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Register a new userRetrograde-rotating exoplanets experience obliquity excitations in an eccentricity-enabled resonance
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Previous studies have shown that planets that rotate retrograde (backwards with respect to their orbital motion) generally experience less severe obliquity variations than those that rotate prograde (the same direction as their orbital motion). Here we examine retrograde-rotating planets on eccentric orbits and find a previously unknown secular spin-orbit resonance that can drive significant obliquity variations. This resonance occurs when the frequency of the planets rotation axis precession becomes commensurate with an orbital eigenfrequency of the planetary system. The planets eccentricity enables a participating orbital frequency through an interaction in which the apsidal precession of the planets orbit causes a cyclic nutation of the planets orbital angular momentum vector. The resulting orbital frequency follows the relationship $f = 2 dot{varpi} - dot{Omega}$, where $dot{varpi}$ and $dot{Omega}$ are the rates of the planets changing longitude of periapsis and ascending node, respectively. We test this mechanism by simulating cases of a simple Earth-Jupiter system, and confirm the predicted resonance. Over the course of 100 Myr, the test Earths with rotation axis precession rates near the predicted resonant frequency experienced pronounced obliquity variations of order $10^circ$-$30^circ$. These variations can be significant, and suggest that while retrograde rotation is a stabilizing influence most of the time, retrograde rotators can experience large obliquity variations if they are on eccentric orbits and enter this spin-orbit resonance.
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Aims. 2015 BZ509 is the first asteroid confirmed to be in retrograde co-orbit resonance (or 1/-1 resonance) with the giant planets in the solar system. While Saturn is the only giant planet whose Trojans are not discovered until now, we identify some small bodies among Centaurs and Damocloids that are potentially in 1/-1 resonance with Saturn in the present study. Methods. We integrate numerically the motion of the 1000 clones (include the nominal orbit) of each Centaur whose orbit has a semi-major axis between 9.3 au and 9.8 au and an inclination i > 90 deg. To confirm and evaluate the 1/-1 resonant configurations mentioned above, we introduce a useful one-degree integrable approximation for planar 1/-1 resonance. Results. We identify four candidates potentially in 1/-1 resonance with Saturn. The capture in this particular resonant state during the 40000 yr integration timespan is very common for 2006 RJ2 (906/1000 clones), 2006 BZ8 (878/1000 clones), and 2017 SV13 (998/1000 clones), and it is less likely for 2012 YE8 (426/1000 clones). According to our statistical results, 2006 RJ2 is the best candidate to be currently in a 1/-1 mean motion resonance with Saturn, and 2017 SV13 is another important potential candidate. Moreover, 2012 YE8 and 2006 BZ8 are also Centaurs of interest but their current and long-term 1/-1 resonant state with Saturn is less likely. The proportions of the clones captured in the relative long-term stable co-orbit resonance (over 10000 yr) are also given. Conclusions. Small bodies in retrograde co-orbit resonance with giant planets may be more common than previously expected. Identification of these potential mysterious minor bodies encourages the search for such objects on a larger scale in our solar system. The findings of this paper are also useful for understanding the origin and dynamical evolution of the Centaurs and Damocloids on retrograde orbits.
Constructing dynamical maps from the filtered output of numerical integrations, we analyze the structure of the $ u_odot$ secular resonance for fictitious irregular satellites in retrograde orbits. This commensurability is associated to the secular angle $theta = varpi - varpi_odot$, where $varpi$ is the longitude of pericenter of the satellite and $varpi_odot$ corresponds to the (fixed) planetocentric orbit of the Sun. Our study is performed in the restricted three-body problem, where the satellites are considered as massless particles around a massive planet and perturbed by the Sun. Depending on the initial conditions, the resonance presents a diversity of possible resonant modes, including librations of $theta$ around zero (as found for Sinope and Pasiphae) or 180 degrees, as well as asymmetric librations (e.g. Narvi). Symmetric modes are present in all giant planets, although each regime appears restricted to certain values of the satellite inclination. Asymmetric solutions, on the other hand, seem absent around Neptune due to its almost circular heliocentric orbit. Simulating the effects of a smooth orbital migration on the satellite, we find that the resonance lock is preserved as long as the induced change in semimajor axis is much slower compared to the period of the resonant angle (adiabatic limit). However, the librational mode may vary during the process, switching between symmetric and asymmetric oscillations. Finally, we present a simple scaling transformation that allows to estimate the resonant structure around any giant planet from the results calculated around a single primary mass.
Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde co-orbital asteroid of Jupiter, 2015 BZ509 is confirmed to be in a long-term stable retrograde 1:1 mean motion resonance with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this paper, we investigate the phase-space structure of the retrograde 1:1 resonance in detail within the framework of the circular restricted three-body problem. We construct a simple integrable approximation for the planar retrograde resonance using canonical contact transformation and numerically employ the averaging procedure in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We thoroughly analyze all possible librations in the co-orbital region and uncover a new apocentric libration for the retrograde 1:1 resonance inside the planets orbit. We also observe the significant jumps in orbital elements for outer and inner apocentric librations, which are caused by close encounters with the perturber.
We present a three-species (H$^+$, O$^+$ and e$^-$) multi-fluid magnetohydrodynamic (MHD) model, endowed with the requisite upper atmospheric chemistry, that is capable of accurately quantifying the magnitude of oxygen ion losses from Earth-like exoplanets in habitable zones, whose magnetic and rotational axes are roughly coincidental with one another. We apply this model to investigate the role of planetary obliquity in regulating atmospheric losses from a magnetic perspective. For Earth-like exoplanets orbiting solar-type stars, we demonstrate that the dependence of the total atmospheric ion loss rate on the planetary (magnetic) obliquity is relatively weak; the escape rates are found to vary between $2.19 times 10^{26}$ s$^{-1}$ to $2.37 times 10^{26}$ s$^{-1}$. In contrast, the obliquity can influence the atmospheric escape rate ($sim$ $10^{28}$ s$^{-1}$) by more than a factor of $2$ (or $200%$) in the case of Earth-like exoplanets orbiting late-type M-dwarfs. Thus, our simulations indicate that planetary obliquity may play a weak-to-moderate role insofar as the retention of an atmosphere (necessary for surface habitability) is concerned.
We present observations of the Rossiter-McLaughlin effect for two exoplanetary systems, revealing the orientations of their orbits relative to the rotation axes of their parent stars. HAT-P-4b is prograde, with a sky-projected spin-orbit angle of lambda = -4.9 +/- 11.9 degrees. In contrast, HAT-P-14b is retrograde, with lambda = 189.1 +/- 5.1 degrees. These results conform with a previously noted pattern among the stellar hosts of close-in giant planets: hotter stars have a wide range of obliquities and cooler stars have low obliquities. This, in turn, suggests that three-body dynamics and tidal dissipation are responsible for the short-period orbits of many exoplanets. In addition, our data revealed a third body in the HAT-P-4 system, which could be a second planet or a companion star.
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