Stationary flows in the circumstellar envelopes of M giants

A model is developed for a stellar wind driven by radiation pressure on dust grains in the circumstellar envelopes of Mira variables. This theory couples for the first time the gas temperature and the velocity variations. This coupling forms an essential aspect of the flow. The coupling is present because the escape of cooling photons depends on the local velocity gradient. The topology of the solution of the momentum equation of the gas is described, and it is shown that a critical point exists in the flow, related to the sonic point in the familiar solar wind theory. A solution which connects smoothly the region of subsonic flow close to the inner boundary with the region of supersonic flow at the outer boundary has to pass through this point. Finally, the flow for a typical Mira variable is calculated numerically, and its characteristics are briefly discussed.