  Information about the X-ray luminosity of the supermassive black hole located
at the Galactic center (GC), Sgr A*, and its temporal variations in the past is
imprinted in the scattered emission observed today in the direction towards
giant molecular clouds (GMCs) located in our Galaxy. Due to light travel time
effects these clouds probe the activity of Sgr A* at different times in the
past depending on their position relative to the GC and the observer. In this
paper we combine results of recent ASCA observations along the Galactic plane,
providing upper limits for the scattered flux in the 4-10 keV range produced in
a given direction, with data from CO surveys of the same regions. These CO
surveys map the position and mass of the molecular gas which the GMCs are made
up of. Demanding the scattered flux to be not larger than the observed one,
this data enables us to derive upper limits for the 4-10 keV luminosity of Sgr
A* at certain times during the last 40.000 years down to about 8*10^40 erg/s.
At other times the limits are less tight, of the order of 10^41-10^42 erg/s.
The more extended and continuous HI distribution in the Galactic disk, which
also scatters the radiation emitted by Sgr A*, allows us to extend the time
coverage further into the past, back to about 110.000 years, albeit the limits
are becoming less tight. We thereby can rule out a long term X-ray activity
phase of Sgr A* at one per cent of its Eddington level ending less than about
80.000 years ago. The limits presented in this paper can be improved by
observations of emission in the fluorescent iron K_alpha-line. We study the
feasibility of these methods to investigate past nuclear activity in other
spiral galaxies observed with the angular resolution of X-ray telescopes like
Chandra and XMM-Newton.
