Mean Motion Resonances at High Eccentricities: The 2:1 and the 3:2 Interior Resonances

Mean Motion Resonances at High Eccentricities: The 2:1 and the 3:2 Interior Resonances

Authors:

Wang et al

Abstract:
Mean motion resonances (MMRs) play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system and in exoplanetary systems. Most previous theoretical analyses have focused on the low- to moderate-eccentricity regime, but with new discoveries of high-eccentricity resonant minor planets and even exoplanets, there is increasing motivation to examine MMRs in the high-eccentricity regime. Here we report on a study of the high-eccentricity regime of MMRs in the circular planar restricted three-body problem. Numerical analyses of the 2:1 and the 3:2 interior resonances are carried out for a wide range of planet-to-star mass ratio μ, and for a wide range of eccentricity of the test particle. The surface-of-section technique is used to study the phase space structure near resonances. We find that new stable libration zones appear at higher eccentricity at libration centers that are shifted from those at low eccentricities. We provide physically intuitive explanations for these transitions in phase space, and we present novel results on the mass and eccentricity dependence of the resonance widths. Our results show that MMRs have sizable libration zones at high eccentricities, comparable to those at lower eccentricities.

The Influence of Orbital Resonances on the Water Transport to Objects in the Circumprimary Habitable Zone of Binary Star Systems

The Influence of Orbital Resonances on the Water Transport to Objects in the Circumprimary Habitable Zone of Binary Star Systems

Authors:

Bancelin et al

Abstract:
We investigate the role of secular and mean motion resonances on the water transport from a belt of icy asteroids onto planets or embryos orbiting inside the circumprimary habitable zone (HZ) of a binary star system. In addition, the host-star has an accompanying gas giant planet. For a comparison, we perform two case studies where a secular resonance (SR) is located either inside the HZ close to 1.0 au (causing eccentric motion of a planet or embryos therein) or in the asteroid belt, beyond the snow line. In the latter case, a higher flux of icy objects moving toward the HZ is expected. Collisions between asteroids and objects in the HZ are treated analytically. Our purely dynamical study shows that the SR in the HZ boosts the water transport; however, collisions can occur at very high impact speeds. In this paper, we treat for the first time, realistic collisions using a GPU 3D-SPH code to assess the water loss in the projectile. Including the water loss into the dynamical results, we get more realistic values for the water mass fraction of the asteroid during an impact. We highlight that collisions occurring at high velocities greatly reduce the water content of the projectile and thus the amount of water transported to planets or embryos orbiting inside the HZ. Moreover, we discuss other effects that could modify our results, namely the asteroid's surface rate recession due to ice sublimation and the atmospheric drag contribution on the asteroids' mass loss.

Hot Jupiter WASP-12b's Orbit is Decaying

The Apparently Decaying Orbit of WASP-12b

Authors:
Patra et al

Abstract:

We present new transit and occultation times for the hot Jupiter WASP-12b. The data are compatible with a constant period derivative: $\dot{P}=-29\pm 3$ ms yr−1 and $P/\dot{P}=3.2\,\mathrm{Myr}$. However, it is difficult to tell whether we have observed orbital decay or a portion of a 14-year apsidal precession cycle. If interpreted as decay, the star's tidal quality parameter ${Q}_{\star }$ is about $2\times {10}^{5}$. If interpreted as precession, the planet's Love number is 0.44 ± 0.10. Orbital decay appears to be the more parsimonious model: it is favored by ${\rm{\Delta }}{\chi }^{2}=5.5$ despite having two fewer free parameters than the precession model. The decay model implies that WASP-12 was discovered within the final ~0.2% of its existence, which is an unlikely coincidence but harmonizes with independent evidence that the planet is nearing disruption. Precession does not invoke any temporal coincidence, but it does require some mechanism to maintain an eccentricity of $\approx 0.002$ in the face of rapid tidal circularization. To distinguish unequivocally between decay and precession will probably require a few more years of monitoring. Particularly helpful will be occultation timing in 2019 and thereafter.

Moderately Eccentric Warm Jupiters from Secular Interactions with Exterior Companions

Moderately Eccentric Warm Jupiters from Secular Interactions with Exterior Companions

Authors:

Anderson et al

Abstract:
Recent work suggests 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. Eccentricity growth may arise from an inclined companion (through Lidov-Kozai cycles), or from an eccentric, nearly coplanar companion. 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 ∼40∘) 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.

