ALBERT

Description: Surveys have revealed many multi-planet systems containing super-Earths and Neptunes in orbits of a few days to a few months. There is debate whether in situ assembly or inward migration is the dominant mechanism of the formation of such planetary systems. Simulations suggest that migration creates tightly packed systems with planets whose orbital periods may be expressed as ratios of small integers (resonances), often in a many-planet series (chain). In the hundreds of multi-planet systems of sub-Neptunes, more planet pairs are observed near resonances than would generally be expected, but no individual system has hitherto been identified that must have been formed by migration. Proximity to resonance enables the detection of planets perturbing each other. Here we report transit timing variations of the four planets in the Kepler-223 system, model these variations as resonant-angle librations, and compute the long-term stability of the resonant chain. The architecture of Kepler-223 is too finely tuned to have been formed by scattering, and our numerical simulations demonstrate that its properties are natural outcomes of the migration hypothesis. Similar systems could be destabilized by any of several mechanisms, contributing to the observed orbital-period distribution, where many planets are not in resonances. Planetesimal interactions in particular are thought to be responsible for establishing the current orbits of the four giant planets in the Solar System by disrupting a theoretical initial resonant chain similar to that observed in Kepler-223.〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Mills, Sean M -- Fabrycky, Daniel C -- Migaszewski, Cezary -- Ford, Eric B -- Petigura, Erik -- Isaacson, Howard -- England -- Nature. 2016 May 11;533(7604):509-12. doi: 10.1038/nature17445.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉Department of Astronomy and Astrophysics, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA. ; Institute of Physics and CASA*, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland. ; Torun Centre for Astronomy, Nicolaus Copernicus University, Gagarina 11, 87-100 Torun, Poland. ; Center for Exoplanets and Habitable Worlds, The Pennsylvania State University, University Park, Pennsylvania 16802, USA. ; Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA. ; Center for Astrostatistics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA. ; University of California at Berkeley, Berkeley, California 94720, USA. ; California Institute of Technology, Pasadena, California 91125, USA.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/27225123" target="_blank"〉PubMed〈/a〉

Description: We study the migration of three-planet systems in an irradiated 1+1D α-disc with photoevaporation. We performed 2700 simulations with various planets’ masses and initial orbits. We found that most of the systems which ended up as compact configurations form chains of mean motion resonances (MMRs) of the first and higher orders. Most of the systems involved in chains of MMRs are periodic configurations. The period ratios of such system, though, are not necessarily close to exact commensurability. If a given system resides in a divergent migration zone in the disc, the period ratios increase and evolve along resonant divergent migration paths at ( P 2 / P 1 , P 3 / P 2 ) diagram, where P 1 , P 2 , P 3 are the orbital periods of the first, second and third planet, respectively. The observed systems, though, do not lie on those paths. We show that agreement between the synthetic and the observed system distributions could be achieved if the orbital circularization was slower than it results from models of the planet–disc interactions. Therefore, we conclude that most of those systems unlikely formed as a result of divergent migration out of nominal chains of MMRs.

Description: We study the dynamics of a system of two super-Earths embedded in a protoplanetary disc. We build a simple model of an irradiated viscous disc and use analytical prescriptions for the planet–disc interactions which lead to migration. We show that depending on the disc parameters, planets’ masses and their positions in the disc, the migration of each planet can be inwards or outwards and the migration of a two-planet system can be convergent (which may lead to formation of a first-order mean motion resonance, MMR) or divergent (a system moves away from MMR). We performed 3500 simulations of the migration of two-planet systems with various masses and initial orbits. Almost all of them end up as resonant configurations, although the period ratios may be very distant from the nominal values of a given MMR. We found that almost all the systems resulting from the migration are periodic configurations.

