  Context: The CCO candidate in the center of the supernova remnant shell HESS
J1731-347 / G353.6-0.7 shows no pulsations and exhibits a blackbody-like X-ray
spectrum. If the absence of pulsations is interpreted as evidence for the
emitting surface area being the entire neutron star surface, the assumption of
the measured flux being due to a blackbody emission translates into a source
distance that is inconsistent with current estimates of the remnant's distance.
Aims: With the best available observational data, we extended the pulse period
search down to a sub-millisecond time scale and used a carbon atmosphere model
to describe the X-ray spectrum of the CCO and to estimate geometrical
parameters of the neutron star. Methods: To search for pulsations we used data
of an observation of the source with XMM-Newton performed in timing mode. For
the spectral analysis, we used earlier XMM-Newton observations performed in
imaging mode, which permits a more accurate treatment of the background. The
carbon atmosphere models used to fit the CCO spectrum are computed assuming
hydrostatic and radiative equilibria and take into account pressure ionization
and the presence of spectral lines. Results: Our timing analysis did not reveal
any pulsations with a pulsed fraction above ~8% down to 0.2 ms. This finding
further supports the hypothesis that the emitting surface area is the entire
neutron star surface. The carbon atmosphere model provides a good fit to the
CCO spectrum and leads to a normalization consistent with the available
distance estimates of the remnant. The derived constraints on the mass and
radius of the source are consistent with reasonable values of the neutron star
mass and radius. After the CCO in Cas A, the CCO in HESS J1731-347 / G353.6-0.7
is the second object of this class for which a carbon atmosphere model provides
a consistent description of X-ray emission.
