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Register a new userA Mechanism of Exciting Planetary Inclination and Eccentricity through a Residual Gas Disk
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Accordling to the theory of Kozai resonance, the initial mutual inclination between a small body and a massive planet in an outer circular orbit is as high as $sim39.2^{circ}$ for pumping the eccentricity of the inner small body. Here we show that, with the presence of a residual gas disk outside two planetary orbits, the inclination can be reduced as low as a few degrees. The presence of disk changes the nodal precession rates and directions of the planet orbits. At the place where the two planets achieve the same nodal processing rate, vertical secular resonance would occur so that mutual inclination of the two planets will be excited, which might trigger the Kozai resonance between the two planets further. However, in order to pump an inner Jupiter-like planet, the conditions required for the disk and the outer planet are relatively strict. We develop a set of evolution equations, which can fit the N-body simulation quite well but be integrated within a much shorter time. By scanning the parameter spaces using the evolution equations, we find that, a massive planet ($10M_J$) at 30AU with $6^o$ inclined to a massive disk ($50M_J$) can finally enter the Kozai resonance with an inner Jupiter around the snowline. And a $20^{circ}$ inclination of the outer planet is required for flipping the inner one to a retrograde orbit. In multiple planet systems, the mechanism can happen between two nonadjacent planets, or inspire a chain reaction among more than two planets. This mechanism could be the source of the observed giant planets in moderate eccentric and inclined orbits, or hot-Jupiters in close-in, retrograde orbits after tidal damping.
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We study the excitation of planet inclination by a novel secular-orbital resonance in multiplanet systems perturbed by binary companions which we call ivection. Ivection resonance happens when the nodal precession rate of the planet matches a multiple of the orbital frequency of the binary, and its physical nature is similar to the previously-studied evection resonance. Capture into an ivection resonance requires the nodal precession rate to slowly increase passed the resonant value during planet migration, and will excite the mutual inclination of the planets without affecting their eccentricities. If the system encounters another resonance (e.g., a mean-motion resonance) after being captured into an ivection resonance, resonance overlap can make the system dynamically unstable, ejecting the smaller planet. Using ivection resonance, we are able to explain why planets in Kepler-108 have significant mutual inclination but modest eccentricity. We also find a deficit of multiplanet systems which would have nodal precession period comparable to binary orbital period, suggesting that ivection resonance may inhibit the formation or destablize multiplanet systems with external binary companion.
The ubiquity of planets and diversity of planetary systems reveal planet formation encompass many complex and competing processes. In this series of papers, we develop and upgrade a population synthesis model as a tool to identify the dominant physical effects and to calibrate the range of physical conditions. Recent planet searches leads to the discovery of many multiple-planet systems. Any theoretical models of their origins must take into account dynamical interaction between emerging protoplanets. Here, we introduce a prescription to approximate the close encounters between multiple planets. We apply this method to simulate the growth, migration, and dynamical interaction of planetary systems. Our models show that in relatively massive disks, several gas giants and rocky/icy planets emerge, migrate, and undergo dynamical instability. Secular perturbation between planets leads to orbital crossings, eccentricity excitation, and planetary ejection. In disks with modest masses, two or less gas giants form with multiple super-Earths. Orbital stability in these systems is generally maintained and they retain the kinematic structure after gas in their natal disks is depleted. These results reproduce the observed planetary mass-eccentricity and semimajor axis-eccentricity correlations. They also suggest that emerging gas giants can scatter residual cores to the outer disk regions. Subsequent in situ gas accretion onto these cores can lead to the formation of distant (> 30AU) gas giants with nearly circular orbits.
