Mapping of pre-CE to post-CE orbital separations as done in population synthesis (see Sect. 4.4) when applying the (α,λ)-formalism. The donor is assumed to be our 88M⊙ (Z = Z⊙/ 50) star. The in-spiralling objects (BHs) have masses of between 5 and 80M⊙. Below the dashed GW lines, the post-CE systems will merge within a Hubble time. Below the dotted CE lines, the in-spiral continues to the core of the donor star and leads to coalescence (i.e. the relaxed He-core fills its Roche-lobe, cf. Sect. 4.6, and the binary will not survive). In the upper panel, the different colours mark the mass of the in-spiralling object (using α = 1); in the lower panel, they represent different values of α (for a fixed value of MX = 35M⊙). The dark green (upper) line in the lower panel was calculated for α = 1 and an additional accretion energy of 5 × 1049erg, see Sect. 4.2.3. The hatched regions indicate systems that are expected to successfully produce LIGO sources. The solid dots mark the models shown in Figs. 3 and 4.
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