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.
Planets around binary stars and those in multiplanet systems may experience resonant eccentricity excitation and disruption due to perturbations from a distant stellar companion. This "evection resonance" occurs when the apsidal precession frequency of the planet, driven by the quadrupole associated with the inner binary or the other planets, matches the orbital frequency of the external companion. We develop an analytic theory to study the effects of evection resonance on circumbinary planets and multiplanet systems. We derive the general conditions for effective eccentricity excitation or re…
We present a series of dynamical maps for fictitious 3-planets systems in initially circular coplanar orbits. These maps have unveiled a rich resonant structure involving two or three planets, as well as indicating possible migration routes from secular to double resonances or pure 3-planet commensurabilities. These structures are then compared to the present-day orbital architecture of observed resonant chains. In a second part of the paper we describe N-body simulations of type-I migration. Depending on the orbital decay timescale, we show that 3-planet systems may be trapped in different co…
We present two-dimensional hydrodynamical simulations of pairs of planets migrating simultaneously in the Type I regime in a protoplanetary disc. Convergent migration naturally leads to the trapping of these planets in mean-motion resonances. Once in resonance the planets' eccentricity grows rapidly, and disc-planet torques cause the planets to escape resonance on a time-scale of a few hundred orbits. The effect is more pronounced in highly viscous discs, but operates efficiently even in inviscid discs. We attribute this resonance-breaking to overstable librations driven by moderate eccentrici…
Recent observations of Kepler multi-planet systems have revealed a number of systems with planets very close to second-order mean motion resonances (MMRs, with period ratio $1:3$, $3:5$, etc.) We present an analytic study of resonance capture and its stability for planets migrating in gaseous disks. Resonance capture requires slow convergent migration of the planets, with sufficiently large eccentricity damping timescale $T_e$ and small pre-resonance eccentricities. We quantify these requirements and find that they can be satisfied for super-Earths under protoplanetary disk conditions. For pla…
The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could have both resonance angles associated with the resonance librating if the orbital eccentricities are sufficiently small, because the width of first-order resonances diverges in the limit of vanishingly small eccentricity. We consider a widely-held scenario in which pairs of planets were captured into first-order resonances by migration due to planet-disk interactions…
Tidal force plays an important role in the evolution of the planet-moon system. The tidal force of a moon can excite seismic waves in the planet it is orbiting. A tidal-seismic resonance is expected when a tidal force frequency matches a free-oscillation frequency of the planet. Here we show that when the moon is close to the planet, the tidal-seismic resonance can cause large-amplitude seismic waves, which can change the shape of the planet and in turn exert a negative torque on the moon to cause it to fall rapidly toward the planet. We postulate that the tidal-seismic resonance may be an imp…
We study the establishment of three-planet resonances -similar to the Laplace resonance in the Galilean satellites- and their effects on the mutual inclinations of the orbital planes of the planets, assuming that the latter undergo migration in a gaseous disc. In particular, we examine the resonance relations that occur, by varying the physical and initial orbital parameters of the planets (mass, initial semi-major axis and eccentricity) as well as the parameters of the migration forces (migration rate and eccentricity damping rate), which are modeled here through a simplified analytic prescri…
Planets migrating in their natal discs can be captured into mean-motion resonance (MMR), in which the planets' periods are related by integer ratios. Recent observations indicate that planets in MMR can be either apsidally aligned or anti-aligned. How these different configurations arise is unclear. In this paper, we study the MMR capture process of migrating planets, focusing on the property of the apsidal angles of the captured planets. We show that the standard picture of MMR capture, in which the planets undergo convergent migration and experience eccentricity damping due to planet-disc in…
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 strat…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a mass…
We analyze the distribution of known multi-planet systems ($N \geq 3$) in the plane of mean-motion ratios, and compare it with the resonance web generated by two-planet mean-motion resonances (2P-MMR) and pure 3-planet commensurabilities (pure 3P-MMR). We find intriguing evidence of a statistically significant correlation between the observed distribution of compact low-mass systems and the resonance structure, indicating a possible causal relation. While resonance chains such as Kepler-60, Kepler-80 and TRAPPIST-1 are strong contributors, most of the correlation appears to be caused by system…
