The presence of mean-motion resonances (MMRs) in exoplanetary systems is a new exciting field of celestial mechanics which motivates us to consider this work to study the dynamical behaviour of exoplanetary systems by time evolution of the orbital elements of the planets. Mainly, we study the influence of planetary perturbations on semimajor axis and eccentricity. We identify $(r+1):r$ MMR terms in the expression of disturbing function and obtain the perturbations from the truncated disturbing function. Using the expansion of the disturbing function of three-body problem and an analytical approach, we solve the equations of motion. The solution which is obtained analytically is compared with that of obtained by numerical method to validate our analytical result. In this work, we consider three exoplanetary systems namely Kepler-62, HD 200964 and Kepler-11. We have plotted the evolution of the resonant angles and found that they librate around constant value. In view of this, our opinion is that two planets of each system Kepler-62, HD 200964 and Kepler-11 are in 2:1, 4:3 and 5:4 mean motion resonances, respectively.
Keywords:astrometry - celestial mechanics - planetary systems.
Observations of exoplanetary systems provide clues about the intrinsic distribution of planetary systems, their architectures, and how they formed. We develop a forward modelling framework for generating populations of planetary systems and "observed" catalogues by simulating the Kepler detection pipeline (SysSim). We compare our simulated catalogues to the Kepler DR25 catalogue of planet candidates, updated to include revised stellar radii from Gaia DR2. We constrain our model based on the observed 1D marginal distributions of orbital periods, period ratios, transit depths, transit depth rati…
In favourable conditions, the density of transiting planets in multiple systems can be determined from photometry data alone. Dynamical information can be extracted from light curves, providing modelling is done self-consistently, i.e. using a photodynamical model, which simulates the individual photometric observations instead of the more generally used transit times. We apply this methodology to the Kepler-138 planetary system. The derived planetary bulk densities are a factor of 2 more precise than previous determinations, and we find a discrepancy in the stellar bulk density with respect t…
The measurement of an exoplanet's oblateness and obliquity provides insights into the planet's internal structure and formation history. Previous work using small differences in the shape of the transit light curve has been moderately successful, but was hampered by the small signal and extreme photometric precision required. The measurement of changes in transit depth, caused by the spin precession of an oblate planet, was proposed as an alternative method. Here, we present the first attempt to measure these changes. Using Kepler photometry, we examined the brown dwarf Kepler-39b and the warm…
We propose several descriptive measures to characterize the arrangements of planetary masses, periods, and mutual inclinations within exoplanetary systems. These measures are based in complexity theory and capture the global, system-level trends of each architecture. Our approach considers all planets in a system simultaneously, facilitating both intra-system and inter-system analysis. We find that based on these measures, Kepler's high-multiplicity ($N\geq3$) systems can be explained if most systems belong to a single intrinsic population, with a subset of high-multiplicity systems ($\sim20\%…
We investigate the origins of Kepler-419, a peculiar system hosting two nearly coplanar and highly eccentric gas giants with apsidal orientations librating around anti-alignment, and use this system to place constraints on the properties of their birth protoplanetary disk. We follow the proposal by Petrovich, Wu, & Ali-Dib (2019) that these planets have been placed on these orbits as a natural result of the precessional effects of a dissipating massive disk and extend it by using direct N-body simulations and models for the evolution of the gas disks, including photoevaporation. Based on a par…
$\bf{Context}$. We investigate the validity of the claim that invokes two extreme exoplanetary system candidates around the pulsating B-type subdwarfs KIC 10001893 and KIC 5807616 from the primary $\it{Kepler}$ field. $\bf{Aims}$. Our goal was to find characteristics and the source of weak signals that are observed in these subdwarf light curves. $\bf{Methods}$. To achieve this, we analyzed short- and long-cadence $\it{Kepler}$ data of the two stars by means of a Fourier transform and compared the results to Fourier transforms of simulated light curves to which we added exoplanetary signals. T…
