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Fig. 13

image

Constraints in the mass-luminosity plane for the primary and secondary components (upper, lower panels) of VFTS 450 and VFTS 652 (left, right panels), obtained by assuming that the primaries fill their Roche lobes, with absolute magnitudes and effective temperatures as summarized in Table 8; refer to Sect. 5.5.1 for further details. Thick black solid lines show ML loci for the indicated mass ratios q over a range in continuum brightness ratio, 2/1 (values shown in the vertical scales to the right in each panel, marked at steps of 0.1; log (L/L) is constant for given 2/1, for fixed Teff values). Thin solid and dashed curves, labelled Z and T in the top-left panel, show the zero-age and terminal-age main sequence loci for non-rotating single stars (from Brott et al. 2011a,b). Thin red curves are lines of constant inclination, at i = 90, 60, and 45° (left to right). Grey shaded areas in the lower panels indicate the zones for which 45° ≤ i ≤ 60°, LL(ZAMS), and 2/ ℱ1 ≤ 1. Filled circles show the initial parameter estimates summarised in Table 8 (columns headed “M1”). “Error bars” in the upper panels, and horizontal error bars in the lower panels, show the effects of changing Teff(1) by ±1 kK (this affects the inferred secondary mass, but not its luminosity, all else fixed). Vertical error bars in the lower panels show the effect of varying Teff(2) by ±2 kK (which has no effect on secondary mass). Open circles represent equivalent ML solutions from V-band photometry. Green circles show the effects of (arbitrarily) adjusting 2/1 to bring the secondary masses to 32 M, hence into the grey shaded zones in this plane. (Note that any changes to effective temperatures or absolute magnitudes also change the loci of constant q, so that only M and L can be inferred from this diagram for Teff or M(IC) values that differ from the reference solution; e.g., the V-band solutions have the same q, i values as the IC-band solutions.)

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