Evolution of quasar stochastic variability along its main sequence
  We explore the evolution of the time variability (in the optical $g$-band and
on timescales of weeks to years) of SDSS Stripe 82 quasars along the quasar
main sequence. A parent sample of $1004$ quasars within $0.5\leq z \leq 0.89$
are used for our statistical studies, we then make subsamples from our parent
sample: a subsample of $246$ quasars with similar luminosities, and a subsample
of $399$ quasars with similar Rfe (i.e., the ratio of the equivalent width of
FeII within $4435$--$4685\ \mathrm{\AA}$ to that of \Hbeta). We find the
variability amplitude decreases with luminosity ($L_{\mathrm{bol}}$). The
anti-correlation between the variability amplitude and Rfe is weak but
statistically significant. The characteristic timescale, $\tau$, correlates
mostly with quasar luminosity, its dependence on Rfe is statistically
insignificant. After controlling luminosity and Rfe, the high- and low-FWHM
samples have similar structure functions. These results support the framework
that Rfe is governed by Eddington ratio and FWHM of Hbeta is mostly determined
by orientation. We then provide new empirical relations between variability
parameters and quasar properties (i.e., luminosity and Rfe). Our new relations
are consistent with the scenario that quasar variability is driven by the
thermal fluctuations in the accretion disk, $\tau$ seems to correspond to the
thermal timescale. From our new relations, we find the short-term variability
is mostly sensitive to $L_{\mathrm{bol}}$. Basing on this, we propose that
quasar short-term (a few months) variability might be a new type of "Standard
Candle" and can be adopted to probe cosmology.
