Lidov-Kozai Stability Regions in the Alpha Centauri system

Lidov-Kozai stability regions in the alpha Centauri system

Authors:

Guippone et al

Abstract:
The stability of planets in the alpha-Centauri AB stellar system has been studied extensively. However, most studies either focus on the orbital plane of the binary or consider inclined circular orbits.

Here, we numerically investigate the stability of a possible planet in the alpha-Centauri AB binary system for S-type orbits in an arbitrary spatial configuration. In particular, we focus on inclined orbits and explore the stability for different eccentricities and orientation angles.

We show that large stable and regular regions are present for very eccentric and inclined orbits, corresponding to libration in the Lidov-Kozai resonance. We additionally show that these extreme orbits can survive over the age of the system, despite the effect of tides. Our results remain qualitatively the same for any compact binary system.

Magnetospheric Truncation, Tidal Inspiral, and the Creation of Short-period and Ultra-short-period Planets

Magnetospheric Truncation, Tidal Inspiral, and the Creation of Short-period and Ultra-short-period Planets


Authors:

Lee et al

Abstract:
Sub-Neptunes around FGKM dwarfs are evenly distributed in log orbital period down to ~10 days, but dwindle in number at shorter periods. Both the break at ~10 days and the slope of the occurrence rate down to ~1 day can be attributed to the truncation of protoplanetary disks by their host star magnetospheres at corotation. We demonstrate this by deriving planet occurrence rate profiles from empirical distributions of pre-main-sequence stellar rotation periods. Observed profiles are better reproduced when planets are distributed randomly in disks—as might be expected if planets formed in situ—rather than piled up near disk edges, as would be the case if they migrated in by disk torques. Planets can be brought from disk edges to ultra-short (less than 1 day) periods by asynchronous equilibrium tides raised on their stars. Tidal migration can account for how ultra-short-period planets are more widely spaced than their longer-period counterparts. Our picture provides a starting point for understanding why the sub-Neptune population drops at ~10 days regardless of whether the host star is of type FGK or early M. We predict planet occurrence rates around A stars to also break at short periods, but at ~1 day instead of ~10 days because A stars rotate faster than stars with lower masses (this prediction presumes that the planetesimal building blocks of planets can drift inside the dust sublimation radius).

Stability of Multiplanetary Systems in Star Clusters

Stability of Multiplanetary Systems in Star Clusters

Authors:

Cai et al

Abstract:
Most stars form in star clusters and stellar associated. To understand the roles of star cluster environments in shaping the dynamical evolution of planetary systems, we carry out direct N-body simulations of four planetary systems models in three different star cluster environments with respectively N=2k, 8k and 32k stars. In each cluster, an ensemble of initially identical planetary systems are assigned to solar-type stars with ∼1M⊙ and evolved for 50~Myr. We found that following the depletion of protoplanetary disks, external perturbations and planet-planet interactions are two driving mechanisms responsible for the destabilization of planetary systems. The planet survival rate varies from ∼95% in the N=2k cluster to ∼60% in the N=32k cluster, which suggests that most planetary systems can indeed survive in low-mass clusters, except in the central regions. We also find that planet ejections through stellar encounters are cumulative processes, as only ∼3% of encounters are strong enough to excite the eccentricity by Δe≥0.5. Short-period planets can be perturbed through orbit crossings with long-period planets. When taking into account planet-planet interactions, the planet ejection rate nearly doubles, and therefore multiplicity contributes to the vulnerability of planetary systems. In each ensemble, ∼0.2% of planetary orbits become retrograde due to random directions of stellar encounters. Our results predict that young low-mass star clusters are promising sites for next-generation planet surveys, yet low planet detection rates are expected in dense globular clusters such as 47 Tuc. Nevertheless, planets in denser stellar environments are likely to have shorter orbital periods, which enhances their detectability.

