Disentangling 2:1 resonant radial velocity orbits from eccentric ones and a case study for HD 27894

Abstract

Context. In radial velocity (RV) observations, a pair of extrasolar planets near a 2:1 orbital resonance can be misinterpreted as a single eccentric planet, if data are sparse and measurement precision insufficient to distinguish between these models. Aims. Using the Exoplanet Orbit Database (EOD), we determine the fraction of alleged single-planet RV detected systems for which a 2:1 resonant pair of planets is also a viable model and address the question of how the models can be disentangled. Methods. By simulation we quantified the mismatch arising from applying the wrong model. Model alternatives are illustrated using the supposed single-planet system HD 27894 for which we also study the dynamical stability of near-2:1 resonant solutions. Results. Using EOD values of the data scatter around the fitted single-planet Keplerians, we find that for 74% of the 254 putative single-planet systems, a 2:1 resonant pair cannot be excluded as a viable model, since the error due to the wrong model is smaller than the scatter. For 187 EOD stars χ 2 -probabilities can be used to reject the Keplerian models with a confidence of 95% for 54% of the stars and with 99.9% for 39% of the stars. For HD 27894 a considerable fit improvement is obtained when adding a low-mass planet near half the orbital period of the known Jovian planet. Dynamical analysis demonstrates that this system is stable when both planets are initially placed on circular orbits. For fully Keplerian orbits a stable system is only obtained if the eccentricity of the inner planet is constrained to <0.3. Conclusions. A large part of the allegedly RV detected single-planet systems should be scrutinized in order to determine the fraction of systems containing near-2:1 resonant pairs of planets. Knowing the abundance of such systems will allow us to revise the eccentricity distribution for extrasolar planets and provide direct constraints for planetary system formation.

The SOPHIE search for northern extrasolar planets

“…Several studies have shown that the Keplerian signature of a single eccentric planet might also be fit with a model including two planets on circular (or nearly circular) orbits in 2:1 resonance, depending on the radial velocity accuracy and their time sampling (e.g., Anglada-Escudé et al 2010;Wittenmyer et al 2013;Kürster et al 2015). Numerous pairs of planets near the 2:1 orbital resonance have indeed be detected in transit with Kepler (e.g., Lissauer et al 2011;Delisle & Laskar 2014).…”

juliet: a versatile modelling tool for transiting and non-transiting exoplanetary systems

“…Although PlanetPack and EXOFAST do provide (frequentist) statistics on the fits performed to the data, it is not straightforward to use those to compare different models, as all frequentist statistical measures assume an underlying null hypothesis which does not take into account either prior information nor the reality that there are more models than the one being tested. This is very important for complicated tasks such as calculating the evidence for additional planets in either the transits and/or the radial-velocities (especially in the case in which extra, non-planetary signals such as stellar activity might make this procedure even more difficult), or even for more simple but routine tasks such as finding evidence for an eccentric orbit (or even disentangling between significant eccentricity or additional planets; see e.g., Kürster et al 2015). Although this question has been explored in the literature for the detection of planets in radial-velocities (see, e.g.…”

Bias and robustness of eccentricity estimates from radial velocity data

“…A Bayesian test with a physically motivated prior on eccentricity was devised by Lucy (2013). Also, Anglada-Escudé et al (2010), Wittenmyer et al (2013) and Kürster et al (2015) note that two planets in 2:1 mean motion resonances can appear as an eccentric planet, and propose ways to disentangle those cases. This problem has also been studied in Boisvert et al (2018); Nagel et al (2019); Wittenmyer et al (2019).…”