Gravitational perturbations in multi-planet systems caused by an accompanying star are the subject of this investigation. Our dynamical model is based on the binary star HD41004 AB where a giant planet orbits HD41004 A. We modify the orbital parameters of this system and analyze the motion of a hypothetical test-planet surrounding HD41004 A on an interior orbit to the detected giant planet. Our numerical computations indicate perturbations due to mean motion and secular resonances. The locations of these resonances are usually connected to high eccentricity and highly inclined motion depending…
The resonant perturbations from planets are able to halt the drag-induced migration, and capture the inwardly drifting planetesimals into mean motion resonances. The equilibrium eccentricity of planetesimals in resonances, and the minimum size of planetesimal that can trigger resonance trapping, have been analyzed and formulated. However, the analytical works based on the assumption that the disk is axisymmetric, which is violated by the asymmetric structures developed by planets. We perform long-term 2D hydrodynamic simulations to study the dynamics of planetesimals in the $j:(j+1)$ first-ord…
The multiple-planet systems discovered by the Kepler mission exhibit the following feature: planet pairs near first-order mean-motion resonances prefer orbits just outside the nominal resonance, while avoiding those just inside the resonance. We explore an extremely simple dynamical model for planet formation, in which planets grow in mass at a prescribed rate without orbital migration or dissipation. We develop an analytic version of this model for two-planet systems in two limiting cases: the planet mass grows quickly or slowly relative to the characteristic resonant libration time. In both …
Pairs of migrating extrasolar planets often lock into mean motion resonance as they drift inward. This paper studies the convergent migration of giant planets (driven by a circumstellar disk) and determines the probability that they are captured into mean motion resonance. The probability that such planets enter resonance depends on the type of resonance, the migration rate, the eccentricity damping rate, and the amplitude of the turbulent fluctuations. This problem is studied both through direct integrations of the full 3-body problem, and via semi-analytic model equations. In general, the pr…
I consider the dynamics of mean motion resonances between pairs of co-planar planets and derive a new integrable Hamiltonian model for planets' resonant motion. The new model generalizes previously-derived integrable Hamiltonians for first-order resonances to treat higher-order resonances by exploiting a surprising near-symmetry of the full, non-integrable Hamiltonians of higher-order resonances. Whereas past works have frequently relied on truncated disturbing function expansions to derive integrable approximations to resonant motion, I show that no such expansion is necessary, thus enabling …
Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of convergent migration. However, higher order resonances require high initial orbital eccentricities in order to be formed by this process and these are in general unexpected in a dissipative disk. We present a way of generating large initial eccentricities using additional planets. This procedure allows us to form high order MMRs and predict new planets using a gene…
A commonly noted feature of the population of multi-planet extrasolar systems is the rarity of planet pairs in low-order mean-motion resonances. We revisit the physics of resonance capture via convergent disk-driven migration. We point out that for planet spacings typical of stable configurations for Kepler systems, the planets can routinely maintain a small but nonzero eccentricity due to gravitational perturbations from their neighbors. Together with the upper limit on the migration rate needed for capture, the finite eccentricity can make resonance capture difficult or impossible in Sun-lik…
In spite of planetary resonances being a common dynamical mechanism acting on planetary systems, no general model exists for describing their properties, particularly for commensurabilities of any order and arbitrary values of the eccentricities and inclinations. The present work presents a semi-analytical model that describes the resonance strength, width, location and stability of fixed points, as well as periods of small-amplitude librations. The model is valid to any two gravitationally interacting massive bodies, and thus applicable to planets around single or binary stars. Using a theore…
A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about star. We expand the planet-planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet's obliquity to near 90 or 180 degrees depending upon whether the…
