Kozai Mechanism Research Articles

Cumulative shift of periastron time of binary pulsar with Kozai–Lidov oscillation

ABSTRACT We study a hierarchical triple system with the Kozai–Lidov mechanism, and analyse the cumulative shift of periastron time of a binary pulsar by the emission of gravitational waves. Time evolution of the osculating orbital elements of the triple system is calculated by directly integrating the first-order post-Newtonian equations of motion. The Kozai–Lidov mechanism will bend the evolution curve of the cumulative shift when the eccentricity becomes large. We also investigate the parameter range of mass and semimajor axis of the third companion with which the bending of the cumulative-shift curve could occur within 100 yr.

Mutual orbit orientations of transneptunian binaries

We present Keplerian orbit solutions for the mutual orbits of 17 transneptunian binary systems (TNBs). For ten of them, the orbit had not previously been known: 60458 2000 CM114, 119979 2002 WC19, 160091 2000 OL67, 160256 2002 PD149, 469514 2003 QA91, 469705 ǂKá̦gára, 508788 2000 CQ114, 508869 2002 VT130, 1999 RT214, and 2002 XH91. Seven more are systems where the size, shape, and period of the orbit had been published, but new observations have now eliminated the sky plane mirror ambiguity in its orientation: 90482 Orcus, 120347 Salacia-Actaea, 1998 WW31, 1999 OJ4, 2000 QL251, 2001 XR254, and 2003 TJ58. The dynamical masses we obtain from TNB mutual orbits can be combined with estimates of the objects' sizes from thermal observations or stellar occultations to estimate their bulk densities. The ǂKá̦gára system is currently undergoing mutual events in which one component casts its shadow upon the other and/or obstructs the view of the other. Such events provide valuable opportunities for further characterization of the system. Combining our new orbits with previously published orbits yields a sample of 35 binary orbits with known orientations that can provide important clues about the environment in which outer solar system planetesimals formed, as well as their subsequent evolutionary history. Among the relatively tight binaries, with semimajor axes less than about 5% of their Hill radii, prograde mutual orbits vastly outnumber retrograde orbits. This imbalance is not attributable to any known observational bias. We suggest that this distribution could be the signature of planetesimal formation through gravitational collapse of local density enhancements such as caused by the streaming instability. Wider binaries, with semimajor axes >5% of their Hill radii, are somewhat more evenly distributed between prograde and retrograde orbits, but with mutual orbits that are aligned or anti-aligned with their heliocentric orbits. This pattern could perhaps result from Kozai-Lidov cycles coupled with tidal evolution eliminating high inclination wide binaries.

The mass and density of the dwarf planet (225088) 2007 OR10

The satellite of (225088) 2007 OR10 was discovered on archival Hubble Space Telescope images and along with new observations with the WFC3 camera in late 2017 we have been able to determine the orbit. The orbit's notable eccentricity, e ≈ 0.3, may be a consequence of an intrinsically eccentric orbit and slow tidal evolution, but may also be caused by the Kozai mechanism. Dynamical considerations also suggest that the moon is small, Deff < 100 km. Based on the newly determined system mass of 1.75 ·1021 kg, 2007 OR10 is the fifth most massive dwarf planet after Eris, Pluto, Haumea and Makemake. The newly determined orbit has also been considered as an additional option in our radiometric analysis, provided that the moon orbits in the equatorial plane of the primary. Assuming a spherical shape for the primary this approach provides a size of 1230 ± 50 km, with a slight dependence on the satellite orbit orientation and primary rotation rate chosen, and a bulk density of 1.75 ± 0.07 g cm−3 for the primary. A previous size estimate that assumed an equator-on configuration (1535−225+75 km) would provide a density of 0.92−0.14+0.46 g cm−3, unexpectedly low for a 1000 km-sized dwarf planet.

