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Orbital fitting of imaged planetary companions with high eccentricities and unbound orbits -- Application to Fomalhaut b and PZ Telescopii B

Imaging companions to main-sequence stars often allows to detect a projected orbital motion. MCMC has become very popular in for fitting their orbits. Some of these companions appear to move on very eccentric, possibly unbound orbits. This is the case for the exoplanet Fomalhaut b and the brown dwarf companion PZ Tel B. For such orbits, standard MCMC codes assuming only bound orbits may be inappropriate. We develop a new MCMC implementation able to handle bound and unbound orbits as well in a continuous manner, and we apply it to the cases of Fomalhaut b and PZ Tel B. This code is based on universal Keplerian variables and Stumpff functions formalism. We present two versions of this code, the second one using a different set of angular variables designed to avoid degeneracies arising when the projected orbital motion is quasi-radial, as it is the case for PZ Tel B. We also present additional observations of PZ Tel B. The code is applied to Fomalhaut b and PZ Tel B. Concerning Fomalhaut b, we confirm previous results, but we show that open orbital solutions are also possible. The eccentricity distribution nevertheless peaks around ~0.9 in the bound regime. We present a first successful orbital fit of PZ Tel B, showing in particular that the eccentricity distribution presents a sharp peak very close to e=1, meaning a quasi-parabolic orbit. It was recently suggested that unseen inner companions may lead orbital fitting algorithms to artificially give high eccentricities. We show that this caveat is unlikely to apply to Fomalhaut b. Concerning PZ Tel B, an inner ~12 MJup companion would mimic a e=1 orbit despite a real eccentricity around 0.7, but a dynamical analysis reveals that such a system would not be stable. We conclude that our orbital fit is robust.