Context. The discovery of pulsations in several ultraluminous X-ray sources (ULXs) has demonstrated that a fraction of them are powered by super-Eddington accretion onto neutron stars (NSs). This has raised questions regarding the NS to black hole (BH) ratio within the ULX population and the physical mechanism that allows ULXs to reach luminosities well in excess of their Eddington luminosity. Is this latter the presence of strong magnetic fields or rather the presence of strong outflows that collimate the emission towards the observer? Aims. In order to distinguish between these scenarios, namely, supercritically accreting BHs, weakly magnetised NSs, or strongly magnetised NSs, we study the long-term X-ray spectral evolution of a sample of 17 ULXs with good long-term coverage, 6 of which are known to host NSs. At the same time, this study serves as a baseline to identify potential new NS-ULX candidates. Methods. We combine archival data from Chandra, XMM-Newton, and NuSTAR observatories in order to sample a wide range of spectral states for each source. We track the evolution of each source in a hardness–luminosity diagram in order to identify spectral changes, and show that these can be used to constrain the accretion flow geometry, and in some cases the nature of the accretor. Results. We find NS-ULXs to be among the hardest sources in our sample with highly variable high-energy emission. On this basis, we identify M 81 X-6 as a strong NS-ULX candidate, whose variability is shown to be akin to that of NGC 1313 X-2. For most softer sources with an unknown accretor, we identify the presence of three markedly different spectral states, which we interpret by invoking changes in the mass-accretion rate and obscuration by the supercritical wind/funnel structure. Finally, we report on a lack of variability at high energies (≳10 keV) in NGC 1313 X-1 and Holmberg IX X-1, which we argue may offer a means to differentiate BH-ULXs from NS-ULXs. Conclusions. We support a scenario in which the hardest sources in our sample might be powered by strongly magnetised NSs, meaning that the high-energy emission is dominated by the hard direct emission from the accretion column. Instead, softer sources may be explained by weakly magnetised NSs or BHs, in which the presence of outflows naturally explains their softer spectra through Compton down-scattering, their spectral transitions, and the dilution of the pulsed-emission should some of these sources contain NSs.
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