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 cooler star (1 Del), by including in an approximate manner the diffuse radiation 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-free absorption were assumed to contribute to the rate of energy gain; radiative recombination, collisional excitation, and free-free emission contribute to the rate of energy loss. The kinetic temperature at a particular location is obtained from the requirement that the rates of energy gain and energy loss there be equal. These results, combined with previous investigations, establish the range of temperatures expected in the circumstellar envelopes of Be stars if the primary source of energy input is the radiation field of the star.