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Fig. 3

image

Energy budget of the in-spiral process for the 88M donor star model with Z = Z/ 50 at two different evolutionary epochs: at the beginning of the Hertzsprung gap, R = 194R (upper panel), and when the star reaches its maximum extent as a giant star, R = 3530R (lower panel). The two solid lines mark the integrated binding energy of the material between the given mass coordinate and the surface. The green line (Ebind) includes the total energy (internal and gravitational binding energy, cf. Eq. (1)), while the red line (Egrav) only considers the gravitational binding energy. The six dashed curves represent the released orbital energy, ΔEorb of an in-spiralling object with a given mass between 1.3 and 80M (cf. mass values in the legend). For the values of ΔEorb, it is assumed that the in-spiral stops just when the remaining star would fill its Roche lobe. The vertical dotted line indicates the core boundary according to the XH = 0.10 criterion (cf. Sect. 2), and the arrow marks the location of the maximum-compression point (cf. Sect. 4.1). The hatched regions shown at the top indicate convective layers. The black and grey dots mark the crossings when Ebind = ΔEorb, see Sect. 3.3 for details.

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