Free Access
Volume 520, September-October 2010
Article Number A86
Number of page(s) 16
Section Stellar structure and evolution
Published online 07 October 2010

Online Material

Appendix A: Data

Table A.1:   Properties of the SDSS PCEBs.

Table A.2:   Properties of the previously known PCEBs.

\end{figure} Figure A.1:

Reconstructed values of $\alpha \lambda $ for the three different versions of the energy equation. Black lines are progenitors in the FGB, and blue are for progenitors in the AGB. The results obtained with the PRH and BSE formulations (left and center) are almost identical and significantly higher than those obtained with ILY formulation (right panel) because in the latter case the binding energy at the onset of CE evolution is assumed to be significantly smaller.

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\end{figure} Figure A.2:

Reconstructed values of $\alpha $ for all the possible progenitors of the PCEBs in our sample with $\lambda = 0.5$ (left), $\lambda $ calculated using the BSE code without internal energy (center), and with $\lambda $ calculated including a fraction $\alpha _{\rm int}=\alpha $ of the internal energy (right). Colors are the same as in Fig. A.1. While $\lambda = 0.5$ seems to be a reasonable assumption for most of the FGB progenitors, calculating $\lambda $ and particularly including internal energy becomes important for progenitors on the AGB (blue). While $\alpha $ is only slightly moved towards lower values in the central panel, taking into account the internal energy leads to dramatically lower values of $\alpha $ for AGB progenitors (right panel). For example, we only find solutions for IK Peg in the range $0 \leq \alpha \leq 1$ if a fraction of the internal energy is assumed to contribute to the energy budget. The vertical lines in the right panel correspond to $\alpha =0.2$ and 0.3.

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\end{figure} Figure A.3:

Reconstructed values for $\alpha $ (left) and $\gamma $ (right) for the possible progenitors of our PCEB sample. The structural parameter $\lambda $ has been calculated including a fraction $\alpha _{\rm int}=\alpha $ of the internal energy of the envelope. On the left hand side, the vertical lines indicate the range of values were we find simultaneous solutions for all the systems in our sample, i.e. $\alpha =0.2-0.3$. On the right panel vertical lines show the range of simultaneous solutions for $\gamma $ proposed by NT05.

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\end{figure} Figure A.4:

Left panel: reconstructed values of $\alpha $ for $\gamma $ fixed between 1.5 and 1.75. Right panel: reconstructed values of $\gamma $ for $\alpha $ fixed between 0.2 and 0.3. If constraining $\gamma $ we still find rather broad ranges of possible values for $\alpha $. In contrast, if we constrain the energy efficiency to be $\alpha =0.2-0.3$, the values of $\gamma $ cluster in a small range of values and there is a clear dependency on the evolutionary stage of the progenitor of the primary, which reflects the fact that expelling tightly bound evelopes extracts more angular momentum per unit mass from the binary (see text for details).

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