  The UV radiation from a quasar leaves a characteristic pattern in the
distribution of ionized hydrogen throughout the surrounding space. This pattern
or light echo propagates through the intergalactic medium at the speed of
light, and can be observed by its imprint on the Ly-alpha forest spectra of
background sources. As the echo persists after the quasar has switched off, it
offers the possibility of searching for dead quasars, and constraining their
luminosities and lifetimes. We outline a technique to search for and
characterize these light echoes. To test the method, we create artificial
Ly-alpha forest spectra from cosmological simulations at z=3, apply light
echoes and search for them. We show how the simulations can also be used to
quantify the significance level of any detection. We find that light echoes
from the brightest quasars could be found in observational data. With
absorption line spectra of 100 redshift z~3-3.5 quasars or galaxies in a 1
square degree area, we expect that ~10 echoes from quasars with B band
luminosities L_B=3x10^45 ergs/s exist that could be found at 95% confidence,
assuming a quasar lifetime of ~10^7 yr. Even a null result from such a search
would have interesting implications for our understanding of quasar
luminosities and lifetimes.
