Significant Mutual Inclinations Research Articles

Chasing extreme planetary architectures

Context. Planet(s) in binaries are unique architectures for testing predictions of planetary formation and evolution theories in very hostile environments. Their presence in such a highly perturbed region poses a clear challenge from the early phase of planetesimals accretion to the dynamical evolution and stability through a very long period of time (several Gyrs in some case). Aims. The combination of radial velocity, speckle interferometry, high-contrast imaging and high-precision astrometry with interfer-ometry, offers a unique and unprecedented set of observable to push the exploration of the extreme planetary system HD 196885. By dissecting the physical and orbital properties of each component, we aim at shedding light on its global architecture and stability. Methods. We used the IRDIS dual-band imager of SPHERE at VLT, and the speckle interferometric camera HRCAM of SOAR, to acquire high-angular resolution images of HD 196885 AB between 2015 and 2020. Radial velocity observations started in 1983 with CORAVEL at OHP have been extended with a continuous monitoring with CORALIE at La Silla, and ELODIE and SOPHIE at OHP over almost 40 yr extending the radial velocity measurements HD 196885 A and resolving both the binary companion and the inner giant planet HD 196885 Ab. Finally, we took advantage of the exquisite astrometric precision of the dual-field mode of VLTI/GRAVITY (down to 30 µas) to monitor the relative position of HD 196885 A and B to search for the 3.6 yr astrometric wobble of the circumpri-mary planet Ab imprinted on the binary separation. Results. Our observations enable to accurately constrain the orbital properties of the binary HD 196885 AB, seen on an inclined and retrograde orbit (iAB = 120.43 deg) with a semi-major axis of 19.78 au, and an eccentricity of 0.417. The GRAVITY measurements confirm for the first time the nature of the inner planet HD 196885 Ab by rejecting all families of pole-on solutions in the stellar or brown dwarf masses. The most favored island of solutions is associated with a Jupiter-like planet (MAb = 3.39 MJup), with moderate eccentricity (eAaAb = 0.44), and inclination close to 143.04 deg. This results points toward a significant mutual inclination (Ф = 24.36 deg) between the orbital planes (relative to the star) of the binary companion B and the planet Ab. Our dynamical simulations indicate that the system is dynamically stable over time. Eccentricity and mutual inclination variations could be expected for moderate von Zipele Kozai Lidov cycles that may affect the inner planet.

The 14 Her Planetary System: Companion Masses and Architecture from Radial Velocities and Astrometry

We combine Hubble Space Telescope (HST) Fine Guidance Sensor, Hipparcos, and Gaia DR3 astrometric observations of the K0 V star 14 Her with the results of an analysis of extensive ground-based radial velocity data to determine perturbation orbits and masses for two previously known companions, 14 Her b and c. Radial velocities obtained with the Hobby–Eberly Telescope and from the literature now span over 25 years. With these data we obtain improved radial velocity (RV) orbital elements for both the inner companion, 14 Her b and the long-period outer companion, 14 Her c. We also find evidence of an additional RV signal with P ∼ 3789d. We then model astrometry from Hipparcos, HST, and Gaia with RV results to obtain system parallax and proper motion, perturbation periods, inclinations, and sizes due to 14 Her b and c. We find P b = 1767.6 ± 0.2 days, perturbation semimajor axis α b = 1.3 ± 0.1 mas, and inclination i b = 36° ± 3°, P c = 52160 ± 1028 days, perturbation semimajor axis α c = 10.3 ± 0.7 mas, and inclination i c = 82° ± 14°. In agreement with a past investigation, the 14 Her b, c orbits exhibit significant mutual inclination. Assuming a primary mass M * = 0.98 ± 0.04M ☉, we obtain companion masses and .

On the masses, age, and architecture of the VHS J1256−1257AB b system

ABSTRACT VHS J1256−1257 AB is an ultracool dwarf binary that hosts a wide-separation planetary-mass companion that is a key target of the JWST Exoplanet Early Release Science programme. Using Keck adaptive optics imaging and aperture masking interferometry, we have determined the host binary’s orbit (a = 1.96 ± 0.03 au, P = 7.31 ± 0.02 yr, e = 0.883 ± 0.003) and measured its dynamical total mass (0.141 ± 0.008 M⊙). This total mass is consistent with VHS J1256−1257 AB being a brown dwarf binary or pair of very low-mass stars. In addition, we measured the orbital motion of VHS J1256−1257 b with respect to the barycentre of VHS J1256−1257 AB, finding that the wide companion’s orbit is also eccentric ($e=0.68^{+0.11}_{-0.10}$), with a mutual inclination of 115○ ± 14○ with respect to the central binary. This orbital architecture is consistent with VHS J1256−1257 b attaining a significant mutual inclination through dynamical scattering and thereafter driving Kozai–Lidov cycles to pump the eccentricity of VHS J1256−1257 AB. We derive a cooling age of 140 ± 20 Myr for VHS J1256−1257 AB from low-mass stellar/substellar evolutionary models. At this age, the luminosity of VHS J1256−1257 b is consistent with both deuterium-inert and deuterium-fusing evolutionary tracks. We thus find a bimodal probability distribution for the mass of VHS J1256−1257 b, either 12.0 ± 0.1 MJup or 16 ± 1 MJup, from these models. Future spectroscopic data to measure isotopologues such as HDO and CH3D could break this degeneracy and provide a strong test of substellar models at the deuterium-fusion mass boundary.

