Planetary Perturbers Research Articles

Planetary perturbers: flaring star–planet interactions in Kepler and TESS

ABSTRACT In many star–planet systems discovered so far, the innermost planet orbits within only a few stellar radii. In these systems, planets could become in situ probes of the extended stellar magnetic field. Because they disturb the field as they move, they are expected to trigger flares in the corona. Potential differences to the energies and morphologies of intrinsic flares are poorly constrained. However, as we expect planet-induced flares to correlate with the planet’s orbital period, we can identify them from a clustering of flares in phase with the planet’s orbit. We used the excellent phase coverage from Kepler and the Transiting Exoplanet Survey Satellite to find flaring star–planet systems, compile a catalogue of all their flares, and measure how much they cluster in orbital phase. In the 1811 searched systems, we found 25 single stars with three or more flares each. We quantified the significance of the clustering in each system, and compared it against the theoretically expected power of magnetic interaction that leads to planet-induced flaring. Most systems do not show any clustering, consistent with low expected power. Those we expect to show clustering fall on two branches. An inactive one, without any signs of clustering, and a tentative active one, where the clustering becomes more pronounced as the expected power of interaction increases. The flares in HIP 67522 are prominently clustered (p < 0.006). This young hot Jupiter system is the most promising candidate for magnetic star–planet interaction in our sample.

An inner warp discovered in the disk around HD 110058 using VLT/SPHERE and HST/STIS

Context. An edge-on debris disk was detected in 2015 around the young, nearby A0V star HD 110058. The disk showed features resembling those seen in the disk of β Pictoris that could indicate the presence of a perturbing planetary-mass companion in the system. Aims. We investigated new and archival scattered light images of the disk in order to characterise its morphology and spectrum. In particular, we analysed the disk’s warp to constrain the properties of possible planetary perturbers. Methods. Using data from two VLT/SPHERE observations taken with the Integral Field Spectrograph (IFS) and near InfraRed Dual-band Imager and Spectrograph (IRDIS), we obtained high-contrast images of the edge-on disk. Additionally, we used archival data from HST/STIS with a poorer inner-working angle but a higher sensitivity to detect the outer parts of the disk. We measured the morphology of the disk by analysing vertical profiles along the length of the disk to extract the centroid spine position and vertical height. We extracted the surface brightness and reflectance spectrum of the disk. Results. We detect the disk between 20 au (with SPHERE) and 150 au (with STIS), at a position angle of 159.6° ± 0.6°. Analysis of the spine shows an asymmetry between the two sides of the disk, with a 3.4° ± 0.9° warp between ~20au and 60 au. The disk is marginally vertically resolved in scattered light, with a vertical aspect ratio of 9.3 ± 0.7% at 45 au. The extracted reflectance spectrum is featureless, flat between 0.95 µm and 1.1 µm, and red from 1.1 µm to 1.65 µm. The outer parts of the disk are also asymmetric with a tilt between the two sides compatible with a disk made of forward-scattering particles and seen not perfectly edge-on, suggesting an inclination of <84°. Conclusions. The presence of an undetected planetary-mass companion on an inclined orbit with respect to the disk could explain the warp. The misalignment of the inner parts of the disk with respect to the outer disk suggests a warp that has not yet propagated to the outer parts of the disk, favouring the scenario of an inner perturber as the origin of the warp.

Planet search with the Keck/NIRC2 vortex coronagraph in the Ms band for Vega

Context. Gaps in circumstellar disks can signal the existence of planetary perturbers, making such systems preferred targets for direct imaging observations of exoplanets. Aims. Being one of the brightest and closest stars to the Sun, the photometric standard star Vega hosts a two-belt debris disk structure. Together with the fact that its planetary system is being viewed nearly face-on, Vega has been one of the prime targets for planet imaging efforts. Methods. Using the vector vortex coronagraph on Keck/NIRC2 in the Ms band at 4.67 μm, we report the planet detection limits from 1 au to 22 au for Vega with an on-target time of 1.8 h. Results. We reach a 3 MJupiter limit outward of 12 au, which is nearly an order of magnitude deeper than for other existing studies. Combining our observations with existing radial velocity studies, we can confidently rule out the existence of companions more than ~8 MJupiter from 22 au down to 0.1 au for Vega. Interior and exterior to ~4 au, this combined approach reaches planet detection limits down to ~2–3 MJupiter using radial velocity and direct imaging, respectively. Conclusions. By reaching multi-Jupiter mass detection limits, our results are expected to be complemented by the planet imaging of Vega in the upcoming observations using the James Webb Space Telescope to obtain a more holistic understanding of the planetary system configuration around Vega.