Planetary formation theories and, more specifically, migration models predict that planets can be captured in mean-motion resonances (MMRs) during the disc phase. The distribution of period ratios between adjacent planets shows an accumulation in the vicinity of the resonance, which is not centred on the nominal resonance but instead presents an offset slightly exterior to it. Here we extend on previous works by thoroughly exploring the effect of different disc and planet parameters on the resonance offset during the disc migration phase. The dynamical study is carried out for several first-or…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are both in mean motion resonance and revolve in opposite directions. For a particular two-planet system, we have also obtained a new orbital fit involving such a counter-revolving configuration and consistent with the observational data. In the present paper, we analytically investigate the three-body problem in this particular case of retrograde resonances. W…
Orbital mean motion resonances in planetary systems originate from dissipative processes in disk-planet interactions that lead to orbital migration. In multi-planet systems that host giant planets, the perturbation of the protoplanetary disk strongly affects the migration of companion planets. By studying the well-characterized resonant planetary system around GJ 876 we aim to explore which effects shape disk-driven migration in such a multi-planet system to form resonant chains. We modelled the orbital migration of three planets embedded in a protoplanetary disk using two-dimensional locally …
All of the known circumbinary planets are large (> 3 Earth radii). Whilst observational biases may account for this dearth of small planets, in this paper we propose a theoretical explanation. Most of the known planets are near the stability limit, interspersed between potentially unstable 5 : 1, 6 : 1 and 7 : 1 mean motion resonances with the binary. It is believed that these planets did not form in situ, but rather migrated from farther out in the disc, and hence passed through these resonances. Planets are expected to migrate at a speed proportional to their mass, and a slower rate makes re…
The study of orbital resonances allows for the constraint of planetary properties of compact systems. K2-138 is an early K-type star with six planets, five of which have been proposed to be in the longest chain of 3:2 mean motion resonances. To observe and potentially verify the resonant behavior of K2-138's planets, we run N-body simulations using previously measured parameters. Through our analysis, we find that 99.2% of our simulations result in a chain of 3:2 resonances, although only 11% of them show a five-planet resonance chain. We find we are able to use resonances to constrain the orb…
A fraction of multiple planet candidate systems discovered from transits by the Kepler mission contain pairs of planet candidates that are in orbital resonance or are spaced slightly too far apart to be in resonance. We focus here on the four planet system, KOI 730, that has planet periods satisfying the ratios 8:6:4:3. By numerically integrating four planets initially in this resonant configuration in proximity to an initially exterior cold planetesimal disk, we find that of the order of a Mars mass of planet-orbit-crossing planetesimals is sufficient to pull this system out of resonance. App…
Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent `lone-planet' scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. During the depletion of the disk gas, the planet's secular resonance propagates inward and clears a …
We derive the transit timing variations (TTVs) of two planets near a second order mean motion resonance on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of $j n_2-(j-2)n_1$, where $j \ge 3$ is an integer characterizing the resonance and $n_2$ and $n_1$ are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV depends on the mass of the perturbing planet, relative to the mass of the star, and on both the eccentricities and longitudes of pericenter of each planet. The TTVs of the two planets are approximated…
The process of migration into resonance capture has been well studied for planetary systems where the gravitational potential is generated exclusively by the star and planets. However, massive protoplanetary disks add a significant perturbation to these models. In this paper we consider two limiting cases of disk-induced precession on migrating planets and find that small amounts of precession significantly affect the equilibrium reached by migrating planets. We investigate these effects with a combination of semi-analytic models of the resonance and numerical integrations. We also consider th…
We present spectroscopic measurements of the Rossiter-McLaughlin effect for the planet b of Kepler-9 multi-transiting planet system. The resulting sky-projected spin-orbit angle is $λ=-13^{\circ} \pm 16^{\circ}$, which favors an aligned system and strongly disfavors highly misaligned, polar, and retrograde orbits. Including Kepler-9, there are now a total of 4 Rossiter-McLaughlin effect measurements for multiplanet systems, all of which are consistent with spin-orbit alignment.
