Inferences on relations between distant supermassive black holes and
  their hosts complemented by the galaxy fundamental plane
  The realization of fundamental relations between supermassive black holes and
their host galaxies would have profound implications in astrophysics. To add
further context to studies of their co-evolution, an investigation is carried
out to gain insight as to whether quasars and their hosts at earlier epochs
follow the local relation between black hole (BH) mass and stellar velocity
dispersion. We use 584 SDSS quasars at 0.2 < z < 0.8 with black hole
measurements, and properties of their hosts from the Hyper Suprime-Cam Subaru
Strategic Program. An inference of the stellar velocity dispersion is achieved
for each based on the stellar mass and size of the host galaxy by using the
galaxy mass fundamental plane for inactive galaxies at similar redshifts. In
agreement with past studies, quasars occupy an elevated position from the local
M_BH-sigma relation, considered as a flattening, while maintaining ratios of
M_BH/M* consistent with local values. Based on a forward-modeling of the
sample, we demonstrate that an evolving intrinsic M_BH-sigma relation can match
the observations. However, we hypothesize that these changes may be a
reflection of a non-evolving intrinsic relationship between M_BH and M*.
Reassuringly, there are signs of migration onto the local M_BH-sigma for
galaxies that are either massive, quiescent or compact. Thus, the majority of
the bulges of quasar hosts at high redshift are in a development stage and
likely to align with their black holes onto the mass scaling relation at later
times.
