Rates of Energy Gain and Loss in the Circumstellar Envelopes of Be Stars: The Poeckert‐Marlborough Model

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Abstract
We have determined the kinetic temperature of the electron gas as a function of position in the circumstellar envelopes of early Be stars for the model developed by Poeckert & Marlborough. The rates of energy gain and loss due to photoionization, radiative recombination, collisional transitions between bound levels, free-free emission, and free-free absorption were calculated at a set of grid points in a meridional plane. If the temperature assumed is correct, the ratio of energy gain to energy loss should be exactly 1 at all points in the envelope. Our investigation demonstrates that the choice of a constant temperature of 20,000 K was a reasonable first-order approximation. More importantly, we have also determined the temperature that corresponds to equal rates of energy gain and loss at each grid point throughout the envelope. These temperatures represent a self-consistent solution of the equation of energy conservation.