Black Hole Mass Determination Using X-ray Data

Supermassive black holes are located at the center of basically every galaxy and their mass appears to be tightly correlated with several galaxy properties, suggesting that black hole and galaxy growths are linked together. Determining the mass of black holes provides crucial information on the galaxy evolution and indeed significant progress has been achieved thanks to optically-based methods. However, since these methods are limited by several factors including absorption and galaxy contamination, it is important to develop and test alternative methods that use different energy bands to constrain the black hole mass. In a recent work we demonstrated that a novel X-ray scaling method, originally introduced for stellar mass black holes, can be reliably extended to estimate the mass of highly-accreting supermassive black holes. Here we investigate the limits of applicability of this method to low-accreting black holes, using a control sample of low-luminosity active galactic nuclei with good-quality X-ray data and with dynamically measured black hole masses. We find the threshold value of the accretion rate for which the X-ray scaling method can still be used. Below this threshold, we provide a simple recipe to constrain the black hole mass based on the inverse correlation between X-ray spectral properties and accretion rate, which was found in several low-accreting black holes and confirmed by our sample. Then, we extend the X-ray scaling method to ultraluminous X-ray sources (ULXs), which are off-nuclear, point-like X-ray sources, whose nature is still debated. Their high X-ray brightness can be equally well explained by stellar mass black holes accreting at extreme rates or by intermediate mass black holes accreting at regular rates, therefore, constraining their mass may shed light on one of the outstanding questions of high energy astrophysics. Currently, no direct optically-based methods can dynamically determine the mass of ULXs, making X-ray methods the only viable option. In this work, we systematically applied the X-ray scaling method to a sample of ULXs with multiple high-quality X-ray observations. This allows us to reconstruct the spectral evolution of ULXs and directly compare it with the spectral trend of stellar mass black holes used as reference sources in the X-ray scaling method. We found that the vast majority of the ULX spectral trends are consistent with those of highly-accreting stellar black holes, suggesting that ULXs are not characterized by exotic spectral states. The black hole masses determined with this scaling technique are in agreement with values obtained from different methods and confirm the existence of some intermediate mass black holes, which may play a crucial role in the formation of the seeds for supermassive black holes. However, the vast majority of the ULX masses appear to be consistent with the hypothesis of massive stellar black holes accreting at very high rate. Our findings highlight the importance of the X-ray scaling method as a robust, scale independent technique that can be used to constrain the black hole mass from stellar systems up to supermassive black holes at the center of all galaxies.