Simulations Fail to Explain SuperEarth Resonant Chains

Breaking the Chains: Hot Super-Earth systems from migration and disruption of compact resonant chains
Authors:

Izidoro et al

Abstract:
“Hot super-Earths” (or “Mini-Neptunes”) between 1 and 4 times Earth’s size with period shorter than 100 days orbit 30-50% of Sun-like type stars. Their orbital configuration – measured as the period ratio distribution of adjacent planets in multi-planet systems – is a strong constraint for formation models. Here we use N-body simulations with synthetic forces from an underlying evolving gaseous disk to model the formation and long-term dynamical evolution of super-Earth systems. While the gas disk is present, planetary embryos grow and migrate inward to form a resonant chain anchored at the inner edge of the disk. These resonant chains are far more compact than the observed super-Earth systems. Once the gas dissipates resonant chains may become dynamically unstable. They undergo a phase of giant impacts that spreads the systems out. Disk turbulence has no measurable effect on the outcome. Our simulations match observations if a small fraction of resonant chains remain stable, while most super-Earths undergo a late dynamical instability. Our statistical analysis restricts the contribution of stable systems to less than 25%. Our results also suggest that the large fraction of observed single planet systems does not necessarily imply any dichotomy in the architecture of planetary systems. Finally, we use the low abundance of resonances in Kepler data to argue that, in reality, the survival of resonant chains happens likely only in ∼5% of the cases. This leads to a mystery: in our simulations only 50-60% of resonant chains became unstable whereas at least 75% (and probably 90-95%) must be unstable to match observations.

Dynamically hot Super-Earths from outer giant planet scattering

Dynamically hot Super-Earths from outer giant planet scattering

Authors:

Huang et al

Abstract:

The hundreds of multiple planetary systems discovered by the Kepler mission are typically observed to reside in close-in (≲0.5 AU), low-eccentricity, and low-inclination orbits. We run N-body experiments to study the effect that unstable outer (≳1 AU) giant planets, whose end orbital configurations resemble those in the Radial Velocity population, have on these close-in multiple Super-Earth systems. Our experiments show that the giant planets greatly reduce the multiplicity of the inner Super-Earths and the surviving population can have large eccentricities (e≳0.3) and inclinations (i≳20∘) at levels that anti-correlate with multiplicity. Consequently, this model predicts the existence of a population of dynamically hot single-transiting planets with typical eccentricities and inclinations in the ranges of ∼0.2−0.5 and ∼10∘−40∘. We show that these results can explain the following observations: (i) the recent eccentricity measurements of Kepler super-Earths from transit durations, (ii) the tentative observation that single-transiting systems have a wider distribution of stellar obliquity angles compared to the multiple-transiting systems; (iii) the architecture of some eccentric super-Earths discovered by Radial Velocity surveys such as HD125612c. Future observations from TESS will reveal many more dynamically hot single transiting planets, for which follow up Radial Velocity studies will be able to test our models and see whether they have outer giant planets.

Dynamics of tidally captured planets in the Galactic Center

Dynamics of tidally captured planets in the Galactic Center

Authors:

Trani et al

Abstract:

Recent observations suggest ongoing planet formation in the innermost parsec of the Galactic center (GC). The super-massive black hole (SMBH) might strip planets or planetary embryos from their parent star, bringing them close enough to be tidally disrupted. Photoevaporation by the ultraviolet field of young stars, combined with ongoing tidal disruption, could enhance the near-infrared luminosity of such starless planets, making their detection possible even with current facilities. In this paper, we investigate the chance of planet tidal captures by means of high-accuracy N-body simulations exploiting Mikkola's algorithmic regularization. We consider both planets lying in the clockwise (CW) disk and planets initially bound to the S-stars. We show that tidally captured planets remain on orbits close to those of their parent star. Moreover, the semi-major axis of the planet orbit can be predicted by simple analytic assumptions in the case of prograde orbits. We find that starless planets that were initially bound to CW disk stars have mild eccentricities and tend to remain in the CW disk. However, we speculate that angular momentum diffusion and scattering with other young stars in the CW disk might bring starless planets on low-angular momentum orbits. In contrast, planets initially bound to S-stars are captured by the SMBH on highly eccentric orbits, matching the orbital properties of the G1 and G2 clouds. Our predictions apply not only to planets but also to low-mass stars initially bound to the S-stars and tidally captured by the SMBH.

