  Recent studies of the tight scaling relations between the masses of
supermassive black holes and their host galaxies have suggested that in the
past black holes constituted a larger fraction of their host galaxies' mass.
However, these arguments are limited by selection effects and difficulties in
determining robust host galaxy masses at high redshifts. Here we report the
first results of a new, complementary diagnostic route: we directly determine a
dynamical host galaxy mass for the z=1.3 luminous quasar J090543.56+043347.3
through high-spatial-resolution (0.47", 4kpc FWHM) observations of the host
galaxy gas kinematics over 30x40 kpc using ESO/VLT/SINFONI with LGS/AO.
Combining our result of M_dyn = 2.05+1.68_0.74 x 10^11 M_sun (within a radius
5.25 +- 1.05 kpc) with M_BH,MgII = 9.02 \pm 1.43 x 10^8 M_sun, M_BH,Halpha =
2.83 +1.93-1.13 x 10^8 M_sun, we find that the ratio of black hole mass to host
galaxy dynamical mass for J090543.56+043347.3 matches the present-day relation
for M_BH vs. M_Bulge,Dyn, well within the IR scatter, deviating at most a
factor of two from the mean. J090543.56+043347.3 displays clear signs of an
ongoing tidal interaction and of spatially extended star formation at a rate of
50-100 M_sun/yr, above the cosmic average for a galaxy of this mass and
redshift. We argue that its subsequent evolution may move J090543.56+043347.3
even closer to the z=0 relation for M_BH vs. M_Bulge,Dyn. Our results support
the picture where any substantive evolution in these relations must occur prior
to z~1.3. Having demonstrated the power of this modelling approach we are
currently analyzing similar data on seven further objects to better constrain
such evolution.
