A Statistical Approach to Optimizing Orbit Constraints for Directly Imaged Exoplanets

Direct imaging capabilities for exoplanets are rapidly increasing. Space telescope concepts, such as HabEx and LUVOIR, have the potential to make a dramatic leap forward in this field with the resolving capability to image Earth analogues around Solar type stars. In the 2020 Decadal Survey on Astronomy and Astrophysics, direct imaging of Earth-like worlds around nearby stars was recommended as the top science priority for future space-based missions. These advances will be made possible through sophisticated starshade and/or coronagraph configurations. One major constraint on the effectiveness of these mission concepts is the amount of time that will be spent on orbital characterization follow-up observations. These observations are expected to take a large fraction of the total observing time for each mission, hence, by reducing the time required to constrain exoplanet orbits, we effectively increase time available to characterize the planets themselves (e.g., determine habitability, etc.).

We have developed a statistical method utilizing Markov Chain Monte Carlo sampling techniques combined with orbital integration to dramatically improve orbit characterization time for directly imaged exoplanets. In this method, we find a best fit orbit for existing observations and assume that the real orbit is reasonably close to this fit. Then we make synthetic observations at regular intervals, each a set fraction of the predicted orbital period of the planet. Over all synthetic observations we use an orbital constraint metric to determine the expected location and corresponding time at which orbit uncertainties are minimized. This provides the optimum revisit time at which to observe the system, thus reducing observational degeneracies and, consequently, the number of observations required to constrain the orbit to within acceptable limits. We find that this method yields dramatic improvement in orbit characterization over previously suggested equal timing observations, as well as, other optimization algorithms we tested.