The Discovery of the Long-Period, Eccentric Planet Kepler-88 d and System Characterization with Radial Velocities and Photodynamical Analysis
Lauren M. Weiss, Daniel C. Fabrycky, Eric Agol, Sean M. Mills, Andrew W. Howard, Howard Isaacson, Erik A. Petigura, Benjamin J. Fulton, Lea Hirsch, Evan Sinukoff
We present the discovery of Kepler-88 d ($P_d = 1403\pm14$ days, $M\mathrm{sin}i_d = 965\pm44\,M_\oplus = 3.04\pm0.14\,M_J$, $e_d = 0.41\pm0.03$) based on six years of radial velocity (RV) follow-up from the W. M. Keck Observatory HIRES spectrograph. Kepler-88 has two previously identified planets. Kepler-88 b (KOI-142.01) transits in the NASA \Kepler\ photometry and has very large transit timing variations. \citet{Nesvorny2013} perfomed a dynamical analysis of the TTVs to uniquely identify the orbital period and mass of the perturbing planet (Kepler-88 c), which was later was confirmed with RVs from the Observatoire de Haute-Provence (OHP, Barros et al. 2014). To fully explore the architecture of this system, we performed photodynamical modeling on the \Kepler\ photometry combined with the RVs from Keck and OHP and stellar parameters from spectroscopy and Gaia. Planet d is not detectable in the photometry, and long-baseline RVs are needed to ascertain its presence. A photodynamical model simultaneously optimized to fit the RVs and \Kepler\ photometry yields the most precise planet masses and orbital properties yet for b and c: $P_b = 10.91647\pm0.00014\,\mathrm{days}$, $M_b=9.5\pm1.2\,M_\oplus$, $P_c=22.2649\pm0.0007\,\mathrm{days}$, and $M_c=214.1\pm5.3\,M_\oplus$. The photodynamical solution also finds that planets b and c have low eccentricites and low mutual inclination, are apsidally anti-aligned, and have conjunctions on the same hemisphere of the star. Continued RV follow-up of systems with small planets will improve our understanding of the link between inner planetary system architectures and giant planets.
Context. The Kepler Object of Interest Network (KOINet) is a multi-site network of telescopes around the globe organised for follow-up observations of transiting planet candidate Kepler objects of interest (KOIs) with large transit timing variations (TTVs). The main goal of KOINet is the completion of their TTV curves as the Kepler telescope stopped observing the original Kepler field in 2013. Aims. We ensure a comprehensive characterisation of the investigated systems by analysing Kepler data combined with new ground-based transit data using a photodynamical model. This method is applied to t…
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…
Inferring planetary parameters from transit timing variations is challenging for small exoplanets because their transits may be so weak that determination of individual transit timing is difficult or impossible. We implement a useful combination of tools which together provide a numerically fast global photodynamical model. This is used to fit the TTV-bearing light-curve, in order to constrain the masses of transiting exoplanets in low eccentricity, multi-planet systems - and small planets in particular. We present inferred dynamical masses and orbital eccentricities in four multi-planet syste…
The Kepler Object of Interest Network (KOINet) is a multi-site network of telescopes around the globe organised to follow up transiting planet candidate KOIs with large transit timing variations (TTVs). Its main goal is to complete their TTV curves, as the Kepler telescope no longer observes the original Kepler field. Combining Kepler and new ground-based transit data we improve the modelling of these systems. To this end, we have developed a photodynamical model, and we demonstrate its performance using the Kepler-9 system as an example. Our comprehensive analysis combines the numerical integ…
Photodynamical modeling of TOI-4504 reveals its deeply resonant state and similarity to GJ 876
Observatoire de Genève, Département d’Astronomie, Université de Genève（日内瓦大学天文学系天文台）；School of Physics and Astronomy, Monash University（蒙纳士大学物理与天文学院）；Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、IPAG研究所）；Instituto Tecnológico de Buenos Aires (ITBA)（布宜诺斯艾利斯理工学院）；Instituto de Ciencias Físicas (ICIFI（物理科学研究所（ICIFI；CONICET），ECyT-UNSAM）；CONICET), ECyT-UNSAM
Kepler-33 hosts five validated transiting planets ranging in period from 5 to 41 days. The planets are in nearly co-planar orbits and exhibit remarkably similar (appropriately scaled) transit durations indicative of similar impact parameters. The outer three planets have radii of $3.5\lesssim R_{\rm p}/R_\oplus\lesssim4.7$ and are closely-packed dynamically, and thus transit timing variations can be observed. Photodynamical analysis of transit timing variations provide $2σ$ upper bounds on the eccentricity of the orbiting planets (ranging from $<0.02$ to $<0.2$) and the mean density of the hos…