Eccentricity distributions of eccentric binary black holes in galactic nuclei

Galactic nuclei are expected to be one of the main sites for formations of eccentric binary black holes (EBBHs), with an estimated detection rate of $\mathcal{O}(1-100$ yr$^{-1})$ with Advanced LIGO (aLIGO) detectors operating at design sensitivity. The two main formation channels of these binaries are gravitational capture and the secular Kozai-Lidov mechanism, with expectedly commensurable formation rates. We used Monte Carlo simulations to construct the eccentricity distributions of EBBHs formed through these channels in galactic nuclei, at the time their gravitational-wave signals enter the aLIGO band at $10$ Hz. We have found that the proportion of binary black holes entering the aLIGO band with eccentricities larger than $0.1$ is $\sim 10$ percent for the secular Kozai-Lidov mechanism, and $\sim 75$ percent for gravitational capture. We show that if future EBBH detection rates with aLIGO will be dominated by EBBHs formed in galactic nuclei, then the proportions of EBBHs formed through the two main channels can be constrained to a $\Delta \mathcal{F}= 0.2$ wide one-sigma confidence interval with a few tens of observations, even if parameter estimation errors are taken into account at realistic levels.

A high binary fraction for the most massive close-in giant planets and brown dwarf desert members

ABSTRACT Stellar multiplicity is believed to influence planetary formation and evolution, although the precise nature and extent of this role remain ambiguous. We present a study aimed at testing the role of stellar multiplicity in the formation and/or evolution of the most massive, close-in planetary and substellar companions. Using past and new direct imaging observations, as well as the Gaia DR2 catalogue, we searched for wide binary companions to 38 stars hosting massive giant planets or brown dwarfs (M &amp;gt; 7 MJup) on orbits shorter than ∼1 au. We report the discovery of a new component in the WASP-14 system, and present an independent confirmation of a comoving companion to WASP-18. From a robust Bayesian statistical analysis, we derived a binary fraction of $79.0^{+13.2}_{-14.7}$ per cent between 20 and 10 000 au for our sample, twice as high as for field stars with a 3σ significance. This binary frequency was found to be larger than for lower-mass planets on similar orbits, and we observed a marginally higher binary rate for inner companions with periods shorter than 10 d. These results demonstrate that stellar companions greatly influence the formation and/or evolution of these systems, suggesting that the role played by binary companions becomes more important for higher-mass planets, and that this trend may be enhanced for systems with tighter orbits. Our analysis also revealed a peak in binary separation at 250 au, highlighting a shortfall of close binaries among our sample. This indicates that the mechanisms affecting planet and brown dwarf formation or evolution in binaries must operate from wide separations, although we found that the Kozai–Lidov mechanism is unlikely to be the dominant underlying process. We conclude that binarity plays a crucial role in the existence of very massive short-period giant planets and brown dwarf desert inhabitants, which are almost exclusively observed in multiple systems.

Detection and characterization of an ultra-dense sub-Neptunian planet orbiting the Sun-like star K2-292

We present the discovery and characterization of a new transiting planet from Campaign 17 of the Kepler extended mission K2. The planet K2-292 b is a warm sub-Neptune on a 17 day orbit around a bright (V = 9.9 mag) solar-like G3 V star with a mass and radius of M⋆ = 1.00 ± 0.03 M⊙ and R⋆ = 1.09 ± 0.03 R⊙, respectively. We modeled simultaneously the K2 photometry and CARMENES spectroscopic data and derived a radius of Rp=2.63−0.10+0.12 R⊕ and mass of Mp=24.5−4.4+4.4 M⊕, yielding a mean density of ρp=7.4−1.5+1.6 g cm−3, which makes it one of the densest sub-Neptunian planets known to date. We also detected a linear trend in the radial velocities of K2-292 (γ˙RV = −0.40−0.07+0.07 m s−1 d−1) that suggests a long-period companion with a minimum mass on the order of 33 M⊕. If confirmed, it would support a formation scenario of K2-292 b by migration caused by Kozai-Lidov oscillations.

