  [Context] Recent detections of disks around young high-mass stars support the
idea of massive star formation through accretion rather than coalescence, but
the detailed kinematics in the equatorial region of the disk candidates is not
well known, which limits our understanding of the accretion process. [Aims]
This paper explores the kinematics of the gas around a young massive star with
millimeter-wave interferometry to improve our understanding of the formation of
massive stars though accretion. [Methods] We use Plateau de Bure
interferometric images to probe the environment of the nearby (~1 kpc) and
luminous (~20000 Lsun) high-mass (10-16 Msun) young star AFGL 2591-VLA3 in
continuum and in lines of HDO, H218O and SO2 in the 115 and 230 GHz bands.
Radiative transfer calculations are employed to investigate the kinematics of
the source. [Results] At ~0.5" (500 AU) resolution, the line images clearly
resolve the velocity field of the central compact source (diameter of ~ 800 AU)
and show linear velocity gradients in the northeast-southwest direction.
Judging from the disk-outflow geometry, the observed velocity gradient results
from rotation and radial expansion in the equatorial region of VLA3. Radiative
transfer calculations suggest that the velocity field is consistent with
sub-Keplerian rotation plus Hubble-law like expansion. The line profiles of the
observed molecules suggest a layered structure, with HDO emission arising from
the disk mid-plane, H218O from the warm mid-layer, and SO2 from the upper disk.
[Conclusions] We propose AFGL 2591-VLA3 as a new massive disk candidate, with
peculiar kinematics. The rotation of this disk is sub-Keplerian, probably due
to magnetic braking, while the stellar wind may be responsible for the
expansion of the disk. The expansion motion [...]
