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Trappist-1 hosts 7 planets where period ratios of neighbouring pairs are close to the 8:5, 5:3, 3:2, 3:2, 4:3, and 3:2 ratios in increasing distance from the star. The Laplace angles associated with neighbouring triplets are observed to be librating, proving the resonant nature of the system. This compact, resonant configuration is a manifest sign of disc-driven migration; however, the preferred outcome of such evolution is the establishment of first-order resonances, not the high-order resonances observed in the inner system. Here, we explain the observed orbital configuration in a model that is largely independent on the specific disc migration and orbital circularisation efficiencies. Together with migration, the two key elements of our model are: i) the inner border of the protoplanetary disc receded with time; and ii) the system was initially separated in two sub-systems. Specifically, the inner b, c d and e planets were initially placed in a 3:2 resonance chain and then evolved to the 8:5 -- 5:3 commensurability between planets b, c and d under the effect of the recession of the inner edge of the disc, whereas the outer planets migrated to the inner edge at a later time, establishing the remaining resonances. Our results pivot on the dynamical role of the presently unobservable recession of the inner edge of protoplanetary discs. They also reveal the role of recurring phases of convergent migration followed by resonant repulsion with associated orbital circularisation when resonant chains interact with migration barriers., Comment: To appear in Nature Astronomy

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.

In a previous paper we showed that, like the migration speed, the eccentricity damping efficiency is modulated linearly by the depth of the partial gap a planet carves in the disk surface density profile, resulting in less efficient $e$-damping compared to the prescription commonly used in population synthesis works. Here, we extend our analysis to 3D, refining our $e$-damping formula and studying how the inclination damping efficiency is also affected. We perform high resolution 3D locally isothermal hydrodynamical simulations of planets with varying masses embedded in disks with varying aspect ratios and viscosities. We extract the gap profile and orbital damping timescales for fixed eccentricities and inclinations up to the disk scale height. The limit in gap depths below which vortices appear, in the low-viscosity case, happens roughly at the transition between classical type-I and type-II migration regimes. The orbital damping timescales can be described by two linear trends with a break around gap depths $\sim80\%$ and with slopes and intercepts depending on the eccentricity and inclination. These trends are understood on physical grounds and are reproduced by simple fitting formulas whose error is within the typically uncertainty of type-I torque formulas. Thus, our recipes for the gap depth and orbital damping efficiencies yield a simple description for planet-disk interactions to use in N-body codes in the case of partial gap opening planets that is consistent with high-resolution 3D hydro-simulations. Finally, we show examples of how our novel orbital damping prescription can affect the outcome of population synthesis experiments., Comment: Accepted for publication in ApJ

Following the assumption that the disc substructures observed in protoplanetary discs originate from the interaction between the disc and the forming planets embedded therein, we aim to test if these putative planets could represent the progenitors of the currently observed giant exoplanets. We performed N-body simulations assuming initially three, four, five or seven planets. Our model includes pebble and gas accretion, migration, damping of eccentricities and inclinations, disc-planet interaction and disc evolution. We locate the planets in the positions where the gaps in protoplanetary discs have been observed and we evolve the systems for 100Myr including a few Myr of gas disc evolution, while also testing three values of $\alpha$ viscosity. For planetary systems with initially three and four planets we find that most of the growing planets lie beyond the RV detection limit of 5AU and only a small fraction of them migrate into the inner region. We also find that these systems have too low final eccentricities to be in agreement with the observed giant planet population. Systems initially consisting of five or seven planets become unstable after $\approx$40Kyr of integration time. This clearly shows that not every gap can host a planet. The general outcome of our simulations - too low eccentricities - is independent of the disc's viscosity and surface density. Further observations could either confirm the existence of an undetected population of wide-orbit giants or exclude the presence of such undetected population to constrain how many planets hide in gaps even further., Comment: Accepted for publication in A&A

Earth-sized exoplanets that transit nearby, late spectral type red dwarfs will be prime targets for atmospheric characterization in the coming decade. Such systems, however, are difficult to find via wide-field transit surveys like Kepler or TESS. Consequently, the presence of such transiting planets is unexplored and the occurrence rates of short-period Earth-sized planets around late M dwarfs remain poorly constrained. Here, we present the deepest photometric monitoring campaign of 22 nearby late M dwarf stars, using data from over 500 nights on seven 1-2 meter class telescopes. Our survey includes all known single quiescent northern late M dwarfs within 15 pc. We use transit-injection-and-recovery tests to quantify the completeness of our survey, successfully identify most ($>80\%$) transiting short-period (0.5-1 d) super-Earths ($R > 1.9 R_\oplus$), and are sensitive ($\sim50\%$) to transiting Earth-sized planets ($1.0-1.2 R_\oplus$). Our high sensitivity to transits with a near-zero false positive rate demonstrates an efficient survey strategy. Our survey does not yield a transiting planet detection, yet it provides the most sensitive upper limits on transiting planets orbiting our target stars. Finally, we explore multiple hypotheses about the occurrence rates of short-period planets (from Earth-sized planets to giant planets) around late M dwarfs. We show, for example, that giant planets at short periods ($<1$ day) are uncommon around our target stars. Our dataset provides some insight into occurrence rates of short-period planets around TRAPPIST-1-like stars, and our results can help test planetary formation and system evolution models, as well as guide future observations of nearby late M dwarfs., Comment: 27 pages, 11 figures

