  We study H I Lyman-alpha absorption observed by the Hubble Space Telescope
toward the nearby binary system Alpha Cen (G2 V+K0 V) and its distant companion
star Proxima Cen (M5.5 Ve). Absorption from heliospheric H I heated by the
solar wind/ISM interaction is observed toward both Alpha Cen and Proxima Cen.
Absorption from analogous "astrospheric" material surrounding the stars is
detected toward Alpha Cen, but not Proxima Cen. The nondetection of
astrospheric absorption toward Proxima Cen suggests that the stellar wind of
Proxima Cen must be significantly weaker than that of the Alpha Cen system. We
use hydrodynamic models of the astrospheres computed assuming different
mass-loss rates to predict astrospheric Lyman-alpha absorption for comparison
with the observations. The model that best matches the Alpha Cen data has a
mass-loss rate of twice the solar rate, and the models suggest an upper limit
of 0.2 solar for Proxima Cen. Finally, we note that the heliospheric absorption
observed toward Proxima Cen in 2000 May is identical to the heliospheric
absorption observed toward Alpha Cen in 1995 May, implying that the structure
of the outer heliosphere does not change significantly during the solar
activity cycle.
