolved to a state of synchronous rotation, and have likely preserved their initial inclinations 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 Weywots eccentricity and semi-major axis. Accordingly, it appears that Weywots 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.
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The Kepler-186 system consists of five planets orbiting an early-M dwarf. The planets have physical radii of 1.0-1.50 R$_oplus$ and orbital periods of 4 to 130 days. The $1.1~$R$_oplus$ Kepler-186f with a period of 130 days is of particular interest. Its insolation of roughly $0.32~S_odot$places it within the liquid water habitable zone. We present a multi-faceted study of the Kepler-186 system. First, we show that the distribution of planet masses can be roughly reproduced if the planets accreted from a high-surface density disk presumably sculpted by an earlier phase of migration. However, our simulations predict the existence of 1-2 undetected planets between planets e and f. Next, we present a dynamical analysis of the system including the effect of tides. The timescale for tidal evolution is short enough that the four inner planets must have small obliquities and near-synchronous rotation rates. Tidal evolution of Kepler-186f is slow enough that its current spin state depends on a combination of its dissipation rate and the stellar age. Finally, we study the habitability of Kepler-186f with a 1-D climate model. The planets surface temperature can be raised above 273 K with 0.5-5 bars of CO$_2$, depending on the amount of N$_2$ present. Kepler-186f represents a case study of an Earth-sized planet in the cooler regions of the habitable zone of a cool star.
We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state where consecutive planets are linked by first order resonances and consecutive triples, apart from planets c, d and e, by connected three body Laplace resonances. The system expands with period ratios increasing and mean eccentricities decreasing with time. This evolution is largely driven by tides acting on the innermost planets which then influence the outer ones. In order that deviations from commensurability become significant only on $Gy$ time scales or longer, we require that the tidal parameter associated with the planets has to be such that $Q > sim 10^{2-3}.$ At the same time, if we start with two subsystems, with the inner three planets comprising the inner one, $Q$ associated with the planets has to be on the order (and not significantly exceeding) $10^{2-3}$ for the two subsystems to interact and end up in the observed configuration. This scenario is also supported by modelling of the evolution through disk migration which indicates that the whole system cannot have migrated inwards together. Also in order to avoid large departures from commensurabilities, the system cannot have stalled at a disk inner edge for significant time periods. We discuss the habitability consequences of the tidal dissipation implied by our modelling, concluding that planets d, e and f are potentially in habitable zones.
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.
While the vast majority of multiple-planet systems have their orbital angular momentum axes aligned with the spin axis of their host star, Kepler-56 is an exception: its two transiting planets are coplanar yet misaligned by at least 40 degrees with respect to their host star. Additional follow-up observations of Kepler-56 suggest the presence of a massive, non-transiting companion that may help explain this misalignment. We model the transit data along with Keck/HIRES and HARPS-N radial velocity data to update the masses of the two transiting planets and infer the physical properties of the third, non-transiting planet. We employ a Markov Chain Monte Carlo sampler to calculate the best-fitting orbital parameters and their uncertainties for each planet. We find the outer planet has a period of 1002 $pm$ 5 days and minimum mass of 5.61 $pm$ 0.38 Jupiter masses. We also place a 95% upper limit of 0.80 m/s/yr on long-term trends caused by additional, more distant companions.
Forming the Moon by a high-angular momentum impact may explain the Earth-Moon isotopic similarities, however, the post-impact angular momentum needs to be reduced by a factor of 2 or more to the current value (1 L_EM) after the Moon forms. Capture into the evection resonance, occurring when the lunar perigee precession period equals one year, could remove the angular momentum excess. However the appropriate angular momentum removal appears sensitive to the tidal model and chosen tidal parameters. In this work, we use a constant-time delay tidal model to explore the Moons orbital evolution through evection. We find that exit from formal evection occurs early and that subsequently, the Moon enters a quasi-resonance regime, in which evection still regulates the lunar eccentricity even though the resonance angle is no longer librating. Although not in resonance proper, during quasi-resonance angular momentum is continuously removed from the Earth-Moon system and transferred to Earths heliocentric orbit. The final angular momentum, set by the timing of quasi-resonance escape, is a function of the ratio of tidal strength in the Moon and Earth and the absolute rate of tidal dissipation in the Earth. We consider a physically-motivated model for tidal dissipation in the Earth as the mantle cools from a molten to a partially molten state. We find that as the mantle solidifies, increased terrestrial dissipation drives the Moon out of quasi-resonance. For post-impact systems that contain >2 L_EM, final angular momentum values after quasi-resonance escape remain significantly higher than the current Earth-Moon value.
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