The variational slope of quasar light curves is not a distance indicator

Abstract

When the time difference quotients, or variational slopes, of quasar light curves are plotted against their absolute magnitudes, there is a tight positive correlation of $\sim 0.16$ dex in the variational slope direction or $\sim 0.5$ dex in the absolute magnitude direction. This finding resulted in suggestions that a variational slope -- luminosity relation could be used as a distance indicator. However, I show that this relation can be explained almost entirely from self-correlation with luminosity. After properly accounting for the self-correlation component, the relation has a true scatter of $\sim 1.5$ dex in luminosity, consistent with established correlations for quasar variability amplitudes. Given this large scatter, correlation with variational slope or variability amplitude and luminosity is not by itself a suitable distance indicator for quasars.