A diversity of resonance configurations may be formed under different migration of two giant planets. And the researchers show that the HD 128311 and HD 73526 planetary systems are involved in a 2:1 mean motion resonance but not in apsidal corotation, because one of the resonance argument circulates over the dynamical evolution. In this paper, we investigate potential mechanisms to form the 2:1 librating-circulating resonance configuration.
In the late stage of planetary formation, scattering or colliding among planetesimals and planetary embryos can frequently occur. Hence, in our model, we consider a planetary configuration of two giants together with few terrestrial planets. We find that both colliding or scattering events at very early stage of dynamical evolution can influence the configurations trapped into resonance. A planet-planet scattering of a moderate terrestrial planet, or multiple scattering of smaller planets in a crowded planetary system can change the resonant configuration. In addition, collision or merging can alter the masses and location of the giant planets, which also play an important role in shaping the resonant configuration during the dynamical evolution. In this sense, the librating-circulating resonance configuration is more likely to form by a hybrid mechanism of scattering and collision.
We study the orbital evolution of a three planet system with masses in the super-Earth regime resulting from the action of tides on the planets induced by the central star which cause orbital circularization. We consider systems either in or near to a three body commensurability for which adjacent pairs of planets are in a first order commensurability. We develop a simple analytic solution, derived from a time averaged set of equations, that describes the expansion of the system away from strict commensurability as a function of time, once a state where relevant resonant angles undergo small a…
We present six years of new radial-velocity data from the Anglo-Australian and Magellan Telescopes on the HD 73526 2:1 resonant planetary system. We investigate both Keplerian and dynamical (interacting) fits to these data, yielding four possible configurations for the system. The new data now show that both resonance angles are librating, with amplitudes of 40 degrees and 60 degrees, respectively. We then perform long-term dynamical stability tests to differentiate these solutions, which only differ significantly in the masses of the planets. We show that while there is no clearly preferred s…
Resonant chains are groups of planets for which each pair is in resonance, with an orbital period ratio locked at a rational value (2/1, 3/2, etc.). Such chains naturally form as a result of convergent migration of the planets in the proto-planetary disk. In this article, I present an analytical model of resonant chains of any number of planets. Using this model, I show that a system captured in a resonant chain can librate around several possible equilibrium configurations. The probability of capture around each equilibrium depends on how the chain formed, and especially on the order in which…
The multi-planetary system HD128311 hosts at least two planets. Its dynamical formation history has been studied extensively in the literature. We reanalyse the latest radial velocity data for this system with the affine-invariant Markov chain Monte Carlo sampler EMCEE. Using the high order integrator IAS15, we perform a fully dynamical fit, allowing the planets to interact during the sampling process. A stability analysis using the MEGNO indicator reveals that the system is located in a stable island of the parameter space. In contrast to a previous study, we find that the system is locked in…
We present an updated analysis of radial velocity data of the HD 82943 planetary system based on 10 years of measurements obtained with the Keck telescope. Previous studies have shown that the HD 82943 system has two planets that are likely in 2:1 mean-motion resonance (MMR), with the orbital periods about 220 and 440 days (Lee et al. 2006). However, alternative fits that are qualitatively different have also been suggested, with two planets in a 1:1 resonance (Gozdziewski & Konacki 2006) or three planets in a Laplace 4:2:1 resonance (Beauge et al. 2008). Here we use \c{hi}2 minimization combi…
We investigate the dynamical stability of the Kepler-60 planetary system with three super-Earths. We first determine their orbital elements and masses by Transit Timing Variation (TTV) data spanning quarters Q1-Q16 of the KEPLER mission. The system is dynamically active but the TTV data constrain masses to ~4 Earth masses and orbits in safely wide stable zones. The observations prefer two types of solutions. The true three-body Laplace MMR exhibits the critical angle librating around 45 degrees and aligned apsides of the inner and outer pair of planets. In the Laplace MMR formed through a chai…
Spin-orbit coupling is often described in the "MacDonald torque" approach which has become the textbook standard. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (1964; Rev. Geophys. 2, 467), is combined with an assumption that the Q factor is frequency-independent (i.e., that the geometric lag angle is constant in time). This makes the approach unphysical because MacDonald's derivation of the said formula was implicitly based on keeping the time lag frequency-independent, which is equivalent to setting Q to scale as the inverse tidal frequency…
We present evidence for a new two-planet system around the giant star HD202696 (= HIP105056, BD+26 4118). The discovery is based on public HIRES radial velocity measurements taken at Keck Observatory between July 2007 and September 2014. We estimate a stellar mass of 1.91$^{+0.09}_{-0.14}M_\odot$ for HD202696, which is located close to the base of the red giant branch. A two-planet self-consistent dynamical modeling MCMC scheme of the radial velocity data followed by a long-term stability test suggests planetary orbital periods of $P_{\rm b}$ = 517.8$_{-3.9}^{+8.9}$ days and $P_{\rm c}$ = 946.…
