Mutual Inclination Research Articles

The Prevalence of Resonance Among Young, Close-in Planets

Multiple planets undergoing disk migration may be captured into a chain of mean-motion resonances with the innermost planet parked near the disk’s inner edge. Subsequent dynamical evolution may disrupt these resonances, leading to the nonresonant configurations typically observed among Kepler planets that are Gyr old. In this scenario, resonant configurations are expected to be more common in younger systems. This prediction can now be tested, thanks to recent discoveries of young planets, in particular those in stellar clusters, by NASA’s TESS mission. We divided the known planetary systems into three age groups: young (<100 Myr old), adolescent (0.1–1 Gyr old), and mature (>1 Gyr old). The fraction of neighboring planet pairs having period ratios within a few percent of a first-order commensurability (e.g., 4:3, 3:2, or 2:1) is 70% ± 15% for young pairs, 24% ± 8% for adolescent pairs, and 15% ± 2% for mature pairs. The fraction of systems with at least one nearly commensurable pair (either first- or second-order) is 86% ± 13% among young systems, 38% ± 12% for adolescent systems, and 23% ± 3% for mature systems. First-order commensurabilities prevail across all age groups, with an admixture of second-order commensurabilities. Commensurabilities are more common in systems with high planet multiplicity and low mutual inclinations. Observed period ratios often deviate from perfect commensurability by ∼1% even among young planets, too large to be explained by resonant repulsion with equilibrium eccentricity tides. We also find that super-Earths in the radius gap (1.5–1.9R ⊕) are less likely to be near-resonant (11.9% ± 2.0%) compared to Earth-sized planets (R p < 1R ⊕; 25.3% ± 4.4%) or mini-Neptunes (1.9R ⊕ ≤ R p < 2.5R ⊕; 14.4% ± 1.8%).

Diversities and similarities exhibited by multi-planetary systems and their architectures. I. Orbital spacings

The rich diversity of multi-planetary systems and their architectures is greatly contrasted by the uniformity exhibited within many of these systems. Previous studies have shown that compact Kepler systems tend to exhibit a peas-in-a-pod architecture: Planets in the same system tend to have similar sizes and masses and be regularly spaced in orbits with low eccentricities and small mutual inclinations. This work extends on previous research and examines a larger and more diverse sample comprising all the systems with a minimum of three confirmed planets, resulting in 282 systems and a total of 991 planets. We investigated the system architectures, focusing on the orbital spacings between adjacent planets as well as their relationships with the planets' sizes and masses. We also quantified the similarities of the sizes, masses, and spacings of planets within each system, conducting both intra- and inter-system analyses. Our results corroborate previous research showing that planets orbiting the same star tend to be regularly spaced and that pairs of adjacent planets with radii $&lt; 1\, R_ predominantly have orbital period ratios (PRs) smaller than two. In contrast to other studies, we identified a significant similarity of adjacent orbital spacings not only at PRs &lt; 4 but also at 1.17 &lt; PRs &lt; 2662 . For the systems with transiting planets, we additionally found that the reported correlation between the orbital PRs and the average sizes of adjacent planets disappears when planet pairs with $R &lt; 1\, R_ are excluded. Furthermore, we examined the data for possible correlations between the intra-system dispersions of the orbital spacings and those of the planetary radii and masses. Our findings indicate that these dispersions are uncorrelated for the systems in which all the pairs of adjacent planets have PRs &lt; 6 and even for the compact systems where all PRs &lt; 2 . Notably, planets in the same system can be similarly spaced even if they do not have similar masses or sizes.

Empirical Stability Criteria for 3D Hierarchical Triple Systems. I. Circumbinary Planets

In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We derive critical semimajor axes based on simulating and analyzing the dynamical behavior of 3 × 108 binary star–planet configurations. For the first time, three-dimensional and eccentric planetary orbits are considered. We explore systems with a variety of binary and planetary mass ratios, binary and planetary eccentricities from 0 to 0.9, and orbital mutual inclinations ranging from 0° to 180°. Planetary masses range between the size of Mercury and the lower fusion boundary (approximately 13 Jupiter masses). The stability of each system is monitored over 106 planetary orbital periods. We provide empirical expressions in the form of multidimensional, parameterized fits for two borders that separate dynamically stable, unstable, and mixed zones. In addition, we offer a machine learning model trained on our data set as an alternative tool for predicting the stability of circumbinary planets. Both the empirical fits and the machine learning model are tested for their predictive capabilities against randomly generated circumbinary systems with very good results. The empirical formulae are also applied to the Kepler and TESS circumbinary systems, confirming that many planets orbit their host stars close to the stability limit of those systems. Finally, we present a REST application programming interface with a web-based application for convenient access to our simulation data set.

