  Context: Both the absolute mass-loss rates and the mechanisms that drive the
mass loss of late-type supergiants are still not well known. Binaries such as
alpha Sco provide the most detailed empirical information about the winds of
these stars.
  Aims: The goal was to improve the binary technique for the determination of
the mass-loss rate of alpha Sco A by including a realistic density distribution
and velocity field from hydrodynamic and plasma simulations.
  Methods: We performed 3D hydrodynamic simulations of the circumstellar
envelope of alpha Sco in combination with plasma simulations accounting for the
heating, ionization, and excitation of the wind by the radiation of alpha Sco
B. These simulations served as the basis for an examination of circumstellar
absorption lines in the spectrum of alpha Sco B as well as of emission lines
from the Antares nebula.
  Results: The present model of the extended envelope of alpha Sco reproduces
some of the structures that were observed in the circumstellar absorption lines
in the spectrum of alpha Sco B. Our theoretical density and velocity
distributions of the outflow deviate considerably from a spherically expanding
model, which was used in previous studies. This results in a higher mass-loss
rate of (2 +/- 0.5) x 10^-6 M_sun/yr. The hot H II region around the secondary
star induces an additional acceleration of the wind at large distances from the
primary, which is seen in absorption lines of Ti II and Cr II at -30 km/s.
