Stability Limits in Resonant Planetary Systems
The Astrophysical Journal, 665 (1):
L67-L70 (2007)cite arxiv:0706.3721Comment: 13 pages, 3 figures, 2 tables, accepted for publication in ApJ Letters. A version with full resolution figures is available at http://www.lpl.arizona.edu/~rory/research/xsp/resstab.pdf.DOI: 10.1086/521144
Abstract
The relationship between the boundaries for Hill and Lagrange stability in <p>orbital element space is modified in the case of resonantly interacting <p>planets. Hill stability requires the ordering of the planets to remain constant <p>while Lagrange stability also requires all planets to remain bound to the <p>central star. The Hill stability boundary is defined analytically, but no <p>equations exist to define the Lagrange boundary, so we perform numerical <p>experiments to estimate the location of this boundary. To explore the effect of <p>resonances, we consider orbital element space near the conditions in the HD <p>82943 and 55 Cnc systems. Previous studies have shown that, for non-resonant <p>systems, the two stability boundaries are nearly coincident. However the Hill <p>stability formula are not applicable to resonant systems, and our investigation <p>shows how the two boundaries diverge in the presence of a mean-motion <p>resonance, while confirming that the Hill and Lagrange boundaries are similar <p>otherwise. In resonance the region of stability is larger than the domain <p>defined by the analytic formula for Hill stability. We find that nearly all <p>known resonant interactions currently lie in this extra stable region, i.e. <p>where the orbits would be unstable according to the non-resonant Hill stability <p>formula. This result bears on the dynamical packing of planetary systems, <p>showing how quantifying planetary systems' dynamical interactions (such as <p>proximity to the Hill-stability boundary) provides new constraints on planet <p>formation models.
Description
Stability Limits in Resonant Planetary Systems