Modified method of round Gaussian rings. Application to the two-planetary problem

A scheme of the modified method of round Gaussian rings, designed to study the secular evolution of orbits in systems consisting of a central star and two planets, is presented. The reason for the secular evolution of the nodes and inclinations of the orbits of the planets is their mutual gravitational attraction. The orbits of the planets are modeled by homogeneous round Gaussian rings, to which the masses, sizes and angles of inclination of the orbits, as well as orbital angular momenta of the planets, are transferred. The method takes into account the fact that, in general, the ascending nodes of the orbits may not coincide. The mutual gravitational energy of the rings 𝑊𝑚𝑢𝑡 is represented as a series in the quadratic approximation in powers of small inclination angles. Using this function 𝑊𝑚𝑢𝑡, a closed system of four differential equations describing the secular evolution of the planets’ orbits is composed. The solution to the equations is obtained in finite analytic form, which simplifies the interpretation of the investigated planetary motions. The method was tested on the example of the Sun-Jupiter-Saturn system; for it, in particular, the difference in the longitudes of the nodes of the orbits of Jupiter and Saturn was calculated as a function of time. New approach is also used to study the precession of nodes in the exoplanetary system K2-36; graphs of all unknown quantities are obtained. It has been established that in the course of evolution the mutual inclination angle of the orbits remains constant, and the librations of the orbits in the inclination angle and in the motion of the nodes occur synchronously.

The HD 191939 Exoplanet System is Well Aligned and Flat

We report the sky-projected spin–orbit angle λ for HD 191939 b, the innermost planet in a six-planet system, using Keck/KPF to detect the Rossiter–McLaughlin (RM) effect. Planet b is a sub-Neptune with radius 3.4 ± 0.8 R ⊕ and mass 10.0 ± 0.7 M ⊕ with an RM amplitude <1 m s−1. We find the planet is consistent with a well-aligned orbit, measuring λ = 3.°7 ± 5.°0. Additionally, we place new constraints on the mass and period of the distant super-Jupiter, planet f, finding it to be 2.88 ± 0.26 M J on a 2898 ± 152 days orbit. With these new orbital parameters, we perform a dynamical analysis of the system and constrain the mutual inclination of the nontransiting planet e to be smaller than 12° relative to the plane shared by the inner three transiting planets. Additionally, the further planet f is inclined off this shared plane, the greater the amplitude of precession for the entire inner system, making it increasingly unlikely to measure an aligned orbit for planet b. Through this analysis, we show that this system’s wide variety of planets are all well-aligned with the star and nearly coplanar, suggesting that the system formed dynamically cold and flat out of a well-aligned protoplanetary disk, similar to our own solar system.

KPF Confirms a Polar Orbit for KELT-18 b

We present the first spectroscopic transit results from the newly commissioned Keck Planet Finder on the Keck-I telescope at W. M. Keck Observatory. We observed a transit of KELT-18 b, an inflated ultrahot Jupiter orbiting a hot star (T eff = 6670 K) with a binary stellar companion. By modeling the perturbation to the measured cross-correlation functions using the Reloaded Rossiter–McLaughlin technique, we derived a sky-projected obliquity of λ = − 94.°8 ± 0.°7 ( ψ=93.8−1.8+1.6° for isotropic i ⋆). The data are consistent with an extreme stellar differential rotation (α = 0.9), though a more likely explanation is moderate center-to-limb variations of the emergent stellar spectrum. We see additional evidence for the latter from line widths increasing toward the limb. Using loose constraints on the stellar rotation period from observed variability in the available TESS photometry, we were able to constrain the stellar inclination and thus the true 3D stellar obliquity to ψ=91.7−1.8+2.2° . KELT-18 b could have obtained its polar orbit through high-eccentricity migration initiated by Kozai–Lidov oscillations induced by the binary stellar companion KELT-18 B, as the two likely have a large mutual inclination as evidenced by Gaia astrometry. KELT-18 b adds another data point to the growing population of close-in polar planets, particularly around hot stars.

