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In the context of low-viscosity protoplanetary discs (PPDs), the formation scenarios of the Solar System should be revisited. In particular, the Jupiter-Saturn pair has been shown to lock in the 2:1 mean motion resonance while migrating generally inwards, making the Grand Tack scenario impossible. We explore what resonant chains of multiple giant planets can form in a low-viscosity disc, and whether these configurations can evolve into forming the Solar System in the post gas disc phase. We used hydrodynamical simulations to study the migration of the giant planets in a disc with viscosity $\alpha=10^{-4}$. After a transition phase to a gas-less configuration, we studied the stability of the obtained resonant chains through their interactions with a disc of leftover planetesimals by performing N-body simulations using rebound. The gaps open by giant planets are wider and deeper for lower viscosity, reducing the damping effect of the disc and thus weakening resonant chains. Exploring numerous configurations, we found five stable resonant chains of four or five planets. In a thin PPD, the four giant planets revert their migration and migrate outwards. After disc dispersal, under the influence of a belt of planetesimals, some resonant chains undergo an instability phase while others migrate smoothly over a billion years. For three of our resonant chains, about 1% of the final configurations pass the four criteria to fit the Solar System. The most successful runs are obtained for systems formed in a cold PPD with a massive planetesimal disc. This work provides a fully consistent study of the dynamical history of the Solar System's giant planets, from the protoplanetary disc phase up to the giant planet instability. Although building resonant configurations is difficult in low-viscosity discs, we find it possible to reproduce the Solar System from a cold, low-viscosity protoplanetary disc., Comment: 13 Pages, 13 Figures, Accepted for publications in A&A

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

The emergence of orbital resonances among planets is a natural consequence of the early dynamical evolution of planetary systems. While it is well-established that convergent migration is necessary for mean-motion commensurabilities to emerge, recent numerical experiments have shown that the existing adiabatic theory of resonant capture provides an incomplete description of the relevant physics, leading to an erroneous mass scaling in the regime of strong dissipation. In this work, we develop a new model for resonance capture that self-consistently accounts for migration and circularization of planetary orbits, and derive an analytic criterion based upon stability analysis that describes the conditions necessary for the formation of mean-motion resonances. We subsequently test our results against numerical simulations and find satisfactory agreement. Our results elucidate the critical role played by adiabaticity and resonant stability in shaping the orbital architectures of planetary systems during the nebular epoch, and provide a valuable tool for understanding their primordial dynamical evolution., Comment: 12 pages, 4 figures, accepted for publication in ApJL

Capture into mean motion resonance (MMR) is an important dynamical mechanism as it shapes the final architecture of a planetary system. We simulate systems of two or three planets undergoing migration with varied initial parameters such as planetary mass and disk surface density and analyse the resulting resonant chains. In contrast to previous studies, our results show that the disk properties have the dominant impact on capture into mean motion resonance, while the total planetary mass barely affects the final system configuration as long as the planet does not open a gap in the disk. We confirm that the adiabatic resonant capture is the correct framework to understand the conditions leading to MMR formation, since its predictions are qualitatively similar to the numerical results. However, we find that the eccentricity damping can facilitate the capture in a given resonance. We find that under typical disk conditions, planets tend to be captured into 2:1 or 3:2 MMRs, which agrees well with the observed exoplanet MMRs. Our results predict two categories of systems: those that have uniform chains of wide resonances (2:1 or 3:2 MMRs) and those that have a more compact inner pair than the outer pair such as 4:3:2 chains. Both categories of resonant chains are present in observed exoplanet systems. On the other hand, chains with a wider inner pair than the outer one are very rare and emerge from stochastic capture. Our work here can be used to link current configuration of exoplanetary systems to the formation conditions within protoplanetary disks., Comment: Accepted in A&A

Observations and models of giant planets indicate that such objects are enriched in heavy elements compared to solar abundances. The prevailing view is that giant planets accreted multiple Earth masses of heavy elements after the end of core formation. Such late solid enrichment is commonly explained by the accretion of planetesimals. Planetesimals are expected to form at the edges of planetary gaps, and here we address the question of whether these planetesimals can be accreted in large enough amounts to explain the inferred high heavy element contents of giant planets. We perform a series of N-body simulations of the dynamics of planetesimals and planets during the planetary growth phase, taking into account gas drag as well as the enhanced collision cross-section caused by the extended envelopes. We consider the growth of Jupiter and Saturn via gas accretion after reaching the pebble isolation mass and we include their migration in an evolving disk. We find that the accretion efficiency of planetesimals formed at planetary gap edges is very low: less than 10% of the formed planetesimals are accreted even in the most favorable cases, which in our model corresponds to a few Earth-masses. When planetesimals are assumed to form beyond the feeding zone of the planets, extending to a few Hill radii from a planet, accretion becomes negligible. Furthermore, we find that the accretion efficiency increases when the planetary migration distance is increased and that the efficiency does not increase when the planetesimal radii are decreased. Based on these results we conclude that it is difficult to explain the large heavy element content of giant planets with planetesimal accretion during the gas accretion phase. Alternative processes most likely are required, e.g. accretion of vapor deposited by drifting pebbles., Comment: Accepted for publication in A&A

