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 4636s 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.
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