On the Dynamical Evolution of the Asteroid Belt in a Massive Star–Neutron Star Binary

Some fast radio bursts (FRBs) exhibit repetitive behaviors, and their origins remain enigmatic. It has been argued that repeating FRBs could be produced by the interaction between a neutron star and an asteroid belt. Here, we consider the systems in which an asteroid belt dwells around a massive star, while a neutron star, as a companion of the massive star, interacts with the belt through gravitational force. Various orbital configurations are assumed for the system. Direct N-body simulations are performed to investigate the dynamical evolution of the asteroids' belt. It is found that a larger orbital eccentricity of the neutron star will destroy the belt more quickly, with a large number of asteroids being scattered out of the system. A low inclination not only suppresses the collisions but also inhibits the ejection rate at early stages. However, highly inclined systems may undergo strong oscillations, resulting in the Kozai–Lidov instabilities. Among the various configurations, a clear periodicity is observed in the collision events for the case with an orbital eccentricity of 0.7 and mutual inclination of 0◦. It is found that such a periodicity can be sustained for at least eight neutron star orbital periods, supporting this mechanism as a possible explanation for periodically repeating FRBs. Our studies also suggest that the active stage of these kinds of FRB sources should be limited, since the asteroid belt would finally be destroyed by the neutron star after multiple passages.

Dynamical and Secular Stability of Mutually Inclined Planetary Systems

Multiple analytical, semi-analytical, and empirical stability criteria have been derived in the literature for two-planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well modeled by previous stability criteria. Here, we derive a semi-analytical stability criteria for two-planet systems, at arbitrary inclinations, in which the inner planet is a test particle. Using perturbation theory we calculate the characteristic fractional change in the semimajor axis of the inner binary β = δ a 1/a 1 caused by perturbations from the companion. Stability criteria can be derived by setting a threshold on β. Focusing initially on circular orbits, we derive an analytical expression for β for coplanar prograde and retrograde orbits. For noncoplanar configurations, we evaluate a semi-analytical expression. We then generalize to orbits with arbitrary eccentricities and account for the secular effects. Our analytical and semi-analytical results are in excellent agreement with direct N-body simulations. In addition, we show that contours of β ∼ 0.01 can serve as criteria for stability. More specifically, we show that (1) retrograde orbits are generally more stable than prograde ones; (2) systems with intermediate mutual inclination are less stable due to von Ziepel–Lidov–Kozai (vZLK) dynamics; and (3) mean motion resonances (MMRs) can stabilize intermediate inclination secularly unstable regions in phase space, by quenching vZLK secular processes (4) MMRs can destabilize some of the dynamically stable regions. We also point out that these stability criteria can be used to constrain the orbital properties of observed systems and their age.

Sculpting of Exoplanetary Systems Driven by a Misaligned Disk and Stellar Oblateness: Origin of Perpendicular Orbits in HD 3167

A significant proportion of exoplanets have been detected with highly tilted or even polar orbits relative to their host stars’ equatorial planes. These unusual orbital configurations are often linked to postdisk secular interactions among multiple bodies. However, many aspects remain elusive. In this study, we investigate the role of disk-induced spin–orbit misalignments in shaping the architecture of multiplanet systems, taking into account the combined effect of the host star’s oblateness and the full-space disk potential. We demonstrate that large mutual planetary inclinations can arise from a saddle-center bifurcation occurring during the photoevaporation of the disk. This bifurcation triggers an instant, nonadiabatic transition in the planet’s libration. Following this process, the orbital evolution diverges into several distinct patterns. Notably, in scenarios involving a near-polar primordial misalignment, the orbit, consistently librating about a coplanar equilibrium axis, can be captured by an orthogonal equilibrium during the decay of the stellar oblateness. However, the orbit will be eventually recaptured by the coplanar equilibrium, aligned or antialigned with the orientation of the outer orbit, resulting in either a prograde or retrograde inner–outer orbit configuration. Additionally, general relativity contributes to maintaining eccentricity stability within these dynamic scenarios. Through the proposed mechanism, we can provide a plausible explanation for the unique, near-perpendicular, and likely retrograde orbit architecture observed in the HD 3167 system, enhancing our understanding of exoplanetary system dynamics.

Why are inner planets not inclined?

