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Context. A low-mass brown dwarf has been recently imaged around HR 2562 (HD50571), a star hosting a debris disk resolved in the far infrared.Interestingly, the companion location is compatible with an orbit coplanar withthe disk and interior to the debris belt. This feature makes the system avaluable laboratory to analyze the formation of substellar companions in acircumstellar disk and potential disk-companion dynamical interactions. Aims.We aim to further characterize the orbital motion of HR 2562 B and itsinteractions with the host star debris disk. Methods. We performed a monitoringof the system over ~10 months in 2016 and 2017 with the VLT/SPHERE exoplanetimager. Results. We confirm that the companion is comoving with the star anddetect for the first time an orbital motion at high significance, with acurrent orbital motion projected in the plane of the sky of 25 mas (~0.85 au)per year. No orbital curvature is seen in the measurements. An orbital fit ofthe SPHERE and literature astrometry of the companion without priors on theorbital plane clearly indicates that its orbit is (quasi-)coplanar with thedisk. To further constrain the other orbital parameters, we used empirical lawsfor a companion chaotic zone validated by N-body simulations to test theorbital solutions that are compatible with the estimated disk cavity size.Non-zero eccentricities (>0.15) are allowed for orbital periods shorter than100 yr, while only moderate eccentricities up to ~0.3 for orbital periodslonger than 200 yr are compatible with the disk observations. A comparison ofsynthetic Herschel images to the real data does not allow us to constrain theupper eccentricity of the companion.

VLT/SPHERE astrometric confirmation and orbital analysis of the brown dwarf companion HR 2562 B