Recent works on three-planet mean motion resonances (MMRs) have highlighted their importance for understanding the details of the dynamics of planet formation and evolution. While the dynamics of two-planet MMRs are well understood and approximately described by a one degree of freedom Hamiltonian, little is known of the exact dynamics of three-bodies resonances besides the cases of zeroth-order MMRs or when one of the body is a test particle. In this work, I propose the first general integrable model for first-order three-planet mean motion resonances. I show that one can generalize the strategy proposed in the two-planet case to obtain a one degree of freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application I show how this model could improve our understanding of the capture into MMRs as well as their role on the stability of planetary systems., Comment: Accepted in Celestial Mechanics and Dynamical Astronomy

The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While for a two-planet system a sharp stability boundary exists, numerical simulations of three and more planet systems show that they can experience instability on timescales up to billions of years. Moreover, an exponential trend between the planet orbital separation measured in units of Hill radii and the survival time has been reported. While these findings have been observed in numerous numerical simulations, little is known of the actual mechanism leading to instability. Contrary to a constant diffusion process, planetary systems seem to remain dynamically quiescent for most of their lifetime before a very short unstable phase. In this work, we show how the slow chaotic diffusion due to the overlap of three-body resonances dominates the timescale leading to the instability for initially coplanar and circular orbits. While the last instability phase is related to scattering due to two-planet mean motion resonances (MMR), for circular orbits the two-planets MMR are too far separated to destabilize systems initially away from them. We develop an analytical model to generalize the empirical trend obtained for equal mass and equally-spaced planets to general systems. We obtain an analytical estimate of the survival time consistent with simulations over four orders of magnitude for the planet to star mass ratio $\epsilon$, and 6 to 8 orders of magnitude for the instability time. We also confirm that measuring the orbital spacing in terms of Hill radii is not adapted and that the right spacing unit scales as $\epsilon^{1/4}$. We predict that beyond a certain spacing, the three-planet resonances are not overlapped, which results in an increase of the survival time. We finally discuss the extension of our result to more general systems, containing more planets on initially non circular orbits., Comment: Accepted in A&A. Added numerical tests with test particles and non uniform systems. A notebook as well as python scripts to reproduce the article figure are available at https://github.com/acpetit/PlanetSysSurvivalTime

K2-19 hosts a planetary system composed of two outer planets, b and c, with size of $7.0\pm 0.2~R_\oplus$ and $4.1\pm0.2~R_\oplus$ , and an inner planet, d, with a radius of $1.11\pm 0.05 R_\oplus$. A recent analysis of Transit-Timing Variations (TTVs) suggested b and c are close to but not in 3:2 mean motion resonance (MMR) because the classical resonant angles circulate. Such an architecture challenges our understanding of planet formation. Indeed, planet migration through the protoplanetary disk should lead to a capture into the MMR. Here, we show that the planets are in fact, locked into the 3:2 resonance despite circulation of the conventional resonant angles and aligned periapses. However, we show that such an orbital configuration cannot be maintained for more than a few hundred million years due to the tidal dissipation experienced by planet d. The tidal dissipation remains efficient because of a secular forcing of the innermost planet eccentricity by planets b and c. While the observations strongly rule out an orbital solution where the three planets are on close to circular orbits, it remains possible that a fourth planet is affecting the TTVs such that the four planet system is consistent with the tidal constraints., Comment: Accepted in MNRAS, replaced with published version

We present the obliquity measurement, that is, the angle between the normal angle of the orbital plane and the stellar spin axis, of the sub-Neptune planet HD3167 c, which transits a bright nearby K0 star. We study the orbital architecture of this multi-planet system to understand its dynamical history. We also place constraints on the obliquity of planet d based on the geometry of the planetary system and the dynamical study of the system. New observations obtained with HARPS-N at the Telescopio Nazionale Galileo (TNG) were employed for our analysis. The sky-projected obliquity was measured using three different methods: the Rossiter-McLaughlin anomaly, Doppler tomography, and reloaded Rossiter-McLaughlin techniques. We performed the stability analysis of the system and investigated the dynamical interactions between the planets and the star. HD3167 c is found to be nearly polar with sky-projected obliquity, $\lambda$ = -97$^{\circ} \pm$ 23$^{\circ}$. This misalignment of the orbit of planet c with the spin axis of the host star is detected with 97\% confidence. The analysis of the dynamics of this system yields coplanar orbits of planets c and d. It also shows that it is unlikely that the currently observed system can generate this high obliquity for planets c and d by itself. However, the polar orbits of planets c and d could be explained by the presence of an outer companion in the system. Follow-up observations of the system are required to confirm such a long-period companion., Comment: 13 pages, 11 figures, 2 tables. Accepted for publication in A&A, Updated to match the published version

