The Structure of Close Binaries in Two Dimensions

The structure and evolution of close binary stars has been studied using the two-dimensional stellar structure algorithm developed by Deupree. We have calculated a series of solar composition stellar evolution sequences of binary models in which the mass of the two-dimensional model is 8 M ☉ with a point-mass 5 M ☉ companion. We have also studied the structure of the companion in two dimensions by considering the zero-age main sequence (ZAMS) structure of a 5 M ☉ model with an 8 M ☉ point-mass companion. This result suggests that treating the 5 M ☉ star as a point source for the 8 M ☉ evolution is reasonable. In all cases, the binary orbit was assumed to be circular and corotating with the rotation rate of the stars. We considered binary models with three different initial separations, a = 10, 14, and 20 R ☉ . These models were evolved through central hydrogen burning or until the more massive star expanded to fill its critical potential surface or Roche lobe. The model with a separation of 20 R ☉ will be expected to go through case B-type mass transfer during the shell H-burning phase. The 14 R ☉ model is expected to go through mass transfer much earlier, near the middle of core hydrogen burning, and the 10 R ☉ model is very close to this situation at the ZAMS. The calculations show that evolution of the deep interior quantities is only slightly modified from those of single-star evolution. Describing the model surface as a Roche equipotential is also satisfactory until very close to the time of Roche lobe overflow, when the self-gravity of the model about to lose mass develops a noticeable aspherical component and the surface timescale becomes sufficiently short, so that it is conceivable that the actual surface is not an equipotential.