Warm Jupiters-giant exoplanets with orbital periods between 10 and 200 days-exhibit a broad range of eccentricities and are often accompanied by nearby low-mass planets. Understanding the origins of their orbital architectures requires examining both their migration histories and subsequent dynamical interactions. In this study, we perform extensive N-body simulations to explore how distant giant planet perturbers affect the eccentricity evolution of warm Jupiters and the role of nearby super-Earth companions in mediating these interactions. We find that while distant perturbers can induce large-amplitude eccentricity oscillations in warm Jupiters via the von Zeipel-Lidov-Kozai mechanism, the presence of nearby super-Earth companions often suppresses these variations via strong dynamical coupling. This mechanism naturally leads to a bimodal eccentricity distribution: warm Jupiters with nearby companions tend to maintain low eccentricities, whereas those without exhibit significantly broader eccentricity distributions. We show that reproducing the observed eccentricity distribution of warm Jupiters lacking nearby companions is most naturally explained if a substantial fraction of distant perturbers occupy dynamically extreme orbits, either with large mutual inclinations or high orbital eccentricities. These results support a scenario in which warm Jupiters experience substantial post-disk dynamical evolution, shaped jointly by distant perturbers and nearby companions.
The origin of warm Jupiters (gas giant planets with periods between 10 and 200 days) is an open question in exoplanet formation and evolution. We investigate a particular migration theory in which a warm Jupiter is coupled to a perturbing companion planet that excites secular eccentricity oscillations in the warm Jupiter, leading to periodic close stellar passages that can tidally shrink and circularize its orbit. If such companions exist in warm Jupiter systems, they are likely to be massive and close-in, making them potentially detectable. We generate a set of warm Jupiter-perturber populati…
Among a hundred transiting planets with a measured projected spin-orbit angle λ, several systems are suggested to be counter-orbiting. While they may be due to the projection effect, the mechanism to produce a counter-orbiting planet is not established. A promising scenario for the counter-orbiting planets is the extreme eccentricity evolution in near-coplanar hierarchical triple systems with eccentric inner and outer or- bits. We examine this scenario in detail by performing a series of systematic numerical simulations, and consider the possibility of forming hot Jupiters, especially counter-…
Torques from a mutually inclined perturber can change a transiting planet's impact parameter, resulting in variations in the transit shape and duration. Detection of and upper limits on changes in impact parameter yield valuable constraints on a planetary system's three dimensional architecture. Constraints for warm Jupiters are particularly interesting because they allow us to test origins theories that invoke a mutually inclined perturber. Because of warm Jupiters' high signal-to-noise transits, changes in impact parameter are feasible to detect. However, here we show that allowing the impac…
The behavior of an interior test particle in the secular 3-body problem has been studied extensively. A well-known feature is the Lidov-Kozai resonance in which the test particle's argument of periapse librates about $\pm 90^\circ$ and large oscillations in eccentricity and inclination are possible. Less explored is the inverse problem: the dynamics of an exterior test particle and an interior perturber. We survey numerically the inverse secular problem, expanding the potential to hexadecapolar order and correcting an error in the published expansion. Four secular resonances are uncovered that…
We present a semi-analytical correction to the seminal solution for the secular motion of a planet's orbit under gravitational influence of an external perturber derived by Heppenheimer (1978). A comparison between analytical predictions and numerical simulations allows us to determine corrective factors for the secular frequency and forced eccentricity in the co-planar restricted three-body problem. The correction is given in the form of a polynomial function of the system's parameters that can be applied to first-order forced eccentricity and secular frequency estimates. The resulting secula…
Planet-Planet Scattering Explains the Mass-Eccentricity Relation of Warm Jupiters
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；National Center for Supercomputing Applications（国家超级计算应用中心）；University of California, San Diego（加州大学圣地亚哥分校）；National Astronomical Observatory of Japan（日本国立天文台）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；U.S. National Science Foundation National Optical-Infrared Astronomy Research Laboratory（美国国家科学基金会国家光学-红外天文研究实验室）
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…