AbstractPoincaré’s work more than one century ago, or Laskar’s numerical simulations from the 1990’s on, have irrevocably impaired the long-held belief that the Solar System should be stable. But mathematical mechanisms explaining this instability have remained mysterious. In 1968, Arnold conjectured the existence of “Arnold diffusion” in celestial mechanics. We prove Arnold’s conjecture in the planetary spatial 4-body problem as well as in the corresponding hierarchical problem (where the bodies are increasingly separated), and show that this diffusion leads, on a long time interval, to some large-scale instability. Along the diffusive orbits, the mutual inclination of the two inner planets is close to $\pi /2$ π / 2 , which hints at why even marginal stability in planetary systems may exist only when inner planets are not inclined. More precisely, consider the normalised angular momentum of the second planet, obtained by rescaling the angular momentum by the square root of its semimajor axis and by an adequate mass factor (its direction and norm give the plane of revolution and the eccentricity of the second planet). It is a vector of the unit 3-ball. We show that any finite sequence in this ball may be realised, up to an arbitrary precision, as a sequence of values of the normalised angular momentum in the 4-body problem. For example, the second planet may flip from prograde nearly horizontal revolutions to retrograde ones. As a consequence of the proof, the non-recurrent set of any finite-order secular normal form accumulates on circular motions – a weak form of a celebrated conjecture of Herman.

Dynamics of Two Planets near a 2:1 Resonance: Case Studies of Known and Synthetic Exosystems on a Grid of Initial Configurations

The distribution of period ratios for 580 known two-planet systems is apparently nonuniform, with several sharp peaks and troughs. In particular, the vicinity of the 2:1 commensurability seems to have a deficit of systems. Using Monte Carlo simulations and an empirically inferred population distribution of period ratios, we prove that this apparent dearth of near-resonant systems is not statistically significant. The excess of systems with period ratios in the wider vicinity of the 2:1 resonance is significant, however. Long-term WHFast integrations of a synthetic two-planet system on a grid period ratios from 1.87 through 2.12 reveal that the eccentricity and inclination exchange mechanism between non-resonant planets represents the orbital evolution very well in all cases, except at the exact 2:1 mean motion resonance. This resonance destroys the orderly exchange of eccentricity, while the exchange of inclination still takes place. Additional simulations of the Kepler-113 system on a grid of initial inclinations show that the secular periods of eccentricity and inclination variations are well fitted by a simple hyperbolic cosine function of the initial mutual inclination. We further investigate the six known two-planet systems with period ratios within 2% of the exact 2:1 resonance (TOI-216, KIC 5437945, Kepler-384, HD 82943, HD 73526, HD 155358) on a grid of initial inclinations and for two different initial periastron longitudes corresponding to the aligned and anti-aligned states. All these systems are found to be long-term stable except HD 73526, which is likely a false positive. The periodic orbital momentum exchange is still at work in some of these systems, albeit with much shorter cycling periods of a few years.

Orbital architectures of planet-hosting binaries III. Testing mutual inclinations of stellar and planetary orbits in triple-star systems

Abstract Transiting planets in multiple-star systems, especially high-order multiples, make up a small fraction of the known planet population but provide unique opportunities to study the environments in which planets would have formed. Planet-hosting binaries have been shown to have an abundance of systems in which the stellar orbit aligns with the orbit of the transiting planet, which could give insights into the planet formation process in such systems. We investigate here if this trend of alignment extends to planet-hosting triple-star systems. We present long-term astrometric monitoring of a novel sample of triple-star systems that host Kepler transiting planets. We measured orbit arcs in 21 systems, including 12 newly identified triples, from a homogeneous analysis of our Keck adaptive optics data and, for some systems, Gaia astrometry. We examine the orbital alignment within the nine most compact systems (≲ 500 au), testing if either (or both) of the stellar orbits align with the edge-on orbits of their transiting planets. Our statistical sample of triple systems shows a tendency toward alignment, especially when assessing the alignment probability using stellar orbital inclinations computed from full orbital fits, but is formally consistent with isotropic orbits. Two-population tests where half of the stellar orbits are described by a planet-hosting-binary-like moderately aligned distribution give the best match when the other half (non-planet-hosting) has a Kozai-like misaligned distribution. Overall, our results suggest that our sample of triple-star planet-hosting systems are not fully coplanar systems and have at most one plane of alignment.

Irregular fixation: I. Fixed points and librating orbits of the Brown Hamiltonian

ABSTRACT In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel–Lidov–Kozai oscillations. Stable systems with a mild hierarchy, where the period ratio is not too small, require an additional corrective term, known as the Brown Hamiltonian, to adequately account for their long-term evolution. Although the Brown Hamiltonian has been used to accurately describe the highly eccentric systems on circulating orbits where the periapse completes a complete revolution, the analysis near its elliptical fixed points had been overlooked. We derive analytically the modified fixed points including the Brown Hamiltonian and analyse its librating orbits (where the periapse motion is limited in range). We compare our result to the direct three-body integrations of millions of orbits and discuss the regimes of validity. We numerically discover the regions of orbital instability, allowed and forbidden librating zones with a complex, fractal, structure. The retrograde orbits, where the mutual inclination is $\iota \ \gt\ 90\ \rm deg$, are more stable and allowed to librate for larger areas of the parameter space. We find numerical fits for the librating-circulating boundary. Finally, we discuss the astrophysical implications for systems of satellites, stars, and compact objects. In a companion paper (Paper II), we apply our formalism to the orbits of irregular satellites around giant planets.

