Conditions of dynamical stability for the HD 160691 planetary system

Author(s)

Eric Bois, Nicolas Rambaux, Elke Pilat-Lohinger

Abstract

In our previous paper we showed that the currently determined orbital

parameters placed four recently announced planetary systems (HD 12661,

HD 38529, HD 37124, and HD 160691) in very different situations from the

point of view of dynamical stability. In the present paper we deal with

the last of these systems, whose orbital parameters of the outer planet

are yet uncertain. We discover a stabilizing mechanism that could be

the key to its existence. The paper is devoted to the study of this

mechanism by a global dynamics analysis in the orbital parameter space

related to the HD 160691 system. We obtained our results using a new

technique called the mean exponential growth factor of nearby orbits

(MEGNO), and verified them with the fast Lyapunov indicator technique

(FLI). In order to be dynamically stable, the HD 160691 planetary system

has to satisfy the following conditions: (1) it should have a 2 : 1

mean motion resonance, (2) combined with an apsidal secular resonance,

(3) in a configuration P_c(ap)-S-P_b(ap) (which means that the planets c and b may be considered as initially located at their apoastron around the central star S),

and (4) it must satisfy specific conditions for the respective sizes of

the eccentricities. High eccentricity for the outer orbit (e_c > 0.52) is the most probable necessary condition, while the eccentricity of the inner orbit e_b becomes relatively unimportant when e_c

> 0.7. We also show that there is an upper limit for planetary

masses (in the interval permitted by the undetermined line-of-sight

inclination factor sin i_l) due to the dynamical stability mechanism. More generally, in this original orbital topology, where the resonance variables θ₁ and θ₃ librate about 180° while θ₂

librates about 0°, the HD 160691 system and its mechanism have revealed

aspects of the 2 : 1 orbital resonances that have not been observed nor

analyzed before. The present topology with antialigned apsidal lines,

combined with the 2 : 1 resonance, is indeed more wide-ranging than the

particular case of the HD 160691 planetary system. It is a new

theoretical possibility that is suitable for a stable regime despite

relatively small semimajor axes with respect to the important masses in

interactions.

Organisation(s)

Department of Astrophysics

External organisation(s)

Université Bordeaux

Journal

The Astrophysical Journal: an international review of astronomy and astronomical physics

Volume

598

Pages

1312-1320

No. of pages

9

ISSN

0004-637X

DOI

https://doi.org/10.1086/378796

Publication date

2003

Peer reviewed

Yes

Austrian Fields of Science 2012

103003 Astronomy

Portal url

https://ucrisportal.univie.ac.at/en/publications/bb78f687-9def-4189-b781-8430b5cf6e7e