HD 155358's Interacting Gas Giants

The orbital configuration of the two interacting Jupiters in HD 155358 system
Authors:

Ma et al

Abstract:
Recent observation reveals two interacting Jupiters possibly trapped in a 2:1 mean motion resonance (MMR) around the star HD 155358. For the 2:1 MMR, Beaugé et al. found that as long as the orbital decay was sufficiently slow, the trapped planets should also be in apsidal co-rotation. So it is very interesting to explore whether HD 155358 did undergo such an evolution and presents an apsidal co-rotation. Based on the existing results of spectroscopic orbital determination, the global dynamics of the system shows that the two planets are in an apsidal co-rotation if the eccentricity of the outer planet (ec) takes values very close to the lower limit of its 1σ confidence interval. This makes us conjecture that the globally minimizing solution could be missed in the previous orbital determination. Using an efficient global optimization method, we do find a better solution, reducing χ2 from 1.4 to 1.2. This new solution is significantly different from the previous one, and in particular, with smaller ec. However, the increased possibility for the system to be trapped in a 2:1 MMR with apsidal co-rotation is still not high. A set of simulations of the adiabatic convergent migration process are then performed. The results consistently indicate that the 2:1 MMR forms before apsidal co-rotation. Finally, the long-term stability of the formed system and of its resonant structure are extensively explored, and the resulting statistics are given. A conclusion is that the 2:1 MMR with apsidal co-rotation is a very stable structure.

The Fate of Tatooine-like Circumbinary Exoplanets

TATOOINE'S FUTURE: THE ECCENTRIC RESPONSE OF KEPLER'S CIRCUMBINARY PLANETS TO COMMON-ENVELOPE EVOLUTION OF THEIR HOST STARS

Authors:

Kostov et al

Abstract:

Inspired by the recent Kepler discoveries of circumbinary planets orbiting nine close binary stars, we explore the fate of the former as the latter evolve off the main sequence. We combine binary star evolution models with dynamical simulations to study the orbital evolution of these planets as their hosts undergo common-envelope (CE) stages, losing in the process a tremendous amount of mass on dynamical timescales. Five of the systems experience at least one Roche-lobe overflow and CE stage (Kepler-1647 experiences three), and the binary stars either shrink to very short orbits or coalesce; two systems trigger a double-degenerate supernova explosion. Kepler's circumbinary planets predominantly remain gravitationally bound at the end of the CE phase, migrate to larger orbits, and may gain significant eccentricity; their orbital expansion can be more than an order of magnitude and can occur over the course of a single planetary orbit. The orbits these planets can reach are qualitatively consistent with those of the currently known post-CE, eclipse-time variations circumbinary candidates. Our results also show that circumbinary planets can experience both modes of orbital expansion (adiabatic and nonadiabatic) if their host binaries undergo more than one CE stage; multiplanet circumbinary systems like Kepler-47 can experience both modes during the same CE stage. Additionally, unlike Mercury orbiting the Sun, a circumbinary planet with the same semimajor axis can survive the CE evolution of a close binary star with a total mass of 1 ${M}_{\odot }$.

Understanding the Dynamics of TIghtly Packed Systems

The study of dynamics, the movement of objects in space under the influence of each other's gravity, gets more complicated the more objects you throw into your system. At this year’s Division for Planetary Sciences/European Planetary Science Congress meeting, the Exoplanet Dynamics session was packed full of talks on tightly-packed multi-planet systems and their instabilities.

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The Stability of Tidal Equilibrium for Hierarchical Star-Planet-Moon Systems

The Stability of Tidal Equilibrium for Hierarchical Star-Planet-Moon Systems

Authors:

Adams et al

Abstract:

Motivated by the current search for exomoons, this paper considers the stability of tidal equilibrium for hierarchical three-body systems containing a star, a planet, and a moon. In this treatment, the energy and angular momentum budgets include contributions from the planetary orbit, lunar orbit, stellar spin, planetary spin, and lunar spin. The goal is to determine the optimized energy state of the system subject to the constraint of constant angular momentum. Due to the lack of a closed form solution for the full three-body problem, however, we must use use an approximate description of the orbits. We first consider the Keplerian limit and find that the critical energy states are saddle points, rather than minima, so that these hierarchical systems have no stable tidal equilibrium states. We then generalize the calculation so that the lunar orbit is described by a time-averaged version of the circular restricted three-body problem. In this latter case, the critical energy state is a shallow minimum, so that a tidal equilibrium state exists. In both cases, however, the lunar orbit for the critical point lies outside the boundary (roughly half the Hill radius) where (previous) numerical simulations indicate dynamical instability. These results suggest that star-planet-moon systems have no viable long-term stable states analogous to those found for two-body systems.

