tokens: except when the wind speed at the orbital separation is so low compared to the orbital speed that the effective cross section given by the BHL formula is larger than the orbital separation and looses any meaning: relying on the Roche lobe instead makes much more sense in this regime. Fig. 3. Comparison of the mass-transfer rates we measure as a function of η (solid lines) to the BHL mass-accretion-rate formula (dashed lines) for a filling factor of 90% and mass ratios of 2 ( upper panel ) and 15 ( lower panel ). The BHL prescription leads to mass-accretion rates much lower than the mass-transfer rates we derive, sometimes by more than an order of magnitude. 3.2. Accretion luminosity Another insight revealed by this analysis is the identification of the configurations where ULXs cannot be the product of mass transfer via wind-RLOF and can be explained only if the star fills its Roche lobe. In Fig. 2 , we represented in black the regions where μ is inferior to 0.2%, the minimum fraction of stellar wind captured under which mass transfer without RLOF is not able to produce a stationary X-ray luminosity of 10 39 erg s −1 , even for a stellar mass-loss rate as high as 10 −4 M ⊙ yr −1 : Given the maximal μ we found at ∼20%, this analysis suggests that mass transfer via wind-RLOF in a ULX is only possible for stellar mass-loss rates above ∼10 −6 M ⊙ yr −1 . We note here that matching a mass-transfer rate Ṁ high enough to reach ULX levels is a necessary but not sufficient condition: the final X-ray luminosity is determined by the physics at stake within the Roche lobe of the accretor, where the flow geometry can be disk-like ( El Mellah et al. 2019 ) or spherical ( Shakura et al. 2012 ) and where, for an accreting NS, the magnetosphere eventually dominates the dynamics ( Bozzo et al. 2008 ). For accreting BHs, powerful disk outflows come into play in the vicinity of the compact object, lowering the final mass-accretion rate ( Pinto et al. 2016 ). Rather than covering the large scope of regimes possible, let us focus on three donor stars in one SgXBs and two ULXs. In the SgXBs Vela X-1, Gimenez-Garcia et al. (2016) reported a stellar mass-loss rate Ṁ ⋆ ∼ 6.3 × 10 −7 M ⊙ yr −1 for the B0.5 Ib supergiant donor star. In M101, Liu et al. (2013) inferred a mass-loss rate of 2 × 10 −5 M ⊙ yr −1 for the Wolf-Rayet donor. In P13, we think the stellar mass-loss rate of the B9 Ia supergiant donor star could have been underestimated: in Motch et al. (2014) , it is assumed that the donor star fills its Roche lobe on the basis that the wind mass-loss rate derived by Kudritzki et al. (1999) would be inferior to 10 −6 M ⊙ yr −1 . However, Kudritzki et al. (1999) did not include late-type B supergiants in their study because of the difficulty to measure their terminal wind speed ( Howarth et al. 1997 ). Vink et al. (2000 , 2001) provided fits for the mass-loss rate and the terminal wind speed which extend below the second bi-stability jump (i.e., for effective
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