Temperature profiles of accretion disks in luminous active galactic nuclei derived from ultraviolet spectroscopic variability

¹ Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566, Korea
² Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China
³ Department of Astronomy, School of Physics, Peking University, Beijing 100871, China

^⋆ Corresponding author; mkim.astro@gmail.com

Received: 2 October 2024
Accepted: 27 February 2025

Abstract

The characteristic timescale (τ) of the continuum variability of the accretion disk in active galactic nuclei (AGNs) is known to be related to the thermal timescale, which is predicted to scale with AGN luminosity (L) and the rest-frame wavelength (λ_RF) as t_th ∝ L^0.5λ_RF² in the standard disk model. Using multi-epoch spectroscopic data from the Sloan Digital Sky Survey Reverberation Mapping project, we constructed ultraviolet ensemble structure functions of luminous AGNs as a function of their luminosity and wavelength. Assuming that AGNs exhibit a single universal structure function when Δt is normalized by τ, wherein τ ∝ L ^aλ^b_RF, we find a = 0.50 ± 0.03 and b = 1.42 ± 0.09. While the value of a aligns with the prediction from the standard disk model, b is significantly smaller than expected, suggesting that the radial temperature (color) profile of the accretion disk is significantly steeper (shallower) than the standard disk model. Notably, this discrepancy with theory has been observed in previous studies based on spectroscopic reverberation mapping and gravitational microlensing. Although no current model of accretion disks fully matches our results, our findings provide valuable constraints for testing future physical models.