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 \mu m becomes over two orders of magnitude fainter within 100 years after the quenching .
We also propose that those “ dying ” AGN could be found using the AGN indicators with different physical scale R such as 12 \mu m band luminosity tracing AGN torus ( R \sim 10 pc ) and the optical [ OIII ] \lambda 5007 emission line narrow line regions ( R = 10 ^ { 2 - 4 } pc ) .