  This is the second in a series of papers reporting on a large reverberation
mapping (RM) campaign to measure black hole (BH) mass in high accretion rate
active galactic nuclei (AGNs). The goal is to identify super-Eddington
accreting massive black holes (SEAMBHs) and to use their unique properties to
construct a new method for measuring cosmological distances. Based on
theoretical models, the saturated bolometric luminosity of such sources is
proportional to the BH mass which can be used to obtain their distance. Here we
report on five new RM measurements and show that in four of the cases we can
measure the BH mass and three of these sources are SEAMBHs. Together with the
three sources from our earlier work, we now have six new sources of this type.
We use a novel method based on a minimal radiation efficiency to identify nine
additional SEAMBHs from earlier RM-based mass measurements. We use a Bayesian
analysis to determine the parameters of the new distance expression, and the
method uncertainties, from the observed properties of the objects in the
sample. The ratio of the newly measured distances to the standard cosmological
ones has a mean scatter of 0.14 dex, indicating that SEAMBHs can be use as
cosmological distance probes. With their high luminosity, long period of
activity and large numbers at high redshifts, SEAMBHs have a potential to
extend the cosmic distance ladder beyond the range now explored by type Ia
supernovae.