Photodynamical analysis of the nearly resonant planetary system WASP-148

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 gravitational interactions between all known bodies in the system. Our analysis simultaneously fits the available radial velocities and transit light curves. In particular, we used the photometry secured by the Transiting Exoplanet Survey Satellite (TESS) and made public after the WASP-148 discovery announcement. The TESS data confirm the transit-timing variations, but only in combination with previously measured transit times. The system parameters we derived agree with those previously reported and have a significantly improved precision, including the mass of the non-transiting planet. We found a significant mutual inclination between the orbital planes of the two planets: I = 41.0+6.2°-7.6 based on the modelling of the observations, although we found I = 20.8 ± 4.6° when we imposed a constraint on the model enforcing long-term dynamical stability. When a third planet was added to the model – based on a candidate signal in the radial velocity – the mutual inclination between planets b and c changed significantly allowing solutions closer to coplanar. We conclude that more data are needed to establish the true architecture of the system. If the significant mutual inclination is confirmed, WASP-148 would become one of the only few candidate non-coplanar planetary systems. We discuss possible origins for this misalignment.

Exciting Mutual Inclination in Planetary Systems with a Distant Stellar Companion: The Case of Kepler-108

Abstract We study the excitation of mutual inclination between planetary orbits by a novel secular-orbital resonance in multi-planet 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 eccentricities. We discuss the possible outcomes of ivection resonance capture, and we use simulations to illustrate that it is a promising mechanism for producing the mutual inclination in systems where planets have significant mutual inclination but modest eccentricity, such as Kepler-108. We also find an apparent deficit of multi-planet systems that would have a nodal precession period comparable to the binary orbital period, suggesting that ivection resonance may inhibit formation of or destablize multi-planet systems with an external binary companion.

The distribution of mutual inclinations arising from the stellar quadrupole moment

ABSTRACT 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 rotation, coupled with a non-zero stellar obliquity. Here, we simulate a population of planetary systems subject to the secular perturbation arising from a tilted, oblate host star as it contracts and spins down subsequent to planet formation. We demonstrate that this mechanism can reproduce the general increase in planet-planet mutual inclinations with proximity to the host star, and delineate a parameter space wherein the host star can drive dynamical instabilities. We suggest that approximately 5–10 per cent of low-mass Kepler systems are susceptible to this instability mechanism, suggesting that a significant number of single-transiting planets may truly be intrinsically single. We also report a novel connection between instability and stellar obliquity reduction and make predictions that can be tested within upcoming TESS observations.

Precise Transit and Radial-velocity Characterization of a Resonant Pair: The Warm Jupiter TOI-216c and Eccentric Warm Neptune TOI-216b

Abstract TOI-216 hosts a pair of warm, large exoplanets discovered by the TESS mission. These planets were found to be in or near the 2:1 resonance, and both of them exhibit transit timing variations (TTVs). Precise characterization of the planets’ masses and radii, orbital properties, and resonant behavior can test theories for the origins of planets orbiting close to their stars. Previous characterization of the system using the first six sectors of TESS data suffered from a degeneracy between planet mass and orbital eccentricity. Radial-velocity measurements using HARPS, FEROS, and the Planet Finder Spectrograph break that degeneracy, and an expanded TTV baseline from TESS and an ongoing ground-based transit observing campaign increase the precision of the mass and eccentricity measurements. We determine that TOI-216c is a warm Jupiter, TOI-216b is an eccentric warm Neptune, and that they librate in 2:1 resonance with a moderate libration amplitude of deg, a small but significant free eccentricity of for TOI-216b, and a small but significant mutual inclination of 1.°2–3.°9 (95% confidence interval). The libration amplitude, free eccentricity, and mutual inclination imply a disturbance of TOI-216b before or after resonance capture, perhaps by an undetected third planet.