Long-term stability of HR 8799

Long-term stability of the HR 8799 planetary system without resonant lock

Authors:

Gotberg et al

Abstract:

HR 8799 is a star accompanied by four massive planets on wide orbits. The observed planetary configuration has been shown to be unstable on a timescale much shorter than the estimated age of the system (~ 30 Myr) unless the planets are locked into mean motion resonances. This condition is characterised by small-amplitude libration of one or more resonant angles that stabilise the system by preventing close encounters. We simulate planetary systems similar to the HR 8799 planetary system, exploring the parameter space in separation between the orbits, planetary masses and distance from the Sun to the star. We find systems that look like HR 8799 and remain stable for longer than the estimated age of HR 8799. None of our systems are forced into resonances. We find, with nominal masses and in a narrow range of orbit separations, that 5 of 100 systems match the observations and lifetime. Considering a broad range of orbit separations, we find 12 of 900 similar systems. The systems survive significantly longer because of their slightly increased initial orbit separations compared to assuming circular orbits from the observed positions. A small increase in separation leads to a significant increase in survival time. The low eccentricity the orbits develop from gravitational interaction is enough for the planets to match the observations. With lower masses, but still comfortably within the estimated planet mass uncertainty, we find 18 of 100 matching and long-lived systems in a narrow orbital separation range. In the broad separation range, we find 82 of 900 matching systems. Our results imply that the planets in the HR 8799 system do not have to be in strong mean motion resonances.

Exoplanets Around Binary Stars are Ejected, Don't Collide

Planet Scattering Around Binaries: Ejections, Not Collisions

Authors:

Smullen et al

Abstract:

Transiting circumbinary planets discovered by Kepler provide unique insight into binary star and planet formation. Several features of this new found population, for example the apparent pile-up of planets near the innermost stable orbit, may distinguish between formation theories. In this work, we determine how planet-planet scattering shapes planetary systems around binaries as compared to single stars. In particular, we look for signatures that arise due to differences in dynamical evolution in binary systems. We carry out a parameter study of N-body scattering simulations for four distinct planet populations around both binary and single stars. While binarity has little influence on the final system multiplicity or orbital distribution, the presence of a binary dramatically effects the means by which planets are lost from the system. Most circumbinary planets are lost due to ejections rather than planet-planet or planet-star collisions. The most massive planet in the system tends to control the evolution. Systems similar to the only observed multi-planet circumbinary system, Kepler-47, can arise from much more tightly packed, unstable systems. Only extreme initial conditions introduce differences in the final planet populations. Thus, we suggest that any intrinsic differences in the populations are imprinted by formation.

Studying the HD 41004AB Circumbinary System

Circumstellar multi-planetary systems in binary stars: secular resonances and a semi-analytical approach to determine the location

Authors:

Pilat-Lohinger et al

Abstract:

Binary stars are of special interest for studies of planetary motion and habitability as most of the stars in the solar neighborhood are part of such stellar systems. Since a secondary star causes gravitational perturbations the planetary motion is restricted to certain regions of the phase space depending on the binary configuration. In case a binary system hosts a giant planet it is obvious that additional perturbations will occur. These perturbations will be studied in detail in this investigation where we take into account various binary-planet configurations. We show how the dynamics of another test-planet is influenced by mean motion and secular resonances. Therefore, it is important to know the locations of these resonances. First, we study the binary system HD41004AB to visualize the perturbations on the dynamics of test-planets caused by the secondary star and the detected giant planet. Then we perform a frequency analysis of the orbits to identify of the secular resonance. And finally, we develop a new semi-analytical approach to determine the location of this resonance.

