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Register a new userThe Dynamics of Neptune Trojan: I. the Inclined Orbits
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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.
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We evaluate the orbital evolution and several plausible origins scenarios for the mutually inclined orbits of Upsilon Andromedae c and d. These two planets have orbital elements that oscillate with large amplitudes and lie close to the stability boundary. This configuration, and in particular the observed mutual inclination, demands an explanation. The planetary system may be influenced by a nearby low-mass star, Upsilon And B, which could perturb the planetary orbits, but we find it cannot modify two coplanar orbits into the observed mutual inclination of ~30 deg. However, it could incite ejections or collisions between planetary companions that subsequently raise the mutual inclination to >30 deg. Our simulated systems with large mutual inclinations tend to be further from the stability boundary than Upsilon And, but we are able to produce similar systems. We conclude that scattering is a plausible mechanism to explain the observed orbits of Upsilon And c and d, but we cannot determine whether the scattering was caused by instabilities among the planets themselves or by perturbations from Upsilon And B. We also develop a procedure to quantitatively compare numerous properties of the observed system to our numerical models. Although we only implement this procedure to Upsilon And, it may be applied to any exoplanetary system.
We report integrated orbital fits for the inner regular moons of Neptune based on the most complete astrometric data set to date, with observations from Earth-based telescopes, Voyager 2, and the Hubble Space Telescope covering 1981-2016. We summarize the results in terms of state vectors, mean orbital elements, and orbital uncertainties. The estimated masses of the two innermost moons, Naiad and Thalassa, are $GM_{Naiad}$= 0.0080 $pm$ 0.0043 $km^3 s^{-2}$ and $GM_{Thalassa}$=0.0236 $pm$ 0.0064 $km^3 s^{-2}$, corresponding to densities of 0.80 $pm$ 0.48 $g cm^{-3}$ and 1.23 $pm$ 0.43 $g cm^{-3}$, respectively. Our analysis shows that Naiad and Thalassa are locked in an unusual type of orbital resonance. The resonant argument 73 $dot{lambda}_{Thalassa}$-69 $dot{lambda}_{Naiad}$-4 $dot{Omega}_{Naiad}$ $approx$ 0 librates around 180 deg with an average amplitude of ~66 deg and a period of ~1.9 years for the nominal set of masses. This is the first fourth-order resonance discovered between the moons of the outer planets. More high precision astrometry is needed to better constrain the masses of Naiad and Thalassa, and consequently, the amplitude and the period of libration. We also report on a 13:11 near-resonance of Hippocamp and Proteus, which may lead to a mass estimate of Proteus provided that there are future observations of Hippocamp. Our fit yielded a value for Neptunes oblateness coefficient of $J_2$=3409.1$pm$2.9 $times 10^{-6}$.
The so-called dipper stars host circumstellar disks and have optical and infrared light curves that exhibit quasi-periodic or aperiodic dimming events consistent with extinction by transiting dusty structures orbiting in the inner disk. Most of the proposed mechanisms explaining the dips---i.e., occulting disk warps, vortices, and forming planetesimals---assume nearly edge-on viewing geometries. However, our analysis of the three known dippers with publicly available resolved sub-mm data reveals disks with a range of inclinations, most notably the face-on transition disk J1604-2130 (EPIC 204638512). This suggests that nearly edge-on viewing geometries are not a defining characteristic of the dippers and that additional models should be explored. If confirmed by further observations of more dippers, this would point to inner disk processes that regularly produce dusty structures far above the outer disk midplane in regions relevant to planet formation.
We study the interaction between massive planets and a gas disc with a mass in the range expected for protoplanetary discs. We use SPH simulations to study the orbital evolution of a massive planet as well as the dynamical response of the disc for planet masses between 1 and $6 rmn{M_J}$ and the full range of initial relative orbital inclinations. Gap formation can occur for planets in inclined orbits. For given planet mass, a threshold relative orbital inclination exists under which a gap forms. At high relative inclinations, the inclination decay rate increases for increasing planet mass and decreasing initial relative inclination. For an initial semi-major axis of 5 AU and relative inclination of $i_0=80^circ,$ the times required for the inclination to decay by $10^circ$ is $sim10^{6} rmn{yr}$ and $sim10^{5} rmn{yr}$ for $1 rmn{M_J}$ and $6 rmn{M_J}$. Planets on inclined orbits warp the disc by an extent that is negligible for $1 rmn{M_J}$ but increases with increasing mass becoming quite significant for a planet of mass $6 rmn{M_J}$. We also find a solid body precession of both the total disc angular momentum vector and the planet orbital momentum vector about the total angular momentum vector. Our results illustrate that the influence of an inclined massive planet on a protoplanetary disc can lead to significant changes of the disc structure and orientation which can in turn affect the orbital evolution of the planet significantly.
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of its host stars and on the dynamical properties of the planetary orbit. The trajectory of a planet in a double star system can be determined, approximating stars and planets with point masses, by solving numerically the equations of motion of the classical three-body system. In this study, we analyze a large data set of planetary orbits, made up with high precision long integration at varying: the mass of the planet, its distance from the primary star, the mass ratio for the two stars in the binary system, and the eccentricity of the star motion. To simulate the gravitational dynamics, we use a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term integration. In our data analysis, we evaluate if an orbit is stable or not and also provide the statistics of different types of instability: collisions with the primary or secondary star and planets ejected away from the binary star system. Concerning the stability, we find a significant number of orbits that are only marginally stable, according to the classification introduced by Musielak et al. 2005. For planets of negligible mass, we estimate the critical semi-major axis $a_c$ as a function of the mass ratio and the eccentricity of the binary, in agreement with the results of Holman and Wiegert 1999. However, we find that for very massive planets (Super-Jupiters) the critical semi-major axis decrease in some cases by a few percent, compared to cases in which the mass of the planet is negligible.
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