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 $π$ Mensae system, a G0V star at 18.3 pc host to a wide-orbit super-jovian ($M\sin i = 10.02\pm0.15$ $M_{\rm Jup}$) with a 5.7-year period and an inner transiting super-earth ($M=4.82\pm0.85$ $M_\oplus$) 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 $π$ 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 $π$ 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 c's 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.
Pi Men hosts a transiting planet detected by the TESS space mission and an outer planet in a 5.7-yr orbit discovered by RV surveys. We studied this system using new radial velocity (RV) measurements taken with the HARPS spectrograph on ESO's 3.6-m telescope as well as archival data. We constrain the stellar RV semi-amplitude due to the transiting planet, Pi Men c, as K_c = 1.21 +/- 0.12 m/s resulting in a planet mass of M_c = 3.63 +/- 0.38 M_Earth. A planet radius of R_c= 2.145 +/- 0.015 R_Earth yields a bulk density of rho = 2.03 +/- 0.22 g/cm^{-3}. The precisely determined density of this pl…
Early analyses of exoplanet statistics from the Kepler Mission revealed that a model population of multiple-planet systems with low mutual inclinations (${\sim1^{\circ}-2^{\circ}}$) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. This so-called "Kepler dichotomy" signals the existence of a sub-population of multi-planet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically expl…
The {\it Kepler} mission has detected thousands of planetary systems with 1-7 transiting planets packed within 0.7~au from their host stars. There is an apparent excess of single-transit planet systems that cannot be explained by transit geometries alone, when a single planetary mutual inclination dispersion is assumed. This suggests that the observed compact planetary systems have at least two different architectures. We present a scenario where the "Kepler dichotomy" may be explained by the action of an external giant planet or stellar companion misaligned with the inner multi-planet system.…
We study the excitation of mutual inclination between planetary orbits by a novel secular-orbital resonance in multiplanet systems perturbed by binary companions which we call "ivection". The ivection resonance happens when the nodal precession rate of the planet matches a multiple of the orbital frequency of the binary, and its physical nature is similar to the previously-studied evection resonance. Capture into an ivection resonance requires encountering the resonance with slowly increasing nodal precession rate, and it can excite the mutual inclination of the planets without affecting their…
An overabundance of single-transiting Kepler planets suggests the existence of a sub-population of intrinsically multi-planet systems possessing large mutual inclinations. However, the origin of these mutual inclinations remains unknown. Recent work has demonstrated that mutual inclinations can be excited soon after protoplanetary disk-dispersal due to the oblateness of the rapidly-rotating host star, provided the star is tilted. Alternatively, distant giant planets, which are common in systems of close-in Kepler planets, could drive up mutual inclinations. The relative importance of each of t…
In this paper we study numerically the effect of the initial mutual orbital inclination on the stability of hierarchical triple systems with initially circular orbits. Our aim is to investigate the possibility that the stability boundary may be independent of the orbital inclination for certain mass ratios. We integrate numerically the equations of motion of hierarchical triple systems with initially circular orbits and different orbital configurations. The mass ratios cover the range from 0.000001 to 1000000 and the initial mutual inclination angle varies from 0 to 180 degrees. The results fr…
The {\it Kepler} mission revealed a population of compact multiple-planet systems with orbital periods shorter than a year, and occasionally even shorter than a day. By analyzing a sample of 102 {\it Kepler} and {\it K2} multi-planet systems, we measure the minimum difference $ΔI$ between the orbital inclinations, as a function of the orbital distance of the innermost planet. This is accomplished by fitting all the planetary signals simultaneously, constrained by an external estimate of the stellar mean density. We find $ΔI$ to be larger when the inner orbit is smaller, a trend that does not a…
Previous analyses of Doppler and Kepler data have found that Sun-like stars hosting "cold Jupiters" (giant planets with $a\gtrsim 1\,\mathrm{AU}$) almost always host "inner super-Earths" (1-$4\,R_\oplus$, $a\lesssim1\,\mathrm{AU}$). Here, we attempt to determine the degree of alignment between the orbital planes of the cold Jupiters and the inner super-Earths. The key observational input is the fraction of Kepler stars with transiting super-Earths that also have transiting cold Jupiters. This fraction depends on both the probability for cold Jupiters to occur in such systems, and on the mutual…
The angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criteria to constrain the orbital architectures for exoplanetary systems. Previously, He, Ford, & Ragozzine (2019) (arXiv:1907.07773v2) showed through forward modelling (SysSim) that the observed multiplicity distribution can be well reproduced by two populations consisting of a low and a high mutual inclination component. Here, we show that a broad distribution of mutual inclinations arising from systems at the AMD-stability limit c…
Ultra-short-period planets (USPs) provide important clues to planetary formation and migration. Recently, it is found that the mutual inclinations of the planetary systems are larger if the inner orbits are closer ($\lesssim 5R_*$) and if the planetary period ratios are larger ($P_2/P_1 \gtrsim 5$) (Dai et al. 2018). This suggests that the USPs experienced both inclination excitation and orbital shrinkage. Here we investigate the increase in the mutual inclination due to stellar oblateness. We find that the stellar oblateness (within $\sim 1$Gyr) is sufficient to enhance the mutual inclination…
We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric orbit of the outer perturber on the dynamics of a small highly inclined inner body. Our analytical study of the secular perturbations relies on the classical octupole hamiltonian expansion (third-order theory in the ratio of the semi-major axes), as third-order terms are needed to consider the secular variations of the outer perturber and potential secular …
We study the chaotic and secular evolution of hierarchical quadruple systems in the $3+1$ configuration, focusing on the evolution of mutual inclination of the inner binaries as the system undergoes coupled Lidov-Kozai (LK) oscillations. We include short-range forces (SRF; such as those due to tidal and rotational distortions) that control the eccentricity excitation of the inner binary. The evolution of mutual inclination is described, a priori, by two dimensionless parameters, $\pazocal{R}_0$, the ratio between the inner and outer LK time-scales and $ε_{SRF}$, the ratio between the SRF prece…
Recent observations suggest that a large fraction of Kepler super-Earth systems have external giant planet companions (cold Jupiters), which can shape the architecture of the inner planets, in particular their mutual inclinations. The dynamical perturbation from cold Jupiters may account for the population of misaligned planets in the Kepler data. The effectiveness of this mechanism can be hindered by a strong planet--planet coupling in the inner system. In this paper, we study how mean-motion resonances (MMRs) affect this coupling and the expected misalignment. We derive approximate analytica…
Aims. To date, more than 600 multi-planetary systems have been discovered. Due to the limitations of the detection methods, our knowledge of the systems is usually far from complete. In particular, for planetary systems discovered with the radial velocity (RV) technique, the inclinations of the orbital planes, and thus the mutual inclinations and planetary masses, are unknown. Our work aims to constrain the spatial configuration of several RV-detected extrasolar systems that are not in a mean-motion resonance. Methods. Through an analytical study based on a first-order secular Hamiltonian expa…
Systems with ultra-short-period planets (USPs) tend to possess larger mutual inclinations compared to those with planets located farther from their host stars. This could be explained due to precession caused by stellar oblateness at early times when the host star was rapidly spinning. However, stellar oblateness reduces over time due to the decrease in the stellar rotation rate, and this may further shape the planetary mutual inclinations. In this work, we investigate in detail how the final mutual inclination varies under the effect of a decreasing $J_2$. We find that different initial param…
We evaluate the orbital evolution and several plausible origins scenarios for the mutually inclined orbits of Upsilon Andromedae c and d. These two planets have orbital elements that oscillate with large amplitudes and lie close to the stability boundary. This configuration, and in particular the observed mutual inclination, demands an explanation. The planetary system may be influenced by a nearby low-mass star, Upsilon And B, which could perturb the planetary orbits, but we find it cannot modify two coplanar orbits into the observed mutual inclination of ~30 deg. However, it could incite eje…
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…
In this paper we describe an algorithm and deduce the related mathematical formulae that allows the computation of observed fluxes in stellar and planetary systems with arbitrary number of bodies being part of a transit or occultation event. The presented method does not have any limits or constraints for the geometry and can be applied for almost all of the available limb darkening models as well. As a demonstration, we apply this scheme to gather information for the orbital inclinations from multiple transiting planetary systems in cases when mutual transits occur. We also show here that the…
