  We use a new non-parametric Bayesian approach to obtain the most probable
mass distributions and circular velocity curves along with their confidence
ranges, given deprojected density and temperature profiles of the hot gas
surrounding X-ray bright elliptical galaxies. For a sample of six X-ray bright
ellipticals, we find that all circular velocity curves are rising in the outer
parts due to a combination of a rising temperature profile and a logarithmic
pressure gradient that increases in magnitude. Comparing the circular velocity
curves we obtain from X-rays to those obtained from dynamical models, we find
that the former are often lower in the central ~10 kpc. This is probably due to
a combination of: i) Non-thermal contributions of up to ~35% in the pressure
(with stronger effects in NGC 4486), ii) multiple-temperature components in the
hot gas, iii) incomplete kinematic spatial coverage in the dynamical models,
and iv) mass profiles that are insufficiently general in the dynamical
modelling. Complementing the total mass information from the X-rays with
photometry and stellar population models to infer the dark matter content, we
find evidence for massive dark matter haloes with dark matter mass fractions of
~35-80% at 2Re, rising to a maximum of 80-90% at the outermost radii. We also
find that the six galaxies follow a Tully-Fisher relation with slope ~4 and
that their circular velocities at 1Re correlate strongly with the velocity
dispersion of the local environment. As a result, the galaxy luminosity at 1Re
also correlates with the velocity dispersion of the environment. These
relations suggest a close link between the properties of central X-ray bright
elliptical galaxies and their environments (abridged).