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…
Most warm Jupiters (gas-giant planets with $0.1~{\rm AU}\lesssim a \lesssim1$ AU) have pericenter distances that are too large for significant orbital migration by tidal friction. We study the possibility that the warm Jupiters are undergoing secular eccentricity oscillations excited by an outer companion (a planet or star) in an eccentric and/or mutually inclined orbit. In this model the warm Jupiters migrate periodically, in the high-eccentricity phase of the oscillation when the pericenter distance is small, but are typically observed at much lower eccentricities. We show that the steady-st…
Exoplanets discovered over the last decades have provided a new sample of giant exoplanets, hot Jupiters. For lack of enough materials in current locations of hot Jupiters, they are perceived to form outside snowline. Then, migrate to the locations observed through interactions with gas disks or high-eccentricity mechanisms. We examined the efficiencies of different high-eccentricity mechanisms to form hot Jupiters in near coplaner multi-planet systems. These mechanisms include planet-planet scattering, Kozai-Lidov mechanism, coplanar high-eccentricity migration, secular chaos, as well as othe…
The distribution of eccentricities of warm giant exoplanets is commonly explained through planet--planet interactions, although no physically sound argument favours the ubiquity of such interactions. No simple, generic explanation has been put forward to explain the high mean eccentricity of these planets. In this paper, we revisit a simple, plausible explanation to account for the eccentricities of warm Jupiters: migration inside a cavity in the protoplanetary disc. Such a scenario allows to excite the outer eccentric resonances, a working mechanism for higher mass planets, leading to a growt…
A recent observational study suggests that the occurrence of hot Jupiters (HJs) around solar-type stars is correlated with stellar clustering. We study a new scenario for HJ formation, called "Flyby Induced High-e Migration", that may help explain this correlation. In this scenario, stellar flybys excite the eccentricity and inclination of an outer companion (giant planet, brown dwarf, or low-mass star) at large distance (10-300 au), which then triggers high-e migration of an inner cold Jupiter (at a few astronomical units) through the combined effects of von Zeipel-Lidov-Kozai (ZLK) eccentric…
High-eccentricity tidal migration is a potential formation channel for hot Jupiters. During this process, the planetary f-mode may experience a phase of diffusive growth, allowing its energy to quickly build up to large values. In Yu et al. (2021, ApJ, 917, 31), we demonstrated that nonlinear mode interactions between a parent f-mode and daughter f- and p-modes expand the parameter space over which the diffusive growth of the parent is triggered. We extend that study by incorporating (1) the angular momentum transfer between the orbit and the mode, and consequently the evolution of the pericen…
The presence of a stellar companion can place constraints on occurrence and orbital evolution of satellites orbiting exoplanets, i.e., exomoons. In this work we revise earlier orbital stability limits for retrograde orbits in the case of a three body system consisting of star-planet-satellite. The latter reads $a_{\rm sat}^{\rm crit} \approx 0.668(1-1.236e_{\rm p})$ for $e_p \leq 0.8$ in units of the Hill Radius and represents the lower critical orbit as a function of the planetary eccentricity $e_{\rm p}$. A similar formula is determined for exomoons hosted by planets in binary star systems, …
The obliquity of a star, or the angle between its spin axis and the average orbit normal of its companion planets, provides a unique constraint on that system's evolutionary history. Unlike the Solar System, where the Sun's equator is nearly aligned with its companion planets, many hot Jupiter systems have been discovered with large spin-orbit misalignments, hosting planets on polar or retrograde orbits. We demonstrate that, in contrast to stars harboring hot Jupiters on circular orbits, those with eccentric companions follow no population-wide obliquity trend with stellar temperature. This fi…
High-eccentricity migration is an important channel for the formation of hot Jupiters (HJs). In particular, Lidov-Kozai (LK) oscillations of orbital eccentricity/inclination induced by a distant planetary or stellar companion, combined with tidal friction, have been shown to produce HJs on Gyr timescales, provided that efficient tidal dissipation operates in the planet. We re-examine this scenario with the inclusion of dynamical tides. When the planet's orbit is in a high-eccentricity phase, the tidal force from the star excites oscillatory f-modes and r-modes in the planet. For sufficiently l…