$π$ Men hosts a transiting super Earth ($P\approx6.27$ d, $m\approx4.82$ $M_{\oplus}$, $R\approx2.04$ $R_{\oplus}$) discovered by TESS and a cold Jupiter ($P\approx2093$ d, $m \sin I\approx10.02$ $M_{\rm{Jup}}$, $e\approx0.64$) discovered from radial velocity. We use Gaia DR2 and Hipparcos astrometry to derive the star's velocity caused by the orbiting planets and constrain the cold Jupiter's sky-projected inclination ($I_b=41-65^{\circ}$). From this we derive the mutual inclination ($ΔI$) between the two planets, and find that $49^{\circ}< ΔI < 131^{\circ}$ (1$σ$), and $28^{\circ} < ΔI < 152^…
This paper considers whether the population of known transiting exoplanets provides evidence for additional outer planets on inclined orbits, due to the perturbing effect of such planets on the orbits of inner planets. As such, we develop a semi-analytical method for calculating the probability that two mutually inclined planets are observed to transit. We subsequently derive a simplified analytical form to describe how the mutual inclination between two planets evolves due to secular interactions with a wide orbit inclined planet and use this to determine the mean probability that the two inn…
Previous full-lifetime simulations of single-star multi-planet systems across all phases of stellar evolution have predominately assumed coplanar or nearly-coplanar orbits. Here we assess the consequences of this assumption by removing it and exploring the effect of giant branch mass loss on the stability of two-planet systems with small to moderate non-Kozai (<40 degrees) relative inclinations. We run nearly 10^4 simulations over 14 Gyr for F-star, A-star and B-star planet hosts, incorporating main sequence stellar masses of 1.5, 2.0, 2.5, 3.0 and 5.0 solar masses, and initial planetary semim…
Compact multi-planet systems containing super-Earths or sub-Neptunes, commonly found around solar-type stars, may be surrounded by external giant planet or stellar companions, which can shape the architechture and observability of the inner systems. We present a comprehensive study on the evolution of the inner planetary system subject to the gravitational influence of an eccentric, misaligned outer perturber. Analytic results are derived for the inner planet eccentricities ($e_i$) and mutual inclination ($θ_{12}$) of the "2-planet + perturber" system, calibrated with numerical secular and N-b…
Hierarchical two-planet systems, in which the inner body's semi-major axis is between 0.1 and 0.5 AU, usually present high eccentricity values, at least for one of the orbits. As a result of the formation process, one may expect that planetary systems with high eccentricities also have high mutual inclinations. However, here we show that tidal effects combined with gravitational interactions damp the initial mutual inclination to modest values in timescales that are shorter than the age of the system. This effect is not a direct consequence of tides on the orbits, but it results from a secular…
A large proportion of transiting planetary systems appear to possess only a single planet as opposed to multiple transiting planets. This excess of singles is indicative of significant mutual inclinations existing within a large number of planetary systems, but the origin of these misalignments is unclear. Moreover, recent observational characterization reveals that mutual inclinations tend to increase with proximity to the host star. These trends are both consistent with the dynamical influence of a strong quadrupolar potential arising from the host star during its early phase of rapid rotati…
We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.9 degrees. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364 and HD 60532 systems may be in chaotically-evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1 and 3:2 resonances, and for plane…
Planet formation is often considered in the context of one circumstellar disk around one star. Yet stellar binary systems are ubiquitous, and thus a substantial fraction of all potential planets must form and evolve in more complex, dynamical environments. We present the results of a five-year astrometric monitoring campaign studying 45 binary star systems that host Kepler planet candidates. The planet-forming environments in these systems would have literally been shaped by the binary orbits that persist to the present day. Crucially, the mutual inclinations of star-planet orbits can only be …
HD 113337 and HD 38529 host pairs of giant planets, a debris disc, and wide M-type stellar companions. We measure the disc orientation with resolved images from Herschel and constrain the three-dimensional orbits of the outer planets with Gaia DR2 and Hipparcos astrometry. Resolved disc modelling leaves degeneracy in the disc orientation, so we derive four separate planet-disc mutual inclination ($ΔI$) solutions. The most aligned solutions give $ΔI=17-32°$ for HD 113337 and $ΔI=21-45°$ for HD 38529 (both 1$σ$). In both systems, there is a small probability (<0.3 per cent) that the planet and d…
The Kepler Mission has detected dozens of compact planetary systems with more than four transiting planets. This sample provides a collection of close-packed planetary systems with relatively little spread in the inclination angles of the inferred orbits. A large fraction of the observational sample contains limited multiplicity, begging the question whether there is a true diversity of multi transiting systems, or if some systems merely possess high mutual inclinations, allowing them to appear as single-transiting systems in a transit-based survey. This paper begins an exploration of the effe…
