A Six-planet System around the Star HD 34445

A Six-planet System around the Star HD 34445 

Authors:

Vogt et al 

Abstract:

We present a new precision radial velocity (RV) data set that reveals a multi-planet system orbiting the G0V star HD 34445. Our 18-year span consists of 333 precision RV observations, 56 of which were previously published and 277 of which are new data from the Keck Observatory, Magellan at Las Campanas Observatory, and the Automated Planet Finder at Lick Observatory. These data indicate the presence of six planet candidates in Keplerian motion about the host star with periods of 1057, 215, 118, 49, 677, and 5700 days, and minimum masses of 0.63, 0.17, 0.1, 0.05, 0.12, and 0.38 M J, respectively. The HD 34445 planetary system, with its high degree of multiplicity, its long orbital periods, and its induced stellar RV half-amplitudes in the range 2 m s−1 lesssim K lesssim 5 m s−1 is fundamentally unlike either our own solar system (in which only Jupiter and Saturn induce significant reflex velocities for the Sun), or the Kepler multiple-transiting systems (which tend to have much more compact orbital configurations).

Precise Masses in the WASP-47 System

Precise Masses in the WASP-47 System

Authors:

Vanderburg et al

Abstract:
We present precise radial velocity observations of WASP-47, a star known to host a hot Jupiter, a distant Jovian companion, and, uniquely, two additional transiting planets in short-period orbits: a super-Earth in a ~19 hour orbit, and a Neptune in a ~9 day orbit. We analyze our observations from the HARPS-N spectrograph along with previously published data to measure the most precise planet masses yet for this system. When combined with new stellar parameters and reanalyzed transit photometry, our mass measurements place strong constraints on the compositions of the two small planets. We find unlike most other ultra-short-period planets, the inner planet, WASP-47 e, has a mass (6.83 +/- 0.66 Me) and radius (1.810 +/- 0.027 Re) inconsistent with an Earth-like composition. Instead, WASP-47 e likely has a volatile-rich envelope surrounding an Earth-like core and mantle. We also perform a dynamical analysis to constrain the orbital inclination of WASP-47 c, the outer Jovian planet. This planet likely orbits close to the plane of the inner three planets, suggesting a quiet dynamical history for the system. Our dynamical constraints also imply that WASP-47 c is much more likely to transit than a geometric calculation would suggest. We calculate a transit probability for WASP-47 c of about 10%, more than an order of magnitude larger than the geometric transit probability of 0.6%.

The California-Kepler Survey V. Peas in a Pod: Planets in a Kepler Multi-planet System are Similar in Size and Regularly Spaced

The California-Kepler Survey V. Peas in a Pod: Planets in a Kepler Multi-planet System are Similar in Size and Regularly Spaced

Authors:

Weiss et al

Abstract:
We have established precise planet radii, semi-major axes, incident stellar fluxes, and stellar masses for 909 planets in 355 multi-planet systems discovered by Kepler. We find that planets within a single multi-planet system tend to be closer in size than planets drawn randomly from the collection of multi-planet systems. This is true even when considering systems with similar host stars; we find, at most, a weak correlation between planet radius and stellar mass. Evidently, it is not the stellar mass but some other property or process that enforces the similarity of planet sizes. When adjacent planets in a multi-planet system are not similar in size, the inner planet is smaller in 65±6\% of cases. The tendency for the inner planet to be smaller is especially pronounced when the inner planet has a short period (≲10 days) or equivalently, high radiation flux (≳150 times the Earth's insolation). This could be the result of photoevaporation. We also find that adjacent planets within a given system tend to be spaced in a regular geometric progression, with a typical semi-major axis ratio of 1.5. Using empirical mass-radius relationships, we estimate the mutual Hill separations of planet pairs. We find that 93\% of the planet pairs are at least 10 mutual Hill radii apart, and that a spacing of 10-30 mutual Hill radii is most common

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.

Stable habitable zones of single Jovian planet systems

Stable habitable zones of single Jovian planet systems

Authors:

Agnew et al

Abstract:

With continued improvement in telescope sensitivity and observational techniques, the search for rocky planets in stellar habitable zones is entering an exciting era. With so many exoplanetary systems available for follow-up observations to find potentially habitable planets, one needs to prioritise the ever-growing list of candidates. We aim to determine which of the known planetary systems are dynamically capable of hosting rocky planets in their habitable zones, with the goal of helping to focus future planet search programs. We perform an extensive suite of numerical simulations to identify regions in the habitable zones of single Jovian planet systems where Earth mass planets could maintain stable orbits, specifically focusing on the systems in the Catalog of Earth-like Exoplanet Survey Targets (CELESTA). We find that small, Earth-mass planets can maintain stable orbits in cases where the habitable zone is largely, or partially, unperturbed by a nearby Jovian, and that mutual gravitational interactions and resonant mechanisms are capable of producing stable orbits even in habitable zones that are significantly or completely disrupted by a Jovian. Our results yield a list of 13 single Jovian planet systems in CELESTA that are not only capable of supporting an Earth-mass planet on stable orbits in their habitable zone, but for which we are also able to constrain the orbits of the Earth-mass planet such that the induced radial velocity signals would be detectable with next generation instruments.

