External Companion Research Articles

Teetering stars: resonant excitation of stellar obliquities by hot and warm Jupiters with external companions

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 the inner planet) becomes comparable to the nodal precession rate of the inner planet (driven by the companion). Due to the spin-down of the host star via magnetic braking, this resonance may be achieved during the star's main-sequence lifetime for a wide range of planet masses and orbital architectures. Obliquity excitation is accompanied by a decrease in mutual inclination between the inner planet and perturber, and can thus erase high inclinations. For hot Jupiters, the stellar spin axis is strongly coupled to the orbital axis, and obliquity excitation by a giant planet companion requires a strong perturber, usually located within 1-2 AU. For warm Jupiters, the spin and orbital axes are more weakly coupled, and the resonance may be achieved for distant giant planet perturbers (at several to tens of AU). Since warm Jupiters have a high occurrence rate of distant planetary companions with appropriate properties for resonant obliquity excitation, stellar obliquities in warm Jupiter systems may be common, particularly for warm Jupiters orbiting cool stars that have undergone significant spin-down.

Eccentricities and inclinations of multiplanet systems with external perturbers

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 ($\theta_{12}$) of the "2-planet + perturber" system, calibrated with numerical secular and N-body integrations, as a function of the perturber mass $m_p$, semi-major axis $a_p$ and inclination angle $\theta_p$. We find that the dynamics of the inner system is determined by the dimensionless parameter $\epsilon_{12}$, given by the ratio between the differential precession rate driven by the perturber and the mutual precession rate of the inner planets. Loosely packed systems (corresponding to $\epsilon_{12} \gg 1$) are more susceptible to eccentricity/inclination excitations by the perturber than tightly packed inner systems (with $\epsilon_{12} \ll 1$) (or singletons), although resonance may occur around $\epsilon_{12}\sim 1$, leading to large $e_i$ and $\theta_{12}$. Dynamical instability may set in for inner planet systems with large excited eccentricities and mutual inclinations. We present a formalism to extend our analytical results to general inner systems with $N>2$ planets and apply our results to constrain possible external companions to the Kepler-11 system. Eccentricity and inclination excitation by external companions may help explain the observational trend that systems with fewer transiting planets are dynamically hotter than those with more transiting planets.

Effects of disc warping on the inclination evolution of star–disc–binary systems

Several recent studies have suggested that circumstellar disks in young stellar binaries may be driven into misalignement with their host stars due to secular gravitational interactions between the star, disk and the binary companion. The disk in such systems is twisted/warped due to the gravitational torques from the oblate central star and the external companion. We calculate the disk warp profile, taking into account of bending wave propagation and viscosity in the disk. We show that for typical protostellar disk parameters, the disk warp is small, thereby justifying the "flat-disk" approximation adopted in previous theoretical studies. However, the viscous dissipation associated with the small disk warp/twist tends to drive the disk toward alignment with the binary or the central star. We calculate the relevant timescales for the alignment. We find the alignment is effective for sufficiently cold disks with strong external torques, especially for systems with rapidly rotating stars, but is ineffective for the majority of star-disk-binary systems. Viscous warp driven alignment may be necessary to account for the observed spin-orbit alignment in multi-planet systems if these systems are accompanied by an inclined binary companion.

How do external companions affect spin–orbit misalignment of hot Jupiters?

Consider a planet with its orbital angular momentum axis aligned with the spin axis of its host star. To what extent does an inclined distant companion (giant planet or binary star) affect this alignment? We provide an analytic, quantitative answer and apply it to hot Jupiter systems, for which misalignments between the orbital axis and the stellar spin axis have been detected. We also show how similar consideration can be applied to multi-planet systems with distant companions (such as Kepler-56). The result of this paper provides a simple method to assess the dynamical role played by external companions on spin-orbit misalignments in exoplanetary systems.

Moderately eccentric warm Jupiters from secular interactions with exterior companions

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 circular orbit. Eccentricity growth may arise from an inclined companion (through Lidov-Kozai cycles), or from an eccentric, nearly coplanar companion (through apsidal precession resonances). We quantify the necessary conditions (in terms of the eccentricity, semi-major axis and inclination) for external perturbers of various masses to raise the WJ eccentricity. We also consider the sample of eccentric WJs with detected outer companions, and for each system, identify the range of mutual inclinations needed to generate the observed eccentricity. For most systems, we find that relatively high inclinations (at least $\sim 40^\circ$) are needed so that Lidov-Kozai cycles are induced; the observed outer companions are typically not sufficiently eccentric to generate the observed WJ eccentricity in a low-inclination configuration. The results of this paper place constraints on possibly unseen external companions to eccentric WJs. Observations that probe mutual inclinations of giant planet systems will help clarify the origin of eccentric WJs and the role of external companions.

