  We present results from an archival study of 70 medium-redshift QSOs observed
with the Wide Field Planetary Camera 2 on board the Hubble Space Telescope. The
QSOs have magnitudes M_V <= -23 (total nuclear plus host light) and redshifts
$0.06 <= z <= 0.46$. The aim of the present study is to investigate the
connections between the nuclear and host properties of QSOs, using
high-resolution images and removing the central point source to reveal the host
structure. We confirm that more luminous QSO nuclei are found in more luminous
host galaxies. Using central black hole masses from the literature, we find
that nuclear luminosity also generally increases with black hole mass, but it
is not tightly correlated. Nuclear luminosities range from 2.3% to 200% of the
Eddington limit. Those in elliptical hosts cover the range fairly evenly, while
those in spirals are clustered near the Eddington limit. Using a principal
components analysis, we find a kind of fundamental plane relating the nuclear
luminosity to the size and effective surface magnitude of the bulge. Using
optical nuclear luminosity, this relationship explains 96.1% of the variance in
the overall sample, while another version of the relationship uses x-ray
nuclear luminosity and explains 95.2% of the variance. The form of this QSO
fundamental plane shows similarities to the well-studied fundamental plane of
elliptical galaxies, and we examine the possible relationship between them as
well as the difficulties involved in establishing this connection.