Can Habitable Worlds Survive in Unstable Exoplanetary Systems?

Survival of habitable planets in unstable planetary systems

Authors:

Carrera et al

Abstract:

Many observed giant planets lie on eccentric orbits. Such orbits could be the result of strong scatterings with other giant planets. The same dynamical instability that produces giant planet scatterings can also alter the orbits of terrestrial planets. For example, a habitable rocky planet in the system can be ejected or transported to an orbit outside the habitable zone. Therefore, there is a link between observed giant planets and the habitability of smaller planets in the system. We say that a habitable planet has resilient habitability if it is able to avoid ejections and collisions and its orbit remains inside the habitable zone. Here we model the orbital evolution of rocky planets in planetary systems where giant planets become dynamically unstable. We measure the resilience of habitable planets as a function of the observed, present-day masses and orbits of the giant planets. We find that the survival rate of habitable planets depends strongly on the giant planet architecture. Systems with three Jupiters (3J) are far more destructive than systems with four giant planets of unequal masses (4G), akin to the architecture of the solar system. In terms of observables, we find that giant planets with eccentricity above 0.4 originate only in 3J systems and very rarely have habitable interior planets. For a giant planet with an present-day eccentricity of 0.2 and semimajor axis of 5 AU orbiting a Sun-like star, 50% of the orbits in the habitable zone are resilient to the instability. As semimajor axis increases and eccentricity decreases, a higher fraction of habitable planets survive and remain habitable. However, if the habitable planet has rocky siblings, there is a significant risk of rocky planet collisions that would sterilize the planet.

Explaining the Kepler-444 System

Consequences of tidal interaction between disks and orbiting protoplanets for the evolution of multi-planet systems with architecture resembling that of Kepler 444

Authors:

Papaloizou et al

Abstract:

We study orbital evolution of multi-planet systems with masses in the terrestrial planet regime induced through tidal interaction with a protoplanetary disk assuming that this is the dominant mechanism for producing orbital migration and circularization. We develop a simple analytic model for a system that maintains consecutive pairs in resonance while undergoing orbital circularization and migration. Migration times for each planet may be estimated once planet masses, circularization times and the migration time for the innermost planet are given. We applied it to a model system with the current architecture of Kepler 444 interacting with a protoplanetary disk, the evolution time for the system as a whole being comparable to current protoplanetary disk lifetimes.
In addition we performed numerical simulations with input data obtained from this model. These indicate that although the analytic model is inexact, relatively small corrections to estimated migration rates yield systems for which period ratios vary by a minimal extent. Because of relatively large deviations from exact resonance in the observed system of up to 2%, the migration times obtained in this way indicate only weak convergent migration such that a system for which the planets did not interact would contract by only ∼1% although undergoing significant inward migration as a whole. We performed additional simulations to investigate how the system could undergo significant convergent migration before reaching its final state. These indicate migration times have to be significantly shorter and resonances significantly closer. Relative migration rates would then have to decrease allowing period ratios to increase to become more distant from resonances as the system approached its final state in the inner regions of the protoplanetary disk

Secular models and Kozai resonance for planets in coorbital non-coplanar motion

Secular models and Kozai resonance for planets in coorbital non-coplanar motion

Authors:

Guipponne et al

Abstract:

In this work, we construct and test an analytical and a semianalytical secular models for two planets locked in a coorbital non-coplanar motion, comparing some results with the case of restricted three body problem.

The analytical average model replicates the numerical N-body integrations, even for moderate eccentricities (≲ 0.3) and inclinations (≲10∘), except for the regions corresponding to quasi-satellite and Lidov-Kozai configurations. Furthermore, this model is also useful in the restricted three body problem, assuming very low mass ratio between the planets. We also describe a four-degree-of-freedom semianalytical model valid for any type of coorbital configuration in a wide range of eccentricities and inclinations.

