Regular and chaotic orbits in the dynamics of exoplanets

Regular and chaotic orbits in the dynamics of exoplanets

Authors:

Antoniadou et al

Abstract:

Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR), which offers a phase protection mechanism, so that, even highly eccentric planets can avoid close encounters. However, the present estimation of their initial conditions, which may change significantly after obtaining additional observational data in the future, locate most of the systems in chaotic regions and consequently, they are destabilized. Hence, dynamical analysis is imperative for the derivation of proper planetary orbital elements. We utilize the model of spatial general three body problem, in order to simulate such resonant systems through the computation of families periodic orbits. In this way, we can figure out regions in phase space, where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In this review, we summarize our methodology and showcase the fact that stable resonant planetary systems evolve being exactly centered at stable periodic orbits. We apply this process to co-orbital motion and systems HD 82943, HD 73526, HD 128311, HD 60532, HD 45364 and HD 108874.

Stability of Resonant Configurations During the Migration of Exoplanets

Stability of resonant configurations during the migration of planets and constraints on disk-planet interactions

Authors:

Delisle et al

Abstract:

We study the stability of mean-motion resonances (MMR) between two planets during their migration in a protoplanetary disk. We use an analytical model of resonances, and describe the effect of the disk by a migration timescale (T_{m,i}) and an eccentricity damping timescale (T_{e,i}) for each planet (i=1,2 respectively for the inner and outer planet). We show that the resonant configuration is stable if T_{e,1}/T_{e,2} > (e_1/e_2)^2. This general result can be used to put constraints on specific models of disk-planet interactions. For instance, using classical prescriptions for type I migration, we show that when the angular momentum deficit (AMD) of the inner orbit is larger than the outer's orbit AMD, resonant systems must have a locally inverted disk density profile to stay locked in resonance during the migration. This inversion is very untypical of type I migration and our criterion can thus provide an evidence against classical type I migration. That is indeed the case for the Jupiter-mass resonant systems HD 60532b, c (3:1 MMR), GJ 876b, c (2:1 MMR), and HD 45364b, c (3:2 MMR). This result may be an evidence for type II migration (gap opening planets), which is compatible with the large masses of these planets.

Orbital Evolution of Exoplanets in Mean Motion Resonances

Long-lived Chaotic Orbital Evolution of Exoplanets in Mean Motion Resonances with Mutual Inclinations

Authors:

Barnes et al

Abstract:

We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.9 degrees. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364 and HD 60532 systems may be in chaotically-evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1 and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs after several Gyr, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that 1) approximate methods for identifying unstable orbital architectures may have limited applicability, 2) the observed close-in exoplanets may be produced during the high eccentricity phases induced by inclined resonances, 3) those exoplanets' orbital planes may be misaligned with the host star's spin axis, 4) systems with resonances may be systematically younger than those without, 5) the distribution of period ratios of adjacent planets detected via transit may be skewed due to inclined resonances, and 6) potentially habitable planets in resonances may have dramatically different climatic evolution than the Earth. The GAIA spacecraft is capable of discovering giant planets in these types of orbits.