Fig. 9.

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Minimum initial inner binary separation min(ain) to prevent RLOF at periastron at ZAMS (i.e., R1(m1)≤RRL, 1 and R2(m2)≤RRL, 2) as a function of the inner binary mass ratio qin = m2/m1 and eccentricity ein for HD 45485 (top), HD 191495 (middle), and HD 25631 (bottom). The red solid lines mark the present-day observed separation, corresponding to the evolved post-merger aout in the merger-in-a-triple scenario, while the black area in the bottom left corners corresponds the unphysical region with initial inner binary separation with Ri(mi)≤RRL, i. In the bottom row, the boundary of this unphysical region has a kink caused by the change of slope in the assumed mass–radius relation: HD 25631 primary mass is M1 ≃ 7 M⊙, so for qin ≲ 0.2 (the exact threshold depends on fΔ), the expected values of m2 are sufficiently low that the exponent ξ in the RZAMS ≡ RZAMS(m) changes. For the right column with fΔ ≠ 0, our assumptions based on the Blaauw (1961) approximation may be inconsistent (see Sect. 5).
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