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.