  Circumnuclear water masers can respond in two ways to changes in the
luminosity of an active galactic nucleus. First, an increase in the X-ray
luminosity can lead to an increase in the maser emissivity; and second, an
increase in the intrinsic bolometric luminosity may result in a temporary
decrease in the difference between the gas and dust temperature and a
consequent decrease in the maser output. Whilst the latter effect can occur
over a period shorter than the thermal timescale, the former effect cannot.
Quantitative estimates of the response of the water maser emissivity to changes
in either the X-ray or bolometric luminosity are presented, together with
estimates of the relevant timescales. Either mechanism could account for recent
observations by Gallimore et al. which suggest that the water maser variability
in two widely separated regions of the circumnuclear gas in NGC 1068 have been
coordinated by a signal from the active nucleus. For either mechanism, a
minimum H2 density ~ 1.E+8 cm-3 is needed to explain the observed variability
timescale.