Nemesis Class Exoplanets are Truly bad News

The fates of Solar system analogues with one additional distant planet

Author:

Veras

Abstract:

The potential existence of a distant planet ("Planet Nine") in the Solar system has prompted a re-think about the evolution of planetary systems. As the Sun transitions from a main sequence star into a white dwarf, Jupiter, Saturn, Uranus and Neptune are currently assumed to survive in expanded but otherwise unchanged orbits. However, a sufficiently-distant and sufficiently-massive extra planet would alter this quiescent end scenario through the combined effects of Solar giant branch mass loss and Galactic tides. Here, I estimate bounds for the mass and orbit of a distant extra planet that would incite future instability in systems with a Sun-like star and giant planets with masses and orbits equivalent to those of Jupiter, Saturn, Uranus and Neptune. I find that this boundary is diffuse and strongly dependent on each of the distant planet's orbital parameters. Nevertheless, I claim that instability occurs more often than not when the planet is as massive as Jupiter and harbours a semimajor axis exceeding about 300 au, or has a mass of a super-Earth and a semimajor axis exceeding about 3000 au. These results hold for orbital pericentres ranging from 100 to at least 400 au. This instability scenario might represent a common occurrence, as potentially evidenced by the ubiquity of metal pollution in white dwarf atmospheres throughout the Galaxy.

Coupled orbital and spin evolution of the CoRoT-7 two-planet system using a Maxwell viscoelastic rheology

Coupled orbital and spin evolution of the CoRoT-7 two-planet system using a Maxwell viscoelastic rheology

Authors:

Rodriguez et al

Abstract:

We investigate the orbital and rotational evolution of the CoRoT-7 two-planet system, assuming that the innermost planet behaves like a Maxwell body. We numerically resolve the coupled differential equations governing the instantaneous deformation of the inner planet together with the orbital motion of the system. We show that, depending on the relaxation time for the deformation of the planet, the orbital evolution has two distinct behaviours: for relaxation times shorter than the orbital period, we reproduce the results from classic tidal theories, for which the eccentricity is always damped. However, for longer relaxation times, the eccentricity of the inner orbit is secularly excited and can grow to high values. This mechanism provides an explanation for the present high eccentricity observed for CoRoT-7 b, as well as for other close-in super-Earths in multiple planetary systems.

Outer-planet scattering can gently tilt an inner planetary system

Outer-planet scattering can gently tilt an inner planetary system

Authors:

Gratia et al

Abstract:

Chaotic dynamics are expected during and after planet formation, and a leading mechanism to explain large eccentricities of gas giant exoplanets is planet-planet gravitational scattering. The same scattering has been invoked to explain misalignments of planetary orbital planes with respect to their host star's spin. However, an observational puzzle is presented by Kepler-56, which has two inner planets (b and c) that are nearly coplanar with each other, yet are more than 45 degrees inclined to their star's equator. Thus the spin-orbit misalignment might be primordial. Instead, we further develop the hypothesis in the discovery paper, that planets on wider orbits generated misalignment through scattering, and as a result gently torqued the inner planets away from the equator plane of the star. We integrated the equations of motion for Kepler-56 b and c along with an unstable outer system initialized with either two or three Jupiter-mass planets. We address here whether the violent scattering that generates large mutual inclinations can leave the inner system intact, tilting it gently. In almost all of the cases initially with two outer planets, either the inner planets remain nearly coplanar with each other in the star's equator plane, or they are scattered violently to high mutual inclination and high spin-orbit misalignment. On the contrary, of the systems with three unstable outer planets, a spin-orbit misalignment large enough to explain the observations is generated 28% of the time for coplanar inner planets, which is consistent with the observed frequency of this phenomenon reported so far. We conclude that multiple-planet scattering in the outer parts of the system may account for this new population of coplanar planets hosted by oblique stars.

Secular and tidal evolution of circumbinary systems

Secular and tidal evolution of circumbinary systems

Authors:

Corriea et al

Abstract:

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin-orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star-planet-satellite systems and triple stellar systems.

