  According to the standard picture for binary interactions, the outcome of
binaries surviving the evolution through a common envelope (CE) and spiral-in
phase is determined by the internal structure of the donor star at the onset 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 Research Note we
discuss the bifurcation point which separates the ejected, unprocessed 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 demonstrate that the
exact location of this point is very important for evaluating the binding
energy parameter, lambda, which is used to determine the post-CE orbital
separation. Here we compare various methods to define the bifurcation point
(core/envelope boundary) of evolved stars with masses 4, 7, 10 and 20 M_sun. We
consider the specific nuclear energy production rate profile, the change in the
mass-density gradient (Bisscheroux 1998), the inner region containing less than
10% hydrogen, the method suggested by Han et al. (1994) 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 the core boundary for RGB
stars. Hence, this method is not applicable for RGB stars, unless the actual
bifurcation point of a CE is located at the bottom of the outer convection zone
(resulting in larger values of lambda and larger post-CE orbital separations).
On the AGB, where highly degenerate and condensed cores are formed, we find
good agreement between the various methods, except for massive (20 M_sun)
stars.