The case of HD 106906 debris disc: a binary’s revenge

ABSTRACTDebris disc architecture presents [exo-]planetary scientists with precious clues for processes of planet formation and evolution, including constraints on planetary mass perturbers. This is particularly true of the disc in HD 106906, which in early HST, then follow up polarimetric observations, presented asymmetries and needle-like features that have been attributed to perturbations by a massive, and unusually distant external planetary companion. Here, we revisit the long-term secular dynamical evolution of the HD 106906 disc allowing for the combined gravitational action of the planetary companion and the inner stellar binary which holds the system together. We argue that the binary is strong enough to impose a dynamical break at the disc’s location, resulting in distinctive observational signatures which we render via simulated surface density maps and vertical structure profiles. Within uncertainties on the planet’s orbit, we show that the disc can go from being fully dominated by the inner binary to significantly so, and is hardly ever outside its reach. The extent of binary dominance impacts the disc’s mean eccentricity, a metric which we map as a function of the planet’s semimajor axis and orbital eccentricity, with and without radiation pressure. We can thus constrain the planet’s orbit to ease the tension between evident axisymmetry in the millimeter, and apparent asymmetry in scattered light. We discuss phase space structure, then inclination distribution, arguing for the relevance of our results to a variety of hierarchical systems, as we set the stage for generalizations that allow for disc self-gravity and collisional evolution.

Orbital Dynamics Landscape near the Most Distant Known Trans-Neptunian Objects

The most distant known trans-Neptunian objects (TNOs), those with perihelion distance above 38 au and semimajor axis above 150 au, are of interest for their potential to reveal past, external, or present but unseen perturbers. Realizing this potential requires understanding how the known planets influence their orbital dynamics. We use a recently developed Poincaré mapping approach for orbital phase space studies of the circular planar restricted three-body problem, which we have extended to the case of the 3D restricted problem with N planetary perturbers. With this approach, we explore the dynamical landscape of the 23 most distant TNOs under the perturbations of the known giant planets. We find that, counter to common expectations, almost none of these TNOs are far removed from Neptune’s resonances. Nearly half (11) of these TNOs have orbits consistent with stable libration in Neptune’s resonances; in particular, the orbits of TNOs 148209 and 474640 overlap with Neptune’s 20:1 and 36:1 resonances, respectively. Five objects can be ruled currently nonresonant, despite their large orbital uncertainties, because our mapping approach determines the resonance boundaries in angular phase space in addition to semimajor axis. Only three objects are in orbital regions not appreciably affected by resonances: Sedna, 2012 VP113 and 2015 KG163. Our analysis also demonstrates that Neptune’s resonances impart a modest (few percent) nonuniformity in the longitude of perihelion distribution of the currently observable distant TNOs. While not large enough to explain the observed clustering, this small dynamical sculpting of the perihelion longitudes could become relevant for future, larger TNO data sets.

Inclination dynamics of resonant planets under the influence of an inclined external companion

ABSTRACT 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 analytical expressions for the mutual inclination excitations in the inner planet system induced by an inclined companion, for various period ratios and perturber properties. In most cases, the mutual inclination is proportional to a dimensionless parameter that characterizes the strength of the perturber relative to the coupling in the inner system. We show that the MMR strengthens the inner coupling, reducing the mutual inclination induced by the perturber by a factor of a few. We find that the resonance is resilient to the perturbation, and derive a criterion for the libration of the resonant angle. Our results have applications for constraining unseen planetary perturbers, and for understanding the architecture of multiplanet systems.

