Research Note On the binding energy parameter of common envelope evolution

Dependency on the definition of the stellar core boundary during spiral-in

¹ Nordic Institute for Theoretical Physics (NORDITA), Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
² Astronomical Institute , University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
³ Bosscha Observatory, Lembang 40391, Bandung, Indonesia
⁴ Department of Astronomy, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia e-mail: jasinta@astro.uva.nl

Corresponding author: T. M. Tauris, tauris@nordita.dk

Received: 9 November 2000
Accepted: 9 January 2001

Abstract

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, , 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, λ, 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 . 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. ([CITE]) 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 λ 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 (~) stars.