Three planets around HD 27894. A close-in pair with a 2:1 period ratio and an eccentric Jovian planet at 5.4 AU

Three planets around HD 27894. A close-in pair with a 2:1 period ratio and an eccentric Jovian planet at 5.4 AU 

Authors:

Trifonov et al

Abstract:

Aims.

Our new program with HARPS aims to detect mean motion resonant planetary systems around stars which were previously reported to have a single bona fide planet, often based only on sparse radial velocity data.

Methods.

Archival and new HARPS radial velocities for the K2V star HD 27894 were combined and fitted with a three-planet self-consistent dynamical model. The best-fit orbit was tested for long-term stability.

Results.

We find clear evidence that HD 27894 is hosting at least three massive planets. In addition to the already known Jovian planet with a period Pb ≈ 18 days we discover a Saturn-mass planet with Pc ≈ 36 days, likely in a 2:1 mean motion resonance with the first planet, and a cold massive planet (≈ 5.3 MJup) with a period Pd ≈ 5170 days on a moderately eccentric orbit (ed = 0.39).

Conclusions.

HD 27894 is hosting a massive, eccentric giant planet orbiting around a tightly packed inner pair of massive planets likely involved in an asymmetric 2:1 mean motion resonance. HD 27894 may be an important milestone for probing planetary formation and evolution scenarios.

A Multi-planet System of Rapidly Rotating F-Star HD 106315

A Multi-planet System Transiting the V = 9 Rapidly Rotating F-Star HD 106315

Authors:

Rodriguez et al

Abstract:

We report the discovery of a multi-planet system orbiting HD 106315, a rapidly rotating mid F-type star, using data from the K2 mission. HD 106315 hosts a 2.51 ± 0.12 R ⊕ sub-Neptune in a 9.5-day orbit and a ${4.31}_{-0.27}^{+0.24}\,{R}_{\oplus }$ super-Neptune in a 21-day orbit. The projected rotational velocity of HD 106315 (12.9 km s−1) likely precludes precise measurements of the planets' masses but could enable a measurement of the sky-projected spin–orbit obliquity for the outer planet via Doppler tomography. The eccentricities of both planets were constrained to be consistent with 0, following a global modeling of the system that includes a Gaia distance and dynamical arguments. The HD 106315 system is one of few multi-planet systems hosting a Neptune-sized planet for which orbital obliquity measurements are possible, making it an excellent test-case for formation mechanisms of warm-Neptunian systems. The brightness of the host star also makes HD 106315 c a candidate for future transmission spectroscopic follow-up studies.

HD 20794 has at Least Three Exoplanets

Evidence for at least three planet candidates orbiting HD20794

Authors:

Feng et al

Abstract:

We explore the feasibility of detecting Earth analogs around Sun-like stars using the radial velocity method by investigating one of the largest radial velocities datasets for the one of the most stable radial-velocity stars HD20794. We proceed by disentangling the Keplerian signals from correlated noise and activity-induced variability. We diagnose the noise using the differences between radial velocities measured at different wavelength ranges, so-called "differential radial velocities". We apply this method to the radial velocities measured by HARPS, and identify four signals at 18, 89, 147 and 330 d. The two signals at periods of 18 and 89 d are previously reported and are better quantified in this work. The signal at a period of about 147 d is reported for the first time, and corresponds to a super-Earth with a minimum mass of 4.59 Earth mass located 0.51 AU from HD20794. We also find a significant signal at a period of about 330 d corresponding to a super-Earth or Neptune in the habitable zone. Since this signal is close to the annual sampling period and significant periodogram power in some noise proxies are found close to this signal, further observations and analyses are required to confirm it. The analyses of the eccentricity and consistency of signals provide weak evidence for the existence of the previously reported 43 d signal and a new signal at a period of about 11.9 d with a semi amplitude of 0.4 m/s. We find that the detection of a number of signals with radial velocity variations around 0.5\,m/s likely caused by low mass planet candidates demonstrates the important role of noise modeling in searching for Earth analogs.

HD 3167d: Another SuperEarth/Mini Neptune in the System?

