Double core evolution. 6: Effects of gravitational torques

Abstract

The influence of gravitational torques during the late stages of common envelope evolution of a binary star system consisting of a 3 M⊙ red giant and a 1 M⊙ companion star is studied. The numerical results of two-dimensional hydrodynamical simulations of the binary in its orbital plane indicate that gravitational torques are important for distances of ∼3 times the orbital separation of the binary system. It is shown, for the first time, that when the companion has spiraled to a radius of 3 × 1011 cm from the center of the red giant, matter in its immediate vicinity is brought into a state of corotation with the orbital motion. The degree of spin-up is a function of orbital phase with the departure from corotation increasing or matter which experienced the previous companion passage the earliest. A low-density region, consequently, is formed over a significant fraction of the orbit. This region is limited in its radial extent to a width approximately given by the size of the tidal lobe of the low-mass companion. Throughout the remainder of the common envelope, the matter rotates differentially. In particular, exterior to the low-density region, the specific angular momentum tends toward a spatially constant value. As a result of the gravitational interaction, energy is found to be released from the binary orbit at a rate comparable to that obtained from a frictional drag calculation which employs the unmodified Bondi-Hoyle accretion radius. These rates are larger by a factor of a few in comparison with rates deduced from the use of a modified accretion radius which takes into account density gradients in the accretion flow. Termination of the spiral-in phase, as a result of spin-up of envelope material to the orbital velocity, is strongly indicated when the companion has reached a radius of ∼3 × 1011 cm. This effect is facilitated by the condition that a steep density gradient exists in the red giant companion near that radius. Thus, these two-dimensional nonaxisymmetric calculations strengthen the conclusions reached by previous axisymmetric calculations, which also indicated termination near the same radius, but for different physical reasons. This work also indicates that the common envelope phase ends with a slow material outflow; future three-dimensional studies will be required to confirm this conclusion.