Dependence of a planet's chaotic zone on particle eccentricity: the shape of debris disc inner edges
(2012) In Monthly Notices of the Royal Astronomical Society 419(4). p.30743080 Abstract
 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≈ 1.3μ^2/7 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 Nbody integrations. We find that the classical prescription of Wisdom works well for particles on loweccentricity orbits. However, above a critical eccentricity, dependent upon the mass of the planet, the width of the... (More)
 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≈ 1.3μ^2/7 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 Nbody integrations. We find that the classical prescription of Wisdom works well for particles on loweccentricity 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≈ 1.8e^1/5μ^1/5, which agrees well with the encounter map results. The critical eccentricity is given by ecrit≈ 0.21μ^3/7. 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 810 Jovian masses if the disc particles have low eccentricities (≲0.02), but only 48 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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4500273
 author
 Mustill, Alexander ^{LU} and Wyatt, Mark C
 publishing date
 2012
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Astrophysics  Earth and Planetary Astrophysics, celestial mechanics, chaos, circumstellar matter, planets and satellites: dynamical evolution and stability, stars: individual: HR 8799
 in
 Monthly Notices of the Royal Astronomical Society
 volume
 419
 issue
 4
 pages
 3074  3080
 publisher
 WileyBlackwell
 external identifiers

 Scopus:84855572039
 ISSN
 13652966
 DOI
 10.1111/j.13652966.2011.19948.x
 language
 English
 LU publication?
 no
 id
 42c2f638a9be4dceb8e9137d00602685 (old id 4500273)
 date added to LUP
 20140625 15:10:07
 date last changed
 20161127 04:31:57
@misc{42c2f638a9be4dceb8e9137d00602685, abstract = {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≈ 1.3μ^2/7 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 Nbody integrations. We find that the classical prescription of Wisdom works well for particles on loweccentricity 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≈ 1.8e^1/5μ^1/5, which agrees well with the encounter map results. The critical eccentricity is given by ecrit≈ 0.21μ^3/7. 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 810 Jovian masses if the disc particles have low eccentricities (≲0.02), but only 48 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.}, author = {Mustill, Alexander and Wyatt, Mark C}, issn = {13652966}, keyword = {Astrophysics  Earth and Planetary Astrophysics,celestial mechanics,chaos,circumstellar matter,planets and satellites: dynamical evolution and stability,stars: individual: HR 8799}, language = {eng}, number = {4}, pages = {30743080}, publisher = {ARRAY(0x8076df0)}, series = {Monthly Notices of the Royal Astronomical Society}, title = {Dependence of a planet's chaotic zone on particle eccentricity: the shape of debris disc inner edges}, url = {http://dx.doi.org/10.1111/j.13652966.2011.19948.x}, volume = {419}, year = {2012}, }