Hot Jupiters may have formed in situ, or been delivered to their observed short periods through one of two categories of migration mechanisms: disk migration or high-eccentricity migration. If hot Jupiters were delivered by high-eccentricity migration, we would expect to observe some "super-eccentric" Jupiters in the process of migrating. We update a prediction for the number of super-eccentric Jupiters we would expect to observe in the Kepler sample if all hot Jupiters migrated through high-eccentricity migration and estimate the true number observed by Kepler. We find that the observations f…
Characterizing the dependence of the orbital architectures and formation environments on the eccentricity distribution of planets is vital for understanding planet formation. In this work, we perform statistical eccentricity studies of transiting exoplanets using transit durations measured via Kepler combined with precise and accurate stellar radii from the California-Kepler Survey and Gaia. Compared to previous works that characterized the eccentricity distribution from transit durations, our analysis benefits from both high precision stellar radii ($\sim$3%) and a large sample of $\sim$1000 …
The eccentricity distribution of exoplanets is known from radial velocity surveys to be divergent from circular orbits beyond 0.1 AU. This is particularly the case for large planets where the radial velocity technique is most sensitive. The eccentricity of planetary orbits can have a large effect on the transit probability and subsequently the planet yield of transit surveys. The Kepler mission is the first transit survey that probes deep enough into period-space to allow this effect to be seen via the variation in transit durations. We use the Kepler planet candidates to show that the eccentr…
Kepler-1656b is a 5 $R_E$ planet with an orbital period of 32 days initially detected by the prime Kepler mission. We obtained precision radial velocities of Kepler-1656 with Keck/HIRES in order to confirm the planet and to characterize its mass and orbital eccentricity. With a mass of $48 \pm 4 M_E$, Kepler-1656b is more massive than most planets of comparable size. Its high mass implies that a significant fraction, roughly 80%, of the planet's total mass is in high density material such as rock/iron, with the remaining mass in a low density H/He envelope. The planet also has a high eccentric…
We report the first disclosure of the planetary nature of Kepler-432 b (aka Kepler object of interest KOI-1299.01). We accurately constrained its mass and eccentricity by high-precision radial velocity measurements obtained with the CAFE spectrograph at the CAHA 2.2-m telescope. By simultaneously fitting these new data and Kepler photometry, we found that Kepler-432 b is a dense transiting exoplanet with a mass of Mp = 4.87 +/- 0.48 MJup and radius of Rp = 1.120 +/- 0.036 RJup. The planet revolves every 52.5 d around a K giant star that ascends the red giant branch, and it moves on a highly ec…
We conduct a uniform analysis of the transit timing variations (TTVs) of 145 planets from 55 Kepler multiplanet systems to infer planet masses and eccentricities. Eighty of these planets do not have previously reported mass and eccentricity measurements. We employ two complementary methods to fit TTVs: Markov chain Monte Carlo simulations based on N-body integration and an analytic fitting approach. Mass measurements of 49 planets, including 12 without previously reported masses, meet our criterion for classification as robust. Using mass and radius measurements, we infer the masses of planets…
(abridged) Kepler-278 and Kepler-391 are two of the three evolved stars known to date on the RGB to host multiple short-period transiting planets. Moreover, these planets are among the smallest discovered around RGB stars. Here we present a detailed stellar and planetary characterization of these remarkable systems. Based on high-quality spectra from Gemini-GRACES for Kepler-278 and Kepler-391, we obtained refined stellar parameters and precise chemical abundances for 25 elements. Also, combining our new stellar parameters with a photodynamical analysis of the Kepler light curves, we determine…
The existence of planets orbiting a central binary star system immediately raises questions regarding their formation and dynamical evolution. Recent discoveries of circumbinary planets by the Kepler space telescope has shown that some of these planets reside close to the dynamical stability limit where it is very difficult to form planets in situ. For binary systems with nearly circular orbits, such as Kepler-38, the observed proximity of planetary orbits to the stability limit can be understood by an evolutionary process in which planets form farther out in the disk and migrate inward to the…
Highly eccentric orbits are one of the major surprises of exoplanets relative to the Solar System and indicate rich and tumultuous dynamical histories. One system of particular interest is Kepler-1656, which hosts a sub-Jovian planet with an eccentricity of 0.8. Sufficiently eccentric orbits will shrink in semi-major axis due to tidal dissipation of orbital energy during periastron passage. Here our goal was to assess whether Kepler-1656b is currently undergoing such high-eccentricity migration, and to further understand the system's origins and architecture. We confirm a second planet in the …
