Best-fit model of GQ Lup A. a. Spectrum with the veiling continuum subtracted and divided by the telluric model. The observed spectrum is shown in black, the PHOENIX model with optimal linear amplitudes in orange and the ¹³CO lines from the best-fit model in purple. The residuals of the are shown in the bottom panel, the shaded grey region indicates the root-squared diagonal of the covariance matrix with the GP kernel. b. Posterior distributions of the carbon isotope ratio, projected rotational velocity and radial velocity of GQ Lup A.