It is known that gap opening depends on the disc's viscosity; however, eccentricity damping formulas have only been derived at high viscosities, ignoring partial gap opening. We aim at obtaining a simple formula to model $e$-damping of the type-I regime in low viscosity discs, where even small planets may start opening partial. We perform high resolution 2D locally isothermal hydrodynamical simulations of planets with varying masses on fixed orbits in discs with varying aspect ratios and viscosities. We determine the torque and power felt by the planet to derive migration and eccentricity damping timescales. We first find a lower limit to the gap depths below which vortices appear; this happens roughly at the transition between type-I and type-II regimes. For the simulations that remain stable, we obtain a fit to the observed gap depth in the limit of vanishing eccentricities that is similar to the one currently used in the literature but is accurate down to $\alpha=3.16\times 10^{-5}$. We record the $e$-damping efficiency as a function of the observed gap depth and $e$: when the planet has opened a deep enough gap, a linear trend is observed independently of $e$; at shallower gaps this linear trend is preserved at low $e$, while it deviates to more efficient damping when $e$ is comparable to the disc's scale height. Both trends can be understood on theoretical grounds and are reproduced by a simple fitting formula. Our combined fits yield a simple recipe to implement type-I $e$-damping in $N$-body for partial gap opening planets that is consistent with high-resolution 2D hydro-simulations. The typical error of the fit is of the order of a few percent, and lower than the error of type-I torque formulas widely used in the literature. This will allow a more self-consistent treatment of planet-disc interactions of the type-I regime for population synthesis models at low viscosities., Comment: Submitted to A&A

The presence of forming planets embedded in their protoplanetary disks has been inferred from the detection of multiring structures in such disks. Most of these suspected planets are undetectable by direct imaging observations at current measurement sensitivities. Inward migration and accretion might make these putative planets accessible to the Doppler method, but the actual extent of growth and orbital evolution remains unconstrained. Under the premise that the gaps in the disk around HD 163296 originate from new-born planets, we investigate if and under which circumstances the gap-opening planets could represent progenitors of the exoplanet population detected around A-type stars. In particular, we study the dependence of final planetary masses and orbital parameters on the viscosity of the disk. The evolution of the embedded planets was simulated throughout the disk lifetime and up to 100 Myr after the dispersal of the disk, taking the evolving disk structure and a likely range of disk lifetimes into account. We find that the final configuration of the planets is largely determined by the $\alpha$ viscosity parameter of the disk and less dependent on the choice for the disk lifetime and the initial planetary parameters. If we assume that planets such as those in HD 163296 evolve to form the observed exoplanet population of A-type stars, a $\alpha$ parameter on the order of $3.16 \times 10^{-4} \lesssim \alpha \lesssim 10^{-3}$ is required for the disks to induce sufficiently high migration rates. Depending on whether or not future direct imaging surveys will uncover a larger number of planets with $m_\mathrm{pl} \lesssim 3 M_\mathrm{Jup}$ and $a_\mathrm{pl} \gtrsim 10 \mathrm{AU}$ we expect the $\alpha$ parameter to be at the lower or upper end of this range, always under the assumption that such disks indeed harbor wide orbit planets., Comment: Accepted for publication in Astronomy and Astrophysics, 13 pages, 7 figures

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

There is evidence that most chains of mean motion resonances of type $k$:$k-1$ among exoplanets become unstable once the dissipative action from the gas is removed from the system, particularly for large $N$ (the number of planets) and $k$ (indicating how compact the chain is). We present a novel dynamical mechanism that can explain the origin of these instabilities and thus the dearth of resonant systems in the exoplanet sample. It relies on the emergence of secondary resonances between a fraction of the synodic frequency $2 \pi (1/P_1-1/P_2)$ and the libration frequencies in the mean motion resonance. These secondary resonances excite the amplitudes of libration of the mean motion resonances thus leading to an instability. We detail the emergence of these secondary resonances by carrying out an explicit perturbative scheme to second order in the planetary masses and isolating the harmonic terms that are associated with them. Focusing on the case of three planets in the 3:2 -- 3:2 mean motion resonance as an example, a simple but general analytical model of one of these resonances is obtained which describes the initial phase of the activation of one such secondary resonance. The dynamics of the excited system is also briefly described. This scheme shows how one can obtain analytical insight into the emergence of these resonances, and into the dynamics that they trigger. Finally, a generalisation of this dynamical mechanism is obtained for arbitrary $N$ and $k$. This leads to an explanation of previous numerical experiments on the stability of resonant chains, showing why the critical planetary mass allowed for stability decreases with increasing $N$ and $k$., Comment: Submitted to MNRAS