Relating binary-star planetary systems to central configurations

Relating binary-star planetary systems to central configurations

Author:

Veras

Abstract:

Binary-star exoplanetary systems are now known to be common, for both wide and close binaries. However, their orbital evolution is generally unsolvable. Special cases of the N-body problem which are in fact completely solvable include dynamical architectures known as central configurations. Here, I utilize recent advances in our knowledge of central configurations to assess the plausibility of linking them to coplanar exoplanetary binary systems. By simply restricting constituent masses to be within stellar or substellar ranges characteristic of planetary systems, I find that (i) this constraint reduces by over 90 per cent the phase space in which central configurations may occur, (ii) both equal-mass and unequal-mass binary stars admit central configurations, (iii) these configurations effectively represent different geometrical extensions of the Sun-Jupiter-Trojan-like architecture, (iv) deviations from these geometries are no greater than ten degrees, and (v) the deviation increases as the substellar masses increase. This study may help restrict future stability analyses to architectures which resemble exoplanetary systems, and might hint at where observers may discover dust, asteroids and/or planets in binary star systems.

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.

Magnitude and timing of the giant planet instability: A reassessment from the perspective of the asteroid belt

Magnitude and timing of the giant planet instability: A reassessment from the perspective of the asteroid belt

Authors:

Toliou et al

Abstract:

It is generally accepted today that our solar system has undergone a phase during which the orbits of the giant planets became very unstable. In recent years, many studies have identified traces of this event and have provided reasonable justification for this occurrence. The magnitude (in terms of orbital variation) and the timing of the instability though (early or late with respect to the dispersal of the gas disk) still remains an open debate. The terrestrial planets seem to set a strict constraint: either the giant planet instability happened early, while the terrestrial planets were still forming, or the orbits of Jupiter and Saturn had to separate from each other impulsively, with a large enough `jump' in semimajor axis (Brasser et al. 2009; Kaib and Chambers 2016) for the terrestrial planets to remain stable. Because a large orbital jump is a low probability event, the early instability hypothesis seems to be favored. However, the asteroid belt would also evolve in a different way, assuming different instability amplitudes. These two constraints need to match each other in order to favor one scenario over the other. Considering an initially dynamically cold disk of asteroids, Morbidelli et al. (2010) concluded that a comparably large jump is needed to reconstruct the current asteroid belt. Here we confirm the same conclusion, but considering an asteroid population already strongly excited in eccentricity, such as that produced in the Grand Tack scenario (Walsh et al. 2011). Because the asteroids existed since the time of removal of the gas disk, unlike the terrestrial planets, this constraint on the width of the giant planet jump is valid regardless of whether the instability happened early or late. Hence, at this stage, assuming an early instability does not appear to provide any advantage in terms of the probabilistic reconstruction of the solar system structure.

Anomalous precession of planets on a Weyl conformastatic solution

Anomalous precession of planets on a Weyl conformastatic solution

Authors:

Capistrano et al

Abstract:

In this paper, we investigate the anomalous planets precession in the so-called nearly-newtonian gravitational regime. This limit is obtained from the application of the slow motion condition to the geodesic equations without altering the geodesic deviation equations, which leads to an intermediate gravitational field stronger than the newtonian one. Using a non-standard expression for the perihelion advance from the Weyl conformastatic vacuum solution as a model, we can describe the anomaly in planets precession compared with different observational data from Ephemerides of the Planets and the Moon (EPM2008 and EPM2011) and Planetary and Lunar Ephemeris (INPOP10a). As a result, using the Levenberg-Marquardt algorithm and calculating the related Chi-squared statistic, we find that the anomaly is statistical irrelevant in accordance with INPOP10a observations. As a complement to this work, we also do application to the relativistic precession of giant planets using observational data calibrated with the EPM2011.

implications for the formation of hot and warm Jupiters via high-eccentricity migration

Secular dynamics of multiplanet systems: implications for the formation of hot and warm Jupiters via high-eccentricity migration

Authors:

Hamers et al

Abstract:

Hot Jupiters (HJs) are Jupiter-like planets that reside very closely to their host star, within ∼0.1AU. Their formation is not well understood. It is generally believed that they cannot have formed in situ, implying that some form of migration must have occurred after their initial formation. We study the production of HJs through secular evolution in multiplanet systems with three to five planets. In this variant of high-e migration, the eccentricity of the orbit of the innermost planet is excited on secular time-scales, triggering orbital migration due to tidal dissipation. We use a secular dynamics code and carry out a population synthesis study. We find that HJs are only produced if the viscous time-scale is short (≈0.014 yr). In contrast, in up to ≈0.3 of systems, the innermost planet is tidally disrupted. The orbital period distribution is peaked around 5 d, consistent with observations. The median HJ mass is 1MJ with a maximum of ≈2MJ, similar to observed HJs. Approximately 0.1 of the HJs have retrograde orbits with respect to the stellar spin. We do not find any warm Jupiters in our simulations, i.e. planets with semimajor axes between 0.1 and 1 AU.

