Improving Orbit Estimates for Incomplete Orbits with a New Approach to Priors -- with Applications from Black Holes to Planets

Abstract

We propose a new approach to Bayesian prior probability distributions (priors) that can improve orbital solutions for low-phase-coverage orbits, where data cover less than approximately 40% of an orbit. In instances of low phase coverage such as with stellar orbits in the Galactic center or with directly-imaged exoplanets, data have low constraining power and thus priors can bias parameter estimates and produce under-estimated confidence intervals. Uniform priors, which are commonly assumed in orbit fitting, are notorious for this. We propose a new observable-based prior paradigm that is based on uniformity in observables. We compare performance of this observable-based prior and of commonly assumed uniform priors using Galactic center and directly-imaged exoplanet (HR 8799) data. The observable-based prior can reduce biases in model parameters by a factor of two and helps avoid under-estimation of confidence intervals for simulations with less than about 40% phase coverage. Above this threshold, orbital solutions for objects with sufficient phase coverage such as S0-2, a short-period star at the Galactic center with full phase coverage, are consistent with previously published results. Below this threshold, the observable-based prior limits prior influence in regions of prior dominance and increases data influence. Using the observable-based prior, HR 8799 orbital analyses favor lower eccentricity orbits and provide stronger evidence that the four planets have a consistent inclination around 30 degrees to within 1-sigma. This analysis also allows for the possibility of coplanarity. We present metrics to quantify improvements in orbital estimates with different priors so that observable-based prior frameworks can be tested and implemented for other low-phase-coverage orbits.

arXiv commentPublished in AJ. 23 pages, 14 figures. Monte Carlo chains are available in the published article, or are available upon request

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• Rotation Periods, Inclinations, and Obliquities of Cool Stars Hosting Directly Imaged Substellar Companions: Spin-Orbit Misalignments are Common
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• Kinematic Structure of the Galactic Center S-cluster
• Moderate-Resolution $K$-Band Spectroscopy of Substellar Companion $\kappa$ Andromedae b
• The Orbital Eccentricities of Directly Imaged Companions Using Observable-Based Priors: Implications for Population-level Distributions
• Gaia's Detectability of Black Hole-Main Sequence Star Binaries Formed in Open Clusters
• Octofitter: Fast, Flexible, and Accurate Orbit Modelling to Detect Exoplanets
• Detectablity of Black Hole Binaries with Gaia: Dependence on Binary Evolution Models
• Biases in orbit fitting of directly-imaged exoplanets with small orbital coverage
• Stellar Populations in the Central 0.5 pc of Our Galaxy III: The Dynamical Sub-structures
• The Swansong of the Galactic Center Source X7: An Extreme Example of Tidal Evolution near the Supermassive Black Hole
• Spatial and Binary Parameter Distributions of Black Hole Binaries in the Milky Way Detectable with Gaia
• Orbital Modeling of HII 1348B: An Eccentric Young Substellar Companion in the Pleiades
• Analytic Post-Newtonian Astrometric and Spectroscopic Models of Orbits around Black Holes
• Gravitational signatures beyond Newton: exploring hierarchical three-body dynamics
• Closing the gap: Follow-up observations of peculiar dusty objects close to Sgr A* using ERIS
• Interferometric Detection and Orbit Modeling of the Subcomponent in the Hot-dust System $\kappa$ Tuc A: A Low-mass Star on an Eccentric Orbit in a Hierarchical-quintuple System