Cooling timescale of dust tori in dying active galactic nuclei
  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 $T_{\rm dust}=1000$ 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]$\lambda5007$ emission line narrow line regions ($R=10^{2-4}$ pc).
