H0LiCOW VII. Cosmic evolution of the correlation between black hole mass
  and host galaxy luminosity
  Strongly lensed active galactic nuclei (AGN) provide a unique opportunity to
make progress in the study of the evolution of the correlation between the mass
of supermassive black holes ($\mathcal M_{BH}$) and their host galaxy
luminosity ($L_{host}$). We demonstrate the power of lensing by analyzing two
systems for which state-of-the-art lens modelling techniques have been applied
to Hubble Space Telescope imaging data. We use i) the reconstructed images to
infer the total and bulge luminosity of the host and ii) published broad-line
spectroscopy to estimate $\mathcal M_{BH}$ using the so-called virial method.
We then enlarge our sample with new calibration of previously published
measurements to study the evolution of the correlation out to z~4.5. Consistent
with previous work, we find that without taking into account passive luminosity
evolution, the data points lie on the local relation. Once passive luminosity
evolution is taken into account, we find that BHs in the more distant Universe
reside in less luminous galaxies than today. Fitting this offset as $\mathcal
M_{BH}$/$L_{host}$ $\propto$ (1+z)$^{\gamma}$, and taking into account
selection effects, we obtain $\gamma$ = 0.6 $\pm$ 0.1 and 0.8$\pm$ 0.1 for the
case of $\mathcal M_{BH}$-$L_{bulge}$ and $\mathcal M_{BH}$-$L_{total}$,
respectively. To test for systematic uncertainties and selection effects we
also consider a reduced sample that is homogeneous in data quality. We find
consistent results but with considerably larger uncertainty due to the more
limited sample size and redshift coverage ($\gamma$ = 0.7 $\pm$ 0.4 and
0.2$\pm$ 0.5 for $\mathcal M_{BH}$-$L_{bulge}$ and $\mathcal
M_{BH}$-$L_{total}$, respectively), highlighting the need to gather more
high-quality data for high-redshift lensed quasar hosts. Our result is
consistent with a scenario where the growth of the black hole predates that of
the host galaxy.
