Reverberation Mapping of Lamp-post and Wind Structures in Accretion Thin Disks

TL;DR

This study refines accretion disk size estimates by incorporating disk winds and color correction, using analytical models and reverberation mapping data from AGNs to better understand disk structures and improve observational analysis tools.

Contribution

It introduces self-consistent analytical formulas for disk size estimates considering winds and color correction, and applies them to AGN data to explore disk temperature profiles and correlations with accretion rates.

Findings

Disk temperature profile is shallower ($T\propto R^{-0.66}$) than standard models.

Color correction factor is approximately 1.6, aligning with previous research.

Positive correlation between accretion rate and color correction factor.

Abstract

To address the discrepancy where disk sizes exceed those predicted by standard models, we explore two extensions to disk size estimates within the UV/optical wavelength range: disk winds and color correction. We provide detailed, self-consistent derivations and analytical formulas, including those based on a power-law temperature approximation, offering efficient tools for analyzing observational data. Applying our model to four type I AGNs with intensive reverberation mapping observations, we find a shallower temperature slope ($T\propto R^{-0.66}$, compared to $R^{-3/4}$ traditionally) and a color correction factor ($f_{\rm col} \approx 1.6$), consistent with previous studies. We observe a positive correlation between accretion rate and color correction with black hole mass. However, the small sample size limits our conclusions. The strong degeneracy between the temperature slope and accretion rate suggests that incorporating flux spectra or spectral energy distributions could improve fitting accuracy. Our simulation approach rapidly generates quasar light curves while accommodating various observational scenarios for reverberation mapping, making it well-suited for training machine learning algorithms.