Misaligned accretion disc formation via Kozai–Lidov oscillations

We investigate the formation and evolution of misaligned accretion discs around the secondary component of a binary through mass transfer driven by Kozai-Lidov oscillations of the circumprimary disc's eccentricity and inclination. We perform SPH simulations to study the amount of mass transferred to the secondary star as a function of both the disc and binary parameters. For the range of parameters we explore, we find that increasing the disc aspect ratio, viscosity parameter and initial inclination as well as decreasing the binary mass ratio leads to larger amount of mass transfer, up to a maximum of about ten per cent of the initial mass of the primary disc. The circumsecondary disc forms with a high eccentricity and a high inclination and is also able to undergo KL oscillations. The circumsecondary disc oscillations have a shorter period than those in the disc around the primary. We find that some of the material that escapes the Roche-lobe of the two components forms a narrow misaligned circumbinary accretion disc. This study has implications for disc evolution in young binary star systems.

Revisiting the dynamics of planets in binaries: evolutionary timescales and the effect of early stellar evolution

The discovery of planets in binaries is one the most interesting outcomes of planetary research. With the growing number of discoveries has also grown the interest on describing their formation, long-term evolution and potential habitability. In this work we revisit the dynamics of planets in S-type binary systems. For that purpose we develop explicit formulas for the secularized octupolar Hamiltonian, coupled with general relativistic corrections and non-conservative interactions. We implemented those formulas in an open-source package \texttt{SecDev3B}, that can be used to reproduce our results or test improved versions of the models. In order to test it, we study the long-term dynamical evolution of S-type binary planets during the pre-main-sequence phase of stellar evolution. During that phase, stellar radius significantly changes in timescales similar to secular timescales. We hypothesize that when close-encounters between the planet and its host star happens (e.g. via Lidov-Kozai effect), particularities in the secular formalism plus changes in stellar radius may alter significantly the dynamical evolution. We study the well-known binary planet HD 80606b and found that an octupolar expansion of the conservative Hamiltonian is required to properly predict its dynamical evolution. We also apply the dynamical model, enriched with results coming from stellar evolutionary models, to demonstrate that in S-type systems around low-mass stars, with relative high inclinations ($\itot\ge 60^\circ$), moderate eccentricities ($0.2\le e\le 0.4$) and planets located around 1 AU, the evolution of stellar radius during the first few hundreds of Myr, alters significantly the timescales of dynamical evolution.

Chaotic Tides in Migrating Gas Giants: Forming Hot and Transient Warm Jupiters via Lidov-Kozai Migration

High-eccentricity migration is an important channel for the formation of hot Jupiters (HJs). In particular, Lidov-Kozai (LK) oscillations of orbital eccentricity/inclination induced by a distant planetary or stellar companion, combined with tidal friction, have been shown to produce HJs on Gyr timescales, provided that efficient tidal dissipation operates in the planet. We re-examine this scenario with the inclusion of dynamical tides. When the planet's orbit is in a high-eccentricity phase, the tidal force from the star excites oscillatory f-modes and r-modes in the planet. For sufficiently large eccentricity and small pericentre distance, the mode can grow chaotically over multiple pericentre passages and eventually dissipate non-linearly, drawing energy from the orbit and rapidly shrinking the semi-major axis. We study the effect of such chaotic tides on the planet's orbital evolution. We find that this pathway produces very eccentric ($e\gtrsim 0.9$) warm Jupiters (WJs) on short timescales (a few to 100 Myrs). These WJs efficiently circularize to become HJs due to their persistently small pericentre distances. Chaotic tides can also save some planets from tidal disruption by truncating the LK eccentricity oscillations, significantly increasing the HJ formation fraction for a range of planet masses and radii. Using a population synthesis calculation, we determine the characteristics of WJs and HJs produced in this scenario, including the final period distribution, orbital inclinations and stellar obliquities. Chaotic tides endow LK migration with several favorable features to explain observations of HJs. We expect that chaotic tides are also important in other flavours of high-$e$ migration.

Temporal Earth Coorbital Types of Asteroid 2016 HO3

A newly discovered asteroid 2016 HO3 has coorbital type of retrograde (or quasi) satellite with respect to Earth. The discovery enlarges number of known retrograde satellites of Earth. In this work numerical studies have been performed to investigate orbital dynamics of the asteroid by including all planets and the Moon as perturbers. Hypothetical asteroids were also generated to assess its general dynamics. Results show that since several hundreds thousands years ago the asteroid has been trapped in alternating coorbital types of retrograde satellite (RS) and horseshoe (HS). The RS and HS types, respectively, have taken place for some hundreds and some thousands years, and so those for the future. Long term orbital evolution for one million years predicts that about a few hundreds thousands years from the epoch the asteroid will completely escape its coorbital configuration with Earth. Orbit of the asteroid does not follow Kozai resonance state, and by this study it is found that asteroid 2016 HO3 may behave a coorbital pair with asteroid 2000 WN10.

