Rates of energy gain and loss in the circumstellar envelopes of Be stars: Diffuse radiation

We have determined an upper limit to the kinetic temperature of the gas in the circumstellar envelopes of two Be stars,a hot star (gamma Cas) and a co oler star (1 Del), by including in an approximate manner the diffuse radiat ion produced in the envelope. We computed the temperature as a function of position by balancing at each position the rates of energy gain and energy loss. Photoionization, collisional deexcitation of bound levels, and free-f ree absorption were assumed to contribute to the rate of energy gain; radia tive recombination, collisional excitation, and free-free emission contribu te to the rate of energy loss. The kinetic temperature at a particular loca tion is obtained from the requirement that the rates of energy gain and ene rgy loss there be equal. These results, combined with previous investigatio ns, establish the range of temperatures expected in the circumstellar envel opes of Be stars if the primary source of energy input is the radiation fie ld of the star.