The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While a sharp stability boundary exists for a two-planet system, numerical simulations of three-planet systems and higher 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 (MMRs), for circular orbits the two-planets MMRs are too far separated to destabilise systems initially away from them. The studied mechanism reproduces the qualitative behaviour found in numerical simulations very well. We develop an analytical model to generalise the empirical trend obtained for equal-mass and equally spaced planets to general systems on initially circular orbits. We obtain an analytical estimate of the survival time consistent with numerical simulations over four orders of magnitude for the planet-to-star-mass ratio ε, 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 ε1∕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 confirm these findings with the aid of numerical simulations of three-planet systems with different masses. We finally discuss the extension of our result to more general systems, containing more planets on initially non-circular orbits.

Massive planets form within the lifetime of protoplanetary disks and therefore they are subject to orbital migration due to planet-disk interactions. When the first planet reaches the inner edge of the disk its migration stops and consequently the second planet ends up locked in resonance with the first one. We detail how the resonant trapping works comparing semi-analytical formulae and numerical simulations. We restrict to the case of two equal-mass coplanar planets trapped in first order resonances but the method can be easily generalised. We first describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using series expansions up to different orders in eccentricity as well as a non-expanded Hamiltonian. Then we show that during convergent migration the planets evolve along these families of equilibrium points. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict precisely analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that in most cases the resonant configurations achieved by migration become unstable after the removal of the protoplanetary disk. Here we probe the stability of the resonances as a function of planetary mass. For this purpose, we fictitiously increase the masses of resonant planets, adiabatically maintaining the low-amplitude libration regime until instability occurs. We discuss two hypotheses for the instability, that of a low-order secondary resonance of the libration frequency with a fast synodic frequency of the system, and that of 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 nevertheless play the decisive role in the destabilisation of resonant pairs. We show evidence 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.

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 multiresonant 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.