On the binding energy parameter of common envelope evolution - Dependency on the definition of the stellar core boundary during spiral-in

According to the standard picture for binary interactions, the outcome of b inaries surviving the evolution through a common envelope (CE) and spiral-i n phase is determined by the internal structure of the donor star at the on set of the mass transfer, as well as the poorly-known efficiency parameter, eta (CE), for the ejection of the H-envelope of the donor. In this Researc h Note we discuss the bifurcation point which separates the ejected, unproc essed H-rich material from the inner core region of the donor (the central part of the star which will later contract to form a compact object). We de monstrate that the exact location of this point is very important for evalu ating the binding energy parameter, X, which is used to determine the post- CE orbital separation. Here we compare various methods to define the bifurc ation point (core/envelope boundary) of evolved stars with masses 4, 7, 10 and 20 M.. We consider the specific nuclear energy production rate profile, the change in tile mass-density gradient (Bisscheroux 1998) the inner regi on containing less than 10% hydrogen, the method suggested hy Han et al. (1 994) and the entropy profile. We also calculated effective polytropic index profiles. The entropy profile method measures the convective boundary (at the onset of flatness in the specific entropy) which is not equivalent to t he core boundary for RGB stars. Hence, this method is not applicable for RG B stars, unless the actual bifurcation point of a CE is located at the bott om of the outer convection zone (resulting in larger values of lambda and l arger post-CE orbital separations). On the AGE, where highly degenerate and condensed cores are formed, we find good agreement between the various met hods. except for massive (similar to 20 M.) stars.