  Diffuse intracluster light (ICL) and cD galaxy halos are believed to
originate from galaxy evolution and disruption. We present a kinematic study of
the ICL in the Hydra I cluster core, using planetary nebulas (PNs) as tracers.
We used multi-slit imaging spectroscopy with FORS2 on VLT-UT1 to detect 56 PNs
associated with diffuse light in the central 100 x 100 kpc^2 of Hydra I. We
measured their [OIII] magnitudes, sky positions, and velocity distribution
(LOSVD), and compared with the phase-space distribution of nearby galaxies. The
luminosity function of the detected PNs is consistent with that expected at a
distance of ~50 Mpc. Their number density is ~4 times lower for the light seen
than expected, and we discuss ram pressure stripping of the PNs by the hot ICM
as one of the possible explanations. The LOSVD histogram of the PNs is highly
non-Gaussian and multipeaked: it is dominated by a broad central component with
sigma~500 km/s at around the average velocity of the cluster, and shows two
additional narrower peaks at 1800 km/s and 5000 km/s. The main component is
broadly consistent with the outward continuation of the intracluster halo of
NGC 3311, which was earlier shown to have a velocity dispersion of ~470 km/s at
radii of >50". Galaxies with velocities in this range are absent in the central
100 x 100 kpc^2 and may have been disrupted earlier to build this component.
The PNs in the second peak in the LOSVD at 5000 km/s are coincident spatially
and in velocities with a group of dwarf galaxies in the MSIS field. They may
trace the debris from the ongoing tidal disruption of these galaxies. Most of
the diffuse light in the core of Hydra is still not phase-mixed. The build-up
of ICL and the dynamically hot cD halo around NGC 3311 are ongoing, through the
accretion of material from galaxies falling into the cluster core and tidally
interacting with its potential well.