A significant mutual inclination between the planets within the π Mensae system

Context. Measuring the geometry of multi-planet extrasolar systems can provide insight into their dynamical history and the processes of planetary formation. These types of measurements are challenging for systems that are detected through indirect techniques such as radial velocity and transit, having only been measured for a handful of systems to date. Aims. We aim to place constraints on the orbital geometry of the outer planet in the π Mensae system, a G0V star at a distance of 18.3 pc that is host to a wide-orbit super-Jovian (M sin i = 10.02 ± 0.15MJup) with a 5.7-yr period and an inner transiting super-Earth (M = 4.82 ± 0.85M⊕) with a 6.3-d period. Methods. The reflex motion induced by the outer planet on the π Mensae star causes a significant motion of the photocenter of the system on the sky plane over the course of the 5.7-year orbital period of the planet. We combined astrometric measurements from the HIPPARCOS and Gaia satellites with a precisely determined spectroscopic orbit in an attempt to measure this reflex motion, and in turn we constrained the inclination of the orbital plane of the outer planet. Results. We measure an inclination of ib = 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 MJup. We find a significant mutual inclination between the orbital planes of the two planets, with a 95% credible interval for imut of between 34.°5 and 140.°6 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 piece of direct evidence that giant planets with large mutual inclinations have a role to play in the origins and evolution of some super-Earth systems.

The Resilience of Kepler Systems to Stellar Obliquity

Abstract The Kepler mission and its successor K2 have brought forth a cascade of transiting planets. Many of these planetary systems exhibit multiple members, but a large fraction possess only a single transiting example. This overabundance of singles has led to the suggestion that up to half of Kepler systems might possess significant mutual inclinations between orbits, reducing the transiting number (the so-called “Kepler Dichotomy”). In a recent paper, Spalding & Batygin demonstrated that the quadrupole moment arising from a young, oblate star is capable of misaligning the constituent orbits of a close-in planetary system enough to reduce their transit number, provided that the stellar spin axis is sufficiently misaligned with respect to the planetary orbital plane. Moreover, tightly packed planetary systems were shown to be susceptible to becoming destabilized during this process. Here, we investigate the ubiquity of the stellar obliquity-driven instability within systems with a range of multiplicities. We find that most planetary systems analyzed, including those possessing only two planets, underwent instability for stellar spin periods below ∼3 days and stellar tilts of order 30°. Moreover, we are able to place upper limits on the stellar obliquity in systems such as K2-38 (obliquity ≲20°), where other methods of measuring the spin–orbit misalignment are not currently available. Given the known parameters of T-Tauri stars, we predict that up to one-half of super-Earth-mass systems may encounter the instability, in general agreement with the fraction typically proposed to explain the observed abundance of single-transiting systems.

SPIN–ORBIT MISALIGNMENT AS A DRIVER OF THE KEPLER DICHOTOMY

ABSTRACT During its five-year mission, the Kepler spacecraft has uncovered a diverse population of planetary systems with orbital configurations ranging from single-transiting planets to systems of multiple planets co-transiting the parent star. By comparing the relative occurrences of multiple to single-transiting systems, recent analyses have revealed a significant over-abundance of singles. Dubbed the “Kepler Dichotomy,” this feature has been interpreted as evidence for two separate populations of planetary systems: one where all orbits are confined to a single plane, and a second where the constituent planetary orbits possess significant mutual inclinations, allowing only a single member to be observed in transit at a given epoch. In this work, we demonstrate that stellar obliquity, excited within the disk-hosting stage, can explain this dichotomy. Young stars rotate rapidly, generating a significant quadrupole moment, which torques the planetary orbits, with inner planets influenced more strongly. Given nominal parameters, this torque is sufficiently strong to excite significant mutual inclinations between planets, enhancing the number of single-transiting planets, sometimes through a dynamical instability. Furthermore, as hot stars appear to possess systematically higher obliquities, we predict that single-transiting systems should be relatively more prevalent around more massive stars. We analyze the Kepler data and confirm this signal to be present.

Decoupling of a giant planet from its disk in an inclined binary system

We explore the dynamical evolution of a planet embedded in a disk surrounding a star part of a binary system where the orbital plane of the binary is significantly tilted respect to the initial disk plane. Our aim is to test whether the planet remains within the disk and continues to migrate towards the star in a Type I/II mode in spite of the secular perturbations of the companion star. This would explain observed exoplanets with significant inclination respect to the equatorial plane of their host star. We have used two different SPH codes, vine and phantom, to model the evolution of a system star+disk+planet and companion star with time. After an initial coupled evolution, the inclination of the disk and that of the planet begin to differ significantly. The period of oscillation of the disk inclination, respect to the initial plane, is shorter than that of the planet which evolves independently after about 10^4 yr following a perturbed N-body behavior. However, the planet keeps migrating towards the star because during its orbital motion it crosses the disk plane and the friction with the gas causes angular momentum loss. Disk and planet in a significantly inclined binary system are not dynamically coupled for small binary separations but evolve almost independently. The planet abandons the disk and, due to the onset of a significant mutual inclination, it interacts with the gas only when its orbit intersects the disk plane. The drift of the planet towards the star is not due to type I/II with the planet embedded in the disk but to the friction with the gas during the disk crossing.