Three's Company: An additional non-transiting super-Earth in the bright HD 3167 system, and masses for all three planets

Authors:

Christiansen et al

Abstract:

HD 3167 is a bright (V = 8.9), nearby K0 star observed by the NASA K2 mission (EPIC 220383386), hosting two small, short-period transiting planets. Here we present the results of a multi-site, multi-instrument radial velocity campaign to characterize the HD 3167 system. The masses of the transiting planets are 5.02+/-0.38 MEarth for HD 3167 b, a hot super-Earth with a likely rocky composition (rho_b = 5.60+2.15-1.43 g/cm^3), and 9.80+1.30-1.24 MEarth for HD 3167 c, a warm sub-Neptune with a likely substantial volatile complement (rho_c = 1.97+0.94-0.59 g/cm^3). We explore the possibility of atmospheric composition analysis and determine that planet c is amenable to transmission spectroscopy measurements, and planet b is a potential thermal emission target. We detect a third, non-transiting planet, HD 3167 d, with a period of 8.509+/-0.045 d (between planets b and c) and a minimum mass of 6.90+/-0.71 MEarth. We are able to constrain the mutual inclination of planet d with planets b and c: we rule out mutual inclinations below 1.3 degrees as we do not observe transits of planet d. From 1.3-40 degrees, there are viewing geometries invoking special nodal configurations which result in planet d not transiting some fraction of the time. From 40-60 degrees, Kozai-Lidov oscillations increase the system's instability, but it can remain stable for up to 100Myr. Above 60 degrees, the system is unstable. HD 3167 promises to be a fruitful system for further study and a preview of the many exciting systems expected from the upcoming NASA TESS mission.

HD 3167 System has a SuperEarth & Mini Neptune

The transiting multi-planet system HD3167: a 5.7 MEarth Super-Earth and a 8.3 MEarth mini-Neptune

Authors:

Gandolfi et al

Abstract: 

HD3167 is a bright (V=8.9 mag) K0V star observed by the NASA's K2 space mission during its Campaign 8. It has been recently found to host two small transiting planets, namely, HD3167b, an ultra short period (0.96 d) super-Earth, and HD3167c, a mini-Neptune on a relatively long-period orbit (29.85 d). Here we present an intensive radial velocity follow-up of HD3167 performed with the FIES@NOT, HARPS@ESO-3.6m, and HARPS-N@TNG spectrographs. We revise the system parameters and determine radii, masses, and densities of the two transiting planets by combining the K2 photometry with our spectroscopic data. With a mass of 5.69+/-0.44 MEarth, radius of 1.574+/-0.054 REarth, and mean density of 8.00(+1.0)(-0.98) g/cm^3, HD3167b joins the small group of ultra-short period planets known to have a rocky terrestrial composition. HD3167c has a mass of 8.33 (+1.79)(-1.85) MEarth and a radius of 2.740(+0.106)(-0.100) REarth, yielding a mean density of 2.21(+0.56)(-0.53) g/cm^3, indicative of a planet with a composition comprising a solid core surrounded by a thick atmospheric envelope. The rather large pressure scale height (about 350 km) and the brightness of the host star make HD3167c an ideal target for atmospheric characterization via transmission spectroscopy across a broad range of wavelengths. We found evidence of additional signals in the radial velocity measurements but the currently available data set does not allow us to draw any firm conclusion on the origin of the observed variation.

New Insights on Planet Formation in WASP-47 from a Simultaneous Analysis of Radial Velocities and Transit Timing Variations

New Insights on Planet Formation in WASP-47 from a Simultaneous Analysis of Radial Velocities and Transit Timing Variations 

Authors:

Weiss et al

Abstract:
Measuring precise planet masses, densities, and orbital dynamics in individual planetary systems is an important pathway toward understanding planet formation. The WASP-47 system has an unusual architecture that motivates a complex formation theory. The system includes a hot Jupiter ("b") neighbored by interior ("e") and exterior ("d") sub-Neptunes, and a long-period eccentric giant planet ("c"). We simultaneously modeled transit times from the Kepler K2 mission and 118 radial velocities to determine the precise masses, densities, and Keplerian orbital elements of the WASP-47 planets. Combining RVs and TTVs provides a better estimate of the mass of planet d ($13.6\pm 2.0\,{M}_{\oplus }$) than that obtained with only RVs ($12.75\pm 2.70\,{M}_{\oplus }$) or TTVs ($16.1\pm 3.8\,{M}_{\oplus }$). Planets e and d have high densities for their size, consistent with a history of photoevaporation and/or formation in a volatile-poor environment. Through our RV and TTV analysis, we find that the planetary orbits have eccentricities similar to the solar system planets. The WASP-47 system has three similarities to our own solar system: (1) the planetary orbits are nearly circular and coplanar, (2) the planets are not trapped in mean motion resonances, and (3) the planets have diverse compositions. None of the current single-process exoplanet formation theories adequately reproduce these three characteristics of the WASP-47 system (or our solar system). We propose that WASP-47, like the solar system, formed in two stages: first, the giant planets formed in a gas-rich disk and migrated to their present locations, and second, the high-density sub-Neptunes formed in situ in a gas-poor environment.

