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Constraining properties of dusty environments by infrared variability

We present model simulations of time-variable infrared (IR) emission from dust as a consequence of variability of the incident radiation. For that we introduce a generalized treatment for temperature variations in a dusty environment, which is not limited to any specific astronomical source. The treatment has been incorporated into a simplified clumpy torus model, with the radial brightness distribution as the main parameter, to study the IR emission of type 1 active galactic nuclei (AGN). We show that any variability signal in the optical is smoothened stronger if the brightness distribution is very extended, and this smoothing strongly depends on wavelength. This also affects time lags between the optical and near-/mid-IR emission, which can be up to 10s of sublimation radii for long wavelengths and extended brightness distributions. The dependence of time lag on wavelength and distribution can be used to quantify the brightness distribution in an AGN torus, either by comparing optical light curves to near-IR and mid-IR light curves, or by directly comparing near-IR to mid-IR light curves. Moreover, our model has been applied to near-IR data of the nearby Seyfert 1 galaxy NGC 4151. We show that the simple model can reproduce the overall observed variability signal and found that about 40% of the energy in the variability signal in the V-band has been converted into K-band variability. This low value may be explained by a “snowball” model of gradually-sublimating clouds at the inner edge of the torus. We also note that our modeling does not support a change of time lag/sublimation radius over the observed light curve epoch in spite of a significant change in V-band emission.