Constraining the mass of accreting black holes in ultraluminous X-ray
  sources with ultrafast outflows
  The nature of ultraluminous X-ray sources (ULXs) -- off-nuclear
extra-galactic sources with luminosity, assumed isotropic, $\gtrsim 10^{39}$
erg s$^{-1}$ -- is still debated. One possibility is that ULXs are stellar
black holes accreting beyond the Eddington limit. This view has been recently
reinforced by the discovery of ultrafast outflows at $\sim 0.1$-$0.2c$ in the
high resolution spectra of a handful of ULXs, as predicted by models of
supercritical accretion discs. Under the assumption that ULXs are powered by
super-Eddington accretion onto black holes, we use the properties of the
observed outflows to self-consistently constrain their masses and accretion
rates. We find masses $\lesssim 100$ M$_{\odot}$ and typical accretion rates
$\sim 10^{-5}$ M$_{\odot}$ yr$^{-1}$, i.e. $\approx 10$ times larger than the
Eddington limit calculated with a radiative efficiency of 0.1. However, the
emitted luminosity is only $\approx 10\%$ beyond the Eddington luminosity,
because most of the energy released in the inner part of the accretion disc is
used to accelerate the wind, which implies radiative efficiency $\sim 0.01$.
Our results are consistent with a formation model where ULXs are black hole
remnants of massive stars evolved in low-metallicity environments.
