Journal Article

Dependence of a planet’s chaotic zone on particle eccentricity: the shape of debris disc inner edges

Alexander J. Mustill and Mark C. Wyatt

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 419, issue 4, pages 3074-3080
Published in print February 2012 | ISSN: 0035-8711
Published online January 2012 | e-ISSN: 1365-2966 | DOI:
Dependence of a planet’s chaotic zone on particle eccentricity: the shape of debris disc inner edges

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The orbit of a planet is surrounded by a chaotic zone wherein nearby particles’ orbits are chaotic and unstable. It was shown by Wisdom that the chaos is driven by the overlapping of mean motion resonances which occurs within a distance (δa/a)chaos≈ 1.3μ2/7 of the planet’s orbit. However, the width of mean motion resonances grows with the particles’ eccentricity, which will increase the width of the chaotic zone at higher eccentricities. Here we investigate the width of the chaotic zone using the iterated encounter map and N-body integrations. We find that the classical prescription of Wisdom works well for particles on low-eccentricity orbits. However, above a critical eccentricity, dependent upon the mass of the planet, the width of the chaotic zone increases with eccentricity. An extension of Wisdom’s analytical arguments then shows that, above the critical eccentricity, the chaotic zone width is given by (δa/a)chaos≈ 1.8e1/5μ1/5, which agrees well with the encounter map results. The critical eccentricity is given by ecrit≈ 0.21μ3/7. This extended chaotic zone results in a larger cleared region when a planet sculpts the inner edge of a debris disc composed of eccentric planetesimals. Hence, the planet mass estimated from the classical chaotic zone may be erroneous. We apply this result to the HR 8799 system, showing that the mass of HR 8799 b inferred from the truncation of the disc may vary by up to 50 per cent depending on the disc particles’ eccentricities. With a disc edge at 90 au, the necessary mass of planet b to cause the truncation is 8–10 Jovian masses if the disc particles have low eccentricities (≲0.02), but only 4–8 Jovian masses if the disc particles have higher eccentricities. Our result also has implications for the ability of a planet to feed material into an inner system, a process which may explain metal pollution in white dwarf atmospheres.

Keywords: chaos; celestial mechanics; planets and satellites: dynamical evolution and stability; circumstellar matter; stars: individual: HR 8799

Journal Article.  4677 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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