Quasar Main Sequence: a line or a plane?
  A quasar main sequence is widely believed to reveal itself through objects
represented in a plane spanned by two parameters: the full-width at
half-maximum (FWHM) of H$\beta{}$, and the ratio of Fe II to H$\beta{}$
equivalent width. This sequence is related to the application to quasar
properties of principal component analysis (PCA), which reveals that the main
axis of variance (Eigenvector 1) is co-directional with a strong
anti-correlation between these two measurements. We aim to determine whether
the dominance of two Eigenvectors, originally discovered over two decades ago,
is replicated in newer high-quality quasar samples. If so, we aim to test if a
non-linear approach is an improvement on the linear PCA method by finding two
new parameters which represent a more accurate projection of the variances than
the Eigenvectors recovered from PCA. We selected quasars from the XSHOOTER
archive and a major quasar catalog to build high quality samples. These samples
were tested with PCA. We find that the new high-quality samples do indeed have
two dominant Eigenvectors as originally discovered. Subsequently we find that
the fitting of a non-linear decay curve to the main sequence allows a new plane
spanned by linearly independent axes to be defined, based on the distance along
the decay curve as the main axis and the distance of each quasar datapoint from
the curve as the secondary axis respectively. The results show that it is
possible to define a new plane based on the quasar main sequence which accounts
for the majority of the variance. The most likely candidate for the new main
axis is an anti-correlation with black hole mass. In this case the secondary
axis likely represents luminosity. However, given the results of previous
studies, inclination angle likely plays a role in H$\beta{}$ width.
