Normalized angular momentum deficit: a tool for comparing the violence of the dynamical histories of planetary systems

Abstract

Context. Population studies of the orbital characteristics of exoplanets in multi-planet systems have highlighted the existence of an anticorrelation between the average orbital eccentricity of planets and the number of planets of their host system, that is, its multiplicity. This effect was proposed to reflect the varying levels of violence in the dynamical evolution of planetary systems. Aims. Previous work suggested that the relative violence of the dynamical evolution of planetary systems with similar orbital architectures can be compared through the computation of their angular momentum deficit (AMD). We investigated the possibility of using a more general metric to perform analogous comparisons between planetary systems with different orbital architectures. Methods. We considered a modified version of the AMD, the normalized angular momentum deficit (NAMD), and used it to study a sample of 99 multi-planet systems containing both the currently best-characterized extrasolar systems and the solar system, that is, planetary systems with both compact and wide orbital architectures. Results. We verified that the NAMD allows us to compare the violence of the dynamical histories of multi-planet systems with different orbital architectures. We identified an anticorrelation between the NAMD and the multiplicity of the planetary systems, of which the previously observed eccentricity-multiplicity anticorrelation is a reflection. Conclusions. Our results seem to indicate that phases of dynamical instabilities and chaotic evolution are not uncommon among planetary systems. They also suggest that the efficiency of the planetary formation process in producing high-multiplicity systems is likely to be higher than that suggested by their currently known population.

Tracing the Formation History of Giant Planets in Protoplanetary Disks with Carbon, Oxygen, Nitrogen, and Sulfur

“…Furthermore, the architecture of a large fraction of exoplanetary systems shows signatures of a chaotic dynamical evolution (Limbach & Turner 2015;Laskar & Petit 2017;Zinzi & Turrini 2017;Turrini et al 2020), suggesting that not all giant planets have their dynamical histories shaped by early disk-driven migration, but they can reach their final orbits at a later time as a result of planet-planet scattering events, chaotic dynamics, or a combination of early and late migration. Due to these uncertainties, metallicity alone is not enough to fully disclose a giant planet's formation history, aside from the most extreme cases.…”

A sub-Neptune and a non-transiting Neptune-mass companion unveiled by ESPRESSO around the bright late-F dwarf HD 5278 (TOI-130)

“…Stability is violated only in the limit of a true mass of HD 5278 c in excess of 200 M ⊕ , which would imply a true inclination angle of i c 5 deg. Taken at face value, the nonzero eccentricity of HD 5278 b and the hint of its possibly misaligned orbit could indicate a relatively "active" evolutionary history for the HD 5278 system, in which dynamical instabilities and chaos have played an important role (e.g., Chambers 2001;Laskar & Petit 2017;Turrini et al 2020, and references therein), a scenario that is typically favored for low multiplicity systems such as the one under investigation here. However, precisely because of the lack of a statistically significant determination of nonzero orbital eccentricity for either of the two planets (and in the absence of an actual measurement of the spin-orbit angle), the present orbital configuration of the HD 5278 system is also in line with the findings of Mills et al (2019), who show that multiples in the Kepler field have typically e < 0.1.…”

Exploring the link between star and planet formation with Ariel

“…Figure 4 summarizes the results of the study performed by [254], which suggests that enriched giant exoplanets at small orbits have not formed in situ since they must have migrated inward in order to accrete large amounts of heavy elements. As will be discussed in more detail in Section 8, however, recent population studies investigating the architectures of known multi-planets extrasolar systems [262][263][264][265] suggest that a significant fraction of these planetary systems underwent or are crossing phases of chaotic evolution possibly associated to migration by planet-planet scattering [266,267].…”

“…In particular, [264] and [320] have shown how the information provided by normalized angular momentum deficit (NAMD), an architecture-agnostic measure of the dynamical excitation of planetary systems, allows to build a relative scale of violence of their past histories. Intuitively, the NAMD can be interpreted as the "dynamical temperature" of planetary systems: the higher the value, the more excited is the dynamical state of the system.…”

“…As discussed by [264] and [320], Trappist-1 and the Solar System provide two such reference values, the first as a system characterized by an orderly and stable evolution [321,322] while the second as the boundary between orderly and chaotic evolution [323]. As shown in Fig.…”