The effect of dynamical interactions in stellar birth environments on the orbits of young close-in planetary systems

Abstract Stars do not form in isolation but together with other stars, and often in a clustered environment. Depending on the initial conditions in these environments, such as initial density and substructure, the distances of encounters between stars will differ. These encounters can also affect just-formed exoplanetary systems. Using N-body simulations, we show the effect of a single fly-by on a common type of exoplanetary system: close-in Super-Earths/sub-Neptunes with or without a distant Giant planet. Even a single encounter can significantly modify the architecture of these exoplanetary systems over their long lifetimes. We test fly-bys with different characteristics, such as distance and mass, and show how they perturb the inner planets long after the encounter, leading to collisions and mutual inclination excitation, which can significantly modify the observed architecture of these systems in transit. We find that our initially four-planet inner systems reduce to three or two inner planets depending on their initial separation and that the mutual inclinations of these remaining planets can be high enough to reduce the number of observable, transiting planets. In our 500 Myr simulations, we show that this reduction in the number of transiting planets due to stellar fly-bys can contribute to the observed excess of single-transit systems.

3D Orbital Architecture of Exoplanetary Systems: KAM-Stability Analysis

We study the KAM-stability of several single star two-planetnonresonant extrasolar systems. It is likely that the observedexoplanets are the most massive of the system considered. Therefore,their robust stability is a crucial and necessary condition for thelong-term survival of the system when considering potentialadditional exoplanets yet to be seen. Our study is based on theconstruction of a combination of lower-dimensional elliptic and KAMtori, so as to better approximate the dynamics in the framework ofaccurate secular models. For each extrasolar system, we explore theparameter space of both inclinations: the one with respect to theline of sight and the mutual inclination between the planets. Ourapproach shows that remarkable inclinations, resulting inthree-dimensional architectures that are far from being coplanar,can be compatible with the KAM stability of the system. We findthat the highest values of the mutual inclinations are comparable tothose of the few systems for which the said inclinations are determinedby the observations.

Obliquity Constraints for the Extremely Eccentric Sub-Saturn Kepler-1656 b

The orbits of close-in exoplanets provide clues to their formation and evolutionary history. Many close-in exoplanets likely formed far out in their protoplanetary disks and migrated to their current orbits, perhaps via high-eccentricity migration (HEM), a process that can also excite obliquities. A handful of known exoplanets are perhaps caught in the act of HEM, as they are observed on highly eccentric orbits with tidal circularization timescales shorter than their ages. One such exoplanet is Kepler-1656 b, which is also the only known nongiant exoplanet (<100 M ⊕) with an extreme eccentricity (e = 0.84). We measured the sky-projected obliquity of Kepler-1656 b by observing the Rossiter–McLaughlin effect during a transit with the Keck Planet Finder. Our data are consistent with an aligned orbit but are also consistent with moderate misalignment with λ < 50° at 95% confidence, with the most likely solution of 35.0−21.6+14.9 deg. A low obliquity would be an unlikely outcome of most eccentricity-exciting scenarios, but we show that the properties of the outer companion in the system are consistent with the coplanar HEM mechanism. Alternatively, if the system is not relatively coplanar (≲20° mutual inclination), Kepler-1656 b may be presently at a rare snapshot of long-lived eccentricity oscillations that do not induce migration. Kepler-1656 b is only the fourth exoplanet with e > 0.8 to have its obliquity constrained; expanding this population will help establish the degree to which orbital misalignment accompanies migration. Future work that constrains the mutual inclinations of outer perturbers will be key for distinguishing plausible mechanisms.

