We present new radial velocities for 289 globular clusters around NGC 4636,
the southernmost giant elliptical galaxy of the Virgo cluster. The data were
obtained with FORS2/MXU at the Very Large Telescope. Together with data
analysed in an earlier study (Schuberth et al. 2006), we now have a sample of
460 globular cluster velocities out to a radius of 12 arcmin (60 kpc) available
- one of the largest of its kind. This new data set also provides a much more
complete angular coverage. Moreover, we present new kinematical data of the
inner stellar population of NGC 4636. We perform an updated Jeans analysis,
using both stellar and GC data, to better constrain the dark halo properties.
We find a stellar M/L-ratio of 5.8 in the R-band, higher than expected from
single stellar population synthesis. We model the dark halo by cored and cuspy
analytical halo profiles and consider different anisotropies for the tracer
populations. Properties of NFW halos lie well within the expected range of
cosmological simulations. Cored halos give central dark matter densities, which
are typical for elliptical galaxies of NGC 4636’s luminosity. The surface
densities of the dark matter halos are higher than those of spiral galaxies. We
compare the predictions of Modified Newtonian Dynamics with the derived halo
properties and find satisfactory agreement. Therefore NGC 4636 therefore falls
onto the baryonic Tully-Fisher relation for spiral galaxies. The comparison
with the X-ray mass profile of Johnson et al. (2009) reveals satisfactory
agreement only, if the abundance gradient of hot plasma has been taken into
account. This might indicate a general bias towards higher masses for X-ray
based mass profiles in all systems, including galaxy clusters, with strong
abundance gradients.