Disentangling Planets from Photoelectric Instability in Gas-rich Optically Thin Dusty Disks

Abstract Structures in circumstellar disks such as gaps and rings are often attributed to planets. This connection has been difficult to show unequivocally, as other processes may also produce these features. In particular, a photoelectric instability (PEI) has been proposed, operating in gas-rich optically thin disks, that generates structures predicted by planet–disk interactions. We examine the question of how to disentangle the planetary effects on disk structure from the effects of the PEI. We use the Pencil Code to perform 2D global hydrodynamical models of the dynamics of gas and dust in a thin disk with and without planetary perturbers. Photoelectric heating is modeled with an equation of state where pressure is proportional to dust surface density. The drag force on grains and its backreaction on the gas are included. Analyzing the situation without PEI, we find that gas–dust interactions alter the shape of the planetary gap from the dust-free case when the local dust-to-gas ratio ε approaches unity. This result also applies to primordial disks, because dust drifting inward accumulates at the edge of the planetary gap, and any initial dust-to-gas ratio eventually achieves ε = 1 if the dust reservoir is sufficient. We find a result particular to high dust-to-gas ratio disks as well: as dust drifts inward, the dust front becomes a sharp transition, and the backreaction triggers the Rossby wave instability. When PEI is included, we find that it obscures structures induced by planets unless the planet’s mass is sufficiently large to carve a noticeable gap. Specifically, the instability generates arcs and rings of regular spacing: a planet is discernible when it carves a dust gap wider than the wavelength of the PEI.

Effects of unseen additional planetary perturbers on compact extrasolar planetary systems

Motivated by the large number of compact extrasolar planetary systems discovered by the Kepler Mission, this paper considers perturbations due to possible additional outer planets. The discovered compact systems sometimes contain multiple transiting planets, so that their orbital angular momentum vectors are tightly aligned. Since planetary orbits are susceptible to forced oscillations of their inclination angles, the highly aligned nature of these systems places constraints on possible additional (non-transiting) planets. If planets in the outer regions of these solar systems have sufficiently large mass or sufficiently small semi-major axis, they will induce the compact inner orbits to oscillate in and out of a transiting configuration. This paper considers the dynamics of the compact systems discovered to host five or more planets. In order to not perturb these systems out of a continually, mutually transiting state, additional planetary companions must generally have periastron $p>10$ AU. Specific constraints are found for each of the 18 planetary systems considered, which are obtained by marginalising over other orbital parameters using three different choices of priors for the companion properties (a uniform prior, a transit-inspired prior, and an non-transiting disk prior). A separate ensemble of numerical experiments shows that these compact systems generally cannot contain Jupiter-analogs without disrupting the observed orbits. We also consider how these constraints depend on system properties and find that the surface density of the planetary system is one of the most important variables. Finally, we provide specific results for two systems, WASP-47 and Kepler-20, for which this analysis provides interesting constraints.

CONSTRAINING THE MOVEMENT OF THE SPIRAL FEATURES AND THE LOCATIONS OF PLANETARY BODIES WITHIN THE AB AUR SYSTEM

ABSTRACT We present a new analysis of multi-epoch, H-band, scattered light images of the AB Aur system. We use a Monte Carlo radiative transfer code to simultaneously model the system’s spectral energy distribution (SED) and H-band polarized intensity (PI) imagery. We find that a disk-dominated model, as opposed to one that is envelope-dominated, can plausibly reproduce AB Aur’s SED and near-IR imagery. This is consistent with previous modeling attempts presented in the literature and supports the idea that at least a subset of AB Aur’s spirals originate within the disk. In light of this, we also analyzed the movement of spiral structures in multi-epoch H-band total light and PI imagery of the disk. We detect no significant rotation or change in spatial location of the spiral structures in these data, which span a 5.8-year baseline. If such structures are caused by disk–planet interactions, the lack of observed rotation constrains the location of the orbit of planetary perturbers to be >47 au.

