VLT/SPHERE robust astrometry of the HR8799 planets at milliarcsecond-level accuracy

Context. HR8799 is orbited by at least four giant planets, making it a prime target for the recently commissioned Spectro-Polarimetric High-contrast Exoplanet REsearch (VLT/SPHERE). As such, it was observed on five consecutive nights during the SPHERE science verification in December 2014. Aims. We aim to take full advantage of the SPHERE capabilities to derive accurate astrometric measurements based on H-band images acquired with the Infra-Red Dual-band Imaging and Spectroscopy (IRDIS) subsystem, and to explore the ultimate astrometric performance of SPHERE in this observing mode. We also aim to present a detailed analysis of the orbital parameters for the four planets. Methods. We performed thorough post-processing of the IRDIS images with the Vortex Imaging Processing (VIP) package to derive a robust astrometric measurement for the four planets. This includes the identification and careful evaluation of the different contributions to the error budget, including systematic errors. Combining our astrometric measurements with the ones previously published in the literature, we constrain the orbital parameters of the four planets using PyAstrOFit, our new open-source python package dedicated to orbital fitting using Bayesian inference with Monte-Carlo Markov Chain sampling. Results. We report the astrometric positions for epoch 2014.93 with an accuracy down to 2.0 mas, mainly limited by the astrometric calibration of IRDIS. For each planet, we derive the posterior probability density functions for the six Keplerian elements and identify sets of highly probable orbits. For planet d, there is clear evidence for nonzero eccentricity (e ~ 0.35), without completely excluding solutions with smaller eccentricities. The three other planets are consistent with circular orbits, although their probability distributions spread beyond e = 0.2, and show a peak at e ≃ 0.1 for planet e. The four planets have consistent inclinations of approximately 30° with respect to the sky plane, but the confidence intervals for the longitude of the ascending node are disjointed for planets b and c, and we find tentative evidence for non-coplanarity between planets b and c at the 2σ level