This paper focuses on two-planet systems in a first-order $(q+1):q$ mean motion resonance and undergoing type-I migration in a disc. We present a detailed analysis of the resonance valid for any value of $q$. Expressions for the equilibrium eccentricities, mean motions and departure from exact resonance are derived in the case of smooth convergent migration. We show that this departure, not assumed to be small, is such that period ratio normally exceeds, but can also be less than, $ (q+1)/q.$ Departure from exact resonance as a function of time for systems starting in resonance and undergoing …
A number of multiplanet systems are observed to contain planets very close to mean motion resonances, although there is no significant pileup of precise resonance pairs. We present theoretical and numerical studies on the outcome of capture into first-order mean motion resonances (MMRs) using a parametrized planet migration model that takes into account nonlinear eccentricity damping due to planet-disk interaction. This parametrization is based on numerical hydrodynamical simulations and is more realistic than the simple linear parametrization widely used in previous analytic studies. We find …
Planets close to their stars are thought to form farther out and migrate inward due to angular momentum exchange with gaseous protoplanetary disks. This process can produce systems of planets in co-orbital (Trojan or 1:1) resonance, in which two planets share the same orbit, usually separated by 60 degrees. Co-orbital systems are detectable among the planetary systems found by the Kepler mission either directly or by transit timing variations. However, no co-orbital systems have been found within the thousands of Kepler planets and candidates. Here we study the orbital evolution of co-orbital …
The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic orbit resonances, leading to long-term stable planet and moon orbits in solar or stellar systems. The distance pattern of planets was originally described by the empirical Titius-Bode law, and by a generalized version with a constant geometric progression factor (corresponding to logarithmic spacing). We find that the orbital periods $T_i$ and planet distance…
It has been established theoretically that atmospheric thermal tides on rocky planets can lead to significant modifications of rotational evolution, both close to synchronous rotation and at faster rotations if certain resonant conditions are met. Here it is demonstrated that the normally considered dissipative gravitational tidal evolution of rocky planet rotation could, in principle, be 'stalled' by thermal tide resonances for Earth-analog worlds in the liquid water orbital zone of stars more massive than ~0.3 Msolar. The possibility of feedback effects between a planetary biosphere and the …
The gravitational influence of a planet on a nearby disk provides a powerful tool for detecting and studying extrasolar planetary systems. Here we demonstrate that gaps can be opened in dynamically cold debris disks at the mean-motion resonances of an orbiting planet. The gaps are opened away from the orbit of the planet itself, revealing that not all disk gaps need contain a planetary body. These gaps are large and deep enough to be detectable in resolved disk images for a wide range of reasonable disk-planet parameters, though we are not aware of any such gaps detected to date. The gap shape…
The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected for type II migration. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity resonances different from those found by Lee (2004). This new family has outer orbita…
We investigate the inclination-growth mechanisms for two-planet systems during the late protoplanetary disc phase. In previous works, much attention has been directed to the inclination-type resonance, and it has been shown that it asks for high eccentricities to be acquired during the migration of the giant planets. By adopting eccentricity and inclination damping formulae based on hydrodynamical simulations (instead of the K-prescription), we have carried out 20 000 numerical simulations, where we vary the initial planetary eccentricities, the migration rate, and the dispersal time of the ga…
It has been proposed that mean motion resonances (MMRs) between Planet Nine and distant objects of the scattered disk might inform the semimajor axis and instantaneous position of Planet Nine. Within the context of this hypothesis, the specific distribution of occupied MMRs largely determines the available constraints. Here we characterize the behavior of scattered Kuiper Belt objects arising in the presence of an eccentric Planet Nine ($e_9 \in 0.1$, $0.7$), focusing on relative sizes of populations occupying particular commensurabilities. Highlighting the challenge of predicting the exact MM…
We perform several suites of highly detailed dynamical simulations to investigate the architectures of the 24 Sextantis and HD 200964 planetary systems. The best fit orbital solution for the two planets in the 24 Sex system places them on orbits with periods that lie very close to 2:1 commensurability, while that for the HD 200964 system places the two planets therein in orbits whose periods lie close to a 4:3 commensurability. In both cases, the proposed best-fit orbits are mutually crossing - a scenario that is only dynamically feasible if the planets are protected from close encounters by t…
We present 8 years of high-precision radial velocity (RV) data for HD 204313 from the 2.7 m Harlan J. Smith Telescope at McDonald Observatory. The star is known to have a giant planet (M sin i = 3.5 M_J) on a ~1900-day orbit, and a Neptune-mass planet at 0.2 AU. Using our own data in combination with the published CORALIE RVs of Segransan et al. (2010), we discover an outer Jovian (M sin i = 1.6 M_J) planet with P ~ 2800 days. Our orbital fit suggests the planets are in a 3:2 mean motion resonance, which would potentially affect their stability. We perform a detailed stability analysis, and ve…