ON SHOCKS DRIVEN BY HIGH-MASS PLANETS IN RADIATIVELY INEFFICIENT DISKS. II. THREE-DIMENSIONAL GLOBAL DISK SIMULATIONS

ABSTRACT Recent high-resolution, near-infrared images of protoplanetary disks have shown that these disks often present spiral features. Spiral arms are among the structures predicted by models of disk–planet interaction and thus it is tempting to suspect that planetary perturbers are responsible for these signatures. However, such interpretation is not free of problems. The observed spirals have large pitch angles, and in at least one case (HD 100546) it appears effectively unpolarized, implying thermal emission of the order of 1000 K (465 ± 40 K at closer inspection). We have recently shown in two-dimensional models that shock dissipation in the supersonic wake of high-mass planets can lead to significant heating if the disk is sufficiently adiabatic. Here we extend this analysis to three dimensions in thermodynamically evolving disks. We use the Pencil Code in spherical coordinates for our models, with a prescription for thermal cooling based on the optical depth of the local vertical gas column. We use a 5M J planet, and show that shocks in the region around the planet where the Lindblad resonances occur heat the gas to substantially higher temperatures than the ambient gas. The gas is accelerated vertically away from the midplane to form shock bores, and the gas falling back toward the midplane breaks up into a turbulent surf. This turbulence, although localized, has high α values, reaching 0.05 in the inner Lindblad resonance, and 0.1 in the outer one. We find evidence that the disk regions heated up by the shocks become superadiabatic, generating convection far from the planet’s orbit.

PROBING FOR EXOPLANETS HIDING IN DUSTY DEBRIS DISKS: DISK IMAGING, CHARACTERIZATION, AND EXPLORATION WITHHST/STIS MULTI-ROLL CORONAGRAPHY

Spatially resolved scattered-light images of circumstellar (CS) debris in exoplanetary systems constrain the physical properties and orbits of the dust particles in these systems. They also inform on co-orbiting (but unseen) planets, systemic architectures, and forces perturbing starlight-scattering CS material. Using HST/STIS optical coronagraphy, we have completed the observational phase of a program to study the spatial distribution of dust in ten CS debris systems, and one "mature" protoplanetrary disk all with HST pedigree, using PSF-subtracted multi-roll coronagraphy. These observations probe stellocentric distances > 5 AU for the nearest stars, and simultaneously resolve disk substructures well beyond, corresponding to the giant planet and Kuiper belt regions in our Solar System. They also disclose diffuse very low-surface brightness dust at larger stellocentric distances. We present new results inclusive of fainter disks such as HD92945 confirming, and better revealing, the existence of a narrow inner debris ring within a larger diffuse dust disk. Other disks with ring-like sub-structures, significant asymmetries and complex morphologies include: HD181327 with a posited spray of ejecta from a recent massive collision in an exo-Kuiper belt; HD61005 suggested interacting with the local ISM; HD15115 & HD32297, discussed also in the context of environmental interactions. These disks, and HD15745, suggest debris system evolution cannot be treated in isolation. For AU Mic's edge-on disk, out-of-plane surface brightness asymmetries at > 5 AU may implicate one or more planetary perturbers. Time resolved images of the MP Mus proto-planetary disk provide spatially resolved temporal variability in the disk illumination. These and other new images from our program enable direct inter-comparison of the architectures of these exoplanetary debris systems in the context of our own Solar System.

