Measuring the black hole mass in Ultraluminous X-ray Sources with the X-ray Scaling Method

In our recent work, we demonstrated that a novel X-ray scaling method, originally introduced for Galactic black holes, could be reliably extended to estimate the mass of supermassive black holes accreting at moderate to high level. Here, we apply this X-ray scaling method to ultraluminous X-ray sources (ULXs) to constrain their \mbh. Using 49 ULXs with multiple \xmm\ observations, we infer that ULXs host both stellar mass BHs and intermediate mass BHs. The majority of the sources of our sample seem to be consistent with the hypothesis of highly accreting massive stellar BHs with $M_{\rm BH}\sim100\,M_{\odot}$. Our results are in general agreement with the \mbh\ values obtained with alternative methods, including model-independent variability methods. This suggests that the X-ray scaling method is an actual scale-independent method that can be applied to all BH systems accreting at moderate-high rate.