The late-stage formation of giant planetary systems is rich in interesting dynamical mechanisms. Previous simulations of three giant planets initially on quasi-circular and quasi-coplanar orbits in the gas disc have shown that highly mutually inclined configurations can be formed, despite the strong eccentricity and inclination damping exerted by the disc. Much attention has been directed to inclination-type resonance, asking for large eccentricities to be acquired during the migration of the planets. Here we show that inclination excitation is also present at small to moderate eccentricities …
We aim to investigate the influence of the eccentricity and inclination damping due to planet-disc interactions on the final configurations of the systems, generalizing previous studies on the combined action of the gas disc and planet-planet scattering during the disc phase. Instead of the simplistic $K$-prescription, our n-body simulations adopt the damping formulae for eccentricity and inclination provided by the hydrodynamical simulations of our companion paper. We follow the evolution of $11000$ numerical experiments of three giant planets in the late stage of the gas disc, exploring diff…
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…
The orbits of giant extrasolar planets often have surprisingly small semi-major axes, large eccentricities, or severe misalignments between their normals and their host stars' spin axes. In some formation scenarios invoking Kozai-Lidov oscillations, an external planetary companion drives a planet onto an orbit having these properties. The mutual inclinations for Kozai-Lidov oscillations can be large and have not been confirmed observationally. Here we deduce that observed eccentric warm Jupiters with eccentric giant companions have mutual inclinations that oscillate between 35-65 deg. Our infe…
It is often assumed that the "Kepler dichotomy" -- the apparent excess of planetary systems with a single detected transiting planet in the Kepler catalog -- reflects an intrinsic bimodality in the mutual inclinations of planetary orbits. After conducting 600 simulations of planet formation followed by simulated Kepler observations, we instead propose that the apparent dichotomy reflects a divergence in the amount of migration and the separation of planetary semimajor axes into distinct "clusters". We find that our simulated high-mass systems migrate rapidly, bringing more planets into orbital…
We present a combined analysis of previously published high-precision radial velocities and astrometry for the GJ876 planetary system using a self-consistent model that accounts for the planet-planet interactions. Assuming the three planets so far identified in the system are coplanar, we find that including the astrometry in the analysis does not result in a best-fit inclination significantly different than that found by Rivera and collaborators from analyzing the radial velocities alone. In this unique case, the planet-planet interactions are of such significance that the radial velocity dat…
We consider planetary systems evolving under the effect of a Stokes-type dissipative force mimicking the outcome of a type II migration process. As inward migration proceeds and the planets follow the circular family (they start on circular orbits) and even though they are initially almost coplanar, resonance capture can be realized. Then, at the \textit{vertical critical orbits} (VCOs), that the circular family possesses, the inclination excitation can abruptly take place. The planets are now guided by the spatial elliptic families, which bifurcate from those critical orbits. We herein, perfo…
We propose a method to be able to decide whether the planets of CoRoT-7 are moving on mutually inclined orbits in the order of i > 10 degrees. The extrasolar system CoRoT-7 is very special with respect to the closeness of the planets to the host star, which results in a fast dynamical development. It would therefore be possible to determine the inclination of the innermost planet CoRoT-7b with respect to the observer after an observation of at least three years from space with the satellite CoRoT with sufficient precision. Different inclinations would cause different duration of the transit ti…
The Kepler satellite has discovered a number of transiting planets around close binary stars. These circumbinary systems have highly aligned planetary and binary orbits. In this paper, we explore how the mutual inclination between the planetary and binary orbits may reflect the physical conditions of the assembly of protoplanetary disks and the interaction between protostellar binaries and circumbinary disks. Given the turbulent nature of star-forming molecular clouds, it is possible that the gas falling onto the outer region of a circumbinary disk and the central protostellar binary have diff…
HD 164604 c: a second giant planet on a 15-yr orbit and the constraint of the planet-planet mutual inclination
