Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAn Integrable Model for the Dynamics of Planetary Mean Motion Resonances
74
0
0.0
(
0
)
Authors
Sam Hadden
Ask ChatGPT about the research
No Arabic abstract
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 the new model to accurately capture the dynamics of both first- and higher-order resonances for eccentricities up to orbit-crossing. I demonstrate that predictions of the new integrable model agree well with numerical integrations of resonant planet pairs. Finally, I explore the secular evolution of resonant planets eccentricities. I show that the secular dynamics are governed by conservation of an AMD-like quantity. I also demonstrate that secular frequencies depend on planets resonant libration amplitude and this generally gives rise to a secular resonance inside the mean motion resonance at large libration amplitudes. Outside of the secular resonance the long-term dynamics are characterized small adiabatic modulations of the resonant motion while inside the secular resonance planets can experience large variations of the resonant trajectory over secular timescales. The integrable model derived in this work can serve as a framework for analyzing the dynamics of planetary MMRs in a wide variety of contexts.
rate research
Read More
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 strategy proposed in the two-planet case to obtain a one degree of freedom Hamiltonian. The dynamics of these resonances are governed by the second fundamental model of resonance. The model is valid for any mass ratio between the planets and for every first-order resonance. I show the agreement of the analytical model with numerical simulations. As examples of application I show how this model could improve our understanding of the capture into MMRs as well as their role on the stability of planetary systems.
We present preliminary though statistically significant evidence that shows that multiplanetary systems that exhibit a 2/1 period commensurability are in general younger than multiplanetary systems without commensurabilities, or even systems with other commensurabilities. An immediate possible conclusion is that the 2/1 mean-motion resonance in planetary systems, tends to be disrupted after typically a few Gyrs.
The dynamical interactions that occur in newly formed planetary systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital resonances by migrating planets in the terrestrial mass range. Migration time scales varying between millions of years and thousands of years are considered. In the former case, for which the migration time is comparable to the lifetime of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter, relatively rapid migration regime commensurabilities of high degree such as 8:7 or 11:10 may be formed. However, in any one large-scale migration several different commensurabilities may be formed sequentially, each being associated with significant orbital evolution. We also use a simple analytic theory to develop conditions for first order commensurabilities to be formed. These depend on the degree of the commensurability, the imposed migration and circularization rates, and the planet mass ratios. These conditions are found to be consistent with the results of our simulations.
In circumstellar discs, collisional grinding of planetesimals produces second-generation dust. While it remains unclear whether this ever becomes a major component of the total dust content, the presence of such dust, and potentially the substructure within, it can be used to explore a discs physical conditions. A perturbing planet produces nonaxisymmetric structures and gaps in the dust, regardless of its origin. The dynamics of planetesimals, however, will be very different than that of small dust grains due to weaker gas interactions. Therefore, planetesimal collisions could create dusty disc structures that would not exist otherwise. In this work, we use N-body simulations to investigate the collision rate profile of planetesimals near mean-motion resonances. We find that a distinct bump or dip feature is produced in the collision profile, the presence of which depends on the libration width of the resonance and the separation between the peri- and apocenter distances of the edges of the resonance. The presence of one of these two features depends on the mass and eccentricity of the planet. Assuming that the radial dust emission traces the planetesimal collision profile, the presence of a bump or dip feature in the dust emission at the 2:1 mean-motion resonance can constrain the orbital properties of the perturbing planet. This assumption is valid, so long as radial drift does not play a significant role during the collisional cascade process. Under this assumption, these features in the dust emission should be marginally observable in nearby protoplanetary disks with ALMA.
The identification of mean motion resonances in exoplanetary systems or in the Solar System might be cumbersome when several planets and large number of smaller bodies are to be considered. Based on the geometrical meaning of the resonance variable, an efficient method is introduced and described here, by which mean motion resonances can be easily find without any a priori knowledge on them. The efficiency of this method is clearly demonstrated by using known exoplanets engaged in mean motion resonances, and also some members of different families of asteroids and Kuiper-belt objects being in mean motion resonances with Jupiter and Neptune respectively.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
