Left panel: J1357 spectra showing the BAs evolution during its 2011 outburst, zoomed into the Balmer $\mathrm{H}\beta$ and $\mathrm{H}\alpha$ transitions. The colour of the spectra corresponds to the X-ray spectral state, following the same convention as in Fig. C.1. The best fit corresponding with the parameters shown in the right panel is shown as a solid blue line. The rest wavelength of the transition is marked with a black-dashed line, while blue-dotted lines mark velocity shifts of $\pm 2500\mathrm{km}{\mathrm{s}}^{-1}$ as a visual reference. Right panel: Best fitting parameters for the spectroscopic sample of J1357, following the same description as in Fig. C.2, but using black dots for the $\mathrm{H}\alpha$ transition.