  (abridged) The strong winds of Wolf-Rayet (WR) stars are important for the
mechanical and chemical feedback of the most massive stars and determine
whether they end their lives as neutron stars or black holes. In this work we
investigate theoretically the mass-loss properties of H-free WR stars of the
nitrogen sequence (WN stars). We connect stellar structure models for He stars
with wind models for optically-thick winds and assess how both types of models
can simultaneously fulfill their respective sonic-point conditions. Fixing the
outer wind law and terminal wind velocity, we obtain unique solutions for the
mass-loss rates of optically-thick, radiatively-driven winds of WR stars in the
phase of core He-burning. The resulting mass-loss relations as a function of
stellar parameters, agree well with previous empirical relations. Furthermore,
we encounter stellar mass limits below which no continuous solutions exist.
While these mass limits agree with observations of WR stars in the Galaxy, they
are in conflict with observations in the LMC. While our results confirm in
particular the slope of oft-used empirical mass-loss relations, they imply that
only part of the observed WN population can be understood in the framework of
the standard assumptions of a smooth transonic flow and compact stellar core.
This means that alternative approaches, such as a clumped and inflated wind
structure, or deviations from the diffusion limit at the sonic point may have
to be invoked. Qualitatively, the existence of mass limits for the formation of
WR-type winds may be relevant for the non-detection of low-mass WR stars in
binary systems, which are believed to be progenitors of Type Ib/c supernovae.
The sonic-point conditions derived in this work may provide a possibility to
include optically-thick winds in stellar evolution models in a more physically
motivated form than in current models.
