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Fig. 6.

image

Left-hand panel: an example of binary system with an orbital period of 23.6 min where direct impact accretion can occur: the parameters are M1 = 0.35 M, M2 = 0.14 M. The separation between the centre of the two stellar components is defined as unity. Right-hand panel: region of M1, M2 values that lead to direct impact. Below the curved part of the boundary, the accretor is too small for a direct impact to occur (Eq. (31) from Marsh et al. 2004). The diagonal sloping dashed lines mark the upper bound of stable accretion in the absence of tides for the different values of the logarithmic derivative of radius with respect to mass, ζ2 = d ln(R2)/d ln(M2). We arbitrarily take the case ζ2 = 1 to define the upper boundary which leads to q < 0.87. Models of helium star donors give lower values (ζ2 ≈ 0.2), while degenerate stars have ζ2 < 0, suggesting that the donor mass should lie in the lower half of the shaded region. The arrow shows the direction in which a given system would evolve in this diagram if undergoing conservative mass transfer. Along with the expectation that the donor must have started with mass >0.1 M this leads to the sloping boundary on the lower-left, although its exact location depends upon the assumed upper limit on ζ2.

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