2015
DOI: 10.1088/0004-637x/808/2/120
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The Stability and Fates of Hierarchical Two-Planet Systems

Abstract: We study the dynamical stability and fates of hierarchical (in semi-major axis) two-planet systems with arbitrary eccentricities and mutual inclinations. We run a large number of long-term numerical integrations and use the Support Vector Machine algorithm to search for an empirical boundary that best separates stable systems from systems experiencing either ejections or collisions with the star. We propose the following new criterion for dynamical stability:1/3 (a out /a in ) 1/2 + 1.15, which should be appli… Show more

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Cited by 105 publications
(100 citation statements)
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“…On the other hand, only -+ 3.9 % 2.0 4.5 of hot Jupiters have stellar companions with separations between 1 and 50 au, while  16.4% 0.7% of field stars have stellar companions in this range, corresponding to a s 2.7 difference. We choose a lower limit of 1 au to avoid systems where the stellar companion could eject the hot Jupiter (Mardling & Aarseth 2001;Petrovich 2015b). We note that if we relax this lower limit and considered all companions with separations less than 50 au, we find that hot Jupiter hosts have a companion fraction of -+ 3.9 % 2.0 4.6 while field stars have a companion fraction of  22% 1%, which is a difference of s 3.8 .…”
Section: Stellar Companion Fraction For Hot Jupiter Hosts Versus Fielmentioning
confidence: 99%
“…On the other hand, only -+ 3.9 % 2.0 4.5 of hot Jupiters have stellar companions with separations between 1 and 50 au, while  16.4% 0.7% of field stars have stellar companions in this range, corresponding to a s 2.7 difference. We choose a lower limit of 1 au to avoid systems where the stellar companion could eject the hot Jupiter (Mardling & Aarseth 2001;Petrovich 2015b). We note that if we relax this lower limit and considered all companions with separations less than 50 au, we find that hot Jupiter hosts have a companion fraction of -+ 3.9 % 2.0 4.6 while field stars have a companion fraction of  22% 1%, which is a difference of s 3.8 .…”
Section: Stellar Companion Fraction For Hot Jupiter Hosts Versus Fielmentioning
confidence: 99%
“…1/3 and a in (a out ) is the semimajor axis of the inner (outer) planet (Chambers et al 1996;Yoshinaga et al 1999;Fang & Margot 2013;Pu & Wu 2015;Petrovich 2015). When all planets have e = 0.03 (e = 0.10), the maximum number of stable Earth-mass planets within 0.4-1 AU is 7-8 (4-5).…”
Section: Frequency Of Earth-mass Planets At 025-2 Au Around Solar-tymentioning
confidence: 99%
“…This distinction is only significant for the very massive planets we consider here. Recently, Petrovich (2015) has also explored the role of high eccentricity in modifying the stability boundary.…”
Section: Previous Workmentioning
confidence: 99%