The orbit of Mercury has large values of eccentricity and inclination that cannot be easily explained if this planet formed on a circular and coplanar orbit. Here, we study the evolution of Mercury's orbit during the instability related to the migration of the giant planets in the framework of the jumping Jupiter model. We found that some instability models are able to produce the correct values of Mercury's eccentricity and inclination, provided that relativistic effects are included in the precession of Mercury's perihelion. The orbital excitation is driven by the fast change of the normal o…
Hot Jupiters (HJs) are Jupiter-like planets orbiting their host star in tight orbits of a few days. They are commonly believed not to have formed in situ, requiring inwards migration towards the host star. One of the proposed migration scenarios is secular high-eccentricity or high-$e$ migration, in which the orbit of the planet is perturbed to high eccentricity by secular processes, triggering strong tidal evolution and orbital migration. Previous theoretical studies have considered secular excitation in stellar binaries. Recently, a number of HJs have been observed in stellar triple systems.…
Stellar spin-orbit misalignments (obliquities) in hot Jupiter systems have been extensively probed. Such obliquities may reveal clues about hot Jupiter dynamical histories. Common explanations for generating obliquities include high-eccentricity migration and primordial disk misalignment. This paper investigates another mechanism for producing stellar spin-orbit misalignments in systems hosting a close-in planet with an external, modestly inclined companion. Spin-orbit misalignment may be excited due to a secular resonance, occurring when the precession rate of the stellar spin axis (driven by…
All the giant planets in the solar system host a large number of natural satellites. Moons in extrasolar systems are difficult to detect, but a Neptune-sized exomoon candidate has been recently found around a Jupiter-sized planet in the Kepler-1625bsystem. Due to their relative ease of detection, hot Jupiters (HJs), which reside in close orbits around their host stars with a period of a few days, may be very good candidates to search for exomoons. It is still unknown whether the HJ population can host (or may have hosted) exomoons. One suggested formation channel for HJs is high-eccentricity m…
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…
Warm Jupiters -- defined here as planets larger than 6 Earth radii with orbital periods of 8--200 days -- are a key missing piece in our understanding of how planetary systems form and evolve. It is currently debated whether Warm Jupiters form in situ, undergo disk or high eccentricity tidal migration, or have a mixture of origin channels. These different classes of origin channels lead to different expectations for Warm Jupiters' properties, which are currently difficult to evaluate due to the small sample size. We take advantage of the \TESS survey and systematically search for Warm Jupiter …
Hot Jupiters (HJs) are short-period giant planets that are observed around ~ 1% of solar-type field stars. One possible formation scenario for HJs is high-eccentricity (high-e) migration, in which the planet forms at much larger radii, is excited to high eccentricity by some mechanism, and migrates to its current orbit due to tidal dissipation occurring near periapsis. We consider high-e migration in dense stellar systems such as the cores of globular clusters (GCs), in which encounters with passing stars can excite planets to the high eccentricities needed to initiate migration. We study this…
Hot Jupiters (HJs) are Jupiter-like planets that reside very closely to their host star, within $\sim 0.1\,\mathrm{AU}$. Their formation is not well understood. It is generally believed that they cannot have formed in situ, implying that some form of migration must have occurred after their initial formation. We study the production of HJs through secular evolution in multiplanet systems with three to five planets. In this variant of high-$e$ migration, the eccentricity of the orbit of the innermost planet is excited on secular time-scales, triggering orbital migration due to tidal dissipation…
The population of giant planets on short-period orbits can potentially be explained by some flavours of high-eccentricity migration. In this paper we investigate one such mechanism involving "secular chaos", in which secular interactions between at least three giant planets push the inner planet to a highly eccentric orbit, followed by tidal circularization and orbital decay. In addition to the equilibrium tidal friction, we incorporate dissipation due to dynamical tides that are excited inside the giant planet. Using the method of Gaussian rings to account for planet-planet interactions, we e…