Misaligned protoplanetary disks in a young binary star system.

Many extrasolar planets follow orbits that differ from the nearly coplanar and circular orbits found in our Solar System; their orbits may be eccentric or inclined with respect to the host star's equator, and the population of giant planets orbiting close to their host stars suggests appreciable orbital migration. There is at present no consensus on what produces such orbits. Theoretical explanations often invoke interactions with a binary companion star in an orbit that is inclined relative to the planet's orbital plane. Such mechanisms require significant mutual inclinations between the planetary and binary star orbital planes. The protoplanetary disks in a few young binaries are misaligned, but often the measurements of these misalignments are sensitive only to a small portion of the inner disk, and the three-dimensional misalignment of the bulk of the planet-forming disk mass has hitherto not been determined. Here we report that the protoplanetary disks in the young binary system HKTauri are misaligned by 60 to 68degrees, such that one or both of the disks are significantly inclined to the binary orbital plane. Our results demonstrate that the necessary conditions exist for misalignment-driven mechanisms to modify planetary orbits, and that these conditions are present at the time of planet formation, apparently because of the binary formation process.

TRANSIT TIMING OBSERVATIONS FROM KEPLER . I. STATISTICAL ANALYSIS OF THE FIRST FOUR MONTHS

The architectures of multiple planet systems can provide valuable constraints on models of planet formation, including orbital migration, and excitation of orbital eccentricities and inclinations. NASA's Kepler mission has identified 1235 transiting planet candidates (Borcuki et al 2011). The method of transit timing variations (TTVs) has already confirmed 7 planets in two planetary systems (Holman et al. 2010; Lissauer et al. 2011a). We perform a transit timing analysis of the Kepler planet candidates. We find that at least ~12% of planet candidates currently suitable for TTV analysis show evidence suggestive of TTVs, representing at least ~65 TTV candidates. In all cases, the time span of observations must increase for TTVs to provide strong constraints on planet masses and/or orbits, as expected based on n-body integrations of multiple transiting planet candidate systems (assuming circular and coplanar orbits). We find that the fraction of planet candidates showing TTVs in this data set does not vary significantly with the number of transiting planet candidates per star, suggesting significant mutual inclinations and that many stars with a single transiting planet should host additional non-transiting planets. We anticipate that Kepler could confirm (or reject) at least ~12 systems with multiple transiting planet candidates via TTVs. Thus, TTVs will provide a powerful tool for confirming transiting planets and characterizing the orbital dynamics of low-mass planets. If Kepler observations were extended to at least six years, then TTVs would provide much more precise constraints on the dynamics of systems with multiple transiting planets and would become sensitive to planets with orbital periods extending into the habitable zone of solar-type stars.

Planet dispersal in binary systems during transient multiple star phases

Aims. If a significant fraction of binary star systems spent some time as inclined triple systems, either during their formation process or as the outcome of several close dynamical encounters in a crowded stellar environemnt, then the number of planets in binaries would be significantly lower than around single stars. The stellar chaotic phase preceding the instability of the triple system and the wide oscillations in eccentricity and inclination of the companion star due to the high mutual inclination between the companion and the singleton would quickly eject planets orbiting the binary in S-type orbits. Methods. We perform numerical simulations of the dynamical evolution of hierarchical triple star systems with planets hosted around the primary star of the inner binary. Different values of mutual inclination, binary separation and singleton initial semimajor axis are explored in a statistical way. Results. We find that a significant mutual inclination i m between the singleton and the binary is a key factor for instability of the planetary system. When i m is larger than ~$40^{\circ}$ the fraction of planets in the binary surviving the chaotic phase of the triple declines dramatically. The combination of eccentricity and inclination oscillations of the binary companion induced by the secular perturbations of the singleton and the sequence of close encounters preceding the ejection of one star fully destabilize a planetary system extending beyond 1 AU from the star. For i m around $90^{\circ}$ the percentage of surviving planets is lower than 20% for all binaries with a semimajor axis smaller than 200 AU. Conclusions. The frequency of planets in binaries with low separation may be strongly reduced by the residence of the pair in the past in a temporary inclined hierarchical triple.