A diversity of resonance configurations may be formed under different migration of two giant planets. And the researchers show that the HD 128311 and HD 73526 planetary systems are involved in a 2:1 mean motion resonance but not in apsidal corotation, because one of the resonance argument circulates over the dynamical evolution. In this paper, we investigate potential mechanisms to form the 2:1 librating-circulating resonance configuration. In the late stage of planetary formation, scattering or colliding among planetesimals and planetary embryos can frequently occur. Hence, in our model, we c…
We explore scenarios for the origin of two different density planets in the Kepler 36 system in adjacent orbits near the 7:6 mean motion resonance. We find that fine tuning is required in the stochastic forcing amplitude, the migration rate and planet eccentricities to allow two convergently migrating planets to bypass mean motion resonances such as the 4:3, 5:4 and 6:5, and yet allow capture into the 7:6 resonance. Stochastic forcing can eject the system from resonance causing a collision between the planets, unless the disk inducing migration and stochastic forcing is depleted soon after res…
Motivated by the population of multi-planet systems with orbital period ratios 1<P2/P1<2, we study the long-term stability of packed two planet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits near a first order mean motion resonance can be reduced to a one degree of freedom problem (Sessin & Ferraz Mello (1984), Wisdom (1986), Henrard et al. (1986)). Using this analytically tractable Hamiltonian, we apply the resonance overlap criterion to predict the onset of large scale chaotic motion in close two planet systems. The reduced Hamiltonian has only…
In this paper we investigate the possibility of a migration-induced resonance locking in systems containing three planets, namely an Earth analog, a super-Earth and a gas giant. The planets have been listed in order of increasing orbital periods. All three bodies are embedded in a locally isothermal gaseous disc and orbit around a solar mass star. We are interested in answering the following question: Will the low-mass planets form the same resonant structures with each other in the vicinity of the gas giant as in the case when the gas giant is absent? When there is no gas giant in the system,…
In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant pla…
We consider the dynamical evolution of two planets orbiting in the vicinity of a first order mean motion reso- nance while simultaneously undergoing eccentricity damping and convergent migration. Following Goldreich & Schlichting (2014), we include a coupling between the dissipative semimajor axis evolution and the damping of the eccentricities. In agreement with past studies, we find that this coupling can lead to overstability of the resonance and that for a certain range of parameters capture into resonance is only temporary. Using a more general model, we show that whether overstable motio…
Convergent migration allows pairs of planet to become trapped into mean motion resonances. Once in resonance, the planets' eccentricities grow to an equilibrium value that depends on the ratio of migration time scale to the eccentricity damping timescale, $K=τ_a/τ_e$, with higher values of equilibrium eccentricity for lower values of $K$. For low equilibrium eccentricities, $e_{eq}\propto K^{-1/2}$. The stability of a planet pair depends on eccentricity so the system can become unstable before it reaches its equilibrium eccentricity. Using a resonant overlap criterion that takes into account t…
The recent detection of the third planet in Kepler-47 has shown that binary stars can host several planets in circumbinary orbits. To understand the evolution of such systems we have performed two-dimensional hydrodynamic simulations of the circumbinary disc with two embedded planets for several Kepler systems. In two cases, Kepler-47 and -413, the planets are captured in a 1:1 mean-motion resonance at the planet parking position near the inner edge of the disc. The orbits are fully aligned, have mean eccentricities of about 0.25 to 0.30, and the planets are entangled in a horseshoe type of mo…
The Kepler mission has discovered a plethora of multiple transiting planet candidate exosystems, many of which feature putative pairs of planets near mean motion resonance commensurabilities. Identifying potentially resonant systems could help guide future observations and enhance our understanding of planetary formation scenarios. We develop and apply an algebraic method to determine which Kepler 2-planet systems cannot be in a 1st-4th order resonance, given the current, publicly available data. This method identifies when any potentially resonant angle of a system must circulate. We identify…
Exoplanet systems with multiple planets in mean motion resonances have often been hailed as a signpost of disk driven migration. Resonant chains like Kepler-223 and Kepler-80 consist of a trio of planets with the three-body resonant angle librating and/or with a two-body resonant angle librating for each pair. Here we investigate whether close-in super-Earths and mini-Neptunes forming in situ can lock into resonant chains due to dissipation from a depleted gas disk. We simulate the giant impact phase of planet formation, including eccentricity damping from a gaseous disk, followed by subsequen…
Assuming that giant planets are formed in thin protoplanetary discs, a '3D' system can form, provided that the mutual inclination is excited by some dynamical mechanism. Resonant interactions and close planetary encounters are thought to be the primary inclination-excitation mechanisms, resulting in a resonant and non-resonant system, respectively. Here we propose an alternative formation scenario, starting from a system composed of three giant planets in a nearly coplanar configuration. As was recently shown for the case of the Solar system, planetary migration in the gas disc (Type II migrat…