{Using a N-body integrator, we have found that the phase space of the General Three Body Problem is different to the restricted case for inclined systems, and establish the location of the Lidov-Kozai equilibrium configurations depending on mass ratio. We study the stability of periodic orbits in the inclined systems, and find that apart from the robust configurations L4, AL4, and QS is possible to harbour two Earth-like planets in orbits previously identified as unstable U and also in Euler L3 configurations, with bounded chaos.

Chaotic Diffusion in the Gliese-876 Planetary System

Chaotic Diffusion in the Gliese-876 Planetary System

Authors:

Martí et al

Abstract:

Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disk, and a natural consequence of irregular motion. In this paper we show that resonant multi-planetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over timescales comparable to their age.Using the GJ-876 system as an example, we analyze the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding regions of the Laplace resonance. We numerically integrate ensembles of close initial conditions, compute Poincar\'e maps and estimate the chaotic diffusion present in this system. Our results show that, the Laplace resonance contains two different regions: an inner domain characterized by low chaoticity and slow diffusion, and an outer one displaying larger values of dynamical indicators. In the outer resonant domain, the stochastic borders of the Laplace resonance seem to prevent the complete destruction of the system. We characterize the diffusion for small ensembles along the parameters of the outermost planet. Finally, we perform a stability analysis of the inherent chaotic, albeit stable Laplace resonance, by linking the behavior of the resonant variables of the configurations to the different sub-structures inside the three-body resonance.

Long-term orbital stability of exosolar planetary systems with highly eccentric orbits

Long-term orbital stability of exosolar planetary systems with highly eccentric orbits

Authors:

Antoniadou et al

Abstract:

Nowadays, many extrasolar planetary systems possessing at least one planet on a highly eccentric orbit have been discovered. In this work, we study the possible long-term stability of such systems. We consider the general three body problem as our model. Highly eccentric orbits are out of the Hill stability regions. However, mean motion resonances can provide phase protection and orbits with long-term stability exist. We construct maps of dynamical stability based on the computation of chaotic indicators and we figure out regions in phase space, where the long-term stability is guaranteed. We focus on regions where at least one planet is highly eccentric and attempt to associate them with the existence of stable periodic orbits. The values of the orbital elements, which are derived from observational data, are often given with very large deviations. Generally, phase space regions of high eccentricities are narrow and thus, our dynamical analysis may restrict considerably the valid domain of the system's location.

Stability of Multi Exoplanetary Systems With Very High Mass Worlds

Orbital Stability of Multi-Planet Systems: Behavior at High Masses

Authors:

Morrison et al

Abstract:

In the coming years, high contrast imaging surveys are expected to reveal the characteristics of the population of wide-orbit, massive, exoplanets. To date, a handful of wide planetary mass companions are known, but only one such multi-planet system has been discovered: HR8799. For low mass planetary systems, multi-planet interactions play an important role in setting system architecture. In this paper, we explore the stability of these high mass, multi-planet systems. While empirical relationships exist that predict how system stability scales with planet spacing at low masses, we show that extrapolating to super-Jupiter masses can lead to up to an order of magnitude overestimate of stability for massive, tightly packed systems. We show that at both low and high planet masses, overlapping mean motion resonances trigger chaotic orbital evolution, which leads to system instability. We attribute some of the difference in behavior as a function of mass to the increasing importance of second order resonances at high planet-star mass ratios. We use our tailored high mass planet results to estimate the maximum number of planets that might reside in double component debris disk systems, whose gaps may indicate the presence of massive bodies.

Attempting to Explain the Kepler-223 System

The four planets of the Kepler-223 star system seem to have little in common with the planets of Earth's own solar system. And yet a new study shows that the Kepler-223 system is trapped in an orbital configuration that Jupiter, Saturn, Uranus, and Neptune may have broken from in the early history of the solar system.

"Exactly how and where planets form is an outstanding question in planetary science," said the study's lead author, Sean Mills, a graduate student in astronomy & astrophysics at the University of Chicago. "Our work essentially tests a model for planet formation for a type of planet we don't have in our solar system."

These puffy, gaseous planets, far more massive than Earth, orbit close to their stars. "That's why there's a big debate about how they form, how they got there, and why don't we have one," Mills said.