Spin–Orbit Misalignment of Merging Black Hole Binaries with Tertiary Companions

Abstract We study the effect of an external companion on the orbital and spin evolution of merging black hole (BH) binaries. A sufficiently nearby and inclined companion can excite Lidov–Kozai (LK) eccentricity oscillations in the binary, thereby shortening its merger time. During such LK-enhanced orbital decay, the spin axis of the BH generally exhibits chaotic evolution, leading to a wide range (0°–180°) of the final spin–orbit misalignment angle from an initially aligned configuration. For systems that do not experience eccentricity excitation, only modest ( ) spin–orbit misalignment can be produced, and we derive an analytic expression for the final misalignment using the principle of adiabatic invariance. The spin–orbit misalignment directly impacts the gravitational waveform and can be used to constrain the formation scenarios of BH binaries and dynamical influences of external companions.

On the Origin of the Spiral Morphology in the Elias 2–27 Circumstellar Disk

Abstract The young star Elias 2–27 has recently been observed to posses a massive circumstellar disk with two prominent large-scale spiral arms. In this Letter, we perform three-dimensional Smoothed Particle Hydrodynamics simulations, radiative transfer modeling, synthetic ALMA imaging, and an unsharped masking technique to explore three possibilities for the origin of the observed structures—an undetected companion either internal or external to the spirals, and a self-gravitating disk. We find that a gravitationally unstable disk and a disk with an external companion can produce morphology that is consistent with the observations. In addition, for the latter, we find that the companion could be a relatively massive planetary-mass companion (≲10–13 M Jup) and located at large radial distances (between ≈300–700 au). We therefore suggest that Elias 2–27 may be one of the first detections of a disk undergoing gravitational instabilities, or a disk that has recently undergone fragmentation to produce a massive companion.

Lidov–Kozai Cycles with Gravitational Radiation: Merging Black Holes in Isolated Triple Systems

Abstract We show that a black-hole binary with an external companion can undergo Lidov–Kozai cycles that cause a close pericenter passage, leading to a rapid merger due to gravitational-wave emission. This scenario occurs most often for systems in which the companion has a mass comparable to the reduced mass of the binary and the companion orbit has a semimajor axis within a factor of ∼10 of the binary semimajor axis. Using a simple population-synthesis model and three-body simulations, we estimate the rate of mergers in triple black-hole systems in the field to be about six per Gpc3 per year in the absence of natal kicks during black-hole formation. This value is within the low end of the 90% credible interval for the total black hole–black hole merger rate inferred from the current LIGO results. There are many uncertainties in these calculations, the largest of which is the unknown distribution of natal kicks. Even modest natal kicks of 40 km s−1 will reduce the merger rate by a factor of 40. A few percent of these systems will have eccentricity greater than 0.999 when they first enter the frequency band detectable by aLIGO (above 10 Hz).

Eccentricity and spin-orbit misalignment in short-period stellar binaries as a signpost of hidden tertiary companions

Eclipsing binaries are observed to have a range of eccentricities and spin-orbit misalignments (stellar obliquities). Whether such properties are primordial, or arise from post-formation dynamical interactions remains uncertain. This paper considers the scenario in which the binary is the inner component of a hierarchical triple stellar system, and derives the requirements that the tertiary companion must satisfy in order to raise the eccentricity and obliquity of the inner binary. Through numerical integrations of the secular octupole-order equations of motion of stellar triples, coupled with the spin precession of the oblate primary star due to the torque from the secondary, we obtain a simple, robust condition for producing spin-orbit misalignment in the inner binary: In order to excite appreciable obliquity, the precession rate of the stellar spin axis must be smaller than the orbital precession rate due to the tertiary companion. This yields quantitative requirements on the mass and orbit of the tertiary. We also present new analytic expressions for the maximum eccentricity and range of inclinations allowing eccentricity excitation (Lidov-Kozai window), for stellar triples with arbitrary masses and including the non-Keplerian potentials introduced by general relativity, stellar tides and rotational bulges. The results of this paper can be used to place constraints on unobserved tertiary companions in binaries that exhibit high eccentricity and/or spin-orbit misalignment, and will be helpful in guiding efforts to detect external companions around stellar binaries. As an application, we consider the eclipsing binary DI Herculis, and identify the requirements that a tertiary companion must satisfy to produce the observed spin-orbit misalignment.