State Key Laboratory of Dark Matter Physics, Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（暗物质物理国家重点实验室，李政道研究所与物理天文学院，上海交通大学）；Earth and Planets Laboratory, Carnegie Institution for Science（地球与行星实验室，卡内基科学机构）；Observatories of the Carnegie Institution for Science（卡内基科学机构天文台）；Department of Astronomy, Tsinghua University（天文学系，清华大学）
HD 164604 c是一颗围绕K3.5矮星运行的巨行星，其轨道周期为15年，研究发现其与另一颗行星的互倾角约束及动态历史。
The Lidov-Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner body, and later extended to the quadrupolar secular nonrestricted three body problem. In this paper, we propose a different point of view on the problem by looking first at the restricted problem where the massless particle is the outer body. In this situation, equilibria at high mutual inclination appear, which correspond to the population of stable particle…
Some systems of close-in "super-Earths" contain five or more planets on non-resonant but compact and nearly coplanar orbits. The Kepler-11 system is an iconic representative of this class of system. It is challenging to explain their origins given that planet-disk interactions are thought to be essential to maintain such a high degree of coplanarity, yet these same interactions invariably cause planets to migrate into chains of mean motion resonances. Here we mine a large dataset of dynamical simulations of super-Earth formation by migration. These simulations match the observed period ratio d…
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 …
We investigate the inclination-growth mechanisms for two-planet systems during the late protoplanetary disc phase. In previous works, much attention has been directed to the inclination-type resonance, and it has been shown that it asks for high eccentricities to be acquired during the migration of the giant planets. By adopting eccentricity and inclination damping formulae based on hydrodynamical simulations (instead of the K-prescription), we have carried out 20 000 numerical simulations, where we vary the initial planetary eccentricities, the migration rate, and the dispersal time of the ga…
[Abridged] The recent discovery of a transiting planet on a non-circular orbit with a massive highly eccentric companion orbiting HAT-P-13 offers the possibility of probing the structure of the short-period planet. The ability to do this relies on the system being in a quasi-equilibrium state in the sense that the eccentricities are constant on the usual secular timescale, and decay on a timescale which is much longer than the age of the system. Since the equilibrium eccentricity is effectively a function only of observable system parameters and the unknown Love number of the short-period plan…
Mutually misaligned circumbinary planets may form in a warped or broken gas disc or from later planet-planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the …
The recent characterization of transiting close-in planets has revealed an intriguing population of sub-Neptunes with highly tilted and even polar orbits relative to their host star's equator. Any viable theory for the origin of these close-in, polar planets must explain (1) the observed stellar obliquities, (2) the substantial eccentricities, and (3) the existence of Jovian companions with large mutual inclinations. In this work, we propose a theoretical model that satisfies these requirements without invoking tidal dissipation or large primordial inclinations. Instead, tilting is facilitated…
The outer architectures of Kepler's compact systems of multiple transiting planets remain poorly constrained and few of these systems have lower bounds on the orbital distance of any massive outer planets. We infer a minimum orbital distance and upper limits on the inclination of a hypothetical Jovian-mass planet orbiting exterior to the six transiting planets at Kepler-11. Our constraints are derived from dynamical models together with observations provided by the Kepler mission. Firstly, the lack of transit timing variations (TTV) in the outermost transiting planet Kepler-11 g imply that the…
The giant impact phase of terrestrial planet formation establishes connections between super-Earths' orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by res…
While there have been many studies examining the stability of hierarchical triple systems, the meaning of ``stability'' is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on ``Lagrange stability'', which roughly refers to the stability against the escape of a body from the system, or ``disruption'' of the triple system, in contrast to ``Lyapunov-like stability'' that is related to the chaotic nature of the system dynamics. We compute the evolution of triple systems using direct $N$-body simulations up to $10^7 P_\mathrm{out}$, which is sig…
Recent studies have proposed that most warm Jupiters (WJs, giant planets with semi-major axes in the range of 0.1-1 AU) probably form in-situ, or arrive in their observed orbits through disk migration. However, both in-situ formation and disk migration, in their simplest flavors, predict WJs to be in low-eccentricity orbits, in contradiction with many observed WJs that are moderately eccentric (e=0.2-0.7). This paper examines the possibility that the WJ eccentricities are raised by secular interactions with exterior giant planet companions, following in-situ formation or migration on a circula…
