Stripped-Envelope Stars in Different Metallicity Environments I.
  Evolutionary Phases, Classification and Populations
  Massive stars that become stripped of their hydrogen envelope through binary
interaction or winds can be observed either as Wolf-Rayet stars, if they have
optically thick winds, or as transparent-wind stripped-envelope stars. We
approximate their evolution through evolutionary models of single helium stars,
and compute detailed model grids in the initial mass range 1.5 to 70
M$_{\odot}$ for metallicities between 0.01 and 0.04, from core helium ignition
until core collapse. Throughout their lifetime, some stellar models expose the
ashes of helium burning. We propose that models that have nitrogen-rich
envelopes are candidate WN stars, while models with a carbon-rich surface are
candidate WC stars during core helium burning, and WO stars afterwards. We
measure metallicity dependance of the total lifetime of our models and the
duration of their evolutionary phases. We propose an analytic estimate of the
wind optical depth to distinguish models of Wolf-Rayet stars from
transparent-wind stripped-envelope stars, and find that the luminosity ranges
at which WN, WC and WO type stars can exist is a strong function of
metallicity. We find that all carbon-rich models produced in our grids have
optically thick winds and match the luminosity distribution of observed
populations. We construct population models and predict the numbers of
transparent-wind stripped-envelope stars and Wolf-Rayet stars, and derive their
number ratios at different metallicities. We find that as metallicity
increases, the number of transparent-wind stripped-envelope stars decreases and
the number of Wolf-Rayet stars increases. At high metallicities WC and WO type
stars become more common. We apply our population models to nearby galaxies,
and find that populations are more sensitive to the transition luminosity
between Wolf-Rayet stars and transparent-wind helium stars than to the
metallicity dependent mass loss rates.
