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Register a new userOn the Dynamics of Inclined Neptunes Trojans
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Li-Yong Zhou Nanjingn University
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The dynamics of artificial asteroids on the Trojan-like orbits around Neptune is investigated in this paper. We describe the dependence of the orbital stability on the initial semimajor axis a and inclination i by constructing a dynamical map on the (a,i)-plane. Rich details are revealed in the dynamical map, especially a unstable gap at i=45 deg is determined and the mechanism triggering chaos in this region is figured out. Our investigation can be used to guide the observations.
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In a previous paper, we have presented a global view of the stability of Neptune Trojan (NT hereafter) on inclined orbit. We discuss in this paper the dependence of stability of NT orbits on the eccentricity. High-resolution dynamical maps are constructed using the results of extensive numerical integrations of orbits initialized on the fine grids of initial semimajor axis (a0) versus eccentricity (e0). The extensions of regions of stable orbits on the (a0, e0) plane at different inclinations are shown. The maximum eccentricities of stable orbits in three most stable regions at low (0, 12deg.), medium (22,36deg.) and high (51, 59deg.) inclination, are found to be 0.10, 0.12 and 0.04, respectively. The fine structures in the dynamical maps are described. Via the frequency analysis method, the mechanisms that portray the dynamical maps are revealed. The secondary resonances, concerning the frequency of the librating resonant angle and the frequency of the quasi 2:1 mean motion resonance between Neptune and Uranus, are found deeply involved in the motion of NTs. Secular resonances are detected and they also contribute significantly to the triggering of chaos in the motion. Particularly, the effects of the secular resonance v8, v18 are clarified. We also investigate the orbital stabilities of six observed NTs by checking the orbits of hundreds clones of them generated within the observing error bars. We conclude that four of them, except 2001 QR322 and 2005 TO74, are deeply inside the stable region. The 2001 QR322 is in the close vicinity of the most significant secondary resonance. The 2005 TO74 locates close to the boundary separating stable orbits from unstable ones, and it may be influenced by a secular resonance.
We aim to locate the stability region for Uranus Trojans (UT hereafter) and find out the dynamical mechanisms responsible for the structures in the phase space. Using the spectral number as the stability indicator, we construct the dynamical maps on the (a0, i0) plane. The proper frequencies of UTs are determined precisely so that we can depict the resonance web via a semi-analytical method. Two main stability regions are found, one each for the low-inclination (0-14deg) and high-inclination regime (32-59deg). There is also an instability strip in each of them, at 9deg and 51deg respectively. All stability regions are in the tadpole regime and no stable horseshoe orbits exist for UTs. The lack of moderate-inclined UTs is caused by the nu5 and nu7 secular resonances. The fine structures in the dynamical maps are shaped by high-degree secular resonances and secondary resonances. During the planetary migration, about 36.3% and 0.4% of the pre-formed orbits survive the fast and slow migrations (with migrating time scales of 1 and 10Myr) respectively, most of which are in high inclination. Since the low-inclined UTs are more likely to survive the age of the solar system, they make up 77% of all such long-life orbits by the end of the migration, making a total fraction up to 4.06E-3 and 9.07E-5 of the original population for the fast and slow migrations, respectively. About 3.81% UTs are able to survive the age of the solar system, among which 95.5% are on low-inclined orbits with i0<7.5deg. However, the depletion of the planetary migration seems to prevent a large fraction of such orbits, especially for the slow migration model.
The stability of Trojan type orbits around Neptune is studied. As the first part of our investigation, we present in this paper a global view of the stability of Trojans on inclined orbits. Using the frequency analysis method based on the FFT technique, we construct high resolution dynamical maps on the plane of initial semimajor axis $a_0$ versus inclination $i_0$. These maps show three most stable regions, with $i_0$ in the range of $(0^circ,12^circ), (22^circ,36^circ)$ and $(51^circ,59^circ)$ respectively, where the Trojans are most probably expected to be found. The similarity between the maps for the leading and trailing triangular Lagrange points $L_4$ and $L_5$ confirms the dynamical symmetry between these two points. By computing the power spectrum and the proper frequencies of the Trojan motion, we figure out the mechanisms that trigger chaos in the motion. The Kozai resonance found at high inclination varies the eccentricity and inclination of orbits, while the $ u_8$ secular resonance around $i_0sim44^circ$ pumps up the eccentricity. Both mechanisms lead to eccentric orbits and encounters with Uranus that introduce strong perturbation and drive the objects away from the Trojan like orbits. This explains the clearance of Trojan at high inclination ($>60^circ$) and an unstable gap around $44^circ$ on the dynamical map. An empirical theory is derived from the numerical results, with which the main secular resonances are located on the initial plane of $(a_0,i_0)$. The fine structures in the dynamical maps can be explained by these secular resonances.
Hubble (HST) spectroscopic transit observations of the temperate sub-Neptune K2-18b were interpreted as the presence of water vapour with potential water clouds. 1D modelling studies also predict the formation of water clouds at some conditions. However, such models cannot predict the cloud cover, driven by atmospheric dynamics and thermal contrasts, and thus their real impact on spectra. The main goal of this study is to understand the formation, distribution and observational consequences of water clouds on K2-18b and other temperate sub-Neptunes. We simulated the atmospheric dynamics, water cloud formation and spectra of K2-18b for H2-dominated atmosphere using a 3D GCM. We analysed the impact of atmospheric composition (with metallicity from 1*solar to 1000*solar), concentration of cloud condensation nuclei and planetary rotation rate. Assuming that K2-18b has a synchronous rotation, we show that the atmospheric circulation in the upper atmosphere essentially corresponds to a symmetric day-to-night circulation. This regime preferentially leads to cloud formation at the substellar point or at the terminator. Clouds form for metallicity >100*solar with relatively large particles. For 100-300*solar metallicity, the cloud fraction at the terminators is small with a limited impact on transit spectra. For 1000*solar metallicity, very thick clouds form at the terminator. The cloud distribution appears very sensitive to the concentration of CCN and to the planetary rotation rate. Fitting HST transit data with our simulated spectra suggests a metallicity of ~100-300*solar. In addition, we found that the cloud fraction at the terminator can be highly variable, leading to a potential variability in transit spectra. This effect could be common on cloudy exoplanets and could be detectable with multiple transit observations.
About 20% of stars in the solar vicinity are in the Hercules stream, a bundle of stars that move together with a velocity distinct from the Sun. Its origin is still uncertain. Here, we explore the possibility that Hercules is made of trojans, stars captured at L4, one the Lagrangian points of the stellar bar. Using GALAKOS--a high-resolution N-body simulation of the Galactic disk--we follow the motions of stars in the co-rotating frame of the bar and confirm previous studies on Hercules being formed by stars in co-rotation resonance with the bar. Unlike previous work, we demonstrate that the retrograde nature of trojan orbits causes the asymmetry in the radial velocity distribution, typical of Hercules in the solar vicinity. We show that trojans remain at capture for only a finite amount of time, before escaping L4 without being captured again. We anticipate that in the kinematic plane the Hercules stream will de-populate along the bar major axis and be visible at azimuthal angles behind the solar vicinity with a peak towards L4. This test can exclude the OLR origin of the Hercules stream and be validated by Gaia DR3 and DR4.
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