Long-term evolution of planetary systems with a terrestrial planet and a giant planet

Long-term evolution of planetary systems with a terrestrial planet and a giant planet

Authors:

Georgakarakos et al

Abstract:

We study the long-term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders, and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equations of motion, and we find that the analytical solution works reasonably well. An interesting finding is that the new analytical estimates improve greatly the predictions for the time-scales of the orbital evolution of the terrestrial planet compared to an octupole order expansion. Finally, we briefly discuss possible applications of the analytical estimates in astrophysical problems.

On stability of planetary motion during stellar approaches

On stability of planetary motion during stellar approaches

Authors:

Gasanov et al

Abstract:

We consider motion of a passive-gravitating body when a test star (perturbing body) approaches the central body. An integral invariant relation – a quasi-integral (Lukyanov, 2010) – is found by using exact expression of the force function, and regions of possible motion of a passive-gravitating body are determined. The surfaces of minimal energy (a generalization of zero velocity surfaces) are plotted, singular points of these surfaces are determined, their type and Lyapunov stability are established. Hill's stability of planetary motion is investigated for the case of a test star approaching the Solar system. Criteria for capture of a passive-gravitating body by a test star being possible and impossible are derived. Based on Hill stability criteria, we find critical parameters of the test star's orbit that leave planets bound to the Solar system.

Coplanar Orbits in Be discs in binary systems

Be discs in binary systems I. Coplanar orbits

Authors:

Panoglou et al

Abstract:

Be stars are surrounded by outflowing circumstellar matter structured in the form of decretion discs. They are often members of binary systems, where it is expected that the decretion disc interacts both radiatively and gravitationally with the companion. In this work we study how various orbital (period, mass ratio, eccentricity) and disc (viscosity) parameters affect the disc structure in coplanar systems. We simulate such binaries with the use of a smoothed particle hydrodynamics code. The main effects of the secondary on the disc are its truncation and the accumulation of material inwards of truncation. In circular or nearly circular prograde orbits, the disc maintains a rotating, constant in shape, configuration, which is locked to the orbital phase. The disc is smaller in size, more elongated and more massive for low viscosity parameter, small orbital separation and/or high mass ratio. Highly eccentric orbits are more complex, with the disc structure and total mass strongly dependent on the orbital phase. We also studied the effects of binarity in the disc continuum emission. Since the infrared and radio SED are sensitive to the disc size and density slope, the truncation and matter accumulation result in considerable modifications in the emergent spectrum. The decretion disc in circular binaries remains constant in shape and phase-locked. Eccentric binaries exhibit strong dependence on the distance to the secondary. We conclude that binarity can serve as an explanation for the variability exhibited in observations of Be stars, and that our model can be used to detect invisible companions.

Dynamical mass and multiplicity constraints on co-orbital bodies around stars

Dynamical mass and multiplicity constraints on co-orbital bodies around stars

Authors:

Veras et al

Abstract:

Objects transiting near or within the disruption radius of both main sequence (e.g. KOI 1843) and white dwarf (WD 1145+017) stars are now known. Upon fragmentation or disintegration, these planets or asteroids may produce co-orbital configurations of nearly equal-mass objects. However, as evidenced by the co-orbital objects detected by transit photometry in the WD 1145+017 system, these bodies are largely unconstrained in size, mass, and total number (multiplicity). Motivated by potential future similar discoveries, we perform N-body simulations to demonstrate if and how debris masses and multiplicity may be bounded due to second-to-minute deviations and the resulting accumulated phase shifts in the osculating orbital period amongst multiple co-orbital equal point masses. We establish robust lower and upper mass bounds as a function of orbital period deviation, but find the constraints on multiplicity to be weak. We also quantify the fuzzy instability boundary, and show that mutual collisions occur in less than 5%, 10% and 20% of our simulations for masses of 10^{21}, 10^{22} and 10^{23} kg. Our results may provide useful initial rough constraints on other stellar systems with multiple co-orbital bodies.