Early dynamical evolution of close-in planetary systems is shaped by an intricate combination of planetary gravitational interactions, orbital migration, and dissipative effects. While the process of convergent orbital migration is expected to routinely yield resonant planetary systems, previous analyses have shown that the semi-major axes of initially resonant pairs of planets will gradually diverge under the influence of long-term energy damping, producing an overabundance of planetary period ratios in slight excess of exact commensurability. While this feature is clearly evident in the orbital distribution of close-in extrasolar planets, the existing theoretical picture is limited to the specific case of the planetary three-body problem. In this study, we generalise the framework of dissipative divergence of resonant orbits to multi-resonant chains, and apply our results to the current observational census of well-characterised three-planet systems. Focusing on the 2:1 and 3:2 commensurabilities, we identify three 3-planet systems, whose current orbital architecture is consistent with an evolutionary history wherein convergent migration first locks the planets into a multi-resonant configuration and subsequent dissipation repels the orbits away from exact commensurability. Nevertheless, we find that the architecture of the overall sample of multi planetary systems is incompatible with this simple scenario, suggesting that additional physical mechanisms must play a dominant role during the early stages of planetary systems' dynamical evolution., Comment: Accepted in Astronomy & Astrophysics

Massive planets form within the lifetime of protoplanetary disks and undergo orbital migration due to planet-disk interactions. When the first planet reaches the inner edge of the disk its migration stops and the second planet is locked in resonance. We detail the resonant trapping comparing semi-analytical formulae and numerical simulations in the case of two equal-mass coplanar planets trapped in first order resonances. We describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using expanded and non-expanded Hamiltonians. We show that during convergent migration the planets evolve along these families of equilibria. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that the resonant configurations achieved by migration can become unstable after the removal of the disk. We probe the stability of the resonances as a function of planetary mass. To do this, we fictitiously increase the masses of the planets, adiabatically maintaining the low-amplitude libration regime until instability. We discuss two hypotheses for instability: low-order secondary resonance of the libration frequency with a fast synodic frequency, and minimal approach distance between planets. We show that secondary resonances do not seem to impact resonant systems at low-amplitude of libration. Resonant systems are more stable than non-resonant ones for a given minimal distance at close encounters, but we show that the latter still play the decisive role in the destabilisation of resonant pairs. We show that, as the planetary mass increases and the minimal distance between planets gets smaller in terms of mutual Hill radius, the region of stability around the resonance center shrinks, until the equilibrium point itself becomes unstable.

It is well known that asteroids and comets fall into the Sun. Metal pollution of white dwarfs and transient spectroscopic signatures of young stars like $\beta$-Pic provide growing evidence that extra solar planetesimals can attain extreme orbital eccentricities and fall onto their parent stars. We aim to develop a general, practically implementable, semi-analytical theory of secular eccentricity excitation of small bodies in mean motion resonances with an eccentric planet valid for arbitrary values of the eccentricities and including the short-range force due to General Relativity. Our semi-analytic model for the restricted planar three-body problem does not make use of any series expansion and therefore is valid for any values of eccentricities and semi-major axes ratios. The model is based on the application of the adiabatic principle, which is valid when the precession period of the longitude of pericenter of the planetesimal is much longer than the libration period in the mean motion resonance. This holds down to vanishingly small eccentricities in resonances of order larger than 1. We provide a Mathematica notebook with the implementation of the model allowing direct use to the interested reader. We confirm that the 4:1 mean motion resonance with a moderately eccentric planet is the most powerful one to lift the eccentricity of planetesimals from nearly circular orbits to star-grazing ones. However, if the planet is too eccentric, we find that this resonances becomes unable to pump the planetesimal's eccentricity to very high value. The inclusion of the General Relativity effect imposes a condition on the mass of the planet to drive the planetsimals into star-grazing orbits. For a planetesimal at $\sim$1 AU around a solar-mass star (or white dwarf), we find a threshold planetary mass of about 17 Earth masses. We finally derive an analytical formula for this critical mass., Comment: In press in Astronomy & Astrophysics