The minor planets on orbits that are dynamically stable in Neptunes 1:1 resonance on Gyr timescales were likely emplaced by Neptunes outward migration. We explore the intrinsic libration amplitude, eccentricity, and inclination distribution of Neptunes stable Trojans, using the detections and survey efficiency of the Outer Solar System Origins Survey (OSSOS) and Pan-STARRS1. We find that the libration amplitude of the stable Neptunian Trojan population can be well modeled as a Rayleigh distribution with a libration amplitude width $sigma_{A_phi}$ of 15$^circ$. When taken as a whole, the Neptune Trojan population can be acceptably modeled with a Rayleigh eccentricity distribution of width $sigma_e$ of 0.045 and a typical sin(i) x Gaussian inclination distribution with a width $sigma_i$ of 14 +/- 2 degrees. However, these distributions are only marginally acceptable. This is likely because, even after accounting for survey detection biases, the known large Hr < 8 and small Hr >= 8 Neptune Trojans appear to have markedly different eccentricities and inclinations. We propose that like the classical Kuiper belt, the stable intrinsic Neptunian Trojan population have dynamically `hot and dynamically `cold components to its eccentricity/inclination distribution, with $sigma_{e-cold}$ ~ 0.02 / $sigma_{i-cold}$ ~ 6$^circ$ and $sigma_{e-hot}$~ 0.05 / $sigma_{i-hot}$ ~ 18$^circ$. In this scenario, the `cold L4 Neptunian Trojan population lacks the Hr >= 8 members and has 13 +11/-6 `cold Trojans with Hr < 8. On the other hand, the `hot L4 Neptunian Trojan population has 136 +57/-48 Trojans with Hr < 10 -- a population 2.4 times greater than that of the L4 Jovian Trojans in the same luminosity range.
We study the evolution of the eccentricity and inclination of protoplanetary embryos and low-mass protoplanets (from a fraction of an Earth mass to a few Earth masses) embedded in a protoplanetary disc, by means of three dimensional hydrodynamics calculations with radiative transfer in the diffusion limit. When the protoplanets radiate in the surrounding disc the energy released by the accretion of solids, their eccentricity and inclination experience a growth toward values which depend on the luminosity to mass ratio of the planet, which are comparable to the discs aspect ratio and which are reached over timescales of a few thousand years. This growth is triggered by the appearance of a hot, under-dense region in the vicinity of the planet. The growth rate of the eccentricity is typically three times larger than that of the inclination. In long term calculations, we find that the excitation of eccentricity and the excitation of inclination are not independent. In the particular case in which a planet has initially a very small eccentricity and inclination, the eccentricity largely overruns the inclination. When the eccentricity reaches its asymptotic value, the growth of inclination is quenched, yielding an eccentric orbit with a very low inclination. As a side result, we find that the eccentricity and inclination of non-luminous planets are damped more vigorously in radiative discs than in isothermal discs.
We establish the three-dimensional architecture of the Kepler-419 (previously KOI-1474) system to be eccentric yet with a low mutual inclination. Kepler-419b is a warm Jupiter at semi-major axis a = 0.370 +0.007/-0.006 AU with a large eccentricity e=0.85 +0.08/-0.07 measured via the photoeccentric effect. It exhibits transit timing variations induced by the non-transiting Kepler-419c, which we uniquely constrain to be a moderately eccentric (e=0.184 +/- 0.002), hierarchically-separated (a=1.68 +/- 0.03 AU) giant planet (7.3 +/- 0.4 MJup). We combine sixteen quarters of Kepler photometry, radial-velocity (RV) measurements from the HIgh Resolution Echelle Spectrometer (HIRES) on Keck, and improved stellar parameters that we derive from spectroscopy and asteroseismology. From the RVs, we measure the mass of inner planet to be 2.5+/-0.3MJup and confirm its photometrically-measured eccentricity, refining the value to e=0.83+/-0.01. The RV acceleration is consistent with the properties of the outer planet derived from TTVs. We find that, despite their sizable eccentricities, the planets are coplanar to within 9 +8/-6 degrees, and therefore the inner planets large eccentricity and close-in orbit are unlikely to be the result of Kozai migration. Moreover, even over many secular cycles, the inner planets periapse is most likely never small enough for tidal circularization. Finally, we present and measure a transit time and impact parameter from four simultaneous ground-based light curves from 1m-class telescopes, demonstrating the feasibility of ground-based follow-up of Kepler giant planets exhibiting large TTVs.
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