HIDING PLANETS BEHIND A BIG FRIEND: MUTUAL INCLINATIONS OF MULTI-PLANET SYSTEMS WITH EXTERNAL COMPANIONS

ABSTRACT The Kepler mission has detected thousands of planetary systems with one to seven transiting planets packed within 0.7 au from their host stars. There is an apparent excess of single-transit planet systems that cannot be explained by transit geometries alone, when a single planetary mutual inclination dispersion is assumed. This suggests that the observed compact planetary systems have at least two different architectures. We present a scenario where the “Kepler dichotomy” may be explained by the action of an external giant planet or stellar companion misaligned with the inner multi-planet system. The external companion excites mutual inclinations of the inner planets, causing such systems to appear as “Kepler singles” in transit surveys. We derive approximate analytic expressions (in various limiting regimes), calibrated with numerical calculations, for the mutual inclination excitations for various planetary systems and perturber properties (mass m p , semimajor axis a p , and inclination ). In general, the excited mutual inclination increases with and , though secular resonances may lead to large mutual inclinations even for small . We discuss the implications of our results for understanding the dynamical history of transiting planet systems with known external perturbers.

Disruption of planetary orbits through evection resonance with an external companion: circumbinary planets and multiplanet systems

Planets around binary stars and those in multiplanet systems may experience resonant eccentricity excitation and disruption due to perturbations from a distant stellar companion. This "evection resonance" occurs when the apsidal precession frequency of the planet, driven by the quadrupole associated with the inner binary or the other planets, matches the orbital frequency of the external companion. We develop an analytic theory to study the effects of evection resonance on circumbinary planets and multiplanet systems. We derive the general conditions for effective eccentricity excitation or resonance capture of the planet as the system undergoes long-term evolution. Applying to circumbinary planets, we show that inward planet migration may lead to eccentricity growth due to evection resonance with an external perturber, and planets around shrinking binaries may not survive the resonant eccentricity growth. On the other hand, significant eccentricity excitation in multiplanet systems occurs in limited parameter space of planet and binary semimajor axes, and requires the planetary migration to be sufficiently slow.

Merging compact binaries in hierarchical triple systems: Resonant excitation of binary eccentricity

We study the secular dynamics of compact binaries (consisting of white dwarfs, neutron stars or black holes) with tertiary companions in hierarchical triple systems. As the inner binary (with initially negligible eccentricity) undergoes orbital decay due to gravitational radiation, its eccentricity can be excited by gravitational forcing from the tertiary. This excitation occurs when the triple system passes through an ``apsidal precession resonance,'' when the precession rate of the inner binary, driven by the gravitational perturbation of the external companion and general relativity, matches the precession rate of the outer binary. The eccentricity excitation requires the outer companion to be on an eccentric orbit, with the mutual inclination between the inner and outer orbits less than $\ensuremath{\sim}40\ifmmode^\circ\else\textdegree\fi{}$. Gravitational wave (GW) signals from the inner binary can be significantly modified as the system evolves through the apsidal precession resonance. For some system parameters (e.g., a white dwarf binary with a brown dwarf tertiary), the resonance can happen when the binary emits GWs in the ${10}^{\ensuremath{-}4}\ensuremath{-}{10}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Hz}$ range (the sensitivity band of LISA).

OBSERVATIONAL SIGNATURES OF PLANETS IN PROTOPLANETARY DISKS: SPIRAL ARMS OBSERVED IN SCATTERED LIGHT IMAGING CAN BE INDUCED BY PLANETS