High eccentricity migration is a possible formation channel for hot Jupiters. However, in order for it to be consistent with the observed population of planets, tides must circularize the orbits in less than $\approx$ a Myr. A potential mechanism for such rapid circularization is the diffusive growth of the tidally driven planetary f-mode. Such growth occurs if the f-mode's phase at pericenter varies chaotically from one pericenter passage to the next. Previous studies focused on the variation of the orbital period due to tidal back-reaction on the orbit as the source of chaos. Here we show th…
High-eccentricity tidal migration is a possible way for giant planets to be emplaced in short-period orbits. If it commonly operates, one would expect to catch proto-Hot Jupiters on highly elliptical orbits that are undergoing high-eccentricity tidal migration. As of yet, few such systems have been discovered. Here, we introduce TOI-3362b (TIC-464300749b), an 18.1-day, 5 $M_{\rm Jup}$ planet orbiting a main-sequence F-type star that is likely undergoing high-eccentricity tidal migration. The orbital eccentricity is 0.815$^{+0.023}_{-0.032}$. With a semi-major axis of 0.153$^{+0.002}_{-0.003}$ …
We investigate the formation of close-in planets in near-coplanar eccentric hierarchical triple systems via the secular interaction between an inner planet and an outer perturber (Coplanar High-eccentricity Migration, CHEM). We generalize the previous work on the analytical condition for successful CHEM for point masses interacting only through gravity by taking into account the finite mass effect of the inner planet. We find that efficient CHEM requires that the systems should have m_1<<m_0 and m_1<<m_2. In addition to the gravity for point masses, we examine the importance of the short-range…
Hot Jupiters (HJs) are giant planets with orbital periods of the order of a few days with semimajor axis within $\sim$0.1 au. Several theories have been invoked in order to explain the origin of this type of planets, one of them being the high-eccentricity migration. This migration can occur through different high-eccentricity mechanisms. Our investigation focused on six different kinds of high-eccentricity mechanisms, namely, direct dispersion, coplanar, Kozai-Lidov, secular chaos, E1 and E2 mechanisms. We investigated the efficiency of these mechanisms for the production of HJ candidates in …
We study the tidal interaction between a low-mass companion (e.g., a protoplanet or a black hole) in orbit about a central mass, and the accretion disk within which it is submerged. We present results for a companion on a coplanar orbit with eccentricity e between 0.1 and 0.6. For these eccentricities, dynamical friction arguments in its local approximation, that is, ignoring differential rotation and the curvature of the orbit, provide simple analytical expressions for the rates of energy and angular momentum exchange between the disk and the companion. We examine the range of validity of the…
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…
High-eccentricity migration is a likely formation mechanism for many observed hot Jupiters, particularly those with a large misalignment between the stellar spin axis and orbital angular momentum axis of the planet. In one version of high-eccentricity migration, an inclined stellar companion excites von Zeipel-Lidov-Kozai (ZLK) eccentricity oscillations of a cold Jupiter, and tidal dissipation causes the planet's orbit to shrink and circularize. Throughout this process, the stellar spin can evolve chaotically, resulting in highly misaligned hot Jupiters. Previous population studies of this mig…
The Discovery of K2-232c: Divergent Formation Histories for Hot and Warm Jupiters Based on Outer Companion Eccentricity
Indiana University（印第安纳大学）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Princeton University（普林斯顿大学）；Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Millennium Institute for Astrophysics（天体物理学千年研究所）；Carnegie Science（卡内基科学）；University of California, Santa Cruz（加州大学圣克鲁兹分校）
The origin of Jupiter-mass planets with orbital periods of only a few days is still uncertain. It is widely believed that these planets formed near the water-ice line of the protoplanetary disk, and subsequently migrated into much smaller orbits. Most of the proposed migration mechanisms can be classified either as disk-driven migration, or as excitation of a very high eccentricity followed by tidal circularization. In the latter scenario, the giant planet that is destined to become a hot Jupiter spends billions of years on a highly-eccentric orbit, with apastron near the water-ice line. Event…
一类重要的热彗星形成理论涉及极端轨道偏心率（e=0.99或更大）的激发，随后在近星点通过时发生潮汐耗散，最终使行星轨道以小于10天的周期循环。在稳定状态下，这种机制需要存在大量的超偏心（e>0.9）迁移彗星，它们具有长的轨道周期和只有几个恒星半径的近星点距离。对于这些超偏心行星，由于轨道角动量守恒，近星点是固定的，每个轨道消耗的能量是常数，这意味着半长轴a的变化率为\dot a \propto a ^0.5，因此数量分布满足dN/dlog a \propto a ^0.5。如果这一形成过程产生了大多数热彗星，开普勒应该会探测到几个超偏心迁移的热彗星祖先，从而可以测试高偏心率迁移的情况。
Where Do Hot Jupiters Come From? Revisiting Tidal Disruption and Ejection in High-Eccentricity Migration
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；CSST Science Center for the Guangdong-HongKong-Macau Great Bay Area, Sun Yat-sen University（中山大学中国空间站科学中心粤港澳大湾区分中心）
