Fitting Resonant Exoplanets Orbits. I. Properties and Applications of Fixed-Point Orbits
Abstract
Intact chains of mean-motion resonances may preserve information about the formation and early dynamical evolution of multiplanet systems. Although most mature multiplanet systems are non-resonant, the resonant fraction may have been substantially higher at young ages. Establishing whether exoplanet data are consistent with a resonant configuration is often challenging because the planetary orbits must be sufficiently well constrained. Moreover, while resonance configurations promote stability, standard orbital fitting methods do not impose such a dynamical constraint, with stability tested only a posteriori. As the first step in a series of papers aimed at favoring stable orbital solutions during the fitting process, we develop a method that restricts solutions to stable fixed-point orbits (fPOs)---coplanar, exactly periodic configurations associated with resonant dynamics. We show that dissipative evolution drive resonant systems toward an fPO state, motivating for fPO-constrained fitting for those planet systems that have avoided large-scale dynamical rearrangements since formation. The fPO model greatly reduces the number of free parameters and yields stable solutions by construction. We determine the best-fitting fPos through χ2 minimization and apply the method to astrometric data for the directly imaged PDS 70 and HR 8799 systems and to radial-velocity data for GJ 876. For HR 8799 we independently recover a previously reported resonant solution, illustrating the fidelity of our method. For PDS 70 we find solutions fall in two groups, with the group where the outer planet c mass exceeds planet b more aligned with previous measurements. Finally, For GJ 876 our fPO fit is on par with previous unconstrained fitting, which strengthens the case that its planets reside deep in resonance.
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BibTeX
@misc{ormel2026fitting,
title = {{Fitting Resonant Exoplanets Orbits. I. Properties and Applications of Fixed-Point Orbits}},
author = {Chris W. Ormel and Tian Yi and Shuo Huang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04332},
eprint = {2611.04332},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04332},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fitting Resonant Exoplanets Orbits. I. Properties and Applications of Fixed-Point Orbits
AU - Chris W. Ormel
AU - Tian Yi
AU - Shuo Huang
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04332
UR - https://arxiv.org/abs/2611.04332
AB - Intact chains of mean-motion resonances may preserve information about the formation and early dynamical evolution of multiplanet systems. Although most mature multiplanet systems are non-resonant, the resonant fraction may have been substantially higher at young ages. Establishing whether exoplanet data are consistent with a resonant configuration is often challenging because the planetary orbits must be sufficiently well constrained. Moreover, while resonance configurations promote stability, standard orbital fitting methods do not impose such a dynamical constraint, with stability tested only a posteriori. As the first step in a series of papers aimed at favoring stable orbital solutions during the fitting process, we develop a method that restricts solutions to stable fixed-point orbits (fPOs)---coplanar, exactly periodic configurations associated with resonant dynamics. We show that dissipative evolution drive resonant systems toward an fPO state, motivating for fPO-constrained fitting for those planet systems that have avoided large-scale dynamical rearrangements since formation. The fPO model greatly reduces the number of free parameters and yields stable solutions by construction. We determine the best-fitting fPos through χ^2 minimization and apply the method to astrometric data for the directly imaged PDS 70 and HR 8799 systems and to radial-velocity data for GJ 876. For HR 8799 we independently recover a previously reported resonant solution, illustrating the fidelity of our method. For PDS 70 we find solutions fall in two groups, with the group where the outer planet c mass exceeds planet b more aligned with previous measurements. Finally, For GJ 876 our fPO fit is on par with previous unconstrained fitting, which strengthens the case that its planets reside deep in resonance.
ER -