Enhanced black hole mergers in binary–binary interactions

We study the orbital evolution of black hole (BH) binaries in quadruple systems, where the tertiary binary excites large eccentricity in the BH binary through Lidov-Kozai (LK) oscillations, causing the binary BHs to merge via gravitational radiation. For typical BH binaries with masses $m_{1,2}\simeq 20M_\odot-30M_\odot$ and initial semimajor axis $a_0\sim100$ AU (such that the binaries have no chance of merging by themselves within $\sim10^{10}$ yrs), we show that binary-binary interactions can significantly increase the LK window for mergers (the range of companion inclinations that allows the BH binary to merge within 10~Gyrs). This increase arises from a secular resonance between the LK oscillation of the BH binary and the nodal precession of the outer (binary-binary) orbit driven by the tertiary binary. Therefore, in the presence of tertiary binary, the BH merger fraction is increased to $10-30\%$, an order of magnitude larger than the merger fraction found in similar triple systems. Our analysis (with appropriate scalings) can be easily adapted to other configurations of systems, such as relatively compact BH binaries and moderately hierarchical triples, which may generate even higher merger fractions. Since the occurrence rate of stellar quadruples in the galactic fields is not much smaller than that of stellar triples, our result suggests that dynamically induced BH mergers in quadruple systems may be an important channel of producing BH mergers observed by LIGO/VIRGO.

Orbital Stability Regions for Hypothetical Natural Satellites of (101955) Bennu

The Origins, Spectral Interpretation, Resource Identification, Security-Regolith Explorer (known as OSIRIS-REx) mission will orbit and return a sample from near-Earth asteroid (101955) Bennu. Ground-based observations determined that no object greater than 15 m in diameter is orbiting around Bennu. This investigation explores the potential size and stability of natural satellites of less than 15 m in diameter to provide predictions for where such small satellites should be searched for upon arrival. The focus is solely on the existence of stable orbits for natural satellites. How the natural satellite migrated to this orbit is purposefully placed outside the bounds of this study. The numerical model includes of Bennu, third-body dynamics from the sun, and solar radiation pressure. This model is used with the initial conditions of various semimajor axes, inclinations, the longitude of the ascending nodes, and natural satellite diameters. To be stable, it is required that a set of initial conditions must remain in orbit for greater than 1000 years. The possible existence of natural satellites in orbit around Bennu as small as 0.75 cm is found. Certain mechanisms such as the modified Laplace plane, the Kozai resonance, and sun-synchronous orbits help explain the stability of some orbits.

Discovery of the first resolved triple white dwarf

We report the discovery of J1953-1019, the first resolved triple white dwarf system. The triplet consists of an inner white dwarf binary and a wider companion. Using Gaia DR2 photometry and astrometry combined with our follow-up spectroscopy, we derive effective temperatures, surface gravities, masses and cooling ages of the three components. All three white dwarfs have pure-hydrogen (DA) atmospheres, masses of 0.60-0.63 Msun and cooling ages of 40-290 Myr. We adopt eight initial-to-final mass relations to estimate the main sequence progenitor masses (which we find to be similar for the three components, 1.6-2.6 Msun) and lifetimes. The differences between the derived cooling times and main sequence lifetimes agree for most of the adopted initial-to-final mass relations, hence the three white dwarfs in J1953-1019 are consistent with coeval evolution. Furthermore, we calculate the projected orbital separations of the inner white dwarf binary (303.25 +- 0.01 au) and of the centre of mass of the inner binary and the outer companion (6398.97 +- 0.09 au). From these values, and taking into account a wide range of possible configurations for the triplet to be currently dynamically stable, we analyse the future evolution of the system. We find that a collision between the two inner white dwarfs due to Lidov-Kozai oscillations is unlikely, though if it occurs it could result in a sub-Chandrasekhar Type Ia supernova explosion.

