Bradley M. S. Hansen

The existence of giant extrasolar planets on short-period orbits (“hot Jupiters”) challenges planet formation theories because such planets are difficult to form close to the star. High-eccentricity migration is a leading explanation, in which giant planets born at large separations are excited to near-unity eccentricities, enabling tidal dissipation at periastron to shrink and circularize their orbits. While observations of orbital misalignments and eccentric planets support this scenario, high-eccentricity migration models struggle to reproduce the observed hot Jupiter occurrence rate. Population synthesis studies often predict that many source “cold Jupiters” are destroyed by tidal disruption at high eccentricities. We revisit this question with improved treatments of mass loss and angular momentum return experienced by tidally perturbed planets. As a test case, we explore eccentricity excitations driven by wide stellar companions via the eccentric Kozai–Lidov mechanism. We show using an analytical framework that planets may avoid complete disruption and ultimately survive as stripped hot Jupiters. To capture detailed planetary mass loss over many orbits, we perform numerical studies that combine secular dynamical evolution with planetary structure evolution. Our new population synthesis studies show that hot Jupiter survival is enhanced by a factor of ∼2–3 relative to previous estimates, yielding occurrence rates (≳0.5% around FGK stars), consistent with observations. Angular momentum return from mass accreted onto the star may also produce a pileup of hot Jupiters near 3 day orbital periods. These results suggest that high-eccentricity migration, when accounting for tidal mass loss, may be a dominant channel for hot Jupiter formation.

We present a set of numerical simulations of the dynamical evolution of compact planetary systems migrating in a protoplanetary disk whose inner edge is sculpted by the interaction with the stellar magnetic field, as described in Yu et al. (2023). We demonstrate that the resulting final distribution of neighbouring planet period ratios contains only a small surviving fraction of resonant systems, in accordance with observations. The resulting planetary architectures are largely in place by the end of the protoplanetary disk phase (within a few Myr), and do not require significant later dynamical evolution. The divergence of planetary pairs during gas disk dispersal also leads to the excitation of eccentricities when pairs cross mean motion resonances in a divergent fashion. The resulting distribution of remnant free eccentricities is consistent with the values inferred from the observation of transit durations and transit timing variations. We furthermore demonstrate that this conclusion is not significantly altered by tides, assuming standard values for tidal dissipation in Earth or Neptune-class planets. These results demonstrate that the observed spacing and residual dynamical excitation of compact planetary systems can be reproduced by migration through a protoplanetary disk, as long as the inner disk boundary is modelled as a gradual rollover, instead of a sharp transition. Such an effect can be achieved when the model accounts for the diffusion of the stellar magnetic field into the disk. The resulting divergence of planetary pairs during the magnetospheric rebound phase breaks the resonant chains, resulting in a better match to observations than disk models with more traditional inner boundaries.

The large eccentricities of cold Jupiters and the existence of hot Jupiters have long challenged theories of planet formation. A proposed solution to both of these puzzles is high-eccentricity migration, in which an initially cold Jupiter is excited to high eccentricities before being tidally circularized. Secular perturbations from an inclined stellar companion are a potential source of eccentricity oscillations, a phenomenon known as the Eccentric Kozai–Lidov (EKL) mechanism. Previous studies have found that the cold Jupiter eccentricity distribution produced by EKL is inconsistent with observations. However, these studies assumed all planets start on circular orbits. Here, we revisit this question, considering that an initial period of planet–planet scattering on ∼Myr timescales likely places planets on slightly eccentric orbits before being modulated by EKL on ∼Myr–Gyr timescales. Small initial eccentricities can have a dramatic effect by enabling EKL to act at lower inclinations. We numerically integrate the secular hierarchical three-body equations of motion, including general relativity and tides, for populations of cold giant planets in stellar binaries with varied initial eccentricity distributions. For populations with modest initial mean eccentricities, the simulated eccentricity distribution produced by EKL is statistically consistent with the observed eccentricities of cold single-planet systems. The lower eccentricities in a multiplanet control sample suggest planetary companions quench stellar EKL. We show that scattering alone is unlikely to reproduce the present-day eccentricity distribution. We also calculate predictions for the inclinations and stellar obliquities in binary systems with cold Jupiters.

More than half of all main-sequence (MS) stars have one or more companions, and many of those with initial masses 10 yr) companions. Furthermore, both BSS binaries and DWDs exhibit signatures of WD birth kicks.

Three-body systems are prevalent in nature, from planetary to stellar to supermassive black hole scales. In a hierarchical triple system, oscillations of the inner orbit’s eccentricity and inclination can be induced on secular timescales. Over many cycles, the octupole-level terms in the secular equations of motion can drive the system to extremely high eccentricities via the eccentric Kozai–Lidov (EKL) mechanism. The overall decrease in the inner orbit’s pericenter distance has potentially dramatic effects for realistic systems, such as tidal disruption events. We present an analytical approximation in the test-particle limit to describe individual stepwise increases in eccentricity of the inner orbit. A second approximation, also in the test-particle limit, is obtained by integrating the equations of motion and calibrating to numerical simulations to estimate the overall octupole-level time evolution of the eccentricity. The latter approach is then extended beyond the test particle to the general case. The three novel analytical approximations are compared to numerical solutions to show that the models accurately describe the form and timescale of the secular descent from large distances to a close-encounter distance (e.g., the Roche limit). By circumventing the need for numerical simulations to obtain the long-term behavior, these approximations can be used to readily estimate properties of close encounters and descent timescales for populations of systems. We demonstrate this by calculating rates of EKL-driven migration for Hot Jupiters in stellar binaries.

Most, if not all, Sun-like stars host one or more planets, making multiplanetary systems commonplace in our Galaxy. We utilize hundreds of multiplanet simulations to explore the origin of such systems, focusing on their orbital architecture. The first set of simulations assumes in situ assembly of planetary embryos, while the second explores planetary migration. After applying observational biases to the simulations, we compare them to 250+ observed multiplanetary systems, including 13 systems with planets in the habitable zone. For all of the systems, we calculate two of the so-called statistical measures: the mass concentration (S _c ) and orbital spacing (S _s ). After analytic and empirical analyses, we find that the measures are related to first order with a power law: S c ∼ S s β . The in situ systems exhibit steeper power-law relations relative to the migration systems. We show that different formation scenarios cover different regions in the S _s –S _c diagram with some overlap. Furthermore, we discover that observed systems with S _s < 30 are likely dominated by the migration scenario, while those with S _s ≥ 30 are likely dominated by the in situ scenario. We apply these criteria to determine that a majority (62%) of observed multiplanetary systems formed via migration, whereas most systems with currently observed habitable planets formed via in situ assembly. This work provides methods of leveraging the statistical measures (S _s and S _c ) to disentangle the formation history of observed multiplanetary systems based on their present-day architectures.