We extract densities and eccentricities of 139 sub-Jovian planets by analyzing transit time variations (TTVs) obtained by the Kepler mission through Quarter 12. We partially circumvent the degeneracies that plague TTV inversion with the help of an analytical formula for the TTV. From the observed TTV phases, we find that most of these planets have eccentricities of order a few percent. More precisely, the r.m.s. eccentricity is 0.018^{+0.005}_{-0.004}, and planets smaller than 2.5R_\earth are around twice as eccentric as those bigger than 2.5R_\earth. We also find a best-fit density-radius rel…
We test the high-eccentricity tidal migration scenario for Kepler-419b, a member of the eccentric warm Jupiter class of planets whose origin is debated. Kepler-419 hosts two known planets (b,c). However, in its current configuration, planet c cannot excite the eccentricity of planet b enough to undergo high-eccentricity tidal migration. We investigate whether the presence of an undiscovered fourth body could explain the orbit of Kepler-419b. We explore the parameter space of this potential third giant planet using a suite of N-body simulations with a range of initial conditions. From the resul…
Doppler planet searches have discovered that giant planets follow orbits with a wide range of orbital eccentricities, revolutionizing theories of planet formation. The discovery of hundreds of exoplanet candidates by NASA's Kepler mission enables astronomers to characterize the eccentricity distribution of small exoplanets. Measuring the eccentricity of individual planets is only practical in favorable cases that are amenable to complementary techniques (e.g., radial velocities, transit timing variations, occultation photometry). Yet even in the absence of individual eccentricities, it is poss…
From Stability to Instability: Characterizing the Eccentricities of Multi-planet Systems in the California Kepler Survey as a Means of Studying Stability
The nearly circular (mean eccentricity <e>~0.06) and coplanar (mean mutual inclination <i>~3 deg) orbits of the Solar System planets motivated Kant and Laplace to put forth the hypothesis that planets are formed in disks, which has developed into the widely accepted theory of planet formation. Surprisingly, the first several hundred extrasolar planets (mostly Jovian) discovered using the Radial Velocity (RV) technique are commonly on eccentric orbits (<e> ~ 0.3). This raises a fundamental question: Are the Solar System and its formation special? The Kepler mission has found thousands of transi…
We characterize the eccentricity distribution of a sample of ~50 short-period planet candidates using transit and occultation measurements from NASA's Kepler Mission. First, we evaluate the sensitivity of our hierarchical Bayesian modeling and test its robustness to model misspecification using simulated data. When analyzing actual data assuming a Rayleigh distribution for eccentricity, we find that the posterior mode for the dispersion parameter is $σ=0.081 \pm^{0.014}_{0.003}$. We find that a two-component Gaussian mixture model for $e \cos ω$ and $e \sin ω$ provides a better model than eith…
Since the launch of the Kepler space telescope in 2009 and the subsequent K2 mission, hundreds of multi-planet systems have been discovered. The study of such systems, both as individual systems and as a population, leads to a better understanding of planetary formation and evolution. Kepler-80, a K-dwarf hosting six super-Earths, was the first system known to have four planets in a chain of resonances, a repeated geometric configuration. Transiting planets in resonant chains can enable us to estimate not only the planets' orbits and sizes but also their masses. Since the original resonance an…
We report the discovery of a long-period brown-dwarf transiting companion of the solar-type star KOI-415. The transits were detected by the Kepler space telescope. We conducted Doppler measurements using the SOPHIE spectrograph at the Observatoire de Haute-Provence. The photometric and spectroscopic signals allow us to characterize a 62.14+-2.69 Mjup, brown-dwarf companion of an evolved 0.94+-0.06 Msun star in a highly eccentric orbit of P = 166.78805+-0.00022 days and e = 0.698+-0.002. The radius of KOI-415 b is 0.79 (-0.07,+0.12) Rjup, a value that is compatible with theoretical predictions …
We study the Kepler object Kepler-432, an evolved star ascending the red giant branch. By deriving precise radial velocities from multi-epoch high-resolution spectra of Kepler-432 taken with the CAFE spectrograph at the 2.2m telescope of Calar Alto Observatory and the FIES spectrograph at the Nordic Optical Telescope of Roque de Los Muchachos Observatory, we confirm the planetary nature of the object Kepler-432 b, which has a transit period of 52 days. We find a planetary mass of Mp=5.84 +\- 0.05 Mjup and a high eccentricity of e=0.478 +\- 0.004. With a semi-major axis of a=0.303 +\- 0.007 AU,…