Mills and his collaborators used brightness data from NASA's Kepler telescope to analyze how the four planets block the starlight and change each other's orbits, thus inferring the planets' sizes and masses. The team performed numerical simulations of planetary migration that generate this system's current architecture, similar to the migration suspected for the solar system's gas giants. These calculations are described in the May 11 Advance Online edition of Nature.

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Stability of a planet in the HD 41004 binary system

Stability of a planet in the HD 41004 binary system

Authors:

Satyal et al

Abstract:

The Hill stability criterion is applied to analyse the stability of a planet in the binary star system of HD 41004 AB, with the primary and secondary separated by 22 AU, and masses of 0.7 M⊙ and 0.4 M⊙, respectively. The primary hosts one planet in an S-type orbit, and the secondary hosts a brown dwarf (18.64 MJ) on a relatively close orbit, 0.0177 AU, thereby forming another binary pair within this binary system. This star-brown dwarf pair (HD 41004 B+Bb) is considered a single body during our numerical calculations, while the dynamics of the planet around the primary, HD 41004 Ab, is studied in different phase-spaces. HD 41004 Ab is a 2.6 MJ planet orbiting at the distance of 1.7 AU with orbital eccentricity 0.39. For the purpose of this study, the system is reduced to a three-body problem and is solved numerically as the elliptic restricted three-body problem (ERTBP). The Hill stability function is used as a chaos indicator to configure and analyse the orbital stability of the planet, HD 41004 Ab. The indicator has been effective in measuring the planet's orbital perturbation due to the secondary star during its periastron passage. The calculated Hill stability time series of the planet for the coplanar case shows the stable and quasi-periodic orbits for at least ten million years. For the reduced ERTBP the stability of the system is also studied for different values of planet's orbital inclination with the binary plane. Also, by recording the planet's ejection time from the system or collision time with a star during the integration period, stability of the system is analysed in a bigger phase-space of the planet's orbital inclination, ≤ 90°, and its semimajor axis, 1.65–1.75 AU. Based on our analysis it is found that the system can maintain a stable configuration for the planet's orbital inclination as high as 65° relative to the binary plane. The results from the Hill stability criterion and the planet's dynamical lifetime map are found to be consistent with each other.

Regular and chaotic orbits in the dynamics of exoplanets

Regular and chaotic orbits in the dynamics of exoplanets

Authors:

Antoniadou et al

Abstract:

Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR), which offers a phase protection mechanism, so that, even highly eccentric planets can avoid close encounters. However, the present estimation of their initial conditions, which may change significantly after obtaining additional observational data in the future, locate most of the systems in chaotic regions and consequently, they are destabilized. Hence, dynamical analysis is imperative for the derivation of proper planetary orbital elements. We utilize the model of spatial general three body problem, in order to simulate such resonant systems through the computation of families periodic orbits. In this way, we can figure out regions in phase space, where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In this review, we summarize our methodology and showcase the fact that stable resonant planetary systems evolve being exactly centered at stable periodic orbits. We apply this process to co-orbital motion and systems HD 82943, HD 73526, HD 128311, HD 60532, HD 45364 and HD 108874.

The Fate of Circumbinary ExoPlanets - Tatooines - in Unstable Orbits

On the Fate of Unstable Circumbinary Planets: Tatooine's Close Encounters with a Death Star

Authors:

Sutherland et al

Abstract:

Circumbinary planets whose orbits become unstable may be ejected, accreted, or even captured by one of the stars. We quantify the relative rates of these channels, for a binary of secondary star's mass fraction 0.1 with an orbit of 1AU. The most common outcome is ejection, which happens ~80% of the time. If binary systems form circumbinary planets readily and sloppily, this process may fill the Milky Way with free-floating planets. A significant fraction of the time, ~20%, the unstable planet strikes the primary or secondary. We tracked whether a Jupiter-like planet would undergo tidal stripping events during close passages, and find that these events are not strong enough to change the trajectory of the planet, though this may be observable from a changed structured for free-floating planets that are produced by this process.