  Context. A low-mass brown dwarf has been recently imaged around HR 2562 (HD
50571), a star hosting a debris disk resolved in the far infrared.
Interestingly, the companion location is compatible with an orbit coplanar with
the disk and interior to the debris belt. This feature makes the system a
valuable laboratory to analyze the formation of substellar companions in a
circumstellar disk and potential disk-companion dynamical interactions. Aims.
We aim to further characterize the orbital motion of HR 2562 B and its
interactions with the host star debris disk. Methods. We performed a monitoring
of the system over ~10 months in 2016 and 2017 with the VLT/SPHERE exoplanet
imager. Results. We confirm that the companion is comoving with the star and
detect for the first time an orbital motion at high significance, with a
current 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 of
the SPHERE and literature astrometry of the companion without priors on the
orbital plane clearly indicates that its orbit is (quasi-)coplanar with the
disk. To further constrain the other orbital parameters, we used empirical laws
for a companion chaotic zone validated by N-body simulations to test the
orbital solutions that are compatible with the estimated disk cavity size.
Non-zero eccentricities (>0.15) are allowed for orbital periods shorter than
100 yr, while only moderate eccentricities up to ~0.3 for orbital periods
longer than 200 yr are compatible with the disk observations. A comparison of
synthetic Herschel images to the real data does not allow us to constrain the
upper eccentricity of the companion.