Using numerical integrations, we find that the orbital eccentricity of Saturn's moon Iapetus undergoes prominent multi-Myr oscillations. We identify the responsible resonant argument to be $\varpi-\varpi_{g5}+Ω-Ω_{eq}$, with the terms being the longitudes of pericenter of Iapetus and planetary secular mode $g_5$, Iapetus's longitude of the node and Saturn's equinox. We find that this argument currently (on a $10^7$~yr timescale) appears to librate with a very large amplitude. On longer timescales, the behavior of this resonant angle is strongly dependent on the resonant interaction between Sat…
Resonant planetary systems contain at least one planet pair with orbital periods librating at a near-integer ratio (2/1, 3/2, 4/3, etc.) and are a natural outcome of standard planetary formation theories. Systems with multiple adjacent resonant pairs are known as resonant chains and can exhibit three-body resonances -- characterized by a critical three-body angle. Here we study three-body angles as a diagnostic of resonant chains through tidally-damped N-body integrations. For each combination of the 2:1, 3:2, 4:3, and 5:4 mean motion resonances (the most common resonances in the known resonan…
Convergent disk migration has long been suspected to be responsible for forming planetary systems with a chain of mean-motion resonances (MMR). Dynamical evolution over time could disrupt the delicate resonant configuration. We present TOI-1136, a 700-Myr-old G star hosting at least 6 transiting planets between $\sim$2 and 5 $R_\oplus$. The orbital period ratios deviate from exact commensurability by only $10^{-4}$, smaller than the $\sim$\,$10^{-2}$ deviations seen in typical Kepler near-resonant systems. A transit-timing analysis measured the masses of the planets (3-8$M_\oplus$) and demonst…
We present simulations of low-mass planet--disc interactions in inviscid three-dimensional discs. We show that a wind-driven laminar accretion flow through the surface layers of the disc does not significantly modify the migration torque experienced by embedded planets. More importantly, we find that 3D effects lead to a dramatic change in the behaviour of the dynamical corotation torque compared to earlier 2D theory and simulations. Although it was previously shown that the dynamical corotation torque could act to slow and essentially stall the inward migration of a low-mass planet, our resul…
Resonant Super-Earths Dancing With EKL Oscillations: TTV Phase Excitation and Resonance Disruption by EKL Interactions between a Cold Jupiter and Stellar Companion
Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Center for Relativistic Astrophysics, School of Physics, Georgia Institute of Technology（佐治亚理工学院物理学院相对论天体物理中心）
We report on the discovery and characterisation of three planets orbiting the F8 star HD~28109, which sits comfortably in \tess's continuous viewing zone. The two outer planets have periods of $\rm 56.0067 \pm 0.0003~days$ and $\rm 84.2597_{-0.0008}^{+0.0010}~days$, which implies a period ratio very close to that of the first-order 3:2 mean motion resonance, exciting transit timing variations (TTVs) of up to $\rm 60\,mins$. These two planets were first identified by \tess, and we identified a third planet in the \textcolor{black}{\tess photometry} with a period of $\rm 22.8911 \pm 0.0004~days$…
Kepler has discovered hundreds of systems with multiple transiting exoplanets which hold tremendous potential both individually and collectively for understanding the formation and evolution of planetary systems. Many of these systems consist of multiple small planets with periods less than ~50 days known as Systems with Tightly-spaced Inner Planets, or STIPs. One especially intriguing STIP, Kepler-80 (KOI-500), contains five transiting planets: f, d, e, b, and c with periods of 1.0, 3.1, 4.6, 7.1, 9.5 days, respectively. We provide measurements of transit times and a transit timing variation …
Dynamical analysis of the 5:1 mean-motion resonance of the HD 202206 system
The University of Hong Kong（香港大学）；Hong Kong Institute for Astronomy and Astrophysics（香港天文与天体物理研究所）；Landessternwarte, Zentrum für Astronomie der Universität Heidelberg（海德堡大学州立天文台天文学中心）；Sofia University “St Kliment Ohridski”（索菲亚大学“圣克利门特奥赫里德斯基”）；Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences（保加利亚科学院天文学研究所与国家天文台）
We present radial-velocity (RV) measurements for the K giant $ν$ Oph (= HIP88048, HD163917, HR6698), which reveal two brown dwarf companions with a period ratio close to 6:1. For our orbital analysis we use 150 precise RV measurements taken at Lick Observatory between 2000 and 2011, and we combine them with RV data for this star available in the literature. Using a stellar mass of $M = 2.7\,M_\odot$ for $ν$ Oph and applying a self-consistent N-body model we estimate the minimum dynamical companion masses to be $m_1\sin i \approx 22.2\,M_{\mathrm{Jup}}$ and $m_2\sin i \approx 24.7\,M_{\mathrm{J…
TOI-4495: A Pair of Aligned, Near-Resonant Sub-Neptunes that Likely Experienced Overstable Migration
Institute for Astronomy, University of Hawai‘i（夏威夷大学天体物理研究所）；School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education（教育部现代天文与天体物理重点实验室）；Department of Earth and Space Science, Osaka University（大阪大学地球宇宙科学系）；Department of Astronomy, California Institute of Technology（加州理工学院天文系）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Department of Astronomy, University of California Berkeley（加州大学伯克利分校天文系）；Centre for Astrophysics, University of Southern Queensland（南昆士兰大学天体物理中心）
