Constraining AGN Torus Sizes with Optical and Mid-Infrared Ensemble Structure Functions

Abstract

We propose a new method to constrain the size of the dusty torus in broad-line active galactic nuclei (AGNs) using optical and mid-infrared (MIR) ensemble structure functions (SFs). Because of the geometric dilution of the torus, the MIR response to optical continuum variations has suppressed variability with respect to the optical that depends on the geometry (e.g., size, orientation, opening angle) of the torus. More extended tori have steeper MIR SFs with respect to the optical SFs. We demonstrate the feasibility of this SF approach using simulated AGN light curves and a geometric torus model. While it is difficult to use SFs to constrain the orientation and opening angle due to insensitivity of the SF on these parameters, the size of the torus can be well determined. Applying this method to the ensemble SFs measured for 587 SDSS quasars, we measure a torus $R-L$ relation of $\log R_{\mathrm{eff}}(\mathrm{pc})=0.51_{-0.04}^{+0.04}\times \log (L_{\mathrm{bol}}/10^{46}\mathrm{erg}{\mathrm{s}}^{-1})-0.38_{-0.01}^{+0.01}$ in the WISE $W1$ band, and sizes $\sim 1.4$ times larger in the $W2$ band, which are in good agreement with dust reverberation mapping measurements. Compared with the reverberation mapping technique, the SF method is much less demanding in data quality and can be applied to any optical+MIR light curves for which a lag measurement may not be possible, as long as the variability process and torus structure are stationary. While this SF method does not extract all information contained in the light curves (i.e., the transfer function), it provides an intuitive interpretation for the observed trends of AGN MIR SFs compared with optical SFs.

16 pages, 10 figures, accepted for publication in ApJ

References in corpus (19)

• A Catalog of Quasar Properties from SDSS DR7
• Modeling the Time Variability of SDSS Stripe 82 Quasars as a Damped Random Walk
• Is Quasar Optical Variability a Damped Random Walk?
• Reverberation Measurements of the Inner Radius of the Dust Torus in 17 Seyfert Galaxies
• The innermost region of AGN tori: implications from the HST/NICMOS Type 1 point sources and near-IR reverberation
• A characteristic optical variability timescale in astrophysical accretion disks
• The characteristic blue spectra of accretion disks in quasars as uncovered in the infrared
• Limitations on the recovery of the true AGN variability parameters using Damped Random Walk modeling
• Dust-Deficient Palomar-Green Quasars and the Diversity of AGN Intrinsic IR Emission
• A compendium of AGN inclinations with corresponding UV/optical continuum polarization measurements
• Reverberation Measurements of the Inner Radii of the Dust Tori in Quasars
• Mid-Infrared Variability from the Spitzer Deep, Wide-Field Survey
• Measuring Quasar Variability with Pan-STARRS1 and SDSS
• Dust Reverberation Mapping in Distant Quasars from Optical and Mid-Infrared Imaging Surveys
• Hard X-Ray to Radio Multiwavelength SED Analysis of Local U/LIRGs in GOALS Sample with Self-consistent AGN Model Including Polar-dust Component
• Dust Reverberation of 3C273: torus structure and lag -- luminosity relation
• Modeling the Infrared Reverberation Response of the Circumnuclear Dusty Torus in AGNs: An Investigation of Torus Response Functions
• Dust Reverberation Mapping of Z229-15
• The mid-infrared variability of the SDSS optical quasars

Cited by in corpus (1)

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