We estimate the dust torus cooling timescale once the active galactic nucleus (AGN) is quenched. In a clumpy torus system, once the incoming photons are suppressed, the cooling timescale of one clump from T dust = 1000 K to several 10 K is less than 10 years, indicating that the dust torus cooling time is mainly governed by the light crossing time of the torus from the central engine. After considering the light crossing time of the torus, the AGN torus emission at 12 μm becomes over two orders of magnitude fainter within 100 years after the quenching. We also propose that those "dying" AGNs could be found using the AGN indicators with a different physical scale R such as 12 μm band luminosity tracing AGN torus (R ∼ 10 pc) and the optical [O iii]λ5007 emission line tracing narrow line regions (R = 102-4 pc).
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