The Kepler mission observed thousands of transiting exoplanet candidates around hundreds of thousands of FGK dwarf stars. He, Ford, & Ragozzine (2019) (arXiv:1907.07773) applied forward modeling to infer the distribution of intrinsic architectures of planetary systems, developed a clustered Poisson point process model for exoplanetary systems (SysSim) to reproduce the marginal distributions of the observed Kepler population, and they showed that orbital periods and planet radii are clustered within a given planetary system. Here, we extend the clustered model to explore correlations between pl…
Architectures of Exoplanetary Systems. IV: A Multi-planet Model for Reproducing the Radius Valley and Intra-system Size Similarity of Planets around Kepler's FGK Dwarfs
NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Penn State University（宾夕法尼亚州立大学）
In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we determine also the extent and rate of the chaotic diffusion as well as the characteristi…
Exomoons are a missing piece of exoplanetary science. Recently, two promising candidates were proposed, Kepler-1625 b-I and Kepler-1708 b-I. While the latter still lacks a dynamical analysis of its stability, Kepler-1625 b-I has already been the subject of several studies regarding its stability and origin. Moreover, previous works have shown that this satellite system could harbour at least two stable massive moons. Motivated by these results, we explored the stability of co-orbital exomoons using the candidates Kepler-1625 b-I and Kepler-1708 b-I as case studies. To do so, we performed numer…
TRADES: A new software to derive orbital parameters from observed transit times and radial velocities. Revisiting Kepler-11 and Kepler-9
目的。为了从观测数据中确定系外行星系统的轨道参数，我们开发了一个名为TRADES（TRAnsits and Dynamics of Exoplanetary Systems）的软件，可以同时拟合观测到的径向速度和凌日时间数据。方法.我们实现了一个N体系统的动力学模拟器，它也适合在轨道集成过程中的可用数据，并确定最佳的轨道参数组合，使用网格搜索，$χ^2$最小化，遗传算法，粒子群优化，和引导分析。结果为了验证TRADES，我们在合成三体系统和开普勒任务发现的两个真实系统上测试了代码：开普勒-9和开普勒-11。这些系统是测试多个系外行星系统的良好基准，这些系统由于行星之间的引力相互作用而显示出过境时间变化（TTV）。我们发现开普勒-11行星的轨道参数与发现论文中提出的值以及同一作者最近的工作非常一致。我们分析了Kepler-9系统的前三个季度，发现与发现论文部分一致的参数。分析涵盖开普勒数据的12个季度的过境时间（T0），我们已经找到了一个新的最佳拟合解决方案。该解决方案输出的质量约为发现论文中提出的值的55%;这导致径向速度的半幅值降低约为12.80 m/s。
Previous works focused on exoplanets discovered with the radial velocity (RV) method reported an anti-correlation between the orbital eccentricities of the exoplanets and the multiplicity M (i.e., number of planets) of their system. We further investigate this reported anti-correlation here using a dataset comprising exoplanets discovered with both the RV and transit methods, searching for hints of its causes by exploring the connection between the number of planets and the dynamical state of the exosystems. To examine the correlation between multiplicity and orbital eccentricity, for every mu…
Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique opportunities to study orbital dynamics in compact environments and the subsequent evolution of orbital parameters. One of the compact {\it Kepler} systems is Kepler-89; a system for which the radial velocity follow-up observations place strong upper limits on the masses of the planets and their Keplerian orbital elements. The potential for non-circular orbits i…
The Kepler space mission has detected a large number of exoplanets in multiple transiting planet systems. Previous studies found that these Kepler multiple planet systems exhibit an intra-system uniformity, namely planets in the same system have similar sizes and correlated orbital spacings. However, it is important to consider the possible role of selection effects due to observational biases. In this paper, we revisit the orbital spacing aspect of the pattern after taking observational biases into account using a forward modeling method. We find that orbital spacings, in terms of period rati…
Based on the model described in Ramos et al., 2017, we present an analytical+numerical study of the resonance capture under Type-I migration for the Kepler-25 (Marcy et al., 2014) and K2-24 (Petigura et al., 2016) Kepler systems, both close to a 2/1 mean-motion resonance. We find that, depending on the flare index and the proximity to the central star, the average value of the period-ratio between two consecutive planets show a significant deviation with respect to the resonant nominal value, up to values well in agreement with the observations.
