We analyze X-ray spectra of heavily obscured (N_H > 10^{24} cm^{-2}) active galaxies obtained with Chandra, concentrating on the iron K alpha fluorescence line. We measure very large equivalent widths in most cases, up to 5 keV in the most extreme example. The geometry of an obscuring torus of material near the active galactic nucleus (AGN) determines the Fe emission, which we model as a function of torus opening angle, viewing angle, and optical depth. The starburst/AGN composite galaxies in this sample require small opening angles. Starburst/AGN composite galaxies in general therefore present few direct lines of sight to their central engines. These composite galaxies are common, and their large covering fractions and heavy obscuration effectively hide their intrinsically bright X-ray continua. While few distant obscured AGNs have been identified, we propose to exploit their signature large Fe K alpha equivalent widths to find more examples in X-ray surveys.
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