Brown dwarf companion with a period of 4.6 yr interacting with the hot Jupiter CoRoT-20 b

We report the discovery of an additional substellar companion in the CoRoT-20 system based on six years of HARPS and SOPHIE radial velocity follow-up. CoRoT-20 c has a minimum mass of 17 ± 1 MJup and orbits the host star in 4.59 ± 0.05 yr, with an orbital eccentricity of 0.60 ± 0.03. This is the first identified system with an eccentric hot Jupiter and an eccentric massive companion. The discovery of the latter might be an indication of the migration mechanism of the hot Jupiter, via the Lidov–Kozai effect. We explore the parameter space to determine which configurations would trigger this type of interactions.

Hidden planetary friends: on the stability of two-planet systems in the presence of a distant, inclined companion

Recent observational campaigns have shown that multi-planet systems seem to be abundant in our Galaxy. Moreover, it seems that these systems might have distant companions, either planets, brown-dwarfs or other stellar objects. These companions might be inclined with respect to the inner planets, and could potentially excite the eccentricities of the inner planets through the Eccentric Kozai-Lidov mechanism. These eccentricity excitations could perhaps cause the inner orbits to cross, disrupting the inner system. We study the stability of two-planet systems in the presence of a distant, inclined, giant planet. Specifically, we derive a stability criterion, which depends on the companion's separation and eccentricity. We show that our analytic criterion agrees with the results obtained from numerically integrating an ensemble of systems. Finally, as a potential proof-of-concept, we provide a set of predictions for the parameter space that allows the existence of planetary companions for the Kepler-419, Kepler-56, Kepler-448, Kepler-88, Kepler-109, and Kepler-36 systems.

Shrinking orbits in hierarchical quadruple star systems

The distribution of the inner orbital periods of solar-type main-sequence (MS) triple star systems is known to be peaked at a few days, and this has been attributed to tidal evolution combined with eccentricity excitation due to Lidov-Kozai oscillations. Solar-type MS quadruple star systems also show peaks in their inner orbital period distributions at a few days. Here, we investigate the natural question whether tidal evolution combined with secular evolution can explain the observed inner orbital period distributions in quadruple stars. We carry out population synthesis simulations of solar-type MS quadruple star systems in both the 2+2 (two binaries orbiting each other's barycentre) and 3+1 (triple orbited by a fourth star) configurations. We take into account secular gravitational and tidal evolution, and the effects of passing stars. We assume that no short-period systems are formed initially, and truncate the initial orbital period distributions below 10 d accordingly. We find that, due to secular and tidal evolution, the inner orbital period distributions develop tails at short periods. Although qualitatively consistent with the observations, we find that our simulated orbital period distributions only quantitatively agree with the observations for the 3+1 systems. The observed 2+2 systems, on the other hand, show an enhancement of systems around 10 d, which is not reproduced in the simulations. This suggests that the inner orbital periods of 2+2 systems are not predominantly shaped by tidal and secular evolution, but by other processes, most likely occurring during the stellar formation and early evolution.

Orbital Characterization of GJ1108A System, and Comparison of Dynamical Mass with Model-derived Mass for Resolved Binaries

Abstract We report an orbital characterization of GJ1108Aab that is a low-mass binary system in the pre-main-sequence phase. Via the combination of astrometry using adaptive optics and radial velocity measurements, an eccentric orbital solution of e = 0.63 is obtained, which might be induced by the Kozai–Lidov mechanism with a widely separated GJ1108B system. Combined with several observed properties, we confirm that the system is indeed young. Columba is the most probable moving group, to which the GJ1108A system belongs, although its membership to the group has not been established. If the age of Columba is assumed for GJ1108A, the dynamical masses of both GJ1108Aa and GJ1108Ab (M dynamical,GJ1108Aa = 0.72 ± 0.04 M ⊙ and M dynamical,GJ1108Ab = 0.30 ± 0.03 M ⊙) are more massive than what an evolutionary model predicts based on the age and luminosities. We consider that the discrepancy in mass comparison can be attributed to an age uncertainty; the system is likely older than stars in Columba, and effects that are not implemented in classical models such as accretion history and magnetic activity are not preferred to explain the mass discrepancy. We also discuss the performance of the evolutionary model by compiling similar low-mass objects in the evolutionary state based on the literature. Consequently, it is suggested that the current model on average reproduces the mass of resolved low-mass binaries without any significant offsets.

