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Register a new userDeparture from the Exact Location of Mean Motion Resonances Induced by the Gas Disk in the Systems Observed by Kepler
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The statistical results of transiting planets show that there are two peaks around 1.5 and 2.0 in the distribution of orbital period ratios. A large number of planet pairs are found near the exact location of mean motion resonances (MMRs). In this work, we find out that the depletion and structures of gas disk play crucial roles in driving planet pairs out of exact location of MMRs. Under such scenario, planet pairs are trapped into exact MMRs during orbital migration firstly and keep migrating in a same pace. The eccentricities can be excited. Due to the existence of gas disk, eccentricities can be damped leading to the change of orbital period. It will make planet pairs depart from the exact location of MMRs. With depletion timescales larger than 1 Myr, near MMRs configurations are formed easily. Planet pairs have higher possibilities to escape from MMRs with higher disk aspect ratio. Additionally, with weaker corotation torque, planet pairs can depart farther from exact location of MMRs. The final location of the innermost planets in systems are directly related to the transition radius from optically thick region to inner optically thin disk. While the transition radius is smaller than 0.2 AU at the late stage of star evolution process, the innermost planets can reach around 10 days. Our formation scenario is a possible mechanism to explain the formation of near MMRs configuration with the innermost planet farther than 0.1 AU.
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This paper focuses on two-planet systems in a first-order $(q+1):q$ mean motion resonance and undergoing type-I migration in a disc. We present a detailed analysis of the resonance valid for any value of $q$. Expressions for the equilibrium eccentricities, mean motions and departure from exact resonance are derived in the case of smooth convergent migration. We show that this departure, not assumed to be small, is such that period ratio normally exceeds, but can also be less than, $ (q+1)/q.$ Departure from exact resonance as a function of time for systems starting in resonance and undergoing divergent migration is also calculated. We discuss observed systems in which two low mass planets are close to a first-order resonance. We argue that the data are consistent with only a small fraction of the systems having been captured in resonance. Furthermore, when capture does happen, it is not in general during smooth convergent migration through the disc but after the planets reach the disc inner parts. We show that although resonances may be disrupted when the inner planet enters a central cavity, this alone cannot explain the spread of observed separations. Disruption is found to result in either the system moving interior to the resonance by a few percent, or attaining another resonance. We postulate two populations of low mass planets: a small one for which extensive smooth migration has occurred, and a larger one that formed approximately in-situ with very limited migration.
We present preliminary though statistically significant evidence that shows that multiplanetary systems that exhibit a 2/1 period commensurability are in general younger than multiplanetary systems without commensurabilities, or even systems with other commensurabilities. An immediate possible conclusion is that the 2/1 mean-motion resonance in planetary systems, tends to be disrupted after typically a few Gyrs.
Exoplanet systems with multiple planets in mean motion resonances have often been hailed as a signpost of disk driven migration. Resonant chains like Kepler-223 and Kepler-80 consist of a trio of planets with the three-body resonant angle librating and/or with a two-body resonant angle librating for each pair. Here we investigate whether close-in super-Earths and mini-Neptunes forming in situ can lock into resonant chains due to dissipation from a depleted gas disk. We simulate the giant impact phase of planet formation, including eccentricity damping from a gaseous disk, followed by subsequent dynamical evolution over tens of millions of years. In a fraction of simulated systems, we find that planets naturally lock into resonant chains. These planets achieve a chain of near-integer period ratios during the gas disk stage, experience eccentricity damping that captures them into resonance, stay in resonance as the gas disk dissipates, and avoid subsequent giant impacts, eccentricity excitation, and chaotic diffusion that would dislodge the planets from resonance. Disk conditions that enable planets to complete their formation during the gas disk stage enable those planets to achieve tight period ratios <= 2 and, if they happen to be near integer period ratios, lock into resonance. Using the weighting of different disk conditions deduced by MacDonald et al. (2020) and forward modeling Kepler selection effects, we find that our simulations of in situ formation via oligarchic growth lead to a rate of observable trios with integer period ratios and librating resonant angles comparable to observed Kepler systems.
Recent studies claimed that planets around the same star have similar sizes and masses and regular spacings, and that planet pairs usually show ordered sizes such that the outer planet is usually the larger one. Here I show that these patterns can be largely explained by detection biases. The emph{Kepler} planet detections are set by the transit signal-to-noise ratio (S/N). For different stellar properties and orbital period values, the same S/N corresponds to different planetary sizes. This variation in the detection threshold naturally leads to apparent correlations in planet sizes and the observed size ordering. The apparently correlated spacings, measured in period ratios, between adjacent planet pairs in systems with at least three detected planets are partially due to the arbitrary upper limit that the earlier study imposed on the period ratio, and partially due to the varying stability threshold for different planets. After these detection biases are taken into account, we do not find strong evidence for the so-called intra-system uniformity or the size ordering effect. Instead, the physical properties of emph{Kepler} planets are largely independent of the properties of their siblings and the parent star. It is likely that the dynamical evolution has erased the memory of emph{Kepler} planets about their initial formation conditions. In other words, it will be difficult to infer the initial conditions from the observed properties and the architecture of emph{Kepler} planets.
Mean motion resonances [MMRs] play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system as well as exo-planetary systems. Most previous theoretical analyses have focused on the low-to-moderate eccentricity regime, but with new discoveries of high eccentricity resonant minor planets and even exoplanets, there is increasing motivation to examine MMRs in the high eccentricity regime. Here we report on a study of the high eccentricity regime of MMRs in the circular planar restricted three-body problem. Non-perturbative numerical analyses of the 2:1 and the 3:2 interior resonances are carried out for a wide range of secondary-to-primary mass ratio, and for a wide range of eccentricity of the test particle. The surface-of-section technique is used to study the phase space structure near resonances. We identify transitions in phase space at certain critical eccentricities related to the geometry of resonant orbits; new stable libration zones appear at high eccentricity at libration centers shifted from those at low eccentricities. We present novel results on the mass and eccentricity dependence of the resonance libration centers and their widths in semi-major axis. Our results show that MMRs have sizable libration zones at high eccentricities, comparable to those at lower eccentricities.
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