Most planet pairs in the Kepler data that have measured transit time variations (TTV) are near first-order mean-motion resonances. We derive analytical formulae for their TTV signals. We separate planet eccentricity into free and forced parts, where the forced part is purely due to the planets' proximity to resonance. This separation yields simple analytical formulae. The phase of the TTV depends sensitively on the presence of free eccentricity: if the free eccentricity vanishes, the TTV will be in phase with the longitude of conjunctions. This effect is easily detectable in current TTV data. …
A number of Kepler planet pairs lie just wide of first-order mean motion resonances (MMRs). Tides have been frequently proposed to explain these pileups, but it is still an ongoing discussion. We contribute to this discussion by calculating an optimistic theoretical estimate on the minimum initial eccentricity required by Kepler planets to explain the current observed spacing, and compliment these calculations with N-body simulations. In particular, we investigate 27 Kepler systems having planets within 6% of the 2:1 MMR, and find that the initial eccentricities required to explain the observe…
The vast majority of well studied giant-planet systems, including the Solar System, are nearly coplanar which implies dissipation within a primordial gas disk. however, intrinsic instability may lead to planet-planet scattering, which often produces non-coplanar, eccentric orbits. Planet scattering theories have been developed to explain observed high eccentricity systems and also hot Jupiters; thus far their predictions for mutual inclination (I) have barely been tested. Here we characterize a highly mutually-inclined (I ~ 15-60 degrees), moderately eccentric (e >~ 0.1) giant planet system: K…
Inspired by the recent Kepler discoveries of circumbinary planets orbiting nine close binary stars, we explore the fate of the former as the latter evolve off the main sequence. We combine binary star evolution models with dynamical simulations to study the orbital evolution of these planets as their hosts undergo common-envelope stages, losing in the process a tremendous amount of mass on dynamical timescales. Five of the systems experience at least one Roche-lobe overflow and common-envelope stages (Kepler-1647 experiences three), and the binary stars either shrink to very short orbits or co…
Due to fortuitous circumstances, the two giant planets around Kepler-419 have well characterized 3-D orbits. They are nearly coplanar to each other; the inner one has a large eccentricity (~0.82); and the apses of the two orbits librate around anti-alignment. Such a state defies available proposals for large eccentricities. We argue that it is instead uniquely produced by a decaying protoplanetary disk. When the disk was massive, its precessional effect on the planets forced the two apses to center around an anti-aligned state. And as the disk is gradually eroded, the pair of planets are adiab…
Despite the severe bias of the transit method of exoplanet discovery toward short orbital periods, a modest sample of transiting exoplanets with orbital periods greater than 100 days is known. Long-term radial velocity (RV) surveys are pivotal to confirming these signals and generating a set of planetary masses and densities for planets receiving moderate to low irradiation from their host stars. Here, we conduct RV observations of Kepler-1514 from the Keck I telescope using the High Resolution Echelle Spectrometer. From these data, we measure the mass of the statistically validated giant ($1.…
Three transiting circumbinary planets (Kepler-16 b, Kepler-34 b, and Kepler-35 b) have recently been discovered from photometric data taken by the Kepler spacecraft. Their orbits are significantly non-Keplerian because of the large secondary-to-primary mass ratio and orbital eccentricity of the binaries, as well as the proximity of the planets to the binaries. We present an analytic theory, with the planet treated as a test particle, which shows that the planetary motion can be represented by the superposition of the circular motion of a guiding center, the forced oscillations due to the non-a…
I report the discovery of non-transiting close companions to two transiting warm Jupiters (WJs), Kepler-448/KOI-12b (orbital period $P=17.9\,\mathrm{days}$, radius $R_{\rm p}=1.23^{+0.06}_{-0.05}\,R_{\rm Jup}$) and Kepler-693/KOI-824b ($P=15.4\,\mathrm{days}$, $R_{\rm p}=0.91\pm0.05\,R_{\rm Jup}$), via dynamical modeling of their transit timing and duration variations (TTVs and TDVs). The companions have masses of $22^{+7}_{-5}\,M_{\rm Jup}$ (Kepler-448c) and $150^{+60}_{-40}\,M_{\rm Jup}$ (Kepler-693c), and both are on eccentric orbits ($e=0.65^{+0.13}_{-0.09}$ for Kepler-448c and $e=0.47^{+0…
