Upper panel: the bisector span measurements of WASP-54 as a function of radial velocity, values are shifted to a zero-mean (⟨ V_span ⟩ _SOPHIE = −29 m s^-1, ⟨ V_span ⟩ _CORALIE = 48 m s^-1). Lower panel: the bisector span measurements as a function of time (BJD – 2 450 000.0). The bisector span shows no significant variation nor correlation with the RVs, suggesting that the signal is mainly due to Doppler shifts of the stellar lines rather than stellar profile variations due to stellar activity or a blended eclipsing binary.