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Register a new userLarge eccentricity, low mutual inclination: the three-dimensional architecture of a hierarchical system of giant planets
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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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Measuring the geometry of multi-planet extrasolar systems can provide insight into their dynamical history and the processes of planetary formation. Such measurements are challenging for systems detected through indirect techniques such as radial velocity and transit, having only been measured for a handful of systems to-date. We aimed to place constraints on the orbital geometry of the outer planet in the $pi$ Mensae system, a G0V star at 18.3 pc host to a wide-orbit super-jovian ($Msin i = 10.02pm0.15$ $M_{rm Jup}$) with a 5.7-year period and an inner transiting super-earth ($M=4.82pm0.85$ $M_oplus$) with a 6.3-d period. We combined astrometric measurements from the Hipparcos and Gaia satellites with a precisely determined spectroscopic orbit in an attempt to constrain the inclination of the orbital plane of the outer planet. We measured an inclination of $i_b=49.9_{-4.5}^{+5.3}$ deg for the orbital plane of $pi$ Mensae b, leading to a direct measurement of its mass of $13.01_{-0.95}^{+1.03}$ $M_{rm Jup}$. We found a significant mutual inclination between the orbital planes of the two planets; a 95% credible interval for $i_{rm mut}$ of between $34.5^circ$ and $140.6^circ$ after accounting for the unknown position angle of the orbit of $pi$ Mensae c, strongly excluding a co-planar scenario for the two planets within this system. All orbits are stable in the present-day configuration, and secular oscillations of planet cs eccentricity are quenched by general relativistic precession. Planet c may have undergone high eccentricity tidal migration triggered by Kozai-Lidov cycles, but dynamical histories involving disk migration or in situ formation are not ruled out. Nonetheless, this system provides the first direct evidence that giant planets with large mutual inclinations have a role to play in the origins and evolution of some super-Earth systems.
We examine the gas circulation near a gap opened by a giant planet in a protoplanetary disk. We show with high resolution 3D simulations that the gas flows into the gap at high altitude over the mid-plane, at a rate dependent on viscosity. We explain this observation with a simple conceptual model. From this model we derive an estimate of the amount of gas flowing into a gap opened by a planet with Hill radius comparable to the scale-height of a layered disk (i. e. a disk with viscous upper layer and inviscid midplane). Our estimate agrees with modern MRI simulations(Gressel et al., 2013). We conclude that gap opening in a layered disk can not slow down significantly the runaway gas accretion of Saturn to Jupiter-mass planets.
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.
In the last few years, the so-called Nice model has got a significant importance in the study of the formation and evolution of the solar system. According to this model, the initial orbital configuration of the giant planets was much more compact than the one we observe today. We study the formation of the giant planets in connection with some parameters that describe the protoplanetary disk. The aim of this study is to establish the conditions that favor their simultaneous formation in line with the initial configuration proposed by the Nice model. We focus in the conditions that lead to the simultaneous formation of two massive cores, corresponding to Jupiter and Saturn, able to achieve the cross-over mass (where the mass of the envelope of the giant planet equals the mass of the core, and gaseous runway starts) while Uranus and Neptune have to be able to grow to their current masses. We compute the in situ planetary formation, employing the numerical code introduced in our previous work, for different density profiles of the protoplanetary disk. Planetesimal migration is taken into account and planetesimals are considered to follow a size distribution between $r_p^{min}$ (free parameter) and $r_p^{max}= 100$ km. The cores growth is computed according to the oligarchic growth regime. The simultaneous formation of the giant planets was successfully completed for several initial conditions of the disk. We find that for protoplanetary disks characterized by a power law ($Sigma propto r^{-p}$), smooth surface density profiles ($p leq 1.5$) favor the simultaneous formation. However, for steep slopes ($psim 2$, as previously proposed by other authors) the simultaneous formation of the solar system giant planets is unlikely ...
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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