The Impact of Vector Resonant Relaxation on the Evolution of Binaries near a Massive Black Hole: Implications for Gravitational-wave Sources

Abstract Binaries within the sphere of influence of a massive black hole (MBH) in galactic nuclei are susceptible to the Lidov–Kozai (LK) mechanism, which can drive orbits to high eccentricities and trigger strong interactions within the binary such as the emission of gravitational waves (GWs) and mergers of compact objects. These events are potential sources for GW detectors such as Advanced LIGO and VIRGO. The LK mechanism is only effective if the binary is highly inclined with respect to its orbit around the MBH (within a few degrees of 90°), implying low rates. However, close to an MBH, torques from the stellar cluster give rise to the process of vector resonant relaxation (VRR). VRR can bring a low-inclination binary into an “active” LK regime in which high eccentricities and strong interactions are triggered in the binary. Here, we study the coupled LK–VRR dynamics, with implications for LIGO and VIRGO GW sources. We carry out Monte Carlo simulations and find that the merger fraction enhancement due to LK–VRR dynamics is up to a factor of ∼10 for the lower end of assumed MBH masses ( ) and decreases sharply with increasing M •. We find that, even in our most optimistic scenario, the baseline BH–BH merger rate is small, and the enhancement by LK–VRR coupling is not large enough to increase the rate to well above the LIGO/VIRGO lower limit, . For the Galactic Center, the LK–VRR-enhanced rate is ∼100 times lower than the LIGO/VIRGO limit, and for , the rate barely reaches .

Quasi-secular evolution of mildly hierarchical triple systems: analytics and applications for GW sources and hot Jupiters

In hierarchical triple systems, the inner binary is perturbed by a distant companion. For large mutual inclinations, the Lidov–Kozai mechanism secularly excites large eccentricity and inclination oscillations of the inner binary. The maximal eccentricity attained, emax, is simply derived and widely used. However, for mildly hierarchical systems (i.e. the companion is relatively close and massive), non-secular perturbations affect the evolution. Here we account for fast non-secular variations and find a new analytic formula for emax, in terms of the system’s hierarchy level, correcting previous work and reproducing the orbital flip criteria. We find that emax is generally enhanced, allowing closer encounters between the inner binary components, thus significantly changing their interaction and its final outcome. We then extend our approach to include additional relativistic and tidal forces. Using our results, we show that the merger time of gravitational-wave (GW) sources orbiting massive black holes in galactic nuclei is enhanced compared with previous analysis accounting only for the secular regime. Consequently, this affects the distribution and rates of such GW sources in the relevant mild-hierarchy regime. We test and confirm our predictions with direct N-body and 2.5-level post-Newtonian codes. Finally, we calculate the formation and disruption rates of hot Jupiters (HJs) in planetary systems using a statistical approach, which incorporates our novel results for emax. We find that more HJs migrate from further out, but they are also tidally disrupted more frequently. Remarkably, the overall formation rate of HJs remains similar to that found in previous studies. Nevertheless, the different rates could manifest in different underlying distribution of observed warm Jupiters.

Detecting hierarchical stellar systems with LISA

A significant fraction of stars are members of gravitationally bound hierarchies containing three or more components. Almost all low mass stars in binaries with periods shorter three days are part of a hierarchical system. We therefore anticipate that a large fraction of compact galactic binaries detected by the Laser Interferometer Space Antenna (LISA) will be members of hierarchical triple or quadruple system. The acceleration imparted by the hierarchical companions can be detected in the gravitational wave signal for outer periods as large as 100 years. For systems with periods that are shorter than, or comparable to, the mission lifetime, it will be possible to measure the period and eccentricity of the outer orbit. LISA observations of hierarchical stellar systems will provide insight into stellar evolution, including the role that Kozai-Lidov oscillations play in driving systems towards merger.