WARM JUPITERS NEED CLOSE “FRIENDS” FOR HIGH-ECCENTRICITY MIGRATION—A STRINGENT UPPER LIMIT ON THE PERTURBER'S SEPARATION

We propose a stringent observational test on the formation of warm Jupiters (gas-giant planets with 10 d <~ P <~ 100 d) by high-eccentricity (high-e) migration mechanisms. Unlike hot Jupiters, the majority of observed warm Jupiters have pericenter distances too large to allow efficient tidal dissipation to induce migration. To access the close pericenter required for migration during a Kozai-Lidov cycle, they must be accompanied by a strong enough perturber to overcome the precession caused by General Relativity (GR), placing a strong upper limit on the perturber's separation. For a warm Jupiter at a ~ 0.2 AU, a Jupiter-mass (solar-mass) perturber is required to be <~ 3 AU (<~ 30 AU) and can be identified observationally. Among warm Jupiters detected by Radial Velocities (RV), >~ 50% (5 out of 9) with large eccentricities (e >~ 0.4) have known Jovian companions satisfying this necessary condition for high-e migration. In contrast, <~ 20 % (3 out of 17) of the low-e (e <~ 0.2) warm Jupiters have detected additional Jovian companions, suggesting that high-e migration with planetary perturbers may not be the dominant formation channel. Complete, long-term RV follow-ups of the warm-Jupiter population will allow a firm upper limit to be put on the fraction of these planets formed by high-e migration. Transiting warm Jupiters showing spin-orbit misalignments will be interesting to apply our test. If the misalignments are solely due to high-e migration as commonly suggested, we expect that the majority of warm Jupiters with low-e (e <~0.2) are not misaligned, in contrast with low-e hot Jupiters.

Effect of main belt perturbers on asteroid-pair age estimation

Context. Asteroid-pair age estimations are usually performed by backward integration of possible orbits of pair components, taking planetary perturbations into account along with the Yarkovsky effect. It is assumed that uncertainties coming from the backward integration process itself are small, so to reduce uncertainties in estimations, effort usually focuses on reducing uncertainties in the initial orbital elements and the dimensions of the pair components. Aims. This work aims to evaluate the role of the frequently ignored nonplanetary perturbers in asteroid-pair age estimation. When their role is not negligible, the ages of the youngest known pairs can be roughly re-estimated. Methods. The orbital evolution of several asteroid-pair components and the close approaches between components during the last ≈43 kyr are investigated. Initially, the force equations consisted of only planetary perturbers. The three largest main belt perturbers were added afterwards. Finally, as many as 262 massive main belt perturbers were included. The effect of main belters on age estimation is assessed by comparing the dates of the closest approaches between pair components. The range of the Yarkovsky effect is simulated very roughly, only for comparison purposes. Results. The estimated age of the youngest known pair (6070) Rheinland – (54827) 2001 NQ8 including the Yarkovsky effect seems to be either 16.3 ± 0.1 kyr for the retrograde rotation or 16.0 ± 0.2 kyr for the prograde rotation of the second component, respectively. This is younger by about 0.7−0.9 kyr than the previous estimate. Several more pairs, namely (88259) 2001 HJ7 − 1999 VA117, (111962) 2002 GP75 − (280008) 2001 UR224, (180906) 2005 KB6 − (217266) 2003 YR67, (229401) 2005 SU152 − 2005 UY97 ,a nd 2005 GS180 − 2008 FK107, had relative encounter velocities within 1. 0m s −1 , suggesting they might also have formed within the interval studied. Some other pairs, including (5026) Martes – 2005 WW113, which was previously reported as very young, had slightly higher encounter velocities and longer nominal minimum distances, calling into question whether they could have formed within the interval studied or in some previous mutual encounter of pair components. Conclusions. The effect of main belt perturbers on asteroid-pair age estimation is buried in the huge age uncertainties caused by the Yarkovsky effect until the rotation direction of pair components is recognized.

Long-Term Cycling of Kozai-Lidov Cycles: Extreme Eccentricities and Inclinations Excited by a Distant Eccentric Perturber

The very long-term evolution of the hierarchical restricted three-body problem is calculated analytically for high inclinations. The Kozai-Lidov Cycles (KLCs) slowly evolve due to the octupole term in the perturber's potential and exhibit striking features, including extremely high eccentricities and the generation of retrograde orbits with respect to the perturber. These features were found in recent numerical experiments of the nonrestricted three-body problem and were attributed inaccurately to the comparable and low masses of the two orbiting companions. Our calculation is done by averaging for the first time the double averaged secular equations of motion over the KLCs and finding a new constant of the motion. These very long-term effects are likely to be important in various astrophysical systems thought to involve KLCs, such as hot Jupiters, irregular moons of planets, and many others.

