J. M. Marlborough

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

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.

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 (γ 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 de-excitation 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.

Rates of Energy Gain and Loss in the Circumstellar Envelopes of Be Stars: The Disk Model

We have investigated the kinetic temperatures assumed by Waters, Cote, & Lamers for the circumstellar envelopes of a group of Be stars. Waters introduced a simple equatorial disk model with ρ ∝ r-n to describe the physical characteristics of Be star disks. Since this equatorial disk model was applied to a large number of stars, it is important to ensure that the kinetic temperatures assumed by Waters et al. were reasonable. We have investigated their choice of kinetic temperature in two ways. Initially we tested the appropriateness of the temperatures assumed by evaluating the rates of energy gain and loss. Then, based on equating the rates of energy gain and loss, we self-consistently determined the temperature structure for these envelopes. Our investigation included the stars γ Cas, δ Cen, ψ Per, and β CMi. For each of the stars examined we discovered that the constant temperature of the envelope assumed by Waters et al. was too high by a factor of 2-3.

Rates of Energy Gain and Loss in the Circumstellar Envelopes of Be Stars. II. 1 Delphini

We have investigated the rates of energy gain and loss in the circumstellar envelope of the cool B8-9e star, 1 Del, using the Poeckert-Marlborough model. We determined iteratively the kinetic temperature of the gas as a function of position in the circumstellar envelope by adjusting the temperature at each grid point until the rates of energy gain and loss there were equal. The gas was assumed to gain energy from photoionization, collisional de-excitation of bound levels, and free-free absorption, and to lose energy by recombination, collisional excitation, and free-free emission. The resultant temperatures are a self-consistent solution of the equation of energy conservation. We were also able to reproduce the gross features of the Hα line with this model and the corresponding temperature grid. Our investigation demonstrates that there is sufficient continuum radiation present to ionize the circumstellar envelope and produce the relative line strength without any additional source of heating in the envelopes of cool Be stars.

A HIDDEN CLASS OF BE STARS

Recently, Brα and Brγ emission was detected in the infrared spectrum of the B0.2V star τ Scorpii, without noticeable emission in Hα (Waters et al. A&A 272,L9-L12, 1993). Here we present simple HI recombination line calculations in the infrared and in the optical that demonstrate that there could be a class of B stars with low-density discs, a factor of 100 lower in density compared to normal Be stars, which may have escaped detection so far.