Abstract
Quasars represent a brief phase in the life-cycle of most massive galaxies, but the evolutionary connection between central black holes and their host galaxies remains unclear. While quasars are active and shining brighter than the Compton-limit luminosity, their radiation heats the surrounding medium to the Compton temperature, forming Compton spheres extending to the Str\omgren radius of Fe$^{26+}$/He$^{2+}$. After the quasars shut off, their ``afterglow'' can be detected through three signatures: (1) an extended X-ray envelope, with a characteristic temperature of $\sim 3\times 10^7$ K; (2) Ly$\alpha$ and Ly$\beta$ lines and the $K-$edge of Fe$^{26+}$; and (3) nebulosity from hydrogen and helium recombination emission lines. We discuss the possibility of detecting these signatures using {\em Chandra}, the planned {\em XEUS} mission, and ground-based optical telescopes. The luminosity and size of quasar afterglows can be used to constrain the lifetime of quasars.
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