We study how close-in systems such as those detected by Kepler are affected by the dynamics of bodies in the outer system. We consider two scenarios: outer systems of giant planets potentially unstable to planet--planet scattering, and wide binaries that may be capable of driving Kozai or other secular variations of outer planets' eccentricities. Dynamical excitation of planets in the outer system reduces the multiplicity of Kepler-detectable planets in the inner system in $\sim20-25\%$ of our systems. Accounting for the occurrence rates of wide-orbit planets and binary stars, $\approx18\%$ of…
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, rad…
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…
The Kepler mission has discovered about a dozen circumbinary planetary systems, all containing planets on ~ 1 AU orbits. We place bounds on the locations in the circumbinary protoplanetary disk, where these planets could have formed through collisional agglomeration starting from small (km-sized or less) planetesimals. We first present a model of secular planetesimal dynamics that accounts for the (1) perturbation due to the eccentric precessing binary, as well as the (2) gravity and (3) gas drag from a precessing eccentric disk. Their simultaneous action leads to rich dynamics, with (multiple…
We analyze the transit timing variations obtained by the Kepler mission for 22 sub-jovian planet pairs (17 published, 5 new) that lie close to mean motion resonances. We find that the TTV phases for most of these pairs lie close to zero, consistent with an eccentricity distribution that has a very low RMS value of e ~ 0.01; but about a quarter of the pairs possess much higher eccentricities, up to 0.1 - 0.4. For the low-eccentricity pairs, we are able to statistically remove the effect of eccentricity to obtain planet masses from TTV data. These masses, together with those measured by radial v…
Solar system planets move on almost circular orbits. In strong contrast, many massive gas giant exoplanets travel on highly elliptical orbits, whereas the shape of the orbits of smaller, more terrestrial, exoplanets remained largely elusive. Knowing the eccentricity distribution in systems of small planets would be important as it holds information about the planet's formation and evolution, and influences its habitability. We make these measurements using photometry from the Kepler satellite and utilizing a method relying on Kepler's second law, which relates the duration of a planetary trans…
The six planets of the Kepler-11 system are the archetypal example of a population of surprisingly low-density transiting planets revealed by the Kepler mission. We have determined the fundamental parameters and chemical composition of the Kepler-11 host star to unprecedented precision using an extremely high quality spectrum from Keck-HIRES (R$\simeq$67,000, S/N per pixel$\simeq$260 at 600 nm). Contrary to previously published results, our spectroscopic constraints indicate that Kepler-11 is a young main-sequence solar twin. The revised stellar parameters and new analysis raise the densities …
Radial velocity (RV) surveys have discovered giant exoplanets on au-scale orbits with a broad distribution of eccentricities. Those with the most eccentric orbits are valuable laboratories for testing theories of high eccentricity migration. However, few such exoplanets transit their host stars thus removing the ability to apply constraints on formation from their bulk internal compositions. We report the discovery of Kepler-1704 b, a transiting 4.15 $M_{\rm J}$ giant planet on a 988.88 day orbit with the extreme eccentricity of $0.921^{+0.010}_{-0.015}$. Our decade-long RV baseline from the K…
We present an extension of the BEER model for eccentric binaries - eBEER, approximating the BEaming, Ellipsoidal and Reflection effects by harmonic series of the Keplerian elements of their orbit. As such, it can be a tool for fast processing of light curves for detecting non-eclipsing eccentric binary systems. To validate the applicability of the eccentric model and its approximations, we applied eBEER to the Kepler light curves, identified a sample of bright non-eclipsing binary candidates, and followed three of them with the Wise observatory eShel spectrograph. After confirming the three sy…
Kepler-22b is the first transiting planet to have been detected in the habitable-zone of its host star. At 2.4 Earth radii, Kepler-22b is too large to be considered an Earth-analog, but should the planet host a moon large enough to maintain an atmosphere, then the Kepler-22 system may yet possess a telluric world. Aside from being within the habitable-zone, the target is attractive due to the availability of previously measured precise radial velocities and low intrinsic photometric noise, which has also enabled asteroseismology studies of the star. For these reasons, Kepler-22b was selected a…
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…
When, in the course of searching for exoplanets, sparse sampling and noisy data make it necessary to disentangle possible solutions to the observations, one must consider the possibility that what appears to be a single eccentric Keplerian signal may in reality be attributed to two planets in near-circular orbits. There is precedent in the literature for such outcomes, whereby further data or new analysis techniques reveal hitherto occulted signals. Here, we perform suites of simulations to explore the range of possible two-planet configurations that can result in such confusion. We find that …