Description: HR 8799 is a nearby star hosting at least four ~10  m Jup planets in wide orbits up to ~70 au, detected through the direct, high-contrast infrared imaging. Large companions and debris discs reported interior to ~10 au, and exterior to ~100 au indicate massive protoplanetary disc in the past. The dynamical state of the HR 8799 system is not yet fully resolved, due to limited astrometric data covering tiny orbital arcs. We construct a new orbital model of the HR 8799 system, assuming rapid migration of the planets after their formation in wider orbits. We found that the HR 8799 planets are likely involved in double Laplace resonance, 1e:2d:4c:8b MMR. Quasi-circular planetary orbits are coplanar with the stellar equator and inclined by ~25° to the sky plane. This best-fitting orbital configuration matches astrometry, debris disc models, and mass estimates from cooling models. The multiple mean motion resonance (MMR) is stable for the age of the star ~160 Myr, for at least 1 Gyr unless significant perturbations to the N -body dynamics are present. We predict four configurations with the fifth hypothetical innermost planet HR 8799f in ~9.7 au, or ~7.5 au orbit, extending the MMR chain to triple Laplace resonance 1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR, respectively. Our findings may establish strong boundary conditions for the system formation and its early history.

Description: We report a linear ordering of orbits in a sample of multiple extrasolar planetary systems with super-Earth planets. We selected 20 cases, mostly discovered by the Kepler mission, hosting at least four planets within ~0.5 au. The semimajor axis a n of an n th planet in each system of this sample obeys a ( n ) =  a 1  + ( n  – 1) a , where a 1 is the semimajor axis of the innermost orbit and a is a spacing between subsequent planets, which are specific for a particular system. For instance, the Kepler-33 system hosting five super-Earth planets exhibits the relative deviations between the observed and linearly predicted semimajor axes of only a few per cent. At least half of systems in the sample fulfil the linear law with a similar accuracy. We explain the linear distribution of semimajor axes as a natural implication of multiple chains of mean-motion resonances between subsequent planets, which emerge due to planet–disc interactions and convergent migration at early stages of their evolution.

Description: We investigate the orbital stability of a putative Jovian planet in a compact binary Octantis reported by Ramm et al. We re-analysed published radial velocity data in terms of a self-consistent Newtonian model and we found stable best-fitting solutions that obey observational constraints. They correspond to retrograde orbits, in accord with an earlier hypothesis of Eberle & Cuntz, with apsidal lines anti-aligned with the apses of the binary. The best-fitting solutions are confined to tiny stable regions of the phase space. These regions have a structure of the Arnold web formed by overlapping low-order mean motion resonances and their sub-resonances. The presence of a real planet is still questionable, because its formation would be hindered by strong dynamical perturbations. Our numerical study makes use of a new computational Message Passing Interface framework mechanic developed to run massive numerical experiments on CPU clusters.

Description: We investigate the dynamical stability of the Kepler-60 planetary system with three super-Earths. We determine their orbital elements and masses by transit timing variation (TTV) data spanning quarters Q1–Q16 of the Kepler mission. The system is dynamically active but the TTV data constrain masses to ~4 M and orbits in safely wide stable zones. The observations prefer two types of solutions. The true three-body Laplace mean-motion resonance (MMR) exhibits the critical angle librating around ~=45° and aligned apsides of the inner and outer pair of planets. In the Laplace MMR formed through a chain of two-planet 5:4 and 4:3 MMRs, all critical angles librate with small amplitudes ~30° and apsidal lines in planet's pairs are anti-aligned. The system is simultaneously locked in a three-body MMR with librations amplitude ~=10 o . The true Laplace MMR can evolve towards a chain of two-body MMRs in the presence of planetary migration. Therefore, the three-body MMR formed in this way seems to be more likely state of the system. However, the true three-body MMR cannot be disregarded a priori and it remains a puzzling configuration that may challenge the planet formation theory.

Description: We analyse the transit timing variation measurements of a system of two super-Earths detected as Kepler-29, in order to constrain the planets’ masses and orbital parameters. A dynamical analysis of the best-fitting configurations constrains the masses to be ~6 and ~5 Earth masses for the inner and the outer planets, respectively. The analysis also reveals that the system is likely locked in the 9:7 mean motion resonance. However, a variety of orbital architectures regarding eccentricities and the relative orientation of orbits is permitted by the observations as well as by stability constraints. We attempt to find configurations preferred by the planet formation scenarios as an additional, physical constraint. We show that configurations with low eccentricities and anti-aligned apsidal lines of the orbits are a natural and most likely outcome of the convergent migration. However, we show that librations of the critical angles are not necessary for the Kepler-29 system to be dynamically resonant, and such configurations may be formed on the way of migration as well. We argue, on the other hand, that aligned configurations with e 0.03 may be not consistent with the migration scenario.