Hot Jupiters from secular planet–planet interactions

About 25 per cent of 'hot Jupiters' (extrasolar Jovian-mass planets with close-in orbits) are actually orbiting counter to the spin direction of the star. Perturbations from a distant binary star companion can produce high inclinations, but cannot explain orbits that are retrograde with respect to the total angular momentum of the system. Such orbits in a stellar context can be produced through secular (that is, long term) perturbations in hierarchical triple-star systems. Here we report a similar analysis of planetary bodies, including both octupole-order effects and tidal friction, and find that we can produce hot Jupiters in orbits that are retrograde with respect to the total angular momentum. With distant stellar mass perturbers, such an outcome is not possible. With planetary perturbers, the inner orbit's angular momentum component parallel to the total angular momentum need not be constant. In fact, as we show here, it can even change sign, leading to a retrograde orbit. A brief excursion to very high eccentricity during the chaotic evolution of the inner orbit allows planet-star tidal interactions to rapidly circularize that orbit, decoupling the planets and forming a retrograde hot Jupiter.

Driving Spiral Arms in the Circumstellar Disks of HD 100546 and HD 141569A

With two-dimensional hydrodynamic simulations of disks perturbed externally by stars, brown dwarfs, or planets we investigate possible scenarios that can account for the spiral structure in circumstellar disks. We consider two scenarios: spiral structure driven by an external bound planet or low-mass star, and that excited by a previous stellar close encounter or flyby. We find that both scenarios produce a morphology similar to that observed in the outer disks of HD 141569A and HD 100546: moderately open two-armed outer spiral structure. Our simulations exhibit some trends. While bound prograde objects effectively truncate a disk, a close encounter by a star instead pulls out spiral arms, spreading out the disk. Following a flyby, the morphology of the spiral structure can be used to limit the mass of the perturbing object and the time since the encounter occurred. Eccentric bound planetary perturbers tend to clear gas away from the planet more efficiently, resulting in a reduction in the excited spiral amplitude. Bound perturbers in thicker disks excite more open but lower amplitude spiral structure. When the bound object has higher mass (stellar), the disk is truncated by the Roche lobe of the planet at periapse, and each time the companion approaches periapse, spiral arms may be pulled out from the disk. Thinner disks tend to exhibit more steeply truncated disk edges. We find that the outer two-armed spiral structure at radii greater than 300 AU observed in the disk of HD 141569A is qualitatively reproduced with tidal perturbations from its companion binary HD 141569B and HD 141569C on a prograde orbit near periapse. Our simulation accounts for the outer spiral arms, but is less successful than the secular model of Augereau and Papaloizou at matching the lopsidedness or asymmetry of the disk edge at 300 AU. Our simulations suggest that the disk has been previously truncated by the tidal force from the binary and has aspect ratio or thickness h/r 0.1. The simulated disk also exhibits an enhanced density at the disk edge. We find that a bound object (stellar or planetary) is unlikely to explain the spiral structure in the disk of HD 100546. A coeval planet or brown dwarf in the disk of sufficient mass to account for the amplitude of the spiral structure would be detectable in NICMOS and Space Telescope Imaging Spectrograph images; however, existing images reveal no such object. A previous encounter could explain the observed structure, provided that the disk is thin, the mass of the perturbing star is greater than ~0.1 M?, and the encounter occurred less than a few thousand years ago. This suggests that the object responsible for causing the spiral structure is currently within a few arcminutes of the star. However, the USNO-B proper motion survey reveals no candidate object associated with HD 100546 or any moving object that could have recently encountered HD 100546. Furthermore, the probability that a field star encountered HD 100546 in the past few thousand years is very low.

Planetary Perturbers in Debris Disks

Neptune dominates the dynamics of the Kuiper Belt. By examining images of debris disks around other stars, we may be able to infer what kinds of planets shape the outer edges of other planetary systems. The last few years have seen a burst of progress in the modeling of azimuthal structures in debris disks created by planetary perturbers; new models incorporate planets on substantially eccentric orbits. I review this recent progress in debris disk dynamics and discuss the Kuiper Belt as a key example.