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.