The universal power spectrum of Quasars in optical wavelengths: Break timescale scales directly with both black hole mass and accretion rate

Abstract

Aims: Establish the dependence of variability properties, such as characteristic timescales and variability amplitude, on basic quasar parameters such as black hole mass and accretion rate, controlling for the rest-frame wavelength of emission. Methods: Using large catalogs of quasars, we selected the g-band light curves for 4770 objects from the Zwicky Transient Facility archive. All selected objects fall into a narrow redshift bin, $0.6<z<0.7$, but cover a wide range of accretion rates in Eddington units (REdd) and black hole masses ($M$). We grouped these objects into 26 independent bins according to these parameters, calculated low-resolution $g$-band variability power spectra for each of these bins, and approximated the power spectra with a simple analytic model that features a break at a timescale $t_b$. Results: We found a clear dependence of the break timescale $t_b$ on REdd, on top of the known dependence of $t_b$ on the black hole mass $M$. In our fits, $t_b\propto M^{0.65 - 0.55}$ REdd $^{0.35 - 0.3}$, where the ranges in the exponents correspond to the best-fitting parameters of different power spectrum models. Scaling $t_b$ to the orbital timescale of the innermost stable circular orbit (ISCO), $t_{\rm ISCO}$, results approximately in $t_{b}/t_{\rm ISCO} \propto ($REdd$/M)^{0.35}$. The observed values of $t_b$ are $\sim 10$ longer than the orbital timescale at the light-weighted average radius of the disc region emitting in the (observer frame) $g$-band. The different scaling of the break frequency with $M$ and REdd shows that the shape of the variability power spectrum cannot be solely a function of the quasar luminosity, even for a single rest-frame wavelength. Finally, the best-fitting models have slopes above the break in the range -2.5 and -3. A slope of -2, as in the damped random walk models, fits the data significantly worse.