Using 3D global hydro simulations coupled with radiative transfer calculations, we study the appearance of density waves induced by giant planets in direct imaging observations at near infrared wavelengths. We find that a 6 MJ planet in a typical disk around a 1 M_sun star can produce prominent and detectable spiral arms both interior and exterior to its orbit. The inner arms have (1) two well separated arms in roughly m=2 symmetry, (2) exhibit ~10-15 degrees pitch angles, (3) ~180-270 degrees extension in the azimuthal direction, and (4) ~150% surface brightness enhancement, all broadly consistent with observed spiral arms in the SAO 206462 and MWC 758 systems. The outer arms cannot explain observations as they are too tightly wound given typical disk scale height. We confirm previous results that the outer density waves excited by a 1 MJ planet exhibit low contrast in the IR and are practically not detectable. We also find that 3D effects of the waves are important. Compared to isothermal models, density waves in adiabatic disks exhibit weaker contrast in surface density but stronger contrast in scattered light images, due to a more pronounced vertical structure in the former caused by shock heating. To drive observed pairs of arms with an external companion on a circular orbit, a massive planet, possibly a brown dwarf, is needed at around [r~0.7", PA~10 degrees] (position angle PA from north to east) in SAO 206462 and [r~0.6", PA~10 degrees] in MWC 758. Their existence may be confirmed by direct imaging planet searches.

A class of warm Jupiters with mutually inclined, apsidally misaligned close friends

The orbits of giant extrasolar planets often have surprisingly small semimajor axes, large eccentricities, or severe misalignments between their orbit normals and their host stars' spin axes. In some formation scenarios invoking Kozai-Lidov oscillations, an external planetary companion drives a planet onto an orbit having these properties. The mutual inclinations for Kozai-Lidov oscillations can be large and have not been confirmed observationally. Here we present evidence that observed eccentric warm Jupiters with eccentric giant companions have mutual inclinations that oscillate between 35° and 65°. Our inference is based on the pairs' observed apsidal separations, which cluster near 90°. The near-orthogonality of periapse directions is effected by the outer companion's quadrupolar and octupolar potentials. These systems may be undergoing a stalled version of tidal migration that produces warm Jupiters over hot Jupiters, and they provide evidence for a population of multiplanet systems that are not flat and have been sculpted by Kozai-Lidov oscillations.

Star–disc–binary interactions in protoplanetary disc systems and primordial spin–orbit misalignments

We study the interactions between a protostar and its circumstellar disc under the influence of an external binary companion to determine the evolution of the mutual stellar spin - disc misalignment angle. The gravitational torque on the disc from an inclined binary makes the disc precess around the binary axis, while the star-disc interaction torque due to the rotation-induced quadrupole makes the stellar spin and the disc angular momentum axes precess around each other. A significant star-disc misalignment angle can be generated from a small initial value as the star-disc system evolves in time such that the two precession frequencies cross each other. This ``secular resonance'' behavior can be understood in a geometric way from the precession dynamics of spin and disc angular momenta. We derive the conditions for such resonance to occur, and find that they can be satisfied for reasonable protostar-disc-binary parameters. The evolution of star-disc inclination is also affected by mass accretion and by magnetic star-disc interaction torques, which can either promote or reduce star-disc misalignment. In general, as long as the initial binary-disc inclination is greater than a few degrees, a variety of star-disc misalignment angles can be generated within the disc lifetimes. We discuss the implications of our results for the stellar spin orientations in binaries, for the alignments/misalignments of protostellar discs and debris discs, and for the stellar obliquities in exoplanetary systems. In particular, if hot Jupiters are produced by the Kozai effect induced by an external stellar companion, then it is likely that ``primordial'' star-disc misalignments are already generated by the star-disc-binary interactions. Even for systems where the Kozai effect is suppressed, misaligned planets may still be produced during the protoplanetary disc phase.

On the equilibrium rotation of Hot Jupiters in eccentric and excited orbits

AbstractHot-Jupiters are a common sub-class of exoplanets, which are enough close to the star to undergo tidal dissipation. The continuous action of tides modify the rotation of the planets until an equilibrium situation is reached. It is often assumed that synchronous motion is the most probable outcome of tidal evolution, since synchronous rotation is observed for the majority of the satellites in the Solar System. This is true for circular orbits, but when the orbits are eccentric, tidal effects are stronger when the planets are closer to the star, and therefore, the rotation rate tends to equalize the orbital speed rate at the pericenter (which is faster than synchronous rotation). An additional complication arises if the eccentricity is not constant and undergoes periodic perturbations from an external companion. Here we obtain an expression for the equilibrium rotation of Hot-Jupiters undergoing tidal dissipation and planetary perturbations. We show that for these planets, the equilibrium rotation rate is faster than for non-perturbed eccentric orbits.