Planetary systems in star clusters

Planetary systems in star clusters

Authors:

Kouwenhoven et al

Abstract:

Thousands of confirmed and candidate exoplanets have been identified in recent years. Consequently, theoretical research on the formation and dynamical evolution of planetary systems has seen a boost, and the processes of planet-planet scattering, secular evolution, and interaction between planets and gas/debris disks have been well-studied. Almost all of this work has focused on the formation and evolution of isolated planetary systems, and neglect the effect of external influences, such as the gravitational interaction with neighbouring stars. Most stars, however, form in clustered environments that either quickly disperse, or evolve into open clusters. Under these conditions, young planetary systems experience frequent close encounters with other stars, at least during the first 1-10 Myr, which affects planets orbiting at any period range, as well as their debris structures.

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.

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.

Mutual Inclinations of Multi-Planet Systems with External Companions

Hiding Planets Behind a Big Friend: Mutual Inclinations of Multi-Planet Systems with External Companions

Authors:

Lai et al

Abstract:

The {\it Kepler} mission has detected thousands of planetary systems with 1-7 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" can 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 mp, semi-major axis ap and inclination θp). In general, the excited mutual inclination increases with mp/a3p and θp, although secular resonances may lead to large mutual inclinations even for small θp.

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.

HIP 41378: an F Class Star Hosting 5 Transiting Exoplanets

Five Planets Transiting a Ninth Magnitude Star

Authors:

Vanderburg et al

Abstract:

The Kepler mission has revealed a great diversity of planetary systems and architectures, but most of the planets discovered by Kepler orbit faint stars. Using new data from the K2 mission, we present the discovery of a five planet system transiting a bright (V = 8.9, K = 7.7) star called HIP 41378. HIP 41378 is a slightly metal-poor late F-type star with moderate rotation (v sin(i) = 7 km/s) and lies at a distance of 116 +/- 18 from Earth. We find that HIP 41378 hosts two sub-Neptune sized planets orbiting 3.5% outside a 2:1 period commensurability in 15.6 and 31.7 day orbits. In addition, we detect three planets which each transit once during the 75 days spanned by K2 observations. One planet is Neptune sized in a likely ~160 day orbit, one is sub-Saturn sized likely in a ~130 day orbit, and one is a Jupiter sized planet in a likely ~1 year orbit. We show that these estimates for the orbital periods can be made more precise by taking into account dynamical stability considerations. We also calculate the distribution of stellar reflex velocities expected for this system, and show that it provides a good target for future radial velocity observations. If a precise orbital period can be determined for the outer Jovian planet through future observations, it will be an excellent candidate for follow-up transit observations to study its atmosphere and measure its oblateness.

K2 Campaigns 5 & 6 Have IDed 152 Exoplanet Candidates

Transiting exoplanet candidates from K2 Campaigns 5 and 6

Authors:

Pope et al

Abstract:

We introduce a new transit search and vetting pipeline for observations from the K2 mission, and present the candidate transiting planets identified by this pipeline out of the targets in Campaigns 5 and 6. Our pipeline uses the Gaussian Process-based K2SC code to correct for the K2 pointing systematics and simultaneously model stellar variability. The systematics-corrected, variability-detrended light curves are searched for transits with the Box Least Squares method, and a period-dependent detection threshold is used to generate a preliminary candidate list. Two or three individuals vet each candidate manually to produce the final candidate list, using a set of automatically-generated transit fits and assorted diagnostic tests to inform the vetting. We detect 147 single-planet system candidates and 5 multi-planet systems, independently recovering the previously-published hot~Jupiters EPIC 212110888b, WASP-55b (EPIC 212300977b) and Qatar-2b (EPIC 212756297b). We also report the outcome of reconnaissance spectroscopy carried out for all candidates with Kepler magnitude Kp less than 13, identifying 12 targets as likely false positives. We compare our results to those of other K2 transit search pipelines, noting that ours performs particularly well for variable and/or active stars, but that the results are very similar overall. All the light curves and code used in the transit search and vetting process are publicly available, as are the follow-up spectra.

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:

Giuppone 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 have two Earth-like planets in orbits previously identified as unstable U and also in Euler L3 configurations, with bounded chaos.