Many multiple-planet systems have been found by the Kepler transit survey and various radial velocity (RV) surveys. Kepler planets show an asymmetric feature, namely, there are small but significant deficits/excesses of planet pairs with orbital period spacing slightly narrow/wide of the exact resonance, particularly near the first order mean motion resonance (MMR), such as 2:1 and 3:2 MMR. Similarly, if not exactly the same, an asymmetric feature (pileup wide of 2:1 MMR) is also seen in RV planets, but only for massive ones. We analytically and numerically study planets' orbital evolutions ne…
We study the effect of dynamical tides associated with the excitation of gravity waves in an interior radiative region of the central star on orbital evolution in observed systems containing Hot Jupiters. We consider WASP-43, Ogle-tr-113, WASP-12, and WASP-18 which contain stars on the main sequence (MS). For these systems there are observational estimates regarding the rate of change of the orbital period. We also investigate Kepler-91 which contains an evolved giant star. We adopt the formalism of Ivanov et al. for calculating the orbital evolution. For the MS stars we determine expected rat…
Transit timing variations in eccentric hierarchical triple exoplanetary systems. I. Perturbations on the time-scale of the orbital period of the perturber
Exoplanet Transit Timing Variations (TTVs) caused by gravitational forces between planets can be used to determine planetary masses and orbital parameters. Most of the observed TTVs are small and sinusoidal in time, leading to degeneracies between the masses and orbital parameters. Here we report a TTV analysis of Kepler-90g and Kepler-90h, which exhibit large TTVs up to 25 hours. With optimization, we find a unique solution which allows us to constrain all of the orbital parameters. The best fit masses for Kepler-90g and 90h are $15.0^{+0.9}_{-0.8}$ $M_{\bigoplus}$ (Earth mass) and $203^{+5}_…
We present a model to study secularly and tidally evolving three-body systems composed by two low-mass planets orbiting a star, in the case where the bodies rotation axes are always perpendicular to the orbital plane. The tidal theory allows us to study the spin and orbit evolution of both stiff Earth-like planets and predominantly gaseous Neptune-like planets. The model is applied to study two recently-discovered exoplanetary systems containing potentially habitable exoplanets (PHE): LHS-1140 b-c and K2-18 b-c. For the former system, we show that both LHS-1140 b and c must be in nearly-circul…
Over the course of the last two decades, traditional models of planet formation have been repeatedly challenged by the emerging census of extrasolar planets. Key among them is the orbital architecture problem: while standard models of orbital migration predict resonant orbits for short-period objects, most planets do not appear to lie in orbital resonances. Here we show that the four-planet system Kepler-221, not previously recognized to have active orbital resonances, has a three-body commensurability relation unique within the Kepler sample. Using a suite of numerical experiments as well as …
As lower-mass stars often host multiple rocky planets, gravitational interactions among planets can have significant effects on climate and habitability over long timescales. Here we explore a specific case, Kepler-62f, a potentially habitable planet in a five-planet system with a K2V host star. N-body integrations reveal the stable range of initial eccentricities for Kepler-62f is $0.00 \leqslant e \leqslant 0.32$, absent the effect of additional, undetected planets. We simulate the tidal evolution of Kepler-62f in this range and find that, for certain assumptions, the planet can be locked in…
NASA's Kepler mission revealed that $\sim 30\%$ of Solar-type stars harbor planets with sizes between that of Earth and Neptune on nearly circular and co-planar orbits with periods less than 100 days. Such short-period compact systems are rarely found with planet pairs in mean-motion resonances (MMRs) -- configurations in which the planetary orbital periods exhibit a simple integer ratio -- but there is a significant overabundance of planet pairs lying just wide of the first-order resonances. Previous work suggests that tides raised on the planets by the host star may be responsible for forcin…
