  Super-Eddington accreting massive black holes (SEAMBHs) reach saturated
luminosities above a certain accretion rate due to photon trapping and
advection in slim accretion disks. We show that these SEAMBHs could provide a
new tool for estimating cosmological distances if they are properly identified
by hard X-ray observations, in particular by the slope of their 2-10 keV
continuum. To verify this idea we obtained black hole mass estimates and X-ray
data for a sample of 60 narrow line Seyfert 1 galaxies that we consider to be
the most promising SEAMBH candidates. We demonstrate that the distances derived
by the new method for the objects in the sample get closer to the standard
luminosity distances as the hard X-ray continuum gets steeper. The results
allow us to analyze the requirements for using the method in future samples of
active black holes and to demonstrate that the expected uncertainty, given
large enough samples, can make them into a useful, new cosmological ruler.
