Hardness–luminosity diagram for the ULX sample selected for this study. All fluxes and luminosities are unabsorbed. PULXs are shown in shades of orange and the epochs for which pulsations have been reported in the literature (Israel et al. 2017a; Fürst et al. 2018; Carpano et al. 2018; Vasilopoulos et al. 2018; Sathyaprakash et al. 2019; Rodríguez-Castillo et al. 2020) are highlighted by a black edge around the marker. The dashed black lines indicate respectively 10 and 100 times the Eddington limit for a NS (∼2 × 10³⁸ erg s⁻¹).