Although most of the circumbinary planets detected by the Kepler spacecraft are on orbits that are closely aligned with the binary orbital plane, the systems Kepler-413 and Kepler-453 exhibit small misalignments of $\sim 2.5^\circ$. One possibility is that these planets formed in a circumbinary disc whose midplane was inclined relative to the binary orbital plane. Such a configuration is expected to lead to a warped and twisted disc, and our aim is to examine the inclination evolution of planets embedded in these discs. We employed 3D hydrodynamical simulations that examine the disc response t…
Exoplanet Orbital Distribution around FGK Sun-like Host Stars I: planet occurrence rate derived from the Kepler Mission and theoretical interpretations from planet formation
University of Oslo（奥斯陆大学）；Harvard University（哈佛大学）；Natural History Museum, University of Oslo（奥斯陆大学自然历史博物馆）；Konkoly Observatory, HUN-REN CSFK（孔科利天文台，匈牙利研究网络科学院）
Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments with Dynamics (ROCKE-3D) is a 3-Dimensional General Circulation Model (GCM) developed at the NASA Goddard Institute for Space Studies for the modeling of atmospheres of Solar System and exoplanetary terrestrial planets. Its parent model, known as ModelE2 (Schmidt et al. 2014), is used to simulate modern and 21st Century Earth and near-term paleo-Earth climates. ROCKE-3D is an ongoing effort to expand the capabilities of ModelE2 to handle a broader range of atmospheric conditions including higher and lower atmospheric…
The Apache Point Observatory Galactic Evolution Experiment (APOGEE) has observed $\sim$600 transiting exoplanets and exoplanet candidates from \textit{Kepler} (Kepler Objects of Interest, KOIs), most with $\geq$18 epochs. The combined multi-epoch spectra are of high signal-to-noise (typically $\geq$100) and yield precise stellar parameters and chemical abundances. We first confirm the ability of the APOGEE abundance pipeline, ASPCAP, to derive reliable [Fe/H] and effective temperatures for FGK dwarf stars -- the primary \textit{Kepler} host stellar type -- by comparing the ASPCAP-derived stell…
Direct imaging of widely separated exoplanets from space will obtain their reflected light spectra and measure atmospheric properties. Previous calculations have shown that a change in the orbital phase would cause a spectral signal, but whether this signal may be used to characterize the atmosphere has not been shown. We simulate starshade-enabled observations of the planet 47 Uma b, using the to-date most realistic simulator SISTER to estimate the uncertainties due to residual starlight, solar glint, and exozodiacal light. We then use the Bayesian retrieval algorithm ExoReL$^\Re$ to determin…
The fields of astronomy and astrophysics are currently engaged in an unprecedented era of discovery as recent missions have revealed thousands of exoplanets orbiting other stars. While the Kepler Space Telescope mission has enabled most of these exoplanets to be detected by identifying transiting events, exoplanets often exhibit additional photometric effects that can be used to improve the characterization of exoplanets. The EXONEST Exoplanetary Explorer is a Bayesian exoplanet inference engine based on nested sampling and originally designed to analyze archived Kepler Space Telescope and CoR…
We identify a set of planetary systems observed by Kepler that merit transit timing variation (TTV) analysis given the orbital periods of transiting planets, the uncertainties for their transit times and the number of transits observed during the Kepler mission. We confirm the planetary nature of 4 KOIs within multicandidate systems. We forward model each of the planetary systems identified to determine which systems are likely to yield mass constraints that may be significantly improved upon with follow-up transit observations. We find projected TTVs diverge by more than 90 minutes after 6000…
Recent studies reveal that the free eccentricities of Kepler-34b and Kepler-413b are much larger than their forced eccentricities, implying that the scattering events may take place in their formation. The observed orbital configuration of Kepler-34b cannot be well reproduced in disk-driven migration models, whereas a two-planet scattering scenario can play a significant role of shaping the planetary configuration. These studies indicate that circumbinary planets discovered by Kepler may have experienced scattering process. In this work, we extensively investigate the scattering outcomes of ci…
Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or fur…
