The universal power spectrum of quasars in optical wavelengths

Break timescale scales directly with both black hole mass and the accretion rate

¹ Instituto de Física y Astronomía, Universidad de Valparaíso, Gran Bretaña 1111, Valparaíso, Chile
e-mail: patricia.arevalo@uv.cl
² Millennium Nucleus on Transversal Research and Technology to Explore Supermassive Black Holes (TITANS), Chile
³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany
⁴ Departamento de Astronomía, Universidad de Chile, Casilla 36D, Santiago, Chile
⁵ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
⁶ Millennium Institute of Astrophysics (MAS), Monseñor Sótero Sanz 100, Providencia, Santiago, Chile

Received: 2 June 2023
Accepted: 10 November 2023

Abstract

Context. The optical variability of quasars is one of the few windows through which we can explore the behaviour of accretion discs around supermassive black holes.

Aims. We aim to establish the dependence of variability properties, such as characteristic timescales and the variability amplitude, on basic quasar parameters such as black hole mass and the accretion rate, controlling for the rest-frame wavelength of emission.

Methods. Using large catalogues of quasars, we selected the g-band light curves for 4770 objects from the Zwicky Transient Facility archive. All the selected objects fall into a narrow redshift bin, 0.6 < z < 0.7, but cover a wide range of accretion rates in Eddington units (R_Edd) 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 find a clear dependence of the break timescale, t_b, on R_Edd, on top of the known dependence of t_b on the black hole mass, M. In our fits, t_b ∝ M^{0.65 − 0.55}R_Edd^0.35−0.3, where the ranges in the exponents correspond to the best-fitting parameters of different power spectrum models. This mass dependence is slightly steeper than that found in other studies. Scaling t_b to the orbital timescale of the innermost stable circular orbit (ISCO), t_ISCO, results approximately in t_b/t_ISCO ∝ (R_Edd/M)^0.35. In the standard thin disc model, (R_Edd/M) ∝ T_max⁴, where T_max is the maximum disc temperature, so that t_b/t_ISCO appears to scale approximately with the maximum temperature of the disc to a small power. The observed values of t_b are ∼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 R_Edd 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 between −2.5 and −3. A slope of −2, as in the damped random walk models, fits the data significantly worse.