A simple scaling for the minimum instability time-scale of two widely spaced planets
Veras, Dimitri and Mustill, Alexander LU
(2013)
In Monthly Notices of the Royal Astronomical Society: Letters
434(1).
p.11-15
- Abstract
- Long-term instability in multiplanet exosystems is a crucial consideration when confirming putative candidates, analysing exoplanet populations, constraining the age of exosystems and identifying the sources of white dwarf pollution. Two planets that are Hill stable are separated by a wide-enough distance to ensure that they will never collide. However, Hill-stable planetary systems may eventually manifest Lagrange instability when the outer planet escapes or the inner planet collides with the star. We show empirically that for two nearly coplanar Hill-stable planets with eccentricities less than about 0.3, instability can manifest itself only after a time corresponding to x initial orbits of the inner planet, where log10 x ~... (More)
- Long-term instability in multiplanet exosystems is a crucial consideration when confirming putative candidates, analysing exoplanet populations, constraining the age of exosystems and identifying the sources of white dwarf pollution. Two planets that are Hill stable are separated by a wide-enough distance to ensure that they will never collide. However, Hill-stable planetary systems may eventually manifest Lagrange instability when the outer planet escapes or the inner planet collides with the star. We show empirically that for two nearly coplanar Hill-stable planets with eccentricities less than about 0.3, instability can manifest itself only after a time corresponding to x initial orbits of the inner planet, where log10 x ~ 5.2[μ/(MJupiter/M☉)]-0.18 and μ is the planet-star mass ratio. This relation applies to any type of equal-mass secondaries, and suggests that two low-eccentricity Hill-stable terrestrial-mass or smaller mass planets should be Lagrange stable throughout the main-sequence lifetime of any white dwarf progenitor. However, Hill-stable giant planets are not guaranteed to be Lagrange stable, particularly within a few tens of per cent beyond the critical Hill separation. Our scaling represents a useful `rule of thumb' for planetary population syntheses or individual systems for which performing detailed long-term integrations is unfeasible. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4500225
- author
- Veras, Dimitri
and Mustill, Alexander
LU
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Astrophysics - Earth and Planetary Astrophysics, Astrophysics - Solar and Stellar Astrophysics, celestial mechanics, chaos, planets and satellites: dynamical evolution and stability
- in
- Monthly Notices of the Royal Astronomical Society: Letters
- volume
- 434
- issue
- 1
- pages
- 11 - 15
- publisher
- Oxford University Press
- external identifiers
-
- scopus:84881595725
- ISSN
- 1745-3933
- DOI
- 10.1093/mnrasl/slt067
- language
- English
- LU publication?
- no
- id
- 041adbc6-3aa0-4f0d-8e02-5d59148738ba (old id 4500225)
- date added to LUP
- 2016-04-04 12:21:14
- date last changed
- 2022-04-24 02:01:03
@article{041adbc6-3aa0-4f0d-8e02-5d59148738ba,
abstract = {{Long-term instability in multiplanet exosystems is a crucial consideration when confirming putative candidates, analysing exoplanet populations, constraining the age of exosystems and identifying the sources of white dwarf pollution. Two planets that are Hill stable are separated by a wide-enough distance to ensure that they will never collide. However, Hill-stable planetary systems may eventually manifest Lagrange instability when the outer planet escapes or the inner planet collides with the star. We show empirically that for two nearly coplanar Hill-stable planets with eccentricities less than about 0.3, instability can manifest itself only after a time corresponding to x initial orbits of the inner planet, where log10 x ~ 5.2[μ/(MJupiter/M☉)]-0.18 and μ is the planet-star mass ratio. This relation applies to any type of equal-mass secondaries, and suggests that two low-eccentricity Hill-stable terrestrial-mass or smaller mass planets should be Lagrange stable throughout the main-sequence lifetime of any white dwarf progenitor. However, Hill-stable giant planets are not guaranteed to be Lagrange stable, particularly within a few tens of per cent beyond the critical Hill separation. Our scaling represents a useful `rule of thumb' for planetary population syntheses or individual systems for which performing detailed long-term integrations is unfeasible.}},
author = {{Veras, Dimitri and Mustill, Alexander}},
issn = {{1745-3933}},
keywords = {{Astrophysics - Earth and Planetary Astrophysics; Astrophysics - Solar and Stellar Astrophysics; celestial mechanics; chaos; planets and satellites: dynamical evolution and stability}},
language = {{eng}},
number = {{1}},
pages = {{11--15}},
publisher = {{Oxford University Press}},
series = {{Monthly Notices of the Royal Astronomical Society: Letters}},
title = {{A simple scaling for the minimum instability time-scale of two widely spaced planets}},
url = {{http://dx.doi.org/10.1093/mnrasl/slt067}},
doi = {{10.1093/mnrasl/slt067}},
volume = {{434}},
year = {{2013}},
}