  Only a small fraction of galactic nuclei in the nearby universe are luminous;
most of them are currently dim. We investigate the feasibility of constraining
the X-ray luminosity in the recent past (up to ~10^6 years ago) of the nucleus
of a cluster dominant galaxy by measuring the contribution of scattered
radiation from the central source to the surface brightness of the intracluster
gas dominated by thermal emission. We show that resonance X-ray lines present
an advantage over the adjacent continuum, because the relative contribution of
the scattered component is typically larger in the line case by a significant
factor of 3-10. As an example, we estimate the level of constraint that could
be derived from future fine spectroscopic observations on the past X-ray
luminosity of the nearby M87 and Cygnus A active galaxies. For instance,
scattered line radiation should be detectable from the Virgo cluster if the
X-ray luminosity of M87 was a few times 10^44 erg s^-1, or 10^-3 of its
Eddington luminosity, until a few times 10^5 years ago. For comparison, upper
limits inferred from the available XMM-Newton and Chandra X-ray continuum data
are typically 1-2 orders of magnitude weaker. The same method can be applied to
distant powerful quasars (at redshifts z~1 if they have cluster-like gaseous
coronae, as suggested by Rosat and Chandra observations of active galaxies at
z<1. Their surface brightness profiles in the X-ray continuum above ~10
keV>>kT/(1+z) (where T is the gas temperature) should be dominated by
redshifted scattered radiation from the quasar. Therefore, measurements with
forthcoming mirror-optics hard X-ray telescopes could give information on the
lifetime of quasars and parameters of the hot gas around them.
