We study H I Ly \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 Ly \alpha absorption for comparison with the observations .
The model that best matches the \alpha Cen data has a mass-loss rate of \dot { M } = 2 ~ { } \dot { M } _ { \odot } , and the models suggest an upper limit of \dot { M } \leq 0.2 ~ { } \dot { M } _ { \odot } 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 .