Tracking Advanced Planetary Systems (TAPAS) with HARPS-N

Aims. The star HD 118203, classified as a K0 subgiant, was known to harbour a transiting hot Jupiter planet on a 6.1-day eccentric orbit. Previous studies also revealed a linear trend in the radial velocity (RV) domain, indicative of a companion on a wide orbit. Such a hierarchical orbital architecture could be helpful in studies of the origins of hot Jupiters. Methods. We acquired precise RV measurements over 17 yr using the 9.2 m Hobby-Eberly Telescope and the 3.6 m Telescopio Nazionale Galileo. Combining these observations with space-born photometric time series from the Transiting Exoplanet Survey Satellite, we constructed a two-planetary model for the system. Astrometric observations from HIPPARCOS and Gaia were used to constrain the orbital inclination of the wide-orbit companion and its mass. Numerical simulations were used to investigate the dynamics of the system. The photometric data were searched for additional transit-like flux drops. Results. We found that the additional companion is an 11-Jupiter mass planet orbiting HD 118203 on a 14-yr moderately eccentric orbit, constituting a hierarchical planetary system with the hot Jupiter. Both planets were found to be dynamically decoupled mainly due to the general relativistic apsidal precession of the inner planet, marginalising secular interactions. The orbits of both planets might have a relatively low mutual inclination unless the longitudes of the ascending node differ substantially. This configuration favours the coplanar high-eccentricity migration as a path to the present-day orbital configuration. No other transiting planets with radii down to 2 Earth radii and orbital periods less than 100 days were found in the system.

Gambling preferences and fund company ownership: Evidence from China

This paper empirically tests the preference of China's public mutual funds for lottery-type equities, analyzing data from equity funds in the country's public mutual fund market from 2005 to 2022. The study finds that this gambling preference positively correlates with short-term fund performance, but negatively impacts long-term outcomes. Further investigation shows that the funds' propensity for gambling increases stock market volatility. However, fund company ownership can mitigate this risk amplification by implementing a risk-sharing structure. Additionally, a significant positive correlation exists between the mutual fund industry's gambling inclination and fund managers' optimism about future market movements. Finally, this article employs text analysis to explore the influence of gambling preferences from a non-quantitative information perspective, which helps control the investing behavior of institutional investors and enhances the real economy's access to the capital market.

V892 Tau: A tidally perturbed circumbinary disc in a triple stellar system

V892 Tau is a young binary star surrounded by a circumbinary disc that shows hints of an interaction with the low-mass nearby star V892 Tau NE. The goal of this paper is to constrain the orbit of V892 Tau NE and to determine the resulting circumbinary disc dynamics. We present new ALMA observations of the V892 Tau circumbinary disc at a twice higher angular and spectral resolution. We modelled the data with V892 Tau as a triple system and performed a grid of hydrodynamical simulations testing several orbits of the companion. The simulation outputs were then post-processed to build synthetic maps that we compared to the observations. The 12CO emission of the disc shows clear non-Keplerian features such as spiral arms. When comparing the data with our synthetic observations, we interpreted these features as ongoing interactions with the companion. Our simulations indicate that an eccentricity of $e of the companion is needed to reproduce the observed disc extent and that a mutual inclination of $ i with the inner binary reproduces the measured disc tilt. In order to explain most of the features of the circumbinary disc, we propose that V892 Tau NE follows an orbit with a mild eccentricity $0.2 &lt; e &lt; 0.5$ and a mutual inclination of $30 i &lt; 60 Such a misaligned companion suggests the disc is oscillating and precessing with time, stabilising in an intermediate plane with a non-zero mutual inclination with the inner binary. Given the orbital configuration, we show that the stability of future planets is compromised in the second half of the disc once the gas has dissipated.

Seven new triply eclipsing triple star systems

Aims. We have identified nearly a hundred close triply eclipsing hierarchical triple star systems from data taken with the space telescope TESS. These systems are noteworthy in that we can potentially determine their dynamical and astrophysical parameters with a high precision. In the present paper, we report the comprehensive study of seven new compact triply eclipsing triple star systems taken from this larger sample: TICs 133771812, 176713425, 185615681, 287756035, 321978218, 323486857, and 650024463. Methods. Most of the data for this study come from TESS observations, but two of them have Gaia measurements of their outer orbits, and we obtained supplemental radial velocity (RV) measurements for three of the systems. The eclipse timing variation curves extracted from the TESS data, the photometric light curves, the RV points, and the spectral energy distribution (SED) are combined in a complex photodynamical analysis to yield the stellar and orbital parameters of all seven systems. Results. Four of the systems are quite compact with outer periods in the range of 41–56 days. All of the systems are substantially flat, with mutual inclination angles of ≲2°. Including the systems reported in this work, we have now studied in considerable detail some 30 triply eclipsing triples with TESS, and are accumulating a meaningful census of these systems.