Issue |
A&A
Volume 378, Number 2, November I 2001
|
|
---|---|---|
Page(s) | 569 - 586 | |
Section | Stellar atmospheres | |
DOI | https://doi.org/10.1051/0004-6361:20011189 | |
Published online | 15 November 2001 |
Global dynamics of planetary systems with the MEGNO criterion
1
Observatoire de Bordeaux, UMR/CNRS/INSU 5804, BP 89, 33270 Floirac, France
2
Toruń Centre for Astronomy, N. Copernicus University, Gagarina 11, 87-100 Toruń, Poland
3
Institute of Astronomy, Zielona Góra University, Lubuska 2, 65-265 Zielona Góra, Poland
4
IGPP, LLNL, L-413, 7000 East Ave, Livermore, CA 94550, USA
5
UC Davis, Dept. of Physics, Davis, CA 95616, USA
Corresponding author: K. Goździewski, chris@astri.uni.torun.pl
Received:
11
June
2001
Accepted:
22
August
2001
In this paper we apply a new technique alternative to the numerically
computed Lyapunov Characteristic Number (LCN) for studying the dynamical
behaviour of planetary systems in the framework of the gravitational N-body
problem. The method invented by P. Cincotta and C. Simó is called the Mean
Exponential Growth of Nearby Orbits (MEGNO). It provides an efficient way for
investigation of the fine structure of the phase space and its regular and
chaotic components in any conservative Hamiltonian system. In this work we use
it to study the dynamical behaviour of the multidimensional planetary
systems. We investigate the recently discovered υ And planetary
system, which consists of a star of and three Jupiter-size
planets. The two outermost planets have eccentric orbits. This system appears
to be one of the best candidates for dynamical studies. The mutual
gravitational interaction between the two outermost planets is strong.
Moreover the system can survive on a stellar evolutionary time scale as it is
claimed by some authors (e.g., Rivera & Lissauer 2000b). As the main
methodological result of this work, we confirm important properties of the
MEGNO criterion such as its fast convergence, and short motion times (of the
order of 104 times the longest orbital period) required to distinguish
between regular and chaotic behaviors. Using the MEGNO technique we found
that the presence of the innermost planet may cause the whole system to become
chaotic with the Lyapunov time scale of the order of 103-104 yr only.
Chaos does not induce in this case visible irregular changes of the orbital
elements, and therefore its presence can be overlooked by studying
variations of the elements. We confirm explicitly the strong and sensitive
dependence of the dynamical behaviour on the companion masses.
Key words: celestial mechanics / stellar dynamics / methods: numerical / methods: N-body simulations / planetary systems / stars: individual: υ And
© ESO, 2001
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