Probing quasar viewing angle with the variability structure function
Given the anisotropic emission from quasar accretion discs, their viewing angle affects estimates of the quasar luminosity, black hole mass, and Eddington ratio. Discs appear overluminous when viewed pole-on and underluminous when viewed at high inclination. In radio-quiet quasars, the viewing angle is usually unknown, although spectroscopic indicators have been proposed. Here, we use a recently discovered universality in the variability structure function (SF) of quasar light curves (LCs), where all quasars show the same SF when clocks run in units of orbital time-scale. As an offset from the mean relation can be caused by incorrect orbital time-scales and thus incorrect luminosities, we correlate these offsets with suggested inclination indicators. We derive SFs from NASA/Asteroid Terrestrial-impact Last Alert System (ATLAS) LCs spanning ~6 yr of observation, using a sample of 183 luminous quasars with measured H β lines as well as 753 quasars with C $\tiny{IV}$ and Mg $\tiny{II}$ lines. Starting from the proposed orientation indicators, we expect quasars with narrower H β lines and with more blueshifted C $\tiny{IV}$ lines to be viewed more pole-on and thus appear overluminous. In contrast, our SF analysis finds that presumed pole-on discs appear underluminous, consistently for both line indicators. We discuss possible explanations for the behaviour of quasars with highly blueshifted C $\tiny{IV}$ lines irrespective of inclination angle, including dusty outflows that might render the accretion disc underluminous and flatter disc temperature profiles with longer orbital time-scales than in thin-disc models but reach no satisfying conclusion.