Algorithmic Speedups and Posterior Biases from Orbit Fitting of Directly Imaged Exoplanets in Cartesian Coordinates

Abstract

Abstract A planet’s orbit encodes information about its formation and history. However, exoplanets detected via direct-imaging are often only observed over a small fraction of their periods. Several problems arise from such unconstraining data, like slow convergence of standard orbit-fitting algorithms and significant biases in the estimation of orbital parameters. One possible way of overcoming some of these problems is performing orbit-fits in orbital bases distinct from the usual Keplerian elements. We explore this approach by fitting orbits in Cartesian coordinates, that is, estimating the position and velocity vectors for a planet at a given epoch. We saw a significant improvement in the MCMC convergence time compared to the Keplerian elements, and different posterior shapes were observed with different priors. In particular, setting Gaussian priors in the line-of-sight components (z and z ˙ ) produced posteriors more similar to the ones obtained via the Keplerian basis compared to uniform priors on them.