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Appendix A: Flux correction LH41-1042

	Fig. A.1 Archival HST/WFC3 image of LH41-1042 (F225W filter, proposal ID 12940, PI Massey). North is up and east to the left. The two X-Shooter slit positions are indicated. The inset shows a zoomed image of the boxed area around LH41-1042, and shows the nearby star that may be contaminating the spectrum.
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As discussed in Sect. 2, the slope of the spectrum of LH41-1042 before extinction correction is steeper than that of WO star models for an LMC metallicity. This may either be a result of a bad flux calibration, or a second object may be contaminating the spectrum. Inspection of a Hubble Space Telescope (HST) near-UV image shows that there is indeed a faint star very close to LH41-1042 (Fig. A.1). We therefore first tried to correct the spectrum by assuming that this object is responsible for the steep slope.

We assume that the flux contribution of the contaminating object follows the Rayleigh-Jeans approximation (F ∝ λ^-4) at the X-Shooter wavelength range. This seems justified, as the slope of the uncorrected spectrum is steeper than the slope of the continuum of an LMC WO-model (which has a free-free emission component and is less steep than a Rayleigh-Jeans slope) even before dereddening.

As we cannot determine the reddening from our spectrum, we use the average value for the region found by Massey et al. (2005) of A_V = 0.4 and a standard total-to-selective extinction of R_V = 3.1. We assume a luminosity of 1.8 × 10⁵L_⊙ for the WO star, equal to that of BAT99-123. While there is no a priori reason for the two stars to have the same luminosity, the resulting model flux is in agreement with the dereddened flux in the near-IR region where the contribution of the contaminator becomes negligible.

The correction is then done by testing different ratios of the flux contributed by the WO star and the contaminator. Ideally, the flux ratio measured from photometry should be used. However, the only image where the individual stars are resolved is the HST/WFC3 image shown in Fig. A.1, which uses a filter with an effective wavelength in the near-UV. From this image, the flux ratio is F_cont/F_WO = 0.1 at 2250Å. As a much higher flux ratio is needed to recover the observed spectrum, this indicates that the flux of the contaminating object peaks at a wavelength between 2250 Å  and the X-Shooter wavelengths (between ~ 2500−3000 Å), and no longer in the Rayleigh-Jeans tail. The contaminating object is therefore likely a B dwarf or giant. This means that the measured flux ratio cannot be used to estimate the flux ratio in the X-Shooter wavelength range. Instead, we try out different combinations of flux ratios to obtain a combined spectrum of the WO model and a Rayleigh-Jeans contribution that matches the observed spectrum (Fig. A.2.)

Using this strategy, we can get a good representation of the slope of the observed spectrum (Fig. A.2). However, when the Rayleigh-Jeans contribution is subtracted from the observed spectrum, the emission lines become roughly twice as strong as in any of the other WO stars. As otherwise the spectrum of LH41-1042 does not show unusual features, we conclude that this is unlikely to be physical. We therefore assume that the steep slope is a result of the flux calibration, and not of contamination by the faint nearby object. We correct for this by artificially altering the slope to the correct value. While this results in a much more realistic spectrum, the luminosity and mass-loss rate that is derived from the modeling are much more uncertain than those of the other WO stars.

	Fig. A.2 Determination of the flux contribution of the companion of LH41-1042. Plotted are the dereddened flux (black), the assumed LMC WO model continuum (blue), the derived Rayleigh-Jeans contribution (red), and the combined continuum from the WO and Rayleigh-Jeans contributions (green).
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Appendix B: Equivalent widths and spectral classification

Appendix C: Best-fit models

	Fig. C.1 Best model of WR102.
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	Fig. C.2 Best model of WR142.
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	Fig. C.3 Best model of WR93b.
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	Fig. C.4 Best model of BAT99-123.
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	Fig. C.5 Best model of LH41-1042.
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Appendix D: Helium-burning models

	Fig. D.1 Same as Fig. 11, but for WR142.
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	Fig. D.2 Same as Fig. 11, but for WR93b.
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	Fig. D.3 Same as Fig. 11, but for BAT99-123.
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	Fig. D.4 Same as Fig. 11, but for LH41-1042.
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	Fig. D.5 Same as Fig. 11, but for DR1.
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© ESO, 2015