WASP-148 is a recently announced extra-solar system harbouring at least two giant planets. The inner planet transits its host star. The planets travel on eccentric orbits and are near the 4:1 mean-motion resonance, which implies significant mutual gravitational interactions. In particular, this causes transit-timing variations of a few minutes, which were detected based on ground-based photometry. This made WASP-148 one of the few cases where such a phenomenon was detected without space-based photometry. Here, we present a self-consistent model of WASP-148 that takes into account the gravitati…
Exoplanet orbital eccentricities offer valuable clues about the history of planetary systems. Eccentric, Jupiter-sized planets are particularly interesting: they may link the "cold" Jupiters beyond the ice line to close-in hot Jupiters, which are unlikely to have formed in situ. To date, eccentricities of individual transiting planets primarily come from radial velocity measurements. Kepler has discovered hundreds of transiting Jupiters spanning a range of periods, but the faintness of the host stars precludes radial velocity follow-up of most. Here we demonstrate a Bayesian method of measurin…
Approximately half of the planets discovered by NASA's Kepler mission are in systems where just a single planet transits its host star, and the remaining planets are observed to be in multi-planet systems. Recent analyses have reported a dichotomy in the eccentricity distribution displayed by systems where a single planet transits compared with that displayed by the multi-planet systems. Using $N$-body simulations, we examine the hypothesis that this dichotomy has arisen because inner systems of super-Earths are frequently accompanied by outer systems of giant planets that can become dynamical…
Exomoons are the natural satellites of planets orbiting stars outside our solar system, of which there are currently no confirmed examples. We present new observations of a candidate exomoon associated with Kepler-1625b using the Hubble Space Telescope to validate or refute the moon's presence. We find evidence in favor of the moon hypothesis, based on timing deviations and a flux decrement from the star consistent with a large transiting exomoon. Self-consistent photodynamical modeling suggests that the planet is likely several Jupiter masses, while the exomoon has a mass and radius similar t…
The Kepler mission's discovery of a number of circumbinary planets orbiting close (a_p < 1.1 au) to the stellar binary raises questions as to how these planets could have formed given the intense gravitational perturbations the dual stars impart on the disk. The gas component of circumbinary protoplanetary disks is perturbed in a similar manner to the solid, planetesimal dominated counterpart, although the mechanism by which disk eccentricity originates differs. This is the first work of a series that aims to investigate the conditions for planet formation in circumbinary protoplanetary disks.…
Recent studies suggest that ultra-short period planets (USPs), Earth-sized planets with sub-day periods, constitute a statistically distinct sub-sample of {\it Kepler} planets: USPs have smaller radii ($1-1.4R_\oplus$) and larger mutual inclinations with neighboring planets than nominal {\it Kepler} planets, and their period distribution is steeper than longer-period planets. We study a "low-eccentricity" migration scenario for the formation of USPs, in which a low-mass planet with initial period of a few days maintains a small but finite eccentricity due to secular forcings from exterior comp…
In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant pla…
Orbital eccentricity is one of the basic planetary properties, whose distribution may shed light on the history of planet formation and evolution. Here, in a series of works on Planetary Orbit Eccentricity Trends (dubbed POET), we study the distribution of planetary eccentricities and their dependence on stellar/planetary properties. In this paper, the first work of the POET series, we investigate whether and how the eccentricities of small planets depend on stellar metallicities (e.g., [Fe/H]). Previous studies on giant planets have found a significant correlation between planetary eccentrici…
A significant fraction of Kepler systems are closely-packed, largely coplanar and circular. We study the stability of a 6-planet system, Kepler-11, to gain insights on the dynamics and formation history of such systems. Using a technique called `frequency maps' as fast indicators for long-term stability, we explore the stability of Kepler-11 system by analyzing the neighbourhood space around its orbital parameters. Frequency maps provide a visual representation of chaos and stability, and their dependence on orbital parameters. We find that the current system is stable, but lies within a few p…
