Extrasolar Planets

Detection Of Separatrices And Chaotic Seas Based On Orbit Amplitudes

By Keith Cowing
Press Release
December 6, 2022
Filed under , , ,
Detection Of Separatrices And Chaotic Seas Based On Orbit Amplitudes
(Top left) Dynamical map using δa for the 2/1 MMR in the representative plane (n1/n2, e1) of initial conditions. Planetary masses are m1 = 0.05 mJup and m2 = 0.1 mJup orbiting a central star with mass M? = 1 M . Angular variables are initially chosen equal to zero. The pericentric branch of zero-amplitude solutions appears as dark blue, while the regions of maximum variation of the semi-major axis appear in light colours. Total integration time is 104 yr. (Bottom left) Landscape of the N-body integration of δa computed over the dashed line of initial conditions at fixed eccentricity e1 = 0.17. (Top right) Corresponding k∆δak map which clearly identifies the separatrices. (Bottom right) Corresponding landscape of k∆δak. — astro-ph.EP

The Maximum Eccentricity Method (MEM) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions.

The present paper leverages on the MEM to introduce a sharp detector of separatrices and chaotic seas. After introducing the MEM analogue for nearly-integrable action-angle Hamiltonians, i.e., diameters, we use low-dimensional dynamical systems with multi-resonant modes and junctions, supporting chaotic motions, to recognise the drivers of the diameter metric.

Once this is appreciated, we present a second-derivative based index measuring the regularity of this application. This quantity turns to be a sensitive and robust indicator to detect separatrices, resonant webs and chaotic seas. We discuss practical applications of this framework in the context of N-body simulations for the planetary case affected by mean-motion resonances, and demonstrate the ability of the index to distinguish minute structures of the phase space, otherwise undetected with the original MEM.

Jerome Daquin, Carolina Charalambous

Comments: Under review at Celestial Mechanics and Dynamical Astronomy. 8 Figures, 59 references, 17 pages. Comments and feedback welcome
Subjects: Earth and Planetary Astrophysics (astro-ph.EP); Instrumentation and Methods for Astrophysics (astro-ph.IM); Chaotic Dynamics (nlin.CD)
Cite as: arXiv:2212.02200 [astro-ph.EP] (or arXiv:2212.02200v1 [astro-ph.EP] for this version)
Submission history
From: Jerome Daquin
[v1] Mon, 5 Dec 2022 12:18:06 UTC (6,431 KB)
https://arxiv.org/abs/2212.02200
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