We present a new mixed variable symplectic (MVS) integrator for planetary systems, that fully resolve close encounters. The method is based on a time regularisation that allows keeping the stability properties of the symplectic integrators, while also reducing the effective step size whenever two planets encounter. We use a high order MVS scheme such that it is possible to integrate with large time steps far away from close encounters. We show that this algorithm is able to resolve almost exact collisions (i.e with a mutual separation of a fraction of the physical radius) while using the same time-step as in weakly perturbed problem such as the Solar System. We demonstrate the long term behaviour on systems of six super-Earths experiencing strong scattering for 50 kyr. We compare our algorithm to hybrid methods such as MERCURY and show that for an equivalent cost we obtain much better energy conservation., Comment: Accepted in Astronomy and Astrophysics, updated to match the published version

In a two-planet system, due to Sundman (1912) inequality, a topological boundary can forbid close encounters between the two planets for infinite time. A system is said Hill stable if it verifies this topological condition. Hill stability is widely used in the study of extra solar planets dynamics. However people often use the coplanar and circular orbits approximation. In this paper, we explain how the Hill stability can be understood in the framework of Angular Momentum Deficit (AMD). In the secular approximation, the AMD allows to discriminate between a priori stable systems and systems for which a more in depth dynamical analysis is required. We show that the general Hill stability criterion can be expressed as a function of only the semi major axes, the masses and the total AMD of the system. The proposed criterion is only expanded in the planets-to-star mass ratio $\epsilon$ and not in the semi-major axis ratio, in eccentricities nor in the mutual inclination. Moreover the expansion in $\epsilon$ remains excellent up to values of about $10^{-3}$ even for two planets with very different mass values. We performed numerical simulations in order to highlight the sharp change of behaviour between Hill stable and Hill unstable systems. We show that Hill stable systems tend to be very regular whereas Hill unstable ones often lead to rapid planet collisions. We also remind that Hill stability does not protect from the ejection of the outer planet., Comment: Accepted for publication in Astronomy & Astrophysics

The AMD-stability criterion allows to discriminate between a-priori stable planetary systems and systems for which the stability is not granted and needs further investigations. AMD-stability is based on the conservation of the Angular Momentum Deficit (AMD) in the averaged system at all orders of averaging. While the AMD criterion is rigorous, the conservation of the AMD is only granted in absence of mean-motion resonances (MMR). Here we extend the AMD-stability criterion to take into account mean-motion resonances, and more specifically the overlap of first order MMR. If the MMR islands overlap, the system will experience generalized chaos leading to instability. The Hamiltonian of two massive planets on coplanar quasi-circular orbits can be reduced to an integrable one degree of freedom problem for period ratios close to a first order MMR. We use the reduced Hamiltonian to derive a new overlap criterion for first order MMR. This stability criterion unifies the previous criteria proposed in the literature and admits the criteria obtained for initially circular and eccentric orbits as limit cases. We then improve the definition of AMD-stability to take into account the short term chaos generated by MMR overlap. We analyze the outcome of this improved definition of AMD-stability on selected multi-planet systems from the Extrasolar Planets Encyclopeadia., Comment: Accepted by A and A 07/10/17

Metal production in galaxies traces star formation, and is highly concentrated toward the centers of galactic discs. This suggests that galaxies should have inhomogeneous metal distributions with strong radial gradients, but observations of present-day galaxies show only shallow gradients with little azimuthal variation, implying the existence of a redistribution mechanism. We study the role of gravitational instability-driven turbulence as a mixing mechanism by simulating an isolated galactic disc at high resolution, including metal fields treated as passive scalars. Since any cylindrical field can be decomposed into a sum of Fourier-Bessel basis functions, we set up initial metal fields characterized by these functions and study how different modes mix. We find both shear and turbulence contribute to mixing, but the mixing strongly depends on the symmetries of the mode. Non-axisymmetric modes have decay times smaller than the galactic orbital period because shear winds them up to small spatial scales, where they are erased by turbulence. The decay timescales for axisymmetric modes are much greater, though for all but the largest-scale inhomogeneities the mixing timescale is still short enough to erase chemical inhomogeneities over cosmological times. These different timescales provide an explanation for why galaxies retain metallicity gradients while there is almost no variation at a fixed radius. Moreover, the comparatively long timescales required for mixing axisymmetric modes may explain the greater diversity of metallicity gradients observed in high redshift galaxies as compared to local ones: these systems